FR2782173A1 - Three-dimensional imaging microscope for generating three-dimensional image of an object, applicable to biological and meteorological microscopy - Google Patents

Abstract

The object is lit by a plane wave front in different directions, such that the separation of phase offsets provides each point of representation concentrated around a constant value. Optical part enables to record on one surface of the sensors (118) wave derived from object (112) by measuring interference figures produced by reference beam (Fr) and wave derived from object. Phase difference between illumination and reference waves is controlled for recording.

Description

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Microscope generating a three-dimensional representation of an object and images generated by this microscope. l.Technical area:
The present invention relates to a microscope generating a three-dimensional representation of the object observed, operating on a principle derived from digital holography and synthetic aperture systems.

2. Prior art:
2. 1. References [Curlander]: Synthetic Aperture Radar Systems and Signal Processing, JC Curlander & RNMcDonough, J.Wiley and Sons, New York 1995.

[Hufnagel]: Restoration ofatmospherically degraded images, vol.II, 1967 (National Academy of Science, Washington D.C.), pp. 239-246, cited in [Goodman] p.33.

[Wolf]: Three-dimensional structure determination of semi-transparent objects from holography data.

Emil Wolf, Optics Communications Volume 1 number 4 p.153, 1969 [Goodman]: Synthetic Aperture Optics, Progress in Optics Volume VIII, 1970, North Holland Publishing Company.

[Vishnyakov]:Interferometric computed-microtomography of 3D phase objects, Gennady N. Vishnyakov & Gennady G. Levin, SPIE proceedings vol.2984 p. 64
2. 2. Description de la technique antérieure. [Turpin 1]: US Patent 5,384,573 [Turpin 2]: Theory of the Synthetic Aperture Microscope, Terry Turpin, Leslie Gesell, Jeffrey Lapides, Craig Price, SPIE proceedings vol. 2566 p.230, 1995 [Turpin 3]: The Synthetic Aperture Microscope, Experimental results, P. Woodford, T. Turpin, M. Rubin, J. Lapides, C. Price, SPIE proceedings vo1.2751 p. 230, 1996 [Lauer]: Patent WO 98/13715 [Kawata]: Optical microscope tomography. I. Support constraint, S.Kawata, O.Nakamura & S.Minami, Journal of the Optical Society of America A, vol.4, No. 1, p.292, January 1987 [Noda]: Three-dimensional phase-contrast imaging by a computed tomography microscope, Tomoya Noda, Satoshi Kawata and Shigeo Minami, Applied Optics vol.31no 5 p. 670, February 10, 1992

[Vishnyakov]: Gennady N. Vishnyakov & G. Gennady G. Levin, SPErgraphical Proceedings, vol. 64
2. 2. Description of the prior art.

 A weakly diffracting three-dimensional object can be characterized by a three-dimensional spatial representation giving in each point of space a complex number whose real part is characteristic of the absorptivity of the object and the imaginary part is characteristic of the index of the 'object.

A three-dimensional Fourier transformation of this representation gives a frequency representation of the object. If this frequency representation has a single non-zero value,

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renvoie une onde de vecteur d'onde fe + fo . Un couple d'ondes (f,,, f,) constitué d'un vecteur d'onde émis et d'un vecteur d'onde reçu permet donc d'obtenir la composante de la représentation fréquentielle

tridimensionnelle de l'objet observé sur le vecteur fréquence fo = fc - fe . Les données obtenues par un système émetteur-récepteur émettant des ondes de vecteur d'onde fe vers l'objet et recevant des ondes de vecteur d'onde fc caractérisent donc une partie de la représentation fréquentielle de l'objet observé. corresponding to a frequency fo, so when the object is illuminated by the wave vector wave fe it

returns a wave vector wave fe + fo. A pair of waves (f ,,, f) consisting of an emitted wave vector and a received wave vector thus makes it possible to obtain the component of the frequency representation

three-dimensional object observed on the frequency vector fo = fc - fe. The data obtained by a transceiver system emitting wave vector waves fe to the object and receiving wave vector waves fc thus characterize a part of the frequency representation of the observed object.

 If the transmitter and the receiver are fixed with respect to each other, this part of frequency representation is limited on the one hand by the opening of the receiver and on the other hand by the trajectory of the transmitter-receiver unit. receiver, these factors limiting the usable values of fe and fc. This limitation of the frequency representation is translated in return by a limitation of the resolution on the spatial image that can be deduced therefrom.

 This physical principle is at the base of the synthetic aperture radar, known since the late 1950s, and a history of which is presented in [Curlander]. The considerations outlined above, however, must be adapted to the fact that in the case of radar, the object is a surface on the ground. The radar determines a representation of this surface and not a general three-dimensional representation as seen above. However, the basic principles and limitations outlined above remain valid. A synthetic aperture radar includes a transmitter that directs a coherent wave to the object, and a receiver that performs coherent detection of the wave coming back from the object. The transmitter and the receiver are usually fixed relative to each other. The transceiver assembly moves relative to the observed object, the transmitter being controlled to permanently aim at a fixed area of the object. From the coherent wave received by the transmitter-receiver unit for various positions of this set, a numerical analysis makes it possible to generate a representation of the observed object. The data concerning the positional variations of the transceiver assembly are available and are used to correct the variations of the path traversed by the wave, which would induce in the absence of correction of the phase displacements making it impossible to generate an image of the observed object. The receiver makes it possible to receive waves coming from the object, characterized by their fc wave vectors. The frequencies received by the receiver are limited by the aperture of the image forming system on the receiver or by the size of the receiver in the absence of an image forming system. The wave arriving at the object from the transmitter is approximately plane, wave vector fe. Very different algorithms can be used to generate an image of the object from the wave received on the transmitter. They depend on the type of transmitter and receiver used, the type of image that one wishes to obtain, and the calculation means employed, which are generally very heavy.

 In the field of optics, [Wolf] has proposed a principle consisting in detecting the wave received on two flat reception surfaces facing each other, the observed object being between the two reception surfaces and the frequency of reception. lighting fo being variable. From the received wave on the receiving surfaces for a set of lighting frequencies fe, [Wolf] exposes a method to reconstruct the

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 three-dimensional frequency representation of the object, over all the frequencies fo obtainable by the formula fo = fc-fe from a given wavelength of illumination. The spatial representation of the object is obtained by Fourier transformation of its frequency representation. [Wolf] also determined the maximum system resolution, which corresponds to a maximum period of Il 2 for the sinusoidal components of the object representation, ie a Nyquist sampling period of 4, which is a resolution much higher than that of conventional microscopes.

 The application of the synthetic aperture radar technique in the optical wavelength domain, for example in the form proposed by [Wolf], would in principle make it possible to obtain images of an observed object. However, for the technique to be feasible, it is necessary to permanently have position values, in a frame linked to the object, of each element of the transceiver assembly. These values must be known at a fraction of a wavelength. This is feasible in the field of radar frequencies, where the wavelengths may for example be a few tens of centimeters. In the field of optics, where the wavelengths are sub-micrometric, this is difficult to achieve. This problem is the essential reason why the system is difficult to adapt to optics, as indicated in [Goodman], pages 36 to 39. This problem will be referred to as <problem A>.

 [Hufnagel], however, proposed an adaptation of this technique in the infrared. The technique proposed by [Hufnagel] consists in using an object rotating around a fixed axis and a fixed transceiver unit. This method allows in principle to solve the <problem A>. Indeed, the position of a fixed axis of rotation can be precisely controlled. The relative position of the transceiver with respect to the object is therefore known with good accuracy. However, the rotation of the object can be performed only around a fixed axis, which limits the set of frequencies fo = fc-fe can be detected, and therefore the accuracy of the system. To improve this accuracy, it would be necessary for example to move the transmitter relative to the receiver, which is impossible because of <problem A>. The problem of improving the set of frequencies used will be noted <problem B>.

 [Turpin] has recently described two systems constituting an adaptation in the field of optical principles of the synthetic aperture radar. These systems will be referred to as <system 1> and <system 2>.

 The <system 1> is the one implemented in [Turpin 3]. The physical configuration used is consistent with the principle used in [Hufnagel] to solve <problem A>, that is to say that the transmitter and the receiver are fixed and the object is rotating around a fixed axis . However, the resolution of the <A problem> implies not only the physical possibility of knowing the variations of the position of the transmitter with respect to the receiver, but also the definition of appropriate compensation algorithms or appropriate control methods, removing the need of such an algorithmic compensation. In the absence of such precisions, <system 1> is not functional.

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 <System 2> is the more general system described in [Turpin 1] and [Turpin 2], of which <System 1> is a special case. It specifies that the light wave and / or the position of the receiver may vary, which in principle makes it possible to solve <problem B>. On the other hand, the physical configurations proposed for <system 2> do not allow the resolution of <problem A>. In the absence of a solution to <problem A>, <system 2> is not functional.

 Compared to [Hufnagel], [Turpin] uses an object positioning system with better precision, a shorter wavelength laser, and modern means of computation and image acquisition. These calculation means allow it to implement the principle described by [Wolf], that is to say that it generates a three-dimensional frequency representation of the object, whose spatial representation of the object can be deduced by Fourier transformation. [Hufnagel] formed the image of the object in the reception plan. To use the method described by [Wolf], the two-dimensional Fourier transformation of the image thus detected must first be carried out. In order to simplify the calculations, [Turpin] uses optical means to perform this Fourier transformation, the image formed on the receiver being directly in the frequency domain.

 A second approach to obtain a three-dimensional image of an object is constituted by digital holography. The microscope described by [Lauer] receives a wave diffracted by the object and reaching a receiving surface. The phase and intensity of the wave on the receiving surface are measured and the 'three-dimensional' frequency representation of the wave is reconstructed. From this frequency representation, the wave in the object is reconstituted by inverse Fourier transformation, and constitutes an elementary representation of the object. If the object is illuminated by a plane wave, the resolution in the propagation direction of the wave is poor. To avoid this problem, [Lauer] superimposes several images obtained from spatially incoherent lighting waves. If he proceeded by summing each elementary representation obtained, they would cancel each other out. This is why the superposition is carried out in intensity, that is to say that the intensity of the different elementary representations is summed at each point. This destroys the phase information, and the representations ultimately obtained characterize only the absorptivity, not the index. The problem of superimposing elementary representations without destroying the phase information will be called <problem C>.

 Another approach to obtaining three-dimensional images is tomography.

Tomography, used for example in X-rays, consists of reconstructing an image from a set of projections of this image in different directions. Each projection depends linearly on a three-dimensional density function characterizing the object, and from a sufficient number of projections it is possible to reconstitute the object, by inverting this linear correspondence.

 Tomography has been adapted to light microscopy by [Kawata]. In his tomographic microscope, a plane and non-coherent lighting wave, of variable direction, is used. This light wave passes through a sample and then a focused microscope objective in the plane of the sample. It is received on a reception surface placed in the plane where the objective forms the image of the sample. Of

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 Since the illumination is non-coherent, the intensities from each point of the object add up and the intensity image produced on the receiving surface thus depends linearly on the three-dimensional density function characterizing the absorption of the object. the object. From a sufficient number of images we can reconstitute the object, by reversing this linear correspondence. This microscope differs from conventional tomography systems in that the linear correspondence between the density function of the object and a given image is not a projection, but is characterized by a three-dimensional optical transfer function.

 This microscope is not very suitable for obtaining images taking into account the index of the sample.

[Noda] realized a modified microscope to take into account this phase. The starting idea of [Noda] 's microscope is to use phase contrast to obtain a sample index dependent image and to adapt to this configuration the linear inversion principle already put in place. implemented by [Kawata]. The use of [Noda's] microscope is, however, limited to the study of non-absorbing objects whose index variations are extremely small. The problem of extending the use of this type of microscope will be noted <problem D>.

 Another approach to adapt the tomography to the realization of live images is that of [Vishnyakov]. [Vishnyakov] introduces a reference wave distinct from the illumination wave and detects the received wave on a reception surface according to a method similar to that used by [Turpin]. It then generates a characteristic profile of the phase difference between the received wave and the illumination wave. This phase difference being considered as the projection of the index along the direction of the illumination wave, it regenerates the distribution of the index in the object according to the tomographic method conventionally used in X-rays. However, the assimilation of the phase difference to the projection of the index along the direction of the illumination wave is unjustified for the following two reasons.

- The wavelength used is of the same order as the definition of the microscope, and not much lower than the definition of the imaging system as in the case of X-ray imaging. The diffraction phenomena are not negligible. , which makes the method not very valid. The problem posed by the need to take into account the diffraction phenomena will be designated as <problem E>.

- The phase difference between the received wave and the light wave is in fact determined to a constant.

de la page 67 du document [Vishnyakov] devrait être remplacée par':P(x,y) = 141 XI Y) + x sin a +q ou q est une valeur caractéristique de la différence de phase entre l'onde d'éclairage et l'onde de référence en un point central de la surface de réception. Lorsque la direction de l'onde d'éclairage varie, la valeur de# varie. La non-détermination de la valeur correcte de# se traduit par l'ajout d'une constante à chaque projection obtenue, cette constante variant aléatoirement entre deux projections. Ceci rend donc non-exacte l'assimilation du profil de phase obtenu à la projection de l'indice. Le problème qui consiste à prendre en compte la valeur de# sera noté <problème F>
L'objet de l'invention est de résoudre les problèmes A,B,C,D,E,F. Indeed, even assimilating the phase to the projection of the index according to the reference surface, equation (2)

from page 67 of [Vishnyakov] should be replaced by ': P (x, y) = 141 XI Y) + x sin a + q where q is a characteristic value of the phase difference between the illumination wave and the reference wave at a central point of the receiving surface. When the direction of the illumination wave varies, the value of # varies. The non-determination of the correct value of # results in the addition of a constant to each projection obtained, this constant varying randomly between two projections. This makes the assimilation of the phase profile obtained to the projection of the index non-exact. The problem of taking into account the value of # will be noted <problem F>
The object of the invention is to solve the problems A, B, C, D, E, F.

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3. 1. Vocabulary and General Considerations
Since a wave is known by its complex value at each point of a receiving surface, it is possible to generate its complex representation in an area observed by a calculation simulating the inverse return of light. The representation thus obtained is a complex function of spatial coordinates.

A frequency representation of the wave can be obtained by Fourier transformation of this spatial representation.

 In frequency representation, the coordinates of a point represent the spatial frequency or wave vector. A plane wave has a frequency representation reduced to a single point whose associated frequency vector is the inverse standard of the wavelength and for direction the direction of propagation of the wave. The complex value of the plane wave on its unique frequency characterizes its phase and its intensity.

The frequency representation of a monochromatic wave comprises only frequencies of constant norm equal to the inverse of the wavelength and it is therefore two-dimensional, that is to say reduced to a portion of sphere centered on the frequency null and whose radius is the inverse of the wavelength. The wave coming from the object or the light wave can be characterized by their frequency or spatial representations.

 According to the same principle, any complex function of the defined position in the observed area can be considered as a spatial representation and can also be converted into a frequency representation. The term representation will be used to denote such a function independently of the spatial or frequency domain in which it can be expressed. The term wave will be used to denote the wave as a physical entity or as a complex quantity in a frequency or space domain. The term two-dimensional frequency representation will be used to denote a frequency representation reduced to a surface of the three-dimensional space, that is to say in general to a portion of sphere.

 A two-dimensional frequency representation of a wave coming from the object can be obtained, as in <system 1> or as in [Lauer], from a plane image representing its projection on a plane, for example that of the reception area. This flat image will be called a plane image in frequency.

vecteur -fe comme dans le <système 1>, on obtient une représentation fréquentielle bidimensionnelle constituant une partie de la représentation tridimensionnelle de l'objet. En superposant un nombre élevé desdites parties bidimensionnelles de la représentation fréquentielle tridimensionnelle de l'objet, on obtient la représentation fréquentielle tridimensionnelle de l'objet comme dans le <système 1>. On appellera sousreprésentation fréquentielle une partie de la représentation fréquentielle de l'objet, qui peut être constituée d'une seule desdites parties bidimensionnelles, de la superposition de plusieurs desdites parties bidimensionnelles, d'une partie d'une desdites parties bidimensionnelles, ou de toute autre partie de la représentation fréquentielle tridimensionnelle de l'objet. On utilisera le terme sous-représentation pour By translating a two-dimensional frequency representation of the wave coming from the object of a

vector -fe as in <system 1>, we obtain a two-dimensional frequency representation constituting a part of the three-dimensional representation of the object. By superimposing a large number of said two-dimensional portions of the three-dimensional frequency representation of the object, the three-dimensional frequency representation of the object is obtained as in <system 1>. Frequency subrepresentation will be referred to as a portion of the frequency representation of the object, which may consist of only one of said two-dimensional portions, the superposition of a plurality of said two-dimensional portions, a portion of one of said two-dimensional portions, or any another part of the three-dimensional frequency representation of the object. We will use the term under-representation for

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 designate this representation independently of whether it is represented in the spatial, frequency domain, or in any other way.

 The term lens will designate, throughout the text, both single lenses and composite lenses or achromats, generally sized to limit optical aberration.

 In the rest of the text, five embodiments are described. Reference will be made to embodiments 1,2,3,4 and 5.

3. 2. Problems to be solved by the invention
In the microscope [Lauer], and in the version or several light waves are used, the characteristics of these waves are not known. The phase shifts induced by the sample therefore occur on a lighting wave of unknown characteristics and can not be distinguished from the phase variations originally present in the illumination wave. To solve <problem C> and obtain a representation taking into account the index of the sample, it is necessary to be able to make this distinction, and therefore it is necessary to know the lighting wave used. This is difficult in the general case of the spatially incoherent wave, but a priori possible in the case of a sufficiently simple illumination wave, characterized by a reduced number of parameters, and in particular in the case of a wave of light. flat lighting. Indeed, in this case, the knowledge of the position of the mechanical elements used to generate a plane wave in principle makes it possible to determine the characteristics of this wave.

 The resolution of the <problem C> is thus facilitated by the use of simple lighting waves, for example plane lighting waves. In this case, solving <problem C> involves solving <problem A>.

 The resolution of the <problem C> also involves the development of an algorithm allowing to superpose the images generated from this plane lighting wave. However, it can be observed that the [Lauer] system modified to use plane lighting waves of variable direction constitutes a system similar to that described in [Turpin] and that it allows the use of algorithms of the same type.

 The resolution of the <problem C> is therefore equivalent, in the case where plane lighting waves of variable direction are used, to the resolution of the <problem A>.

 The microscope of [Noda] was not designed as a synthetic aperture system, however its operation can be interpreted in this context. Indeed, the technique adopted by [Noda] is to use on the receiving surface a reference wave formed by the light wave alone. From the images received for a set of lighting waves of variable direction, a three-dimensional frequency representation is obtained. The complex wave detected on the receiving surface is hereby replaced by a pure imaginary value obtained by multiplying by; the actual value obtained by using the unique reference wave constituted by the illumination wave shifted in phase of # / 2. If the reference wave is sufficiently greater, at each point of the receiving surface, than the diffracted wave, then the quantity thus obtained is the imaginary part of the complex wave actually received on the receiving surface, the

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 phase reference being the phase of the illumination wave. The object generating on the receiving surface a pure imaginary wave equivalent to that detected by [Noda] is constituted by the superposition of the observed real object and a virtual object whose complex spatial representation is obtained from that of the real object by symmetry with respect to the plane of the object corresponding to the receiving surface, and by inversion of the sign of the real part. By using the imaginary part thus detected in a manner similar to that [Turpin] uses the detected complex wave, a function representing the superposition of the real object and the virtual object is thus generated in frequency representation. At each acquisition, the two-dimensional frequency representation obtained by Fourier transform of the value detected on the reception surface comprises a part corresponding to the real object and a part corresponding to the virtual object, which only overlap with each other. corresponding to the lighting frequency. It is therefore possible to select only the part corresponding to the real object, so as to obtain a representation of it. [Noda] actually uses the superposition of the real object with the virtual object that it symmetries with respect to the plane of the object corresponding to the receiving surface, thus obtaining a pure imaginary representation representing the imaginary part of the representation which would be obtained by the method of [Turpin] in which the <problem A> would be supposed to be solved.

 The theoretical explanations given in the document [Noda] are very different from those presented here and are perfectly valid. The principle of inverting a filter by multiplication in the frequency domain, as applied by [Noda], is equivalent to the explanations given above, although obtained by a different reasoning. It can be considered that FIGS. 2 and 3 of [Noda] illustrate how the three-dimensional frequency representation of the object is generated from two-dimensional frequency representations.

 Since the reference wave coincides with the illumination wave, the <problem A> does not arise in [Noda] 's microscope.

 The simplest way to solve the "problem D", ie to extend the conditions of use of the microscope of [Noda], is to use a reference wave distinct from the wave of lighting.

The microscope of [Noda] then becomes a synthetic aperture system similar to that of [Turpin] and the resolution of the <problem D> then involves the resolution of the <problem A>.

 In the [Vishnyakov] microscope, the determination of the value of # is equivalent to a determination of the phase of the transmitted wave and the reference wave, a determination which implies, a priori, knowledge, at a fraction of a micrometer, the position of each element used to generate these beams, that is, the resolution of <problem A>. The <problem E> is therefore equivalent to the <problem A>.

 The [Vishnyakov] microscope constituting a physical system similar to that of [Turpin], the <problem F> is solved if the algorithms used by [Vishnyakov] are replaced by algorithms similar to those of [Turpin]. Since the light wave has a direction and a variable phase, the [Turpin] algorithms are not functional in this case. The resolution of the <problem F> therefore implies the resolution of the <problem A>.

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 The problems C, D, E, F are thus reduced to the resolution of the <problem A>. The main object of the invention is therefore to solve the <problem A> in systems where a reference wave distinct from the illumination wave is used. A second object of the invention is to solve the problem B.

 The basis of reasoning can be <system 2>. The <problem A> is divided into two parts: - <problem Al>: knowledge of the position of the transmitter with respect to the receiver, and algorithmic compensation of the deviations.

- <A2 problem>: knowledge of the position of the receiver with respect to the object, and algorithmic compensation of the deviations.

3. 3. Resolution of the <Al problem>
The light wave is defined by its direction, that is to say its wave vector, and by its complex value, that is to say its intensity and its phase. To solve the <Al problem>, it is necessary to know: - its wave vector, in a frame linked to the receiver.

- its phase, relative to the phase of the reference wave.

 The necessary precision on the direction of the illumination wave is of the order of the degree of angle, and this accuracy can be reasonably achieved by mechanical means.

 The necessary precision on the phase of the light wave is of the order of ten degrees, which results in a precision of the order of # / 10 on the optical path, ie about 50 nm for a HeNe laser. This accuracy can not be achieved by simple mechanical means such as those proposed by [Turpin].

 In <system 2>, a two-dimensional frequency subrepresentation is obtained from each position of the transmitter-object-receiver ensemble by determining the frequency representation of the wave coming from the object and reaching the receiver and by translatant of a vector -fe. Frequency subrepresentation can also be obtained by grouping several of these two-dimensional frequency sub-representations obtained for example when the object is moved, the light wave and the receiver remaining fixed. An uncontrolled variation of the phase of the illumination wave results in an overall variation of the phase of the corresponding frequency subrepresentation, which prevents a correct superposition of this underrepresentation to the other sub-representations.

3. 3.1. In the <system 1>
In <system 1> the <Al problem> is solved by the method generally used in synthetic aperture radars, that is to say by using a transmitter and a receiver fixed relative to each other.

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3.2. According to the invention
Given the considerations developed in 3. 2. and 3. 3., and assuming the <problem A2> solved, the resolution of the <problem A> and / or the <problem C> is thus reduced to the knowledge of the phase of each under-representation of the object. The object of the invention is to solve the problem A1 in the case where the direction of the illumination wave is variable in a frame linked to the receiver, in which case the systems described by [Turpin] are not functional.

 According to the invention, the microscope comprises at least one of two groups of means (i) or (ii): (i) active or passive means for controlling the phase differences between the light waves and the waves so that, on each sensor and for each illumination wave, the phase difference between the illumination wave and the reference wave used on said sensor has a predetermined value.

 (ii) means for generating, from one or more of said interference figure recordings, sub-representations of the observed object, and means for determining the phase differences between sub-representations of the object; observed object.

Various combinations of aspects (i) and (ii) can be realized: - version described in 7.17.2. : phase differences are determined at each acquisition. It is therefore means according to (ii) only.

- version described in 7.18.1. The phase differences were measured in a preliminary phase by a method according to (ii). Phase differences are then known during data acquisition and need not be measured again. In the actual acquisition phase, means according to (i) are therefore used, but are supplemented by means according to (ii) when it is necessary to compensate for the vibrations. The means according to (i) are passive means, in that the phase differences are predetermined but are not actively modified by an external system.

- version described in 7. 18.7. The phase deviations are zero and no algorithmic compensation is performed after the acquisition. This is a method according to (i), but again a method according to (ii) was used in a preliminary phase. The means according to (i) are active means, in that an external phase shift system is used to control these deviations.

 - versions described in 8. 6. and 9.20: phase differences are zero and therefore predetermined. These are means according to (i) only. These means are passive.

 The microscope according to embodiment 4, with the adjustment defined in 8. 6., can operate optionally in configurations employing the means (i) or (ii) separately or associated, and differing only by the control algorithms and calculation employees. The same is true of the system according to embodiment 5.

 The means according to (ii) may optionally be employed in a preliminary phase and in the absence of an object. They make it possible to obtain the phase differences between representations of a part

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 delimited space, part that can be occupied by an object or that can be empty, in which case its three-dimensional representation, and therefore its under-representations, are punctual.

 The means (i) and (ii) in fact cover a single notion, namely that the microscope comprises means for determining the phase shift affecting each acquired image, whether due to an active control of the beams of lighting or reference, preliminary adjustments made, or the use of algorithms allowing the subsequent calculation of these phase differences from the recorded data.

 The calculation of the three-dimensional representation of the object does not necessarily imply the determination of the complex value of the wave received on each receiving surface for a given illumination. For example if the variant described in 7. 18.6. is used, only real values corresponding approximately to the real part of the complex value of said wave are used. If the method described in 7. 18.5. is used, the complex value of the received wave on the receiving surface is not determined either.

3. 4. Solution of <A2 problem>
To solve the <problem A2> it is necessary to know: - the angular position of the receiver relative to the object.

the position in translation of the receiver with respect to the object.

 The necessary precision on the angular position of the receiver is of the order of the degree and can reasonably be reached by mechanical means.

 The reference wave used in the receiver has a virtual point of origin in the object being observed. This virtual point of origin can be used to locate the position of the receiver relative to the object. If we assume that the system is such that the origin point of the reference wave corresponds to a fixed point in the sample, we can show that the three-dimensional spatial representation generated by the <system 2> is centered on this point . A displacement of this point is thus translated by a translation of the generated three-dimensional image. If this point moves with respect to the object during the acquisition phase of two-dimensional frequency representations, the effect is that the representation obtained will be the superposition of partial representations that are translated relative to each other. A displacement of this point with respect to the object thus results in a scrambling of the image over a distance equivalent to the displacement distance. Contrary to the <Al problem>, the <A2 problem> does not automatically result in a disappearance of the image, but by a decrease in resolution.

3.4.1. in the <system 1>
In <system 1>, the adoption of the physical configuration defined by [Hufnagel] makes possible in principle the resolution of the <A2 problem>.

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 However an effective resolution supposes not only a mechanical system allowing the knowledge of the movement of the object, but also in the taking into account of this movement in the definition of the algorithms and / or an appropriate setting of the system. In the absence of special precautions, the origin point of the reference wave moves relative to the object on a circle centered on the axis of rotation of the object. If this displacement is important, this effect destroys the image. If this displacement is small, the resolution in the plane of this circle is affected in proportion to the amplitude of the displacement.

 To solve the <A2 problem> in the absence of a specific compensation algorithm, the origin point of the reference wave must be on the axis of rotation of the object. This condition is a priori difficult to achieve. [Turpin] does not mention this problem and does not specify any suitable means of adjustment.

3. 4.2. According to one version of the invention
The invention solves the <problem Al>. Consequently, a set of two-dimensional frequency representations can be constituted by varying the direction of the illumination beam and it is not necessary to vary the position of the receiver. According to one version of the invention, the receiver is fixed with respect to the object. In the absence of relative movement between the object and the receiver, the position of the object can be known and the <A2 problem> can be solved. In the case where the receiver uses a single reference wave centered on a point of the object, the frequency representations obtained will all be relative to this same point of the object and no algorithmic compensation is therefore necessary.

 3. Application of the invention to render functional systems derived from [Turpinl.

 The <system 1> and the <system 2> are not made functional by the present invention which does not solve the <problem A2> in the most general case.

 From <system 2>, one can derive a simplified system in which the position of the receiver and the position of the object are fixed, and in which the illumination wave has a variable direction. The system thus modified will be called <system 3>. In this system, the <A2 problem> is solved by the absence of relative motion between the object and the receiver. The <Al problem> is solved by the method specified in 3. 3.2.

 In <system 1>, the <A2 problem> can be solved, for example when using a planar sample, by making an adjustment to verify the following conditions: (i) - the image of the reference wave on the CCD array image of FIG. 1 of the document [Turpin 3] must be punctual.

(ii) - When the object rotates 180 degrees, the resulting image must be symmetrical with respect to an axis passing through the image point of the reference wave.

 The position of the CCD array must be adjusted to check (i).

 The position of the receiver assembly must be adjusted to check (ii).

 This solution is however rather imperfect, depending essentially on a visual appreciation.

It can only reasonably be used for very simple objects.

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 Nevertheless, by using this method, <system 1> can be made functional. If from the <system 1> thus made functional is further authorized the variation of the illumination wave, we obtain a device that will be called <system 4> which is also made functional by the present invention. In this system, the <Al problem> is solved by the method specified in 3.3.2.

 <System 3> and <system 4> are embodiments close to the state of the art. Nevertheless, they remain ineffective and differ significantly from embodiments 1 to 5 described later in this patent.

3. 6. Recalibration methods in phase
3. 6.1. General method of phase registration
We consider a part of the three-dimensional representation of the object: - constituted by a subset A of the three-dimensional representation.

characterized by a function a (f) defined on A and conventionally zero out of A, where / is the spatial frequency vector and a (f) the value of the representation on this spatial frequency. affected by a Gaussian noise, the standard deviation of the noise on a given frequency f being # a (f).

 This underrepresentation will be referred to as the RA subrepresentation. We will say that A is the support of RA.

affectée par un bruit gaussien b ( f , désignée par l'expression sous-représentation RB
Ces deux parties de la représentation sont décalées en phase l'une par rapport à l'autre et sont supposées avoir une intersection non vide. A partir de ces deux parties, on va générer une sousreprésentation RC définie sur un ensemble C = A u B (C est la réunion de A et B) et définie par une

fonction c(/) affectée par un bruit gaussien (Je ( fez . Consider a second part of the three-dimensional representation of the object, constituted by a subset B of the three-dimensional representation, characterized by a function b (f) defined on B.

affected by a Gaussian noise b (f, denoted by the expression RB underrepresentation
These two parts of the representation are phase shifted with respect to each other and are assumed to have a non-empty intersection. From these two parts, we will generate a subrepresentation RC defined on a set C = A u B (C is the union of A and B) and defined by a

function c (/) affected by a Gaussian noise (Je (fez.

(/M7) 2 2 les sommes sont sur ensemble vecteurs fré uences inclus dans y = -######-## les sommes sont sur un ensemble E de vecteurs fréquences inclus dans 1 b(J)1 2 les sommes sont sur ensemble vecteurs fréquences inclus dans f eE 07,, (f ) + Ub l'intersection des deux ensembles A et B, soit E c (A # B) . La différence de phase entre les deux représentations est l'argument de r. La différence de phase ainsi calculée est la différence de phase la plus probable connaissant les valeurs des représentations RA et RB sur l'ensemble E. One can proceed in two stages: a complex ratio between the two representations can for example be obtained by the formula:

(/ M7) 2 2 sums are on set frequency vectors included in y = - ###### - ## sums are on a set E of frequency vectors included in 1 b (J) 1 2 sums are on a set of frequency vectors included in f eE 07 ,, (f) + Ub the intersection of the two sets A and B, ie E c (A # B). The phase difference between the two representations is the argument of r. The phase difference thus calculated is the most probable phase difference knowing the values of the representations RA and RB on the set E.

b( f E-- r. b( f ou le signe <- désigne l'affectation. the representation RB can be adjusted in phase with respect to RA by multiplying it by the ratio r:

b (f E - r) b (f or the sign <- indicates the assignment.

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/) , + b(f) 2 2(f) c(f) = 0-; f) Ub 1 1 1~ o- (J) o- (1) Les valeurs ainsi affectées à la représentation RC sont les valeurs les plus probables connaissant les représentations RA et RB recalées en phase.

-la fonction 0- c (1) peut être obtenue par exemple par la formule: 1 1 1 6cl.f) al,Î)+bt.f)
L'ensemble des deux opérations précédentes constitue le regroupement de RA et RB
Des explications plus détaillées sur le calcul de ces fonctions sous forme de tableaux sont données au paragraphe 7.17.1. Les formules indiquées ci-dessus pour le recalage de phase effectuent simultanément une normalisation en intensité, qui toutefois n'est pas indispensable. the function c can be obtained for example by the formula:

/), + b (f) 2 2 (f) c (f) = 0-; f) Ub 1 1 1 ~ o- (J) o- (1) The values thus assigned to the representation RC are the most probable values knowing the representations RA and RB recalibrated in phase.

the function 0 -C (1) can be obtained for example by the formula: ## STR1 ##
All of the two previous operations constitute the grouping of RA and RB
More detailed explanations of the calculation of these functions in tabular form are given in paragraph 7.17.1. The formulas indicated above for the phase registration perform simultaneous intensity normalization, which however is not essential.

 This method makes it possible, from two subrepresentations RA and RB whose supports A and B have a non-empty intersection, to obtain a subrepresentation RC corresponding to the superposition of RA and RB.

 If the three-dimensional frequency representation of the object must be reconstituted from many sub-representations whose phases are not known, the above method, applied iteratively, allows to group all these sub-representations. For example, one can start from a given underrepresentation, group it with a second underrepresentation. We can then start from the underrepresentation generated by this group, and group it with additional subrepresentation. By repeating this grouping operation until all the sub-representations have been integrated into a global representation, the three-dimensional frequency representation of the object is finally obtained. The only conditions that must be satisfied for this method to succeed are: - no under-representation or group of sub-representations has an empty intersection with all other sub-representations.

- that the object does not have a very singular frequency representation, which would be for example zero on a set of points separating in two its three-dimensional frequency representation.

 These conditions are easily satisfied for most biological objects when a large number of representations are acquired.

 For example: - in the case of <system 3>, an underrepresentation is constituted by a two-dimensional frequency representation obtained for a given lighting wave.

in the case of <system 4>, an under-representation is constituted by the set of two-dimensional frequency representations obtained for a given lighting wave when the object is moved in rotation.

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in the case of embodiment 5, paragraph 9. 19., an under-representation is constituted by a two-dimensional frequency representation obtained for a given illumination wave. A reduced number of sub-representations is first grouped into a base representation having a non-zero intersection with all other underrepresentations obtained under similar conditions. The set of representations is then adjusted in phase with respect to the basic representation, then a global representation is generated.

in embodiments 3,4,5, four intermediate sub-representations are generated each time, as explained in 7.17.1.1. These four representations are united in one by application of this general method.

 According to one version of the invention, the microscope comprises means for: - determining, for each underrepresentation RB, a coefficient characterizing the phase difference between this underrepresentation and another underrepresentation, part of underrepresentation or group of subrepresentations RA, this coefficient being calculated from the values of RA and RB on a set included in the intersection of the supports of RA and RB.

- correct the phase of RB so as to obtain for RB the same phase reference as for RA.

 According to one version of the invention, the microscope comprises means for: - determining, for a given subrepresentation RB, the frequency representation RC resulting from the grouping of RB with another subrepresentations RA.

determining a characteristic coefficient of the noise affecting RC defined over the entire RC support, obtained from a characteristic coefficient of the noise affecting RA and defined on the support of RA, and from a characteristic coefficient of the noise affecting RB and defined on the RB support.

 The methods used may differ from the formalism outlined above. For example, in the embodiment 1 the ratio r allowing the phase registration is calculated by a formula differing significantly from that indicated here. In the same embodiment, the quantity 1 / # 2c (f) is assimilated to the number N of frequency representations reaching a given point.

 The calculations can be grouped: phase registration of each subrepresentation, these can be combined into a global representation, without calculating each intermediate under-representation.

This is done in the set of embodiments to group two-dimensional sub-representations into full or partial three-dimensional sub-representations.

 It is possible to calculate representations of the object without formally passing through its three-dimensional frequency representation. For example in 7.17.3.3. a confocal representation of the object is generated by using for the final frequency representation a value at each point which is the sum of the values obtained for each representation reaching this point. The representation thus obtained is not, strictly speaking, a frequency representation of the object but is nevertheless

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 carrier of information about this object. It is also possible to generate real representations of the index or the absorptivity. These representations can be generated in a simple way by passing through the frequency representation of the object, however it is also possible to modify the algorithms to not formally use this intermediate.

3. 6.2. Absolute phase registration
The method explained in 3.6.1. allows to obtain a three-dimensional representation of the object.

However, the overall phase of this three-dimensional representation remains arbitrary.

 In the three-dimensional spatial representation of the object, obtained from the three-dimensional frequency representation by inverse Fourier transformation, the complex number associated with each point characterizes the absorptivity and the index of the object at the point considered. If the overall phase of the three-dimensional representation is appropriately selected, the real part of said complex number characterizes the local absorptivity of the object and the imaginary part of said complex number characterizes the local index of the object. The overall phase is appropriately selected when the origin point of the three-dimensional frequency representation has a real value.

 According to a version of the invention, and in cases where the origin point of the three-dimensional frequency representation is one of the points that have been acquired, the microscope comprises means for dividing, by its value at the origin point, the three-dimensional frequency representation obtained. by the method detailed in 3.6.1. This makes it possible to obtain a spatial representation in which the real part and the imaginary part of the complex numbers respectively represent the local absorptivity and the local index. This also makes it possible to standardize the whole representation.

 When the origin point of the three-dimensional frequency representation is not one of the points that have been acquired, this operation is impossible. The operator who visualizes an image then visualizes for example the real part of the complex number, and must intuitively choose the overall phase of the representation so as to obtain the most contrasted image possible.

3. 6.3. Phase registration with respect to the illumination wave
The general phase alignment algorithms defined above have the defect of being of a relatively complex implementation. A simplified version can be obtained when the acquisition system allows the acquisition of the non-diffracted portion of the illumination wave. This has a point image on the reference surface, which corresponds to the origin point of the three-dimensional frequency representation of the object. This point is common to all two-dimensional frequency representations.

 The phase registration described in 3.6.1. can then be performed with respect to the part of underrepresentation constituted by this single point. This registration may be grouped with the absolute registration described in 3. 6.2. The set of two recalculations then amounts to dividing each plane image into frequency by its value at the image point of the illumination wave. According to one version of the invention, the phase registration of two-dimensional frequency representations is performed by dividing each of these representations by

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 its value at the point corresponding to the illumination wave. This method is used for example in embodiments 1,2,3 and 4.

3. 6.4. Recalibration in uar phase compared to pre-recorded nhase values
A three-dimensional frequency representation of the object is obtained from a series of two-dimensional frequency representations each corresponding to a different lighting beam.

 Each of these two-dimensional frequency representations can be recalibrated in phase with respect to the underrepresentation constituted by the origin point alone, as indicated in 3. 6.4. However, the high intensity of the corresponding point on each two-dimensional frequency representation makes it difficult to simultaneously acquire the remainder of the representation. According to one version of the invention, the acquisition of the plane images in frequency is carried out in two stages: - a preliminary phase, during which are recorded the values obtained at the image point of the illumination wave, for each wave of 'lighting.

- An actual acquisition phase, during which the direct beam can be hidden and during which the values of the frequency-plane images are recorded.

 A plane frequency image, or equivalently a two-dimensional frequency representation, can then be obtained for each illumination wave from these two recordings, the value at the image point of the illumination wave being obtained from the first recording and the value at any other point being obtained from the second record. The method described in 3. 6.4. can then be applied to each two-dimensional frequency representation obtained.

 When a series of two-dimensional frequency representations is performed, for example to 'film' the motion of cells, the preliminary phase should not be repeated. Just do it once before the start of the acquisitions.

 For this method to be functional, the phase difference between the illumination beam and the reference beam at the receiving surface must be reproducible. The lighting beam generation systems used in Embodiments 3,4 and 5 satisfy this condition.

 3. 6.5. Phase registration in relation to a reference image.

 The method described in 3. 6.4. assumes the reproducibility of the lighting beams. The method described in 3. 6.3., In the case where several objectives are used, assumes a constant phase shift between the waves received on each of these objectives. However, in embodiments 3,4 and 5, the vibrations may render these methods inoperative or not robust. For the results to be reliable, it is necessary to compensate for these vibrations.

 For this purpose, the system can periodically acquire a reference image. The reference image consists of a plane frequency image obtained for a fixed illumination wave, which is not modified when the illumination wave used to obtain the 'useful' frequency plane images varies. Each plane frequency image then corresponds to a reference image acquired at a close instant. A reference image acquired at an initial moment is chosen as absolute reference. By 'useful' image is meant a

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 image from which a two-dimensional frequency representation used to generate the representation of the object will be calculated.

h(f ) l'image de référence correspondante. On note ho(J) l'image de référence choisie comme référence absolue, obtenue sur la même surface de réception. freprésente la projection plane de la fréquence et est donc un vecteur à deux dimensions variant sur l'ensemble de la surface de réception. On note cr(/) l'écarttype du bruit gaussien affectant la fonction /?(/) en chaque point. We denote m (f) a plane image in 'useful' frequency obtained on a given reception surface and

h (f) the corresponding reference image. We denote by ho (J) the reference image chosen as absolute reference, obtained on the same reception surface. Frepresents the plane projection of the frequency and is therefore a two-dimensional vector varying over the entire receiving surface. We denote by cr (/) the standard deviation of the Gaussian noise affecting the function /? (/) At each point.

ho ( 2 h(.Î a2 (J) lh(f)12~ f a2(J) qui représente l'écart de phase le plus probable entre les images de référence /?(/) et ho(f).
L'image m(f) peut alors être recalée en phase comme suit :

m(f) r.m(f) ou le signe <- désigne l'affectation. The phase variation of vibratory origin can for example be characterized by the coefficient

ho (2h (.i a2 (J) lh (f) 12 ~ f a2 (J) which represents the most probable phase difference between the reference images /? (/) and ho (f).
The image m (f) can then be recalibrated in phase as follows:

m (f) rm (f) or the sign <- designates the assignment.

 When this phase registration has been carried out, the frequency-plane images thus recalibrated in phase can be used in the algorithms defined in 3. 6.3. and 3.6.4.

 If the system is totally vibration free, this preliminary registration is not necessary.

 If the vibrations are of low frequency, the reference image can be acquired only at a low frequency, however higher than the frequency of the vibrations of the system.

 If the vibrations are strong, it is possible to acquire a reference image to each useful image.

 In the presence of vibrations, this preliminary registration is essential for the application of the algorithm defined in 3.6.4.

- this preliminary registration is not essential for the application of the algorithm defined in 3. 6.3. in the case where only one objective is used. However, in the case where several objectives are used, it makes it possible to fix the phase difference between the plane frequency images generated from each objective. In this case, it is therefore also essential.

 This technique is used in Embodiments 3 and 4 and described in 7.17. It is also used in embodiment 5 when the phase registration is performed in accordance with paragraph 9.18.

 One version of the invention therefore consists in periodically acquiring reference images corresponding to a fixed lighting direction, and in using these images to compensate for phase deviations of vibratory origin affecting the plane frequency images.

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3. 7. Characterization of the wave vector of the illumination wave
In <system 3> it is necessary to control the direction of the light wave, that is to say its wave vector fe. This is possible with mechanical means. Nevertheless, these mechanical means must be of great precision and are expensive to implement.

 Under the conditions defined in 3. 6.3., That is, if the acquisition system allows the acquisition of the non-diffracted portion of the illumination wave, the non-diffracted part of the wave of lighting corresponds to a maximum of illumination on the plane image in corresponding frequency. According to one version of the invention, the microscope comprises means for determining the coordinates of this maximum and for calculating, from these coordinates, the wave vector f e of the illumination wave. The vector thus obtained is expressed in the reference used to calculate the two-dimensional representation of the diffracted wave. This method is used for example in Embodiments 1 and 2.

 However, the presence of the object may slightly distort the value of the wave vector thus obtained.

According to one version of the invention, the wave vectors fe of each illumination wave are obtained in a preliminary phase or the object is deleted or replaced by a transparent plate. The wave vectors thus obtained are therefore not distorted by the presence of the object. This method assumes that the wave vectors are reproducible from one acquisition to another. On the other hand, it avoids having to calculate these wave vectors as a function of mechanical parameters. This method is used in Embodiments 3,4 and 5.

3. 8. Receiver Features
3. 8.1. Using a microscope objective
<System 3> resolves <problem A>, but <problem B> remains significant in this system. To improve the system from the point of view of <problem B>, it is necessary to increase the opening of the receiver. This can be done by replacing the Nikkor lens, used in [Turpin 3] to capture the wave from the object, by a high aperture microscope objective. One version of the invention therefore consists in using as a receiver a microscope objective with a large aperture.

3. 8.2. Using the receiver [Lauerl
The receiver used in [Turpin 3] also has the following two defects: - The wave arriving at the sensor, which carries out a sampling in the frequency domain, must have a limited extension in the space domain, otherwise spectrum folding , due to non-compliance with the Nyquist criterion on the sensor, can significantly degrade the quality of the image. As the illuminated area has no clear limits and in particular may be of different size depending on the arrival angle of the illumination beam, compliance with this condition implies a strong oversampling, the whole of the illuminated area, including the dimly lit part, to be included in the generated image, regardless of the angle of arrival of the lighting beam and the position of the sample.

- The wave received on the receiving surface corresponds to a sphere portion in a three-dimensional space. [Turpin 3] likens it to a portion of a plane, which causes notable disturbances.

In the case of a high-aperture lens, these disturbances are not tolerable.

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 These two faults are removed by using for the receiver the configuration and the algorithms defined by [Lauer]. This makes it possible to effectively obtain portions of the sphere, and to avoid spectrum folding by the presence of a diaphragm.

 One version of the invention therefore consists of using as receiver the system defined by [Lauer].

This version is for example implemented in embodiment 1.

3. 8.3. Using a reception surface in a space plan
Apart from the microscope objective itself, the reception system [Lauer] has a paraxial portion for modifying the optical signal sensed by the objective, to obtain a frequency representation. The signal from the lens first passes through the plane or lens normally forms the image of the observed sample. This plan will be called space plan. It is then transformed by a paraxial system so that in the plane where the receiving surface is placed, a plane wave coming from the object has a point image. This plane, where the receiving surface is placed, will be called the frequency plan. The paraxial portion of the optical system used may comprise intermediate space or frequency planes. The receiving surface may be placed in a space plane, in a frequency plane. or in an intermediate plan. However, to simplify the calculations, it will always be placed either in a space plan or in a frequency plan. In order for the received image to be correct, the following conditions must also be met: - if the receiving surface is in a frequency plane, the reference wave must be centered virtually at a central point of the observed object.

if the reception surface is in a space plane, the reference wave must be the image of a virtual wave which is plane at the crossing of the observed object.

 Under these conditions, the signal detected on a reception surface placed in a frequency plane is the optical Fourier transform of the signal that would be detected in a space plane. A version of the invention constituting an alternative to the receiver [Lauer] is therefore to use a receiving surface positioned in a space plane and a reference wave which is the image of a plane virtual wave at the crossing of the observed object. A digital Fourier transform then replaces the optical Fourier transform.

 Embodiments 1, 3, 4 use receive in a frequency plan and embodiments 2 and 5 use receive in a space plan. The plane image in frequency defined in 3.1. can thus be obtained either directly on a reception surface placed in a frequency plane, or by Fourier transformation of an image received on a reception surface placed in a space plane.

3. 9. Beam attenuation
In the case where the sensor is placed in a space plane, the direct lighting wave has as representation on the sensor a constant module value which is superimposed on the wave diffracted by the object.

A diffracted wave too weak relative to this constant base level can not be detected correctly. However, this basic level is low because the intensity of the reference beam is distributed

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 on the whole sensor, which generally makes it possible to obtain good images. In the case where the sensor is placed in a frequency plane, the illumination wave is concentrated at a point and as before, a diffracted wave too weak relative to this constant base level can not be correctly detected.

Since the wave is concentrated at one point, this basic level is high and this limitation is troublesome.

 According to an advantageous version of the invention, a controlled attenuation device of the beam, having one or more attenuation levels, is introduced to solve this problem. The attenuation device makes it possible to successively obtain several recordings differing by the intensity of the illumination wave. A less noisy value of the diffracted wave is then obtained by combining these recordings. The final value of the diffracted wave is for example calculated at each point from the recording for which the intensity of the wave received at the point considered is the highest, but for which the sensor remains unsaturated at the point considered and in its immediate neighbors for all the interference figures for obtaining said recording.

 In view of the use of a beam attenuation device, the version of the invention in which a plane wave has a point image allows the detection of weaker diffracted waves. Indeed, these are not superimposed on the sensor at any other wave and very low levels can be detected when the intensity of the illumination beam is high.

 Such a device is used in embodiments 1,3 and 4.

3. 10. Lighting beam generation system
Whatever the embodiment, it is necessary to design a method of generating the light beams. The methods proposed by [Turpin] have the disadvantage of requiring significant mechanical displacements and thus of slowing down the system.

 An optical system, for example that described in 8.1.1., Can transform a parallel beam of given spatial extension and of variable direction into a parallel beam whose spatial extension has been decreased and whose directional variations have been amplified. In general, small variations in direction applied to a beam of large spatial extent can be amplified by an optical system by reducing the spatial extent of the beam. Since the spatial extent of the illumination beam needed for a microscope is small, this principle can be used to optically amplify weak mechanical motions.

 A variable direction beam can be transformed by a lens into a beam of variable position in the image focal plane of this lens. A variation in the direction of the beam in part of its optical path is therefore equivalent to a variation of position in another part of its optical path and vice versa. In intermediate planes, the variation is a joint variation of position and direction.

It is therefore not necessary to differentiate a system generating variations in position of the illumination wave of a system generating variations in direction, these systems being equivalent.

 According to one version of the invention, the system for generating the light beams comprises: a beam deflector generating variations of a paraxial beam.

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a high aperture optical element (for example a microscope objective or a condenser) transforming said variations of the incident paraxial beam into significant variations of direction of the outgoing beam.

 It may also include a lens system sized so that the beam is parallel to the output of said optical element of high aperture.

 The beam deflector may be for example a mirror mounted on a positioner for controlling the orientation. This solution is implemented in embodiments 1 and 2.

However, this solution has two defects: - The movement of the mirror generates vibrations that disturb the system. After each movement of the mirror it is necessary to wait for vibration absorption before proceeding with the acquisition.

- the phase difference between the reference beam and the illumination beam is not reproducible, which prohibits the use of the algorithms defined in 3.6.4.

 Each of the beam deviators described in 3.10.1. , 3. 10.2 and 3. 10.3. solves these two problems.

3. 10.1. Beam diverter based on a series of binary deviators
A system that can return the beam in two directions can be constructed using a birefringent prism that transmits the ordinary beam and the extraordinary beam in two different directions. The laser beam used must then be polarized. A polarization rotator placed in front of the prism makes it possible to orient its polarization in the ordinary sense or the extraordinary direction, which implies a different angle of deflection by the prism. However, the available ferroelectric polarization rotators, which have the advantage of being fast, do not allow rotation of 90 degrees but rotation of about 80 degrees. This prevents having both a polarized beam exactly in the ordinary sense, for one of the positions of the polarization rotator, and a polarized beam exactly in the extraordinary direction for the other position. It is thus created, in one of the positions, a parasitic beam deviated in an undesired direction. In order to eliminate this parasitic beam, it is necessary to use at the output of the birefringent prism a polarizer selecting only the desired radius. So that this polarizer does not suppress the ray in the other position of the rotator, it is necessary to introduce between this polarizer and the prism a second rotator, used to bring the electric field vector of the beam in the forward direction of the polarizer, when he is not there directly from the prism.

 A system that can return a beam in many directions can be constituted by serializing several of these elementary systems. By associating two, which produce a deviation of the same amplitude but in two orthogonal directions, a doublet is formed. By combining in series N doublets, each doublet being characterized by birefringent prisms of characteristics such that the deflection angle of the doublet number i is proportional to 2 ', we obtain 2 N possible deflection values in each direction. For example with N = 8 we have a total of 256 x 256 beam deflection directions.

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 According to one version of the invention, the beam deflection system is constituted by the series association of elementary deflectors, each of these elementary deflectors comprising a birefringent prism deviating differently the ordinary ray and the extraordinary ray, preceded by a electronically controlled polarization rotator for directing the electric field vector of the beam along the ordinary axis or the extraordinary axis of said prism, followed by a second rotator and a polarizer for eliminating stray beams.

 Such a device is used in embodiment 3.

3. 10.2. Beam diverter based on space modulators
A spatial modulator is a two-dimensional array of pixels for modulating the phase or intensity of a wave in a plane. Most space modulators are based on liquid crystals.

Common LCD displays are an example of a spatial intensity modulator.

 A space plane, on the path of the light beam, will be defined as a plane in which this beam is parallel and is centered on the optical axis. A frequency plan will be defined as a plane in which this beam has a point image.

de la forme eXP{j2n{fxX + fyy)} ou (x,y) sont les coordonnées d'un point du plan et ou ( fx , f y sont les coordonnées de la projection du vecteur d'onde dans ce plan. Si un dispositif de modulation de phase est placé dans ce plan et si un décalage de phase de la forme 6 = 2nigxx + gyy + c\ est appliqué à l'aide de ce dispositif, l'onde a, après traversée dudit dispositif, une représentation complexe exp 2( fx + gx)x + (ly y + g y ) y + c } . Le dispositif de de modulation spatiale a donc modifié la direction de l'onde incidente. Les vecteurs d'onde que peut générer un tel dispositif de modulation spatiale sont compris dans un cône dont l'ouverture dépend des valeurs maximales de gx et gy permises par le modulateur. Ce cône sera appelé 'cône de déviation'. A parallel beam arriving in a space plane has in this plane a complex representation

of the form eXP {j2n {fxX + fyy)} or (x, y) are the coordinates of a point of the plane and where (fx, fy are the coordinates of the projection of the wave vector in this plane. phase modulation device is placed in this plane and if a phase shift of the form 6 = 2nigxx + gyy + c \ is applied using this device, the wave has, after passing through said device, a complex representation exp 2 (fx + gx) x + (ly y + gy) y + c}. The spatial modulation device has therefore modified the direction of the incident wave. The wave vectors that can be generated by such a modulation device are in a cone whose opening depends on the maximum values of gx and gy allowed by the modulator.This cone will be called the 'cone of deviation'.

est possible d' appliquer une fonction d'atténuation du type cos f 2(gxx+gyy+c) . Après traversée du dispositif, l'onde a alors une forme du type exp{j2n{Vx +gxx+(fy + g y)y + c)} + expJ./2 ((/x -gx)x + (fy -gy)y-ty qui correspond à la superposition de deux ondes planes dont les vecteurs d'onde sont symétriques par rapport à un axe orienté suivant le vecteur d'onde de l'onde qui sortirait du dispositifen l'abscence de modulation. Une des deux ondes peut être arrêtée par un diaphragme, moyennant quoi le dispositif constitue un déviateur de faisceau comparable au précédent. If an intensity modulation device is used instead of the phase modulation device, it

It is possible to apply an attenuation function of the type cos f 2 (gxx + gyy + c). After crossing the device, the wave then has a form of the type exp {j2n {Vx + gxx + (fy + gy) y + c)} + expJ./2 ((/ x -gx) x + (fy -gy) y-ty which corresponds to the superposition of two plane waves whose wave vectors are symmetrical with respect to an axis oriented according to the wave vector of the wave which would come out of the device in the absence of modulation. can be stopped by a diaphragm, whereby the device constitutes a beam deflector comparable to the previous one.

 Intermediate modulation devices, performing a co-modulation of phase and intensity, can also be used.

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 One version of the invention therefore consists in using as a beam deflector a suitably controlled spatial modulator.

B = 2gX x + 8 yY
Les dispositifs de modulation existants fonctionnent pixel par pixel. Cette discrétisation entraîne la génération de fréquences parasites hors du cône de déviation. Une version de l'invention consiste à supprimer ces fréquences parasites à l'aide d'un diaphragme placé dans un plan de fréquence sur le trajet de l'onde issue du modulateur de phase. One version of the invention consists in that said modulator is a phase modulator, controlled so as to generate a phase shift of a shape as close as possible to

B = 2gX x + 8 yY
Existing modulation devices operate pixel by pixel. This discretization causes the generation of parasitic frequencies outside the cone of deviation. One version of the invention consists in suppressing these parasitic frequencies by means of a diaphragm placed in a frequency plane on the path of the wave coming from the phase modulator.

 Modulation devices allowing fast modulation are binary, ie at a given pixel only two possible phase or intensity values correspond. The use of a binary modulation device results in the presence of a parasitic plane wave, symmetrical to the wave that is sought to obtain with respect to an axis constituted by the direction of a non-deflected beam. In the case of binary modulators, this is true even when it is a phase modulator, whereas in the case of modulators generating continuous modulation, this problem can be avoided by using a phase modulator. According to one version of the invention, the parasitic filter diaphragm is dimensioned so as to filter not only the frequencies outside the deflection cone, but also a portion of the frequencies located in the deflection cone, so as to stop the parasitic plane wave.

 Binary modulation devices also have the disadvantage of generating parasitic frequencies included in the deflection cone and constituting a 'noise' in frequency. According to one version of the invention, these frequencies are stopped by an intensity modulator placed in a frequency plane on the beam path from the phase modulator, and controlled to let only the desired frequency.

 Such a device is used in embodiment 4.

 3. 10.3. Beam deflector constituted by a movable mirror whose vibrations are rendered unobtrusive.

 The beam deflectors described in 3.10.1. and 3.10.2. are based on the use of liquid crystal devices and polarizers. These devices are not available in the field of ultraviolet radiation. To use ultraviolet radiation, it is therefore necessary to use other means.

 In previous devices, the entire system was placed on an optical table.

 According to one version of the invention, the beam deflection device is constituted by a mirror placed outside the optical table, the separation between the lighting beam and the reference beam being effected by a separator fixed on the optical table and positioned after said mirror on the path of the beam.

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 The mirror being placed out of the optical table, it does not generate vibrations of this table. Since beam separation takes place after the mirror, its vibrations do not generate phase shifts between the illumination beam and the reference beam either. This solves the problem of vibrations.

 On the other hand, the fact that the beam splitting takes place after the moving mirror implies that the reference beam varies at the same time as the illumination beam. This variation must be taken into account in the design of the system and compensated. For example, if the receiving surface is placed in a space plane, the directional variations of the reference wave result in translations of the plane image into frequency. According to one version of the invention, this effect is compensated by carrying out an inverse translation of the obtained plane frequency images.

 This technique is used for example in embodiment 5.

3. 11. Compensation of errors due to polarization
The image generation method employed in [Turpin] is based on a scalar theory of diffraction and assumes that the wave crossing the object is isotropically diffracted in all directions by each point of the object. Only with this assumption can the theoretical resolution of 4 be obtained. The scalar theory of diffraction is however not valid for the angles of
4 high diffraction. The intensity diffracted by a point of the object depends on the direction of the diffracted wave, the direction of the light wave, the direction of polarization of the light wave and the direction of polarization of the diffracted wave.

3. 11.1. Compensation by multiplication by a real coefficient
The wave diffracted by the object differs from the wave which would be diffracted if the diffraction was isotropic by a real multiplicative factor depending on: - the direction of propagation of the light wave - the polarization of the wave d - the direction of propagation of the diffracted wave - the polarization of the diffracted wave
According to one version of the invention, the microscope comprises means for determining this multiplicative factor and compensating it by multiplying the waves received by the inverse of said factor. Such a version of the invention is described in 7.18.8.

3. 11.2. Compensation in the case of anisotropic material
If the observed object consists essentially of an anisotropic material, the effects of diffraction differ from what they are in an isotropic material. The material is then characterized at each point by 6 crystalline parameters plus absorptivity.

 In the particular case where the observed object is a uniaxial crystal, the diffraction index of the ordinary ray has a constant value. According to one version of the invention, a three-dimensional representation

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 in which the complex numbers obtained characterize the absorptivity and the ordinary index can be calculated. According to this version of the invention, this representation is calculated from plane frequency images obtained for a polarized illumination wave so that it constitutes an ordinary ray.

 Since the direction of ordinary polarization varies with the direction of propagation of the wave, it is necessary to be able to modify the direction of polarization of the light wave. However, since the phenomena are linear, it is sufficient to record the wave received at every point for two directions of polarization of the light wave in order to be able to deduce the wave diffracted by the object for a light wave. any direction. According to one version of the invention, the microscope comprises means for generating two directions of polarization of the illumination wave. According to one version of the invention, the microscope also comprises means for analyzing the diffracted wave in two directions of polarization, which makes it possible to distinguish the ordinary diffracted wave from the extraordinary diffracted wave.

According to this version of the invention, the frequency-plane images are then obtained from four elementary images corresponding to each combination of the two directions of polarization and the two directions of analysis.

 Such a version of the invention is described in 7.18.9. In the version described in 7.18.9. only the analysis direction corresponding to the ordinary radius is used, however it is also possible to take into account the analysis direction corresponding to the extraordinary radius. Two plane frequency images are then obtained for each direction of propagation of the illumination wave, one corresponding to the ordinary index and the other to the extraordinary index. The final frequency representation is obtained from this set of images by taking into account the variations of the extraordinary index at each point of the frequency-plane images corresponding to the extraordinary index.

3. 11.3. Compensation by combination of several directions of polarization and analysis
In the case of isotropic material, the method described in 3.11.1. has the defect of considerably raising the level of noise. One method to avoid this problem is to acquire at least four plane frequency images corresponding to each combination of two distinct polarizations of the illumination wave and two polarization directions distinct from the diffracted wave. An appropriate algorithm then makes it possible, from these four images, to calculate a single image corresponding to the desired scalar quantity. According to one version of the invention, the microscope therefore comprises means for generating two distinct polarizations of the illumination wave, and means for analyzing the diffracted wave in two distinct polarization directions. According to one version of the invention, the microscope comprises means for calculating, from the plane frequency images corresponding to each combination of the two directions of polarization and of the two directions of analysis, a single plane frequency image representing at a magnitude complex scalar satisfying the homogeneous diffraction condition in all directions. This principle is used in embodiments 3,4, and 5. The principle of calculating said scalar quantity is detailed in 7.12.1.

 In the case of visible wavelengths, said means for varying the polarization of the illumination wave may consist of a liquid crystal polarization rotator. Said variation means of

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 the direction of analysis of the diffracted wave may be composed of a polarization rotator associated with a polarizer. In the case of ultraviolet, these devices are not available.

3. 11.4. Variation of the polarization direction of the illumination wave in the UV domain
In the UV domain, the polarization rotators can be replaced by a quartz wave plate rotating about an axis by mechanical means. However, these mechanical movements slow down the system considerably. This is why a system is used where the only mechanical movements are those of shutters and where the beam to be closed has a spatial extension as small as possible, so that the movement of the shutter is as small as possible. It is then possible to use a quick shutter or a crenellated rotary wheel shutter.

 According to one version of the invention, such a system comprises: a beam splitter separating the beam into a beam A and a beam B.

lenses placed on each beam A and B and focusing these beams on focusing points where the shutters are placed.

- A device for superimposing again beams A and B having passed through their respective shutters.

a device placed on the path of one of the beams A or B, in the part of the trajectory where the two beams are distinct, and modifying the polarization of this beam.

 Such a system may also include additional lenses for reforming parallel beams after traversing the shutters. It may also include a second polarization modification device. The device for modifying the polarization of the beam may be a wave plate. The beam splitting and beam superimposing devices may be semi-transparent mirrors. Such a device is used in embodiment 5.

 3. 11.5. Variation of the analysis direction in the UV domain.

 The wave coming from the object can be decomposed into a wave whose electric field vector is parallel to that of the reference wave and a wave whose electric field vector is orthogonal to that of the reference wave. The intensity received on the receiving surface is the sum of the intensity of the electric field wave orthogonal to the reference wave and the intensity produced by the interference of the reference wave and the electric field wave parallel to the reference wave. The first of these intensities does not depend on the phase of the reference wave and thus does not modify the complex value of the wave coming from the measured object by combination of interference figures corresponding to different phases of the reference wave. It is therefore only the electric field vector wave parallel to that of the reference wave which is obtained on the receiving surface.

 The direction of analysis of a wave can thus be modified simply by modifying the direction of polarization of the reference wave or symmetrically by modifying the direction of polarization of the wave coming from the object.

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 According to one version of the invention, the analysis direction is modified by variation of the polarization direction of the reference wave or of the wave coming from the object.

 According to one version of the invention, the polarization of the reference wave or of the wave coming from the object is modified by a device comprising: a beam splitter separating the beam into two beams A and B a blade a wave wave LA disposed in the path of the beam and a wave plate LB disposed in the beam path B, the angle between the neutral axes of these two wave plates being 45 degrees.

 The direction of polarization of the beam having passed through the wave plate LA is then deduced from the direction of polarization of the beam having passed through the wave plate LB by a rotation whose angle is the angle between the neutral axes of the blades. LA and LB waveforms If this angle is 45 degrees, the beams from the blades LA and LB will always have orthogonal polarizations, whatever the direction of polarization of the incident beam.

 The two beams A and B can then be joined by a superposition device after passing through shutters, as in the case of the device described in 3.11.4. This has the disadvantage of requiring the use of shutters at a point in the beam path where the beam direction is variable and the beam can not be focused on a fixed point.

 According to one version of the invention, the two beams A and B are separately superimposed on the beam coming from the object (if they constitute the reference wave) or on the reference wave (if they come from the 'object). The interference patterns corresponding to each polarization direction are then formed on two distinct receiving surfaces.

 Whether the frequency-plane images corresponding to each polarization are obtained on separate reception surfaces or on the same reception surface, a phase shift between these images is created which must be compensated. According to one version of the invention, the wave plates are positioned in such a way that the reference and illumination beams reaching a receiving surface have different polarization directions, preferably at 45 degrees one of the other. Under these conditions, the part of the wave coming from the object which comprises frequencies close to the illumination wave is detected on the two reception surfaces and can be used to calculate the said phase difference.

3. 12. Direct lighting suppression system
The light wave is usually much more intense than the diffracted wave. It can saturate the sensors or significantly reduce the signal-to-noise ratio of the system by requiring high-level acquisition. Removing the non-diffracted portion of the illumination wave during the acquisition phase or during part of the acquisition phase significantly improves system performance. In a frequency plane, the non-diffracted portion of the illumination wave has a point image and can be suppressed by placing an absorbent element thereon. According to one version of the invention, the system thus comprises a device for removing the non-diffracted portion of the illumination wave, placed in a frequency plane, and absorbing the beam over a reduced area around the point corresponding to this waveform. 'lighting.

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 According to one version of the invention, this device is constituted by a spatial intensity modulator controlled to be passing at any point except on a limited area around the point of impact of the non-diffracted part of the illumination wave. This version is implemented in embodiment 4.

 According to another version of the invention, this device consists of a pane movable in translation in a frequency plane, an absorbing black spot placed on the pane having the role of stopping the direct beam, the position of the pane being controlled to make this black point coincide with the point of impact of the non-diffracted part of the illumination wave. This version is implemented in embodiment 5.

 3. 13. Device for using space modulators.

 Space modulators used in 3.10.2. or in 3. 12. may in particular be fast binary modulators operating by reflection. They are generally used with the aid of a polarizing semi-transparent mirror, which is a device of cubic shape returning the incident beams in two different directions depending on their polarization. This device, because of its thickness, generates a slight aberration which widens the point corresponding to a given frequency, which is detrimental to the quality of the images obtained.

* To avoid the use of this device, it is possible to use beams reaching the modulator at an oblique angle. The incident and reflected beams are then separated. However, this method distorts the distribution of generated frequencies. To avoid this deformation, said oblique angle must be small.

 According to one version of the invention, this problem is solved by using a device consisting of a mirror with two orthogonal reflecting faces and a lens traversed in one direction by the beam directed towards the modulator and in the other direction by the beam reflected by the modulator. The incident beam is reflected by one side of the mirror, passes through the lens, is reflected by the modulator, crosses the lens in the opposite direction and is reflected by the second mirror face, returning to its original direction. The incident and reflected beams may overlap partially on the lens but are separated on the two-sided mirror. In order to obtain this separation on the mirror, while having an oblique angle as small as possible, the two-sided mirror must be approximately positioned in a focal plane of the lens and the modulator must be positioned in the other plane focal point of the lens.

3. 14. Using multiple objectives
Any limitations on the direction of the light wave, characterized by its frequency vector, affect the performance of the system because of <problem B>. The maximum accuracy is obtained when all possible directions are used. Similarly, it is desirable to record the wave diffracted by the object in all directions. When only one microscope objective is used, its opening limits the directions in which the wave diffracted by the object can be recorded.

Similarly, if we only illuminate the object by a side opposite the lens, we limit the possible directions of the lighting waves. According to an advantageous version of the invention, several objectives focused on the sample are used, which make it possible to record the wave coming from the following sample in more directions.

The objectives then cover almost all of the space around the sample, and the lighting waves must necessarily cross these objectives to reach the sample. According to one version of the invention,

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 each objective is associated with an optical system allowing firstly the measurement on a sensor of the wave coming from the sample and having crossed the objective, and secondly the formation of a light wave which after crossing of the objective becomes in the sample a plane lighting wave of variable direction.

The illumination waves can then be generated in all the directions covered by the opening of the objectives, and likewise the waves coming from the object can be measured in all these directions. The acquisition and calculation system can take into account all the waves measured on all the sensors for all the lights used and generates from these data the three-dimensional frequency representation of the object.

 It is possible to use a large number of lenses to receive all the waves from the sample, or to increase the working distance using low aperture lenses.

However, most of the samples observed in practice are planar and can conveniently be placed between two lamellae. A version of the invention constituting the best compromise between the difficulty of implementation and the performance is to use two wide aperture microscope objectives positioned opposite, the plane sample being introduced between these two objectives. This solution is used in Embodiments 3,4, and 5. In Embodiments 1 and 2, of lower performance but easier to perform, only one microscope objective is used.

3. 15. Generation of inverse beams
When two or more microscope objectives are used, a frequency-plane image is generated from the wave received by each objective. Each point of a frequency-plane image corresponds to a given wave vector of the diffracted wave. It is necessary, in order to be able to calculate the three-dimensional frequency representation of the object, to correctly determine these wave vectors, and this in a coordinate system common to the wave vectors received by each objective.

représentations bidimensionnelles RA ( avant translation de vecteur - fe ) reconstituées à partir de l'image plane en fréquence obtenue à partir d'un objectif donné est différent de celui utilisé pour les représentations RB obtenues à partir de l'objectif en vis-à-vis. Pour établir une correspondance entre ces deux repères il est nécessaire de déterminer les coordonnées de certains points à la fois dans le repère utilisé pour RA et dans le repère utilisé pour RB. The knowledge of the factor K and the optical center, defined in [Lauer], allows the determination of the wave vectors received on each frequency image. However, the benchmark used for

two-dimensional representations RA (before translation of vector - fe) reconstructed from the plane plane in frequency obtained from a given objective is different from that used for the representations RB obtained from the objective vis-à- screw. To establish a correspondence between these two marks it is necessary to determine the coordinates of certain points at a time in the reference used for RA and in the reference used for RB.

correspond un vecteur d'onde - fe de direction opposée dont l'image est un point PB de la représentation RB. Les coordonnées du point PB dans le repère utilisé pour RA sont l'opposé des coordonnées du point PA dans ce repère. Each point PA of the representation RA is the image of a wave vector fe of the illumination wave which reaches at this point in the abscence of an object, and has for coordinates those of this wave vector . To this vector

corresponds to a wave vector - fe of opposite direction whose image is a point PB of the representation RB. The coordinates of the point PB in the reference used for RA are the opposite of the coordinates of the point PA in this reference.

 The correspondence between the two marks can therefore be established if the coordinates of the point PB are also determined in the reference RB. This can be done by generating by optical means a wave vector beam opposite to the illumination beam and by determining the coordinates of the image point

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 of this beam in the reference used for RB. If this match is established in a sufficient number of points, the relationship between the markers used for RB and RA can be easily determined and these representations can be modified to use a common mark.

 Similarly, it is possible to obtain by optical means a direct correspondence between the reference marks RB and RA. This requires the adjustment of a number of optical elements. To make this adjustment, it is possible to check continuously the correspondence between the coordinates of the point PB obtained in each of the marks used, for a certain number of points PB (three points in principle).

 In both cases, it is necessary to generate a beam of the same characteristics as the lighting beam, but propagating in the opposite direction. In general, given a beam used in the system, the term inverse indicator beam will designate a beam of the same characteristics but propagating in the opposite direction.

 According to one version of the invention, the microscope thus comprises, during the adjustment phase, means for generating a reverse indicator beam of the illumination wave. These means may possibly be deleted after the adjustment phase corresponding to the determination, by means of calculation or by optical means, of the correspondences between the reference marks RB and RA.

 According to one version of the invention. the microscope also comprises means for generating, during a control phase, an indicator beam that is in inverse of the reference wave. This beam will also be used in certain adjustment phases. For example, if the receiving surface is in a frequency plane, the reference wave is virtually centered at a central point of the object. The reference beam reversing the reference wave makes it possible to adjust the position of the objectives so that these objectives are focused on the same point.

 According to one version of the invention, when the receiving surface is in a space plane, an additional beam centered on this space plane is also used during an adjustment phase, as well as its reverse indicator beam. This beam facilitates for example the position adjustment of the objectives in the absence of a reference wave centered on a point of the object.

 In embodiments 3,4, and 5, each beam used has a reverse indicator beam, and the means for generating these reverse flags are described as part of the microscope and are not deleted after the settings have been completed: shutters are simply used to stop these bundles.

 According to one version of the invention, the device generating an inverse indicator beam from an original beam comprises: a semi-transparent mirror separating the original beam into an unmodified beam and a secondary beam.

a lens focusing the secondary beam in a plane of focus.

a mirror placed at the point of focus which returns the inverted beam towards said lens.

 The fact that the mirror is placed at the point of focus ensures that the reflected beam has exactly the reverse direction of the incident beam. The reflected beam crosses the lens in the direction

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 reverse. The part of this beam which is then reflected again by the semi-transparent mirror has the same characteristics as the unmodified beam but is directed in the opposite direction.

 3. 16. Compensation for spherical aberration and misalignment of objectives.

 When two objectives are used, the <A2 problem> is soluble in principle since each objective is fixed with respect to the object. However, as in <system 4>, the resolution of the <A2 problem> implies not only the existence of a physical device that allows in principle its resolution, but also the definition of appropriate compensation algorithms.

 From each objective used, we can generate a three-dimensional representation of the observed object. In spatial representation, this representation is relative to a given point of origin, which will be called the characteristic point of the objective. The <A2 problem> results in the fact that the characteristic points of the objectives used do not coincide. The resolution of the <A2 problem> is reduced to determining the coordinates of the characteristic points of each microscope objective, in a common coordinate system, and then to appropriately translating each representation before superimposing them.

 3. 16.1. determining the coordinates of the points of origin corresponding to each objective.

 According to one version of the invention, this can be obtained by using a beam centered on a central point of the observed object and its inverse indicator beam. This beam is received on a sensor after passing through the objectives, and its reverse indicator is received on another sensor. From the beam received on a sensor, the two-dimensional frequency representation of this beam can be obtained and the coordinates of its point of focus can be determined. The focal point of the beam is the same as that of its reverse indicator beam. The difference between the coordinates of the focal point of the beam obtained from an objective and those of its inverse indicator obtained from another objective is equal to the difference between coordinates of the characteristic points of these objectives in a common reference frame.

 This method can be implemented with any number of objectives, provided that the configuration is such that no group of lenses is optically isolated, i.e. such a lens group if it does not bring together all the objectives used, it can always be reached by a beam from an objective outside the group. For example, if 6 goals are used, they should not be grouped in pairs: objective must receive beams from two other goals.

 This aspect of the invention is implemented in 7.9.1. and in 9.12.

3. 16.2.Determination of the movements of each objective
It is usually necessary to move the objectives to introduce the observed object. This operation modifies the obtained coordinates and makes it necessary to repeat the previous operation.

However, the presence of the object disturbs the beam passing through it and prevents the obtaining of a precise result. According to one version of the invention, this problem is solved by using parallel beams of variable direction. A parallel beam has a flat, point-frequency image and the value obtained at this point is little affected by the local irregularities of the observed sample.

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 The difference between the phase of such a beam received on a sensor before displacement of the objectives and the phase of the same beam after displacement of the objectives depends on the vector characterizing the displacement of the characteristic of the objective receiving the beam with respect to the characteristic point of the beam. objective of where the beam comes from. From these phase differences established for a sufficient number of beams it is possible, by an appropriate algorithm, to determine this displacement. According to this version of the invention, the phase of a set of parallel beams reaching a given sensor is thus measured a first time in the absence of the object and a second time in the presence of the object. From the phase differences and possibly the intensity ratios thus measured, an appropriate algorithm can recalculate the displacement of the characteristic points of each objective. These phase and intensity differences can be characterized, for each parallel beam, by a complex value obtained as a quotient of the value obtained in the presence of the object by the value obtained in the absence of the object at a corresponding point. of the plane plane in frequency. This value will be called the phase and intensity ratio on a given parallel beam.

 Knowing the initial coordinates of the point of origin of each representation and its displacements, its current coordinates can be deduced and the position difference can be compensated.

This method can be implemented with any number of objectives, at the same condition as in 3. 16.1.

 The first measurement in the abscence of the object is carried out for example in 7. 9.2. and in 9.13. In both cases, the correction related to the position values determined as indicated in 3.16.1. is described in the same paragraph as this measure.

 The second measurement in the presence of the object and the calculation of the displacements are for example carried out in 7.11. and in 9.15. In both cases the absolute positions are directly calculated, without moving, the correction related to the position values having already been performed as indicated above.

3. 16.3. Determination of the index and the thickness of the object
When two objectives of the microscope vis-à-vis are used and when the observed object forms a layer between two flat lamellae, the average index of the object, if it differs from the nominal index of the objective (index of the optical liquid intended to be used with the objective), creates a spherical aberration which distorts the three-dimensional representations obtained. This spherical aberration results in phase and intensity variations of the beams measured in 3. 16.2., These variations depending on the index and the thickness of the object. According to one version of the invention, a program uses the values measured in 3. 16.2. to simultaneously determine the displacements of the objectives, the index and the thickness of the object.

 The calculation made in 7. 11. or 9. 15. is an embodiment of this aspect of the invention.

3. 16.4. Minimization algorithm
For given values of the displacements and the index and the thickness of the object it is possible to calculate the phase and intensity ratios on each parallel beam. According to one version of the invention, the calculation algorithm determines the values of the displacements and the index and the thickness of the object which

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 minimize the mean squared difference between the theoretical values thus calculated and the values actually measured.

 This algorithm must determine an absolute minimum on a set of five parameters of a noisy function, the quadratic deviation function having even in the abscence of noise local minima other than the absolute maximum. This problem therefore lends itself badly to conventional minimization methods.

 When the values of the parameters are known in an approximate manner, the algorithm can firstly maximize the value at the origin point obtained by offsetting the phase differences due to these parameters. A maximization of a function being equivalent to a minimization of its opposite, one will use only the term maximization to define the algorithm, but one could as well speak of minimization.

 According to one version of the invention, the algorithm comprises iterative phases during which it determines at each iteration an absolute maximum on a set of values of the parameters varying in a discrete manner, the function to be maximized having been previously filtered to remove the frequencies which would cause a spectrum fold in a sampling at the step of variation of the parameters. According to this version of the invention, the pitch is reduced at each iteration and the central point of the set on which the parameters vary during an iteration is the maximum determined at the previous iteration.

 Such an algorithm generally makes it possible to converge towards the solution despite the local maxima and the high number of parameters.

 Such an algorithm is described in 7.8.2.

 3. 16.5. Determination of the position of the object.

 The exact position of the object has no influence on the values measured in 3.16.2. and therefore can not be obtained from these values. On the other hand, it can modify the three-dimensional representations obtained: the spherical aberration affecting a given three-dimensional representation depends on the position of the object. In the case where the index of the object differs from the nominal index of the objectives, this position must be determined.

 The position of the object in relation to the objectives affects the good superposition of two-dimensional representations recalibrated in phase. If it is not correctly evaluated and taken into account as a correction factor, abnormal phase differences appear between pairs of two-dimensional representations recalibrated in phase, on the part of the frequency space that corresponds to the intersection of these representations.

 According to one version of the invention, the measurement of the position of the object with respect to the objectives comprises an acquisition phase, during which a series of frequency-plane images are acquired, corresponding to a series of optical beams. variable orientation lighting. Knowing the position parameters, the index and the thickness of the object, previously calculated by the maximization algorithm described in 3.16.4., And knowing the desired position, a program can determine the two-dimensional representations corresponding to each image. plane in frequency. According to this version of the invention, the

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 A program for determining the position of the object in relation to the objectives is therefore a minimization program which determines the value of the position parameter which minimizes abnormal phase deviations.

Such a program is detailed in paragraph 17.15.

 3. 16.6. Compensation for spherical aberration and positional deviations.

 When all of the above parameters have been evaluated, they must be used to compensate for the corresponding effects in the procedure of generating a three-dimensional representation of the observed object. This implies: - a modification of the corresponding spatial frequency, in a three-dimensional space, at each point of a plane plane in frequency: spatial frequency depends on the index of the object.

a correction of the phase shifts related to the presence of the object and the displacement of the objectives.

 According to one version of the invention, this correction is performed by multiplying each frequency-plane image by a correction function taking into account the various parameters determined above. The calculation of such a function is explained in 7. 16. and the multiplication operation is performed for example in step 2 of the algorithm described in 7.17.

3. 17. Regular sampling
When two microscope objectives are used, the sampling step on the frequency-plane image generated from one of the receiving surfaces can be taken as the basis of the sampling pitch of the three-dimensional representation of the next two object. corresponding axes. If no precautions are taken: - The image points of the illumination waves on this frequency-plane image do not correspond to integer values of the coordinates in pixels.

In the case where two objectives are used, the sampling pitch and the axes on the frequency-plane image generated from a reception surface associated with the objective opposite do not correspond to the pitch. sampling and the axes of the three-dimensional representation of the object.

 It follows that the sampling of the three-dimensional representation of the object is not regular.

According to one version of the invention, this sampling is made regular along two axes corresponding to the axes of the plane plane representations. The quality of the three-dimensional representation of the object is then significantly improved.

 The frequency-plane image can in particular be modified, because of the imperfections of the optical system, by rotation or by homothety. To obtain a regular sampling, it is necessary to cancel or compensate for these imperfections.

 On the other hand, in Embodiment 4, there must be point-to-point matches between the different SLMs used and the CCDs. The realization of these correspondences requires the same type of adjustments.

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 According to one version of the invention, the microscope thus comprises one or more optical devices allowing a rotation adjustment of the images generated in the frequency planes, and / or one or more devices allowing the magnification adjustment of the images generated in the planes of frequency.

3.17.1. Adjustment of the representation scale (homothety)
This setting is actually a magnification setting. According to one version of the invention, the magnification of an image is adjusted using an optical system of variable focal length. Such a system may for example be composed of two lenses, a variation of the distance between said lenses resulting in a variation of the focal length of the assembly. Such a device is used in Embodiments 4 and 5 and is described in 8.1.4.1.

3. 17.2. Rotational adjustment of an image
According to one version of the invention, this adjustment is performed using a device consisting of a first group of fixed mirrors and a second group of mirrors, verifying the following conditions: the first mirror group mirrors the wave vector of the incident beam with respect to a given axis.

the second group of mirrors symmetries the wave vector of the incident beam with respect to a second axis.

- The second group of mirrors is rotatable about an axis orthogonal to the plane of these two axes.

 The set of two groups of mirrors then has the effect of rotating the beam represented in a frequency plane, the angle of rotation being twice the angle between the two axes of symmetry. Such a device is used in Embodiments 4 and 5 and is described in 8.1.4.2.

 3.18. Microscope objectives adapted.

 Conventional microscope objectives are intended to operate with immersion liquid and a cover glass of index close to that of glass. This is irrelevant in the case where two-dimensional samples are observed. However, in the case where thick samples with an index very different from that of the glass, for example samples in the aqueous phase, are observed, the spherical aberration generated can be such that it greatly degrades the image, despite the algorithms compensation for the aberration used.

 According to one version of the invention, this problem is solved by using an objective intended to operate with an immersion liquid whose index is equal to or close to the average index of the sample observed. The objective can be dimensioned by usual methods of optical calculation, the criteria of dimensioning differing from the usual criteria by the fact that the index of the liquid of immersion, which one will call index nominal of the objective, has been modified . If the sample observed consists essentially of water, the design can be facilitated by the use of a Teflon coverslip.

3. 19. Method of data processing in the case of a limited random access memory
Three-dimensional frequency representation calculations use large amounts of data. Since this data is normally accessed in random order, it can not be

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 not be stored during calculations on sequential access media such as a hard disk and must be stored on random access media such as internal computer memory (RAM).

 According to an advantageous version of the invention, adapted to the case where the system does not have enough RAM to be able to store all the data, the calculation algorithm is modified so as to process the data block by block, a block corresponding to a large amount of data which can then be stored sequentially on a sequential access medium and loaded into the central memory only during the processing time of said block. To this end: the modified algorithm performs, in a three-dimensional space, horizontal plane treatments by horizontal plane, each horizontal plane being stored on the sequential access support in a single block.

 - In order to be able to also perform treatments according to the vertical dimension, the algorithm incorporates axis exchange phases that can temporarily bring the vertical axis in a horizontal plane.

 - The axis exchange procedure operates block by block, the blocks generally having equal or close dimensions along the two axes to be exchanged and having size in bytes the maximum size that can be stored in the system's main memory (RAM memory random access).

 This method is implemented in Embodiment 1 and described in Section 5.21.

 3. 20. Images generated by the microscope.

 The three-dimensional representations generated by the present microscope can be stored and transmitted as a three-dimensional array of complex numbers. According to one version of the invention, it is possible to generate from this table two-dimensional sections or projections representing either the index or the absorbance in the object.

 3. 21. Optical element positioning system.

 The described embodiments require the use of many positioners of good accuracy. These positioners are expensive elements that are not well suited to mass production and that may become unstable over time.

 According to one version of the invention, this problem is solved by using, during the manufacture of the microscope, removable positioners, each element being positioned and then fixed by a binder, for example an adhesive, and the positioner being removed after final solidification of the binder.

 3. 22. Protection system against shock, vibration and dust.

 The described microscopes consist of a set of elements attached to an optical table. During a possible transport, even slight shocks can cause a disturbance of the system. During prolonged use, dust can be deposited on the various optical elements.

 According to one version of the invention, most of the optical device is included in a hermetically sealed box which is itself included in a larger box, the connection between the two boxes being via dampers arranged on each side of said box hermetically

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 closed. This system protects the microscope from shock and dust while allowing a good suspension of the optical table.

4.Design description of the drawings:
Fig.1 to 24 relate to a first embodiment. Fig.1 is an overall diagram of the microscope optics. Figs. 2 and 3 show the detail of the angular positioner (110) already shown in FIG. Fig. 4 is an overall diagram of the vertical mechanical support and antivibration of the microscope. Fig.5 shows the detail of a tensioner of FIG. 4. FIG. 6 represents an example of sizing of the optical part. Figs. 7 to 9 are graphical representations serving as a support for explaining the operating principle of the microscope. Fig. 10 shows the algorithm of a program for setting the control voltages of the piezoelectric (122). Fig. 11 shows the detailed algorithm of an imaging procedure used in the previous program. Fig.12 shows the algorithm of a program for adjusting the intensity attenuator consisting of the polarizer (105) and the polarization rotator (104) and to obtain its characteristics. Fig. 13 shows the detailed algorithm of a low level image taking procedure used in the previous program and in the 2D or 3D image acquisition programs. Fig. 14 shows the algorithm of a focusing program for obtaining a 2D image and focusing the microscope objective (113). FIG. 15 shows the algorithm of a program for adjusting the position of the condenser (111) and obtaining certain parameters of the system. Fig. 16 symbolically represents an image displayed on the screen by the previous progranune. Fig. 17 graphically represents a calculation made by this program. Fig.18 shows the algorithm of the three-dimensional image acquisition program. Fig. 19 represents the algorithm of a computer program generating from the results of the acquisition a three-dimensional representation of the object. Fig. 20 schematically represents an operation performed by the first part of this program. Fig.21represent the detail of the algorithm of this first part. Fig. 22 schematically represents an operation performed by the second part of this program. Fig. 23 represents the algorithm of a third part of this program. Fig.24 shows the algorithm of a last part of this program.

 Figs. 25 and 26 relate to a second embodiment. Fig. 25 is an overall diagram of the optical part of the microscope. Fig.26 shows the algorithm of the 'low level' image acquisition procedure used.

 Fig. 71 illustrates a specific apparatus used in the setting operations for Embodiments 3 to 5.

 Figs. 27 to 59 relate to a third embodiment. Figs. 27 and 28 constitute an overall diagram of the optical part of the microscope. Fig. 29 schematizes the optical path of the rays between the lens and the sensor. Fig. 30 represents the beam attenuation device used. Fig. 31 is a block diagram illustrating its operation in the case where there is actually attenuation. Fig. 32 is a block diagram illustrating its operation in the case where there is no attenuation. Fig. 33 shows the phase shift device used. Fig. 34 is a block diagram illustrating

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 its operation. Fig. 35 shows again the phase shifts of the different vectors. Fig. 36 shows FIG. 34 by indicating the module of the different vectors. Fig. 37 represents an elementary unit of the beam deflection device used. Fig. 38 shows the beam deviation and switching device formed by association of these elementary units. Figs. 39 and 40 are schematic diagrams for understanding the operation of an elementary unit. Fig. 39 corresponds to a deflection direction and Fig. 40 to the other direction of deviation possible. Fig.41 illustrates the calculation of beam deflection by a prism. Figs. 42 to 44 illustrate steps of a phase rotator labeling procedure. Fig. 42 illustrates the first step and Figs. 43 and 44 illustrate a second stage, in two different cases. Fig. 45 illustrates the calculation of the difference in step produced on a parallel beam by an object of given index and thickness. Fig. 46 illustrates the calculation of the path difference produced on a parallel beam by a displacement of the origin point of the reference wave, with respect to which the optical path is calculated. Figs. Figs. 47 to 50 and Fig. 60 illustrate an algorithm for calculating the index and thickness values of the sample as well as the displacement of the origin point of the reference wave. Fig. 47 corresponds to the highest level of this algorithm and Fig. 50 to the lowest level. Fig. 51 represents in a three-dimensional space different vectors used to evaluate the effect on the diffracted wave of the polarization of the illumination beam. Fig. 52 represents in the plane of a sensor vectors deduced from the previous ones. Fig.53 shows an algorithm for obtaining control indices of the beam deflector from the coordinates of the desired direct impact point for the illumination beam. Fig. 54 illustrates the calculation of the difference in operation of a wave coming from a point of the object with respect to a reference wave. Fig. 55 illustrates the calculation of the difference in operation between a wave coming from a point of the object and the reference waves used on the two sensors of the system. Fig. 56 illustrates the trajectory, on one of the sensors, of the point of direct impact of the illumination wave, during an imaging procedure. Fig. 57 represents an algorithm determining the position of the object in relation to the objectives. Fig.58 illustrates how the three-dimensional frequency representation of the object is obtained by superposition of two-dimensional representations. Fig. 59 shows in section the three-dimensional frequency representation of the object.

 Figs. 61 to 70 and 72 relate to a fourth embodiment of the invention, constituting the preferred embodiment. Figs. 61, 62, 63 constitute an overall diagram of the optical part of the microscope. Figs. 64 and 65 illustrate the operation of the beam deflector used in this embodiment. Fig.66 illustrates the operation of a direct illumination wave suppression system.

Figs. 67 and 68 illustrate the principle used to control the path of the beam. Figs. 69 and 70 illustrate a system used for controlled rotation of a beam. Fig. 72 illustrates the image to be obtained in one of the adjustment operations.

 Figs. 73 to 82 relate to a fifth embodiment. Figs. 73 and 74 constitute an overall diagram of the optical part of the system. Figs. 75 and 76 illustrate images obtained during an intermediate calculation step. Fig. 77 illustrates an algorithm used to determine the control sequence of a mirror deflecting the beam and to determine the control sequence of a stopping glass.

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 the direct light wave. Figs. 78 and 79 show images obtained during a setting step.

Fig. 80 illustrates the principle used to vary the polarization of the illumination wave and the direction of analysis. Fig. 81 represents the points corresponding to various illumination waves used in an in-phase registration algorithm. Fig. 82 shows a diaphragm used in this embodiment.

 Figs.83 to 85 relate to a device for definitively positioning and fixing optical elements. Fig. 83 and FIG. 84 represent parts of this device and FIG. 85 represents the whole of this device.

 Figs. 86 to 88 relate to a device for protecting the microscope from shock and dust. Fig. 86 represents a block diagram of the device. Figs. 88 and 88 show a specific configuration adapted to the case of embodiments 4.

5.Description of a first embodiment:
This embodiment is the simplest and is inexpensive.

5.1.characteristics:
A laser beam of wavelength 633 nm polarized in the direction orthogonal to the figure is emitted by the helium-neon laser (100) and passes through the filter (101) consisting of zero, one or more stacked filters, stained glass Schott . It is then separated into a lighting beam Fe and a reference beam Fr by the semi-transparent mirror (102). The illumination beam then passes through a filter (103) of the same type as (101), then a polarization rotator (104) based on ferroelectric liquid crystals and marketed by Displaytech Inc., 2602 Clover Basin Dr., Longmont , CO 80503, USA. It then passes through a polarizer (105). The beam then passes through an achromat (106) then a diaphragm (107) and an achromat (108). It is reflected by a mirror (109) fixed on an angular positioner (110) controlled by two stepper motors. It then passes through a condenser (111) opening 1.2 and reaches the object (112). The object (112) is a sample placed between lamina and lamella, whose absorptivity and index variations are relatively small, and of which we want to obtain a three-dimensional image. The lenses (106) and (108) must be such that the laser beam focuses in the object focal plane of the condenser (111) and has a sufficient opening upon its arrival in this focal plane. The beam is again parallel when it reaches the object (112). The plane of the object must be horizontal so that the optical oil needed to use the lens and the immersion condenser does not run. The optical axis is vertical and the elements of Fig.1 are fixed on a vertical plate (300) shown in Fig.4.

 The angular positioner (110) is detailed in FIGS. 2 and 3. FIG. 2 represents a plate on which the mirror (109) is glued, seen from below. Fig.3 shows the entire devicevu side.

The plate (200) is placed on movable contact pads (205) and (212) whose points of contact with the plate are in (203) and (204), and on a fixed contact pad whose point of contact is in (201), the plate (200) being slightly hollowed at this point. It is held by a spring (210) fixed to the plate (202) and to a fixed stud (211). The movable contact pad (205) moves vertically in translation and is integrated in an actuator a conventional type of axis: it is locked in rotation by a flexible (207) and is driven in

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 translation by rotation of the rod (206) exiting the stepper motor (208) which is for example a stepping motor 400 steps / turn. The drive is done for example via a thread. The contact pad (212) is likewise driven by the rotation of the motor (213). The fixed point of contact (201) must be in the optical axis of the objective (113) and the center of the mirror must be on this point of contact. The motors (208) and (213) are fixed on a plate (209) itself fixed on the support plate (300).

 The wave from the object (112) passes through the microscope objective (113). This objective is a plane objective (which gives a plane image of a plane), with a large aperture (for example 1.25), with immersion, and forming an enlarged image of the object at a finite distance.

 In the plane where the objective normally forms the image of the object to be observed, a diaphragm (114) is interposed for spatial filtering of the image. Behind this plane is positioned an achromat (115) whose object focal plane must be confused with the image focal plane of the objective (113). A second achromat (117) whose image focal plane is in the plane of a CCD sensor (118) forms in the plane of this CCD the image of the image focal plane of the objective (113). The CCD (118) is integrated with a camera (119) outputting an analog video signal.

 The reference beam first passes through a filter (120) of the same type as (101) and is reflected by a mirror (121) mounted on the movable end of a piezoelectric translator (122). It then passes through a lens (123) which focuses the beam at a point. The diverging beam coming from this point is partially reflected by the semi-reflecting mirror (116), which superimposes it on the beam coming from the object and makes it possible to record their interference on the CCD (118). The focal point of the beam from the lens (123) must have its virtual image after reflection on the semi-transparent mirror (116) in the center of the image of the diaphragm (114) by the achromat (115). The piezoelectric translator (122) modulates the phase of the reference beam.

 Manual positioners used in the system are not shown in the figure. The microscope objective (113) is mounted on a focusing device. The laser (100) is mounted on a two-axis positioner to adjust the direction. The fixed portion of the piezoelectric stack (122) is mounted on a two-axis positioner allowing rotation relative to an axis orthogonal to the plane of the figure and passing through the center of the mirror (121), and relative to a second axis located in the plane of the mirror (121), orthogonal to the first axis and passing through the center of the mirror (121). The condenser is mounted on a three-axis positioner in translation. The camera (119) is mounted on a three-axis positioner in translation. The angular position of the semi-transparent mirrors (102) and (116) can be adjusted manually. The lens (106) can be translated along its axis. The object (112) is fixed on a two-dimensional positioner for moving it in a horizontal plane. The diaphragm (114) can be moved in a horizontal plane.

 The assembly is fixed on the support plate (300), on the opposite side of the plate from the point of view of FIG. This plate is attached to two triangular plates (301) and (302) themselves attached to a square base (303). The plate (300) is also attached directly to the square base (303). The plates (300) (301) (302) (303) are rigid aluminum alloy AU4G, for example of thickness 20 mm. Fixing plates can be done by screws and tapped holes, and must be made in a number of points

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 enough to ensure perfect rigidity of the whole. This keeps the system vertical by ensuring sufficient rigidity. The assembly is placed on an antivibration support consisting of a 30 mm thick granite plate (304) placed on a low pressure inflated truck (305) that dampens vibrations and is itself on a rigid wooden table (306). A rigid wooden frame (311) is fixed in height by means of uprights (307) (308) (309) (310) to the table (306). The entire wooden construction is reinforced so as to be perfectly rigid. The top of the plate (300) is connected by tensioners (312) (313) (314) (315) to the corners of the rigid frame. Each tensioner, detailed in FIG. 5, consists of a set of elastic bracelets (316) stretched between two rings (318) (317), these rings being themselves fixed to the plate (300) and the frame ( 311) by cords (320) (319), the assembly being energized. The air chamber (305) makes it possible to have, for the set suspended in AU4G, low resonance frequencies for the translation movements, of the order of 2 Hz. The tensioners (312) to (315) make it possible to limit the sway of the whole. The sway frequency can be evaluated simply by printing a slight pendulum movement to the assembly and measuring the time required to have, for example, ten round trips. The sway frequency is adjusted by changing the number of elastic bracelets used for each tensioner. The higher it is, the more the rocking frequency increases It must be set so that the rocking frequency is of the same order as the resonance frequency for the translation movements, about 2Hz.

 The mounting of the various elements on the plate (300), and in particular semitransparent mirrors and mirrors, must be carried out so as to ensure maximum rigidity of the assembly. All the usual precautions must be taken in order to limit the vibrations.

 The following details relate to a particular example of practical dimensioning of the device. The distances quoted are shown in FIG. 6. The given dimensions are approximate and some of them must be corrected in an adjustment phase. The lens (106) is an achromat with a focal length of 10 mm. The lens (108) is an achromat with a diameter of 24 mm and a focal length of 120 mm. The distance D7 between (106) and (108) is 250 mm. The distance D6 between the lens (108) and the center of the mirror (109) is 100 mm. The distance D5 between the center of the mirror (109) and the object focal plane of the condenser is 140 mm. The condenser is a clear bottom condenser with opening dip 1.2.

The microscope objective is a 1.50 aperture x100 aperture objective, at finite distance, forming the image at 160 mm from the neck of the lens, with a focal length of about 1.8 mm. The distance D4 between the neck of the objective and the diaphragm (114) is 160 mm. The distance D3 between the diaphragm (114) and the achromat (115) is 20 mm. The achromat (115) has a focal length of 200 mm and a diameter of 30 mm and its most domed face is oriented towards the semi-transparent mirror (116). The achromat (117) has the same characteristics and its most domed face is also oriented towards the mirror (116). The distance D2 between the two achromats is 85 mm, to insert a semi-transparent mirror (116) of sufficient size. The distance between the achromat (117) and the CCD (118) is 200 mm. The lens (123) has a diameter of 4mm and a focal length of 6mm. The distance D9 between this lens and the optical axis is about 70 mm. The distance D8 between the achromat (115) and the center of the semi-transparent mirror (116), located on the optical axis, is about 45 mm. The laser (100) is a helium-neon laser of wavelength in vacuum = 633 nm polarized in

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 the direction orthogonal to the figure, of power approximately 0.5 mW, beam diameter 0.5 mm. The CCD sensor is a square pixel sensor, the pixel area being about 8.5 x 8.5 micrometers, and the usable area in pixels being at least 512 x 512 pixels in size. The camera outputs a CCIR video signal and a pixel clock, and its exposure time is equal to half the duration of a field, ie 1 / 50th of a second for a non-interlaced CCIR camera whose fields last 1 / 25th second. This allows a delay between the end of a field and the beginning of the next exposure period, which can be used to change the lighting conditions without the transition affecting the image. The piezoelectric positioner (122) is a prestressed, cylinder-shaped piezoelectric 'battery' whose body is fixed and the end moves 15 micrometers at an applied voltage of 100 volts.

 The calculation system is for example a computer type 'PC', equipped with appropriate acquisition and control cards and possibly additional computing means, operating for example under the Windows 95 operating system. video signal, operating in real time, samples the signal on 8 bits and acquires images of size hpix x vpix or hpix and vpix are greater than 512 and multiples of 4. The pixels are sampled according to the pixel clock, so correspond exactly to the pixels of the CCD. The piezoelectric positioner is controlled directly by a digital / analog conversion card output signal included for example between zero and Umax. with for example Umax = 10 volts. A resistor is interposed between the output of the conversion board and the terminals of the piezoelectric actuator so as to limit the current. Its value is set so that the rise time of the voltage across the actuator (122) is about 1 ms. The polarization rotator (104) is equivalent to a half wave plate whose axis is rotatable and has two equilibrium positions separated by a 45 degree angle. If positioned so that the polarized beam is parallel to this axis in one of the equilibrium positions, it will rotate the beam 90 degrees to the other position. The polarization rotator is controlled by application of a bipolar voltage, -5V corresponding to a position of equilibrium and + 5V to the other. Each terminal of the polarization rotator is connected to a 0 / 5V output of a digital output board, and its two positions are controlled by applying in one OV case to one output and 5V to the other, and inverting for the other position. The stepper motors (208) and (212) are also controlled from the computer, via an appropriate control card and electronics. The computer has sufficient internal memory (at least 32 MB) and a hard disk of sufficient size (at least 4 GB).

5. 2.Conventions
The following conventions will be used in the remainder of this description, including in the other embodiments: The letter represents sometimes an index, sometimes the complex pure complex number of module 1.

In the case where there can be ambiguity the complex number / will be noted 7.

 - the sign = symbolizes, depending on the case, the assignment operation or equality -the expression a + = b means a = a + b -a multiplied by b is written ab, a.bou a * b

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 the module of a complex number z is denoted # z # and its conjugate is denoted z.

1-première permutation: E[i]=E[(i+fdiml2)%fdim] 2- transformation de Fourier usuelle du tableau E 3- permutation inverse: E[i]=E[(i+fdiml2)%fdim] ou le signe % désigne le modulo. - the expression a% b will mean a modulo b - if a is a boolean integer, # is its complementary, ie # = 1 and # = 0 0 - The discrete Fourier transform, in its most usual form, transforms a Dirac originally located in a constant and transforms a constant to a point at the origin. The discrete Fourier transform used throughout this patent transforms a constant into a Dirac located in the middle of the transformed array and transforms a Dirac located at that point into a constant. This means that the 'zero' in frequency or position is placed in the middle of the table and not at the origin of the table. This modified transform is obtained from the usual form by performing a permutation of indices before and after the transformation. An array E of dimension fdim is transformed as follows:

1-first permutation: E [i] = E [(i + fdim1 2)% fdim] 2- usual Fourier transformation of array E 3 inverse permutation: E [i] = E [(i + fdim1 2)% fdim] or the sign% designates the modulo.

 The two-dimensional Fourier transform of an array of rows and columns is obtained by performing the one-dimensional Fourier transform defined above on each row of the array. which generates an intermediate array, then performing this transformation on each column of the intermediate array to obtain the transformed array.

 Likewise, the three-dimensional Fourier transform consists in successively performing, on each axis, one-dimensional transforms extended to the entire array.

5.3.Principles of operation
The value of the light wave coming from the object under a given illumination at a point of the CCD sensor is obtained from the recording of three interference patterns received on the sensor, the phase of the reference wave being offset by 120 degrees between each of these figures.

2r oc trois enregistrement successifs sont: so = s + r, sI = S + re 3 , s2 = s + re 3 . Les intensités enregistrées successivement sont donc:

On peut inverser ces formules et on obtient: If s is the light vibration from the object andr is the light vibration constituting the reference wave during the first recording, the total light vibrations reaching the sensor during

2r oc three successive records are: so = s + r, sI = S + re 3, s2 = s + re 3. The intensities recorded successively are therefore:

We can invert these formulas and we obtain:

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The above value is the light vibration coming from the object alone, the phase reference being conventionally equal to zero for a vibration in phase with the reference wave. This calculation therefore makes it possible to reconstruct the complex value of the wave from the intensity records.

d'entrée dans l'objectif, qui vaut sin (p = , .Îx2 + .%Y2 , ou (/, /u, 7z) sont les coordonnées du f/ + fy 2 + f/ vecteur fréquence spatiale du faisceau en entrée de l'objectif, de norme ou # est la longueur d'onde dans le milieu observé, et de direction la direction du faisceau. Le reste du système optique étant paraxial, la déviation du point d'arrivée du rayon sur le capteur par rapport au centre optique du capteur est également

proportionnelle à cette grandeur, et donc les coordonnées (i - Cx, j - cj de ce point par rapport au centre optique sont proportionnelles à (f," fy) . Dans le cas ou le capteur a des pixels carrés, le vecteur fréquence en entrée de l'objectif du rayon qui illumine le point du capteur de coordonnées (i,j) vaut donc:

ou K est une constante à déterminer. On appellera 'fréquence caractéristique' du point ce vecteur fréquence. By construction, each point of the CCD sensor corresponds to a pure frequency fc of the wave coming from the sample. The optical center of the sensor is the point of the sensor illuminated by a ray entering the objective with a direction strictly parallel to the axis of symmetry of the latter and Cx, Cy its coordinates in pixels. The objective verifying the condition of the sines, the deflection at the lens outlet of a ray originating from a central point of the object is proportional to the sine of its angle.

in the objective, which is equal to sin (p =, .Ix2 +.% Y2, or (/, / u, 7z) are the coordinates of f / + fy 2 + f / vector spatial frequency of the input beam of the objective, standard or # is the wavelength in the observed medium, and direction the direction of the beam.The remainder of the optical system being paraxial, the deflection of the point of arrival of the ray on the sensor compared at the optical center of the sensor is also

proportional to this magnitude, and therefore the coordinates (i - Cx, j - cj of this point with respect to the optical center are proportional to (f, "fy).) In the case where the sensor has square pixels, the frequency vector in entry of the objective of the ray which illuminates the point of the coordinate sensor (i, j) is therefore:

or K is a constant to be determined. This frequency vector will be called the 'characteristic frequency' of the point.

 Knowing the characteristic frequency of each point of the sensor and the light vibration coming from the object and received at this point, the frequency representation of the wave resulting from this sample is thus obtained for a given illumination of the sample.

 When a sufficiently fine, low-absorbing sample and small index variations are traversed by a parallel laser beam, each point of the sample is subjected to a light vibration Ae j2 # fe.r where fe is the spatial frequency vector of the sample. lighting beam andr the ray-vector at the point considered of the object, the origin being taken at the point of virtual origin of the reference wave.

qui se superpose à l'onde d'éclairage. Un petit volume dV crée une onde secondaire Aej2;ife.r u(r)dV ou u(r) est un coefficient complexe dont la partie réelle est liée à l'absorptivité locale de l'échantillon et la partie imaginaire à son indice. L'image tridimensionnelle de l'échantillon que ce microscope génère est l'ensemble des valeurs u(r) en chaque point de l'échantillon. The absorbance and the index variations of the sample result in the appearance of a secondary wave

which is superimposed on the lighting wave. A small volume dV creates a secondary wave Aej2; ife.ru (r) dV where u (r) is a complex coefficient whose real part is related to the local absorptivity of the sample and the imaginary part to its index. The three-dimensional image of the sample that this microscope generates is the set of values u (r) at each point of the sample.

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s(r)e 2'r . Un petit volume dV de l'objet, de rayon-vecteur r, éclairé par une onde plane de fréquence fe , crée donc au point du capteur de fréquence caractéristique fc une vibration 4 -"M()F qui se superpose à la vibration principale. Intégrée sur l'ensemble de l'objet, la vibration reçue en un point du capteur vaut donc s(P) = f Ae2'fe-f Oru(r)dY . Cette vibration est donc un élément de la transformée de Fourier de la fonction u(r) , correspondant à la fréquence de Fourier ft = fe - fc Le principe de ce microscope est d'enregistrer cette vibration pour un ensemble de fréquences fe et fc, puis de reconstituer la représentation fréquentielle de u(r) et finalement u(r) en inversant la transformée de Fourier. When a point of the sample, of radius-vector r, locally emits a light vibration s (r), the light vibration received on the sensor at a characteristic frequency point fc is then

s (r) e 2'r. A small volume dV of the object, radius-vector r, illuminated by a plane wave of frequency fe, therefore creates at the point of the characteristic frequency sensor fc a vibration 4 - "M () F which is superimposed on the main vibration Embedded on the whole of the object, the vibration received at a point of the sensor is thus s (P) = f Ae2'fe-f Oru (r) dY This vibration is therefore an element of the Fourier transform of the function u (r), corresponding to the Fourier frequency ft = fe - fc The principle of this microscope is to record this vibration for a set of frequencies fe and fc, then to reconstruct the frequency representation of u (r) and finally u (r) by inverting the Fourier transform.

 The samples studied are poorly absorbent and have small variations in the refractive index.

As a result, the illumination wave remains very intense and illuminates a point of the CCD, which will be called the point of impact of the illumination wave, and which is the point of the CCD where the light vibration received is the most important. high.

If this point has coordinates (imax, jmax) then the frequency of the light wave is:

Figure 7 shows the set (500) of the characteristic frequencies corresponding to the points of the sensor. It is a portion of a sphere of radius limited by the opening of the lens, centered on the optical axis (501) of the system. An example of a lighting frequency vector (502) is superimposed on this set.

Finally, the set (503) of the corresponding frequencies ft = fc- fe is deduced therefrom. When the lighting frequencies are varied according to a circle (504) as indicated in FIG. 8, all the recorded frequencies are those generated by the rotation of the sphere portion (503) about the axis ( 501) in a horizontal plane, as shown in the sectional view of FIG. 9. We thus obtain a three-dimensional (and no longer two-dimensional) frequency representation as in the case where only one record is used. From this three-dimensional representation in the frequency space, the function u (r) can be generated by inverse Fourier transformation.

 To obtain the frequency representation of u (r) from the set of two-dimensional frequency representations, the average value of the two-dimensional frequency representations reaching this point will be calculated at each point.

 The calculation of the frequency representation of u (r) and finally of u (r) can for example be carried out in 6 steps: step 1: for each lighting wave, the two-dimensional frequency representation of the received wave is determined, which is a portion of sphere of a three-dimensional space.

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issue de l'objet, ce point ayant la fréquence fc(i,j) = # p " C, y - C.,, , K2 -(i - Cx)2 - (; - C y) et ayant comme valeur complexe la valeur complexe obtenue au point considéré du capteur CCD par la

étape 2 : pour chaque onde d'éclairage, on détermine la fréquence fe de l'onde d'éclairage en déterminant les coordonnées (imax jmax) du point d'intensité maximale sur le capteur CCD et en appliquant la formule:

étape 3 : pour chaque onde d'éclairage, on translate la représentation obtenue à l'issue de l'étape 1, d'un

vecteur - feou fe est la fréquence de l'onde d'éclairage, obtenue à l'issue de l'étape 2. étape 4 : pour chaque onde d'éclairage, on divise la représentation fréquentielle bidimensionnelle obtenue à l'issue de l'étape 3 par sa valeur au point de coordonnées (0,0). Cette étape constitue l'opération de recalage en phase décrite en 3 6 3. et est indispensable pour que les représentations fréquentielles bidimensionnelles se superposent de manière cohérente. étape 5 : on superpose l'ensemble des représentations fréquentielles bidimensionnelles obtenues à l'issue de l'étape 4, obtenant la représentation fréquentielle de u(r) . La valeur affectée à un point non atteint est 0 et la valeur affectée à un point atteint est la moyenne des valeurs en ce point de chaque représentation fréquentielle bidimensionnelle atteignant ce point. étape 6 : effectue une transformation de Fourier tridimensionnelle inverse de la représentation fréquentielle, obtenant finalement la fonction u(r) en représentation spatiale. From a point of the CCD sensor with coordinates (i, j) we obtain a point of the representation of the wave

from the object, this point having the frequency fc (i, j) = # p "C, y-C. ,,, K2 - (i-Cx) 2 - (; - C y) and having as a complex value the complex value obtained at the point of interest of the CCD sensor by the

step 2: for each illumination wave, the frequency fe of the illumination wave is determined by determining the coordinates (imax jmax) of the point of maximum intensity on the CCD sensor and applying the formula:

step 3: for each lighting wave, translate the representation obtained at the end of step 1, a

vector - feou fe is the frequency of the light wave, obtained at the end of step 2. step 4: for each light wave, divide the two-dimensional frequency representation obtained at the end of the step 3 by its value at the coordinate point (0,0). This step constitutes the phase registration operation described in 3.sub.3 and is indispensable for the two-dimensional frequency representations to be coherently superimposed. step 5: we superimpose the set of two-dimensional frequency representations obtained at the end of step 4, obtaining the frequency representation of u (r). The value assigned to an unreachable point is 0 and the value assigned to a point reached is the average of the values at that point of each two-dimensional frequency representation reaching that point. step 6: performs a three-dimensional Fourier transformation inverse to the frequency representation, finally obtaining the function u (r) in spatial representation.

On détermine également les coordonnées (imax jmax) du point d'intensité maximale sur le capteur CCD et on divise l'ensemble de l'image plane en fréquence obtenue sur le capteur CCD par sa valeur au point de

coordonnées (imax jmax). phase de calcul tridimensionnel: A partir de chaque onde d'éclairage caractérisée par les valeurs (imax,jmax), et à partir de chaque point de coordonnées (i,j) du capteur, on obtient un point de la représentation fréquentielle tridimensionnelle de fréquence In practice, the steps will be performed in a different order and in a modified form, in order to optimize the calculation time and to limit the memory space required. The method actually used comprises two phases, equivalent to the previous 6 steps: acquisition phase: for each light wave, determines the plane frequency image obtained on the CCD sensor by applying in each point the formula

The coordinates (imax jmax) of the point of maximum intensity on the CCD sensor are also determined, and the entire plane frequency image obtained on the CCD sensor is divided by its value at the point of

coordinates (imax jmax). three-dimensional calculation phase: From each illumination wave characterized by the values (imax, jmax), and from each coordinate point (i, j) of the sensor, a point of the three-dimensional frequential frequency representation is obtained

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Lorsqu'un point n'est pas atteint on y affecte la valeur nulle. Lorsqu'il est atteint plusieurs fois on y affecte la moyenne des valeurs obtenues à chaque fois. Lorsque cette opération a été effectuée pour toutes les ondes d'éclairage et tous les points du capteur, la transformation de Fourier tridimensionnelle inverse peut être effectuée.

When a point is not reached, it is set to zero. When it is reached several times, the average of the values obtained is assigned to it. When this operation has been carried out for all the illumination waves and all the points of the sensor, the inverse three-dimensional Fourier transformation can be performed.

 This method poses a practical problem that the point illuminated directly by the beam passing through the sample is illuminated much more intensely than the points corresponding to the diffracted wave. The three-dimensional representation generated during an image capture essentially contains frequencies close to that of the illumination beam, the other frequencies being embedded in the noise. To remedy this drawback, a controlled attenuation device of the beam is used. The part of the frequency representation corresponding to the frequencies on which the intensity is high is obtained with a strong attenuation and that corresponding to the other frequencies is obtained with a weak attenuation. The values obtained under high attenuation are then multiplied by a complex coefficient characteristic of the phase shift and the amplitude ratio of the illumination wave between the two positions of the controlled attenuation device. This controlled attenuation device consists of the polarization rotator (104) and the polarizer (105).

 The three-dimensional representation obtained from images of size hpix x vpix corresponds to important file sizes. In order to limit the size of the files and the computation time, the size of the images will be divided by two by averaging during the procedure of acquisition of the three-dimensional representation. This is equivalent to grouping pixels 4 by 4, a group of 4 pixels on the original image being equivalent to an effective pixel used for the calculation. The size of the observable object is of course reduced accordingly. The values of Cx, Cy, and K are divided by 2 to account for the new coordinate system. This limitation of the observed image size is of course optional.

 The use of the microscope proper comprises: a focus phase on the sample described in paragraph 5.18.

- a positional adjustment of the condenser, which is not always essential, and which is described in paragraph 5.19.

- the acquisition phase of the standard two-dimensional frequency representations described above and detailed in paragraph 5.20.

- the three-dimensional calculation phase described above and detailed in paragraph 5.21.

- a visualization phase described in paragraph 5.22.

 Before you can use this microscope, various settings must be made:

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 - The settings of the manual positioners, described in sections 5.6, 5.7, 5.8, 5.9, allow the beam path to be adjusted correctly, to ensure that the image of a wave hovers over the camera is actually punctual. , and that the condenser forms well at its output a parallel beam.

- The setting described in paragraph 5.10. allows obtaining the number of steps per pixel, useful for controlling the deflection mirror beam (109).

- The level of the reference wave is adjusted as described in paragraph 5.11.

- The adjustment described in paragraph 5. 12. allows to obtain appropriate control voltages from the piezoelectric actuator.

- The setting described in paragraph 5.13. allows the adjustment of the beam attenuator and obtaining attenuation and phase shift constants characterizing it.

- The setting described in paragraph 5. 14. provides the constant K.

- The opening of the diaphragms and the position of the semi-transparent mirror (116) must be adjusted so as to obtain a centered image without folding of spectrum. This setting is described in part in paragraph 5.14 and is completed in paragraph 5.15.

- The setting described in paragraph 5. 16. allows a precise adjustment of the position of the condenser.

- The reference wave must be recorded as described in paragraph 5.17.

5.4.Manipulation of filters
The adjustment operations require permanent manipulation of the filters to adjust the intensity received on the sensor. These manipulations are not systematically recalled in the rest of the text.

 The filter at (120) determines the intensity of the reference wave. Its value is determined in a particular step of the setting. Subsequently, when a reference wave is needed, the filter thus determined is inserted. When the reference wave is to be removed, an opaque element is inserted at (120).

 The filter at (103) determines the intensity of the illumination wave. Its value depends on the current adjustment operations. For most operations, the filter is adjusted so that the intensity received on the sensor (118) is high, without reaching saturation. For some operations the sensor is saturated. For others the lighting wave must be removed, which is done by inserting an opaque element.

 The filter (101) is used only for adjustment operations requiring a visual tracking of the beam, spotted by its scattering spot on a piece of white paper. The filter is then set so that the diffusion spot is visible without being dangerous to the eye.

 In cases where only the illumination wave is present, the relative intensity of the image received on the CCD sensor will be referred to as the ratio of the intensity received on the sensor to the intensity at the output of the filter (103).

In an operation where the aim is to maximize the relative intensity received on the sensor, it is necessary to change the filter regularly to maintain the intensity at a level measurable by the sensor.

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5.5.Programs in common use
Some simple programs are frequently used during adjustment, without this being recalled: - mirror movement (109): this mirror being motorized, a program is necessary to change the position. This program requests the user a number of steps and an axis number corresponding to either the motor (213) or the motor (208), then has the requested number of steps to this motor.

 -Visualization of the image received on the sensor: program allows the direct display on the screen of the computer of the image received on the sensor (118).

 Image view and characteristics of the maximum: program performs the direct display on the screen of the computer of the image received on the sensor (118). It also displays the maximum value detected by the sensor, the coordinates of the corresponding point, and the ratio between the intensity of this point and the sum of the intensities of its 8 neighbors. This program is used to check the appearance of an image, to check the unsaturation of the sensor (maximum value less than 255), to know the coordinates and the value of the maximum, to appreciate the punctual nature of this maximum by observation direct of the image and by use of the displayed values: the intensity (relative) of the maximum must be as high as possible, as well as the ratio of its intensity to that of its neighbors.

5. 6. setting the position of the laser (100) and the mirror (121)
In a first step, the illumination wave is suppressed and the position of the laser (100) is adjusted so as to effectively aim at the center of the mirror (121), which is verified by following the path of the beam with the aid of a piece of paper to visualize it. The position of the mirror (121) is then adjusted so that the reference beam effectively passes through the lens (123) and reaches the camera.

The reference beam should be centered on the sensor (118).

5. 7. translational adjustment of the camera position and adjustment of the mirror (102)
The position of the camera is set in translation by sending a parallel beam directly to the microscope objective. For this purpose, the elements (106) (108) (111) (105) (104) are temporarily removed, the reference wave is suppressed, the microscope objective is positioned in approximately focused position on the object . The object (112) used is a transparent plate and optical oil is interposed between (112) and (113). The angular position of (102) is then adjusted so that the beam reaches the center of the mirror (109) directly. The position of the mirror (109) is adjusted so that the parallel beam enters directly into the lens (113) and is refined so as to maximize the relative intensity of the signal received on the CCD. The position of the CCD sensor is then set in translation in the direction of the optical axis so that the image produced is perfectly punctual, then is set in translation in the directions orthogonal to the optical axis so that this point either in the center of the useful area of the sensor. This central point is the optical center and its coordinates in pixels are the constants Cx, Cy.

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5. 8. resetting the position of the condenser (111)
The elements (106) (108) (111) are replaced. Microscope oil is interposed between (111) and (112) and between (112) and (113). A piece of white cardboard is placed on the mirror (109) to diffuse the light. The diaphragm (107) is open to the maximum and the opening of the diaphragm (114) is about 8 mm. The microscope objective is set in approximately focused position. The position of the condenser (111) is then set so as to obtain on the CCD a clear disc of high radius, the disc to remain relatively homogeneous (the edges and the center are however a little more enlightened).

5. 9. adjusting the position of the lens (106)
The piece of white cardboard placed on the mirror (109) is removed. The position of the mirror is changed to bring the illuminated point to the edge of the disc previously obtained. The position of the lens (106) is then adjusted along its axis so as to have on the CCD sensor the most punctual image possible.

 5.10.Determination of the number of steps per pixel.

The piece of paper obscuring the mirror is then removed. The motor is moved along an axis of a known number of steps. The position in pixels of the point of maximum intensity is noted before and after the displacement, and the number of pixels traveled is deduced therefrom. We then calculate the ratio number of steps not ~ by ~ pixel = number of steps It is similarly done on the other axis and we retain the smallest number of pixels obtained.

5. 11. setting the reference wave level
If we consider a reference wave and a light wave having the same maximum intensity at their arrival on the sensor, adding in amplitude when they are in phase, the condition of non-saturation of the sensor is that the common amplitude two waves is half the amplitude saturating the sensor, or equivalently that the common intensity of the two waves is one quarter of the intensity saturating the sensor. To adjust the level of the reference wave to this value, the illumination wave is suppressed and the value of the filter (120) is adjusted to obtain an image whose maximum level is about one quarter of the maximum allowed level. the acquisition card, or in the case of 8-bit sampling of the video signal, a level of about 64. Before taking pictures, the maximum level of the lighting the same way.

5.12. adjustment of the control voltages of the piezoelectric actuator,
This calibration of the piezoelectric actuator can be done outside the system by a known interferometric method. Three positions of the actuator are used. The mirror movement between each position must be # / 3 # 2. The control voltages corresponding to each 3 # 2 position must be determined, the actuator having a regular cycle to avoid hysteresis effects.

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 However, it is also possible to perform this adjustment while the actuator is in place.

This makes it possible to compensate for the imprecision on the orientation of the mirror and to have a simple calibration procedure that does not use specific hardware.

 This is done using a program which varies the control voltages and which is described by the algorithm of FIG. 10. Before starting the program, the position of the mirror (109) must be adjusted so that the point produced on the CCD sensor using a completely transparent blade as the object at the center of the sensor. To use this program, the object used must be highly diffusive. For example, a piece of white paper dipped in gelatin can be used and placed between the blade and the coverslip. The paper should be thick enough to stop the direct beam and fine enough to allow a scattered beam to pass through. The diaphragm (107) is open to the maximum and the diaphragm (114) is set for an aperture of about 0.8 mm. The reference wave then interferes on the CCD sensor with the clear disk produced by the wave coming from the object. The intensity of the illumination wave must be adjusted so that the sensor is at saturation limit.

de phase de - 3 0, 3 seront respectivement Umaxl2-diff bas, Umaxl2, Umaxl2+ diff haut, ou diff haut et diff~bas sont choisis pour produire les décalages de phase indiqués. Afin d'éviter tout effet d'hystérésis, à chaque acquisition la tension est initialisée à 0, les différentes images sont acquises dans l'ordre croissant des tensions appliquées à l'actuateur et une tension finale Umax est finalement appliquée, de sorte que le même cycle est toujours utilisé. Ce cycle devra également être utilisé en phase normale de fonctionnement. If the maximum voltage applied to the actuator is Umax, the voltages corresponding to the shifts 2 # 2 #

of the phase of - 3 0, 3 will be respectively Umaxl2-diff low, Umaxl2, Umaxl2 + diff high, or diff high and diff ~ low are chosen to produce the indicated phase shifts. In order to avoid any hysteresis effect, at each acquisition the voltage is initialized to 0, the different images are acquired in the ascending order of the voltages applied to the actuator and a final voltage Umax is finally applied, so that the same cycle is always used. This cycle should also be used in the normal operating phase.

dans laquelle l'onde de référence a été remplacée par une constante et l'expression I(P,[alpha]) désigne l'intensité enregistrée au point P pour un décalage de phase a. The images taken with the phase shifts indicated above make it possible to calculate a frequency representation by applying to each pixel P the formula

wherein the reference wave has been replaced by a constant and the expression I (P, [alpha]) denotes the intensity recorded at the point P for a phase shift a.

fréquence sont donc + #, #, ,21r+ z et correspondent respectivement, en première approximation, aux tensions Umaxl2-diff bas+diff basl2, Umaxl2+(diff bas+diff haut)l2, Umaxl2+ diff haut +diff hautl2. Le programme de réglage calcule l'écart moyen pour des séries de valeurs de diff-haut et The control voltages of the actuator are set to evaluate diff high and diff low. The principle is to obtain two frequency representations shifted together by # / 3. The second image can be recaled in phase by multiplying it by e 3 and the mean difference between the first image and this recaled image can be calculated. This difference is minimal when the diff high and low diff voltages are correctly set. Phase offsets allowing the acquisition of the 2nd elementary image in

frequency are therefore + #, #,, 21r + z and correspond respectively, as a first approximation, to the voltages Umaxl2-diff low + diff basl2, Umaxl2 + (diff low + diff high) l2, Umaxl2 + diff high + diff highl2. The tuning program calculates the average deviation for series of diff-high values and

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 diff low and choose those that correspond to a minimum average difference. Its algorithm is detailed in Figure 10.

d'acquisition, on dispose d'un tableau 1[a, b, ij], l'indice a correspondant à la différence de phase, l'indice b correspondant à l'image (décalée ou non décalée en phase), les indices / et/ étant les coordonnées en pixels et variant respectivement de 0 à hpix-l et de 0 à vpix-1, (601) calcul des deux représentations fréquentielles. Celles-ci sont stockées dans des tableaux de

complexes SO[i,j] et SI [i j], en appliquant les formules:

(602) Le programme modifie le tableau SI en multipliant chacun de ses éléments par e

(603): le programme calcule la valeur maximale mod max = max ISo[l, ill du module sur - 05,i5,hpix-l <-hpix-1 05,j5,vpix-l S0. The essential steps of this algorithm are: (600): image acquisition. The acquisition procedure is specified in Fig.ll. By 'images' is meant 6 interference patterns received consecutively by the CCD sensor. This procedure always performs the same cycle starting with the voltage 0 and ending with the voltage Umax. The waiting time after the application of a zero voltage to the piezoelectric allows it to stabilize. The waiting time before the start of the acquisition avoids acquiring a frame that would have been exposed before the application of the desired exposure conditions. The end of the exposure of an image is indicated on the acquisition cards by the beginning of the transfer of the corresponding image. Using an exposure time less than the image transfer time allows the image to not be affected by the transient states. Setting the process to the highest priority avoids disruption of the acquisition by other system tasks under a multitasking operating system. The 6 images are acquired successively and in real time (no image lost) by the acquisition card to minimize the time during which vibrations can affect the result. Each image has horizontal dimension hpix and vertical dimension vpix. During the acquisition, the images are transferred automatically by the acquisition card into the table reserved for them in the main memory of the computer. At the end of the procedure

acquisition, we have a table 1 [a, b, ij], the index a corresponding to the phase difference, the index b corresponding to the image (shifted or not shifted in phase), the indices and / and / being the coordinates in pixels and varying respectively from 0 to hpix-1 and from 0 to vpix-1, (601) computation of the two frequency representations. These are stored in tables of

complexes SO [i, j] and SI [ij], applying the formulas:

(602) The program modifies the SI array by multiplying each of its elements by e

(603): the program calculates the maximum value mod max = max ISo [l, ill of the module on - 05, i5, hpix-l <-hpix-1 05, j5, vpix-1 S0.

testant la condition (605): ISO[i,j]1 0,5 mod max . Chaque fois que cette condition est réalisé, il effectue les opérations suivantes (606): ecart+ = ISO[i,j]- S*,j]1 nombre valeurs+=I (604): The program calculates the average difference between the two tables as follows:
The program initializes range and number values to 0 and traverses all the points i, j in

testing the condition (605): ISO [i, j] 1 0.5 mod max. Whenever this condition is realized, it performs the following operations (606): deviation + = ISO [i, j] - S *, j] 1 number values + = I

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When the program has finished browsing the indices (i, j) it divides the difference by number values (607), which gives it the average difference. This difference therefore only includes values for which the light wave is sufficiently strong, in order to avoid a too noisy result. It is stored in a table.

(608): the program goes to the next value of the pair (high diff, low diff) and repeats the operations until the series of deviations has been calculated.

 (609): the program applies a low-pass filter to the table obtained to limit the noise due to the vibrations of the system. The low-pass filter used is represented in the frequency domain by a 'step' moving from a value of 1 in low frequencies to a value of 0 in high frequencies, and its bandwidth is determined empirically to have good noise limitation without too much deformation of the curve.

(610): the table is represented graphically to check the pace.

(611): the torque value (low diff, high diff) corresponding to the minimum is displayed.

(diff haut, dtff bas) ) que le programme filtre pour éliminer le bruit (609) et qu'il représente graphiquement (610). La valeur d'indice du tableau correspondant à l'écart minimal correspond alors à la valeur correcte du couple (diff bas,diff haut) et ce couple est affiché (611). The series of values of the pair (low diff, high diff) are determined as follows: In a first step the program varies the values of diff high and diff low by leaving them equal to each other. For example they can vary between 0 and Umax / 4 in steps of 4096 if we use 12 bits
4096 conversion. The result is a table of 1024 items (the calculated differences for each value of

(diff high, dtff low)) that the program filters to eliminate the noise (609) and that it represents graphically (610). The index value of the table corresponding to the minimum deviation then corresponds to the correct value of the torque (diff low, diff high) and this torque is displayed (611).

 In a second step, the program is restarted by fixing diff ~ low to the value previously obtained and by varying only diff high. A new minima is thus obtained, which corresponds to a more precise value of diff high.

 In a third step, the program is restarted by setting diff high to the value previously obtained and varying only low diff, obtaining a more accurate value of low diff.

 The operator can reiterate these steps by varying separately and alternatively diff low and diff high, but the maximum accuracy on these values is obtained rather quickly.

5. 13. adjustment of polarizer (105) and polarization rotator (104)
The next step is to adjust the position of the polarization rotator (104) and the polarizer (105). This device is intended to achieve a controlled attenuation of the lighting beam by control of the phase rotator, and will be called the set 'optical switch'. It has a closed position corresponding to a low intensity crossing it and an open position corresponding to a higher intensity.

 The object used is the same as in the previous step, the adjustment of the mirror (109) and the diaphragms is also the same. The reference wave is first removed. At first, the polarizer is set up and adjusted to maximize the intensity therethrough and received on the sensor (118).

In a second step, the polarization rotator is set up. A voltage corresponding to a state

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(800) : Le programme acquiert d'abord les images en utilisant la procédure acquiert-images décrite Fig.13. Par 'les images' on entend içi 6 figures d'interférences reçues consécutivement par le capteur CCD. Cette procédure effectue toujours le même cycle commençant par la tension 0 et finissant par la tension Umax. Le temps d'attente après l'application d'une tension nulle au piézoélectrique permet à celuici de se stabiliser. Le temps d'attente avant le lancement de l'acquisition évite d'acquérir une trame qui aurait été exposée avant l'application des conditions d'exposition voulues. La fin de l'exposition d'une image est signalée sur les cartes d'acquisition par le début du transfert de l'image correspondante. arbitrarily defined as closed is applied thereto and is rotated to minimize the intensity across the switch assembly. In a third step, the reference wave is restored and a program is used that calculates the ratio of the intensities and the phase difference between the two positions of the polarization rotator, which ratio will be necessary during the image acquisition phases for combine the waves corresponding to the open and closed states of the switch. The algorithm of this program is in Figure 12. The steps are as follows:

(800): The program first acquires the images using the acquires-images procedure described in Fig.13. By 'images' is meant 6 interference patterns received consecutively by the CCD sensor. This procedure always performs the same cycle starting with the voltage 0 and ending with the voltage Umax. The waiting time after the application of a zero voltage to the piezoelectric allows it to stabilize. The waiting time before the start of the acquisition avoids acquiring a frame that would have been exposed before the application of the desired exposure conditions. The end of the exposure of an image is indicated on the acquisition cards by the beginning of the transfer of the corresponding image.

Using an exposure time less than the image transfer time allows the image to not be affected by the transient states. Setting the process to the highest priority avoids disruption of the acquisition by other system tasks under a multitasking operating system. The 6 images are acquired successively and in real time (no image lost) by the acquisition card to minimize the time during which vibrations can affect the result. Each image has horizontal dimension hpix and vertical dimension vpix. During the acquisition, the images are transferred automatically by the acquisition card into the table reserved for them in the main memory of the computer.

(801); the program calculates the two frequency representations SO and SI which differ by the state of the switch. SO is the open switch and SI is the closed switch.

(802): The program calculates the maximum mod max max ISO [I, j] 1 reached by the 0 <irpix-1 '0 <j <-vpix-1 module of the elements of the array SO.

(804): ,S'0[y, y]j 0,5 mod~max Lorsque la condition est vérifiée, il effectue (805): rapport+ =S0[i,j] rapport+ = [..] nombre valeurs+=1 (803): the program calculates the average ratio between the two frequency representations. It initializes ratio and number values to 0 then traverses the set of indices (i, j) by testing the condition

(804):, S'0 [y, y] j 0.5 mod ~ max When the condition is satisfied, it performs (805): ratio + = S0 [i, j] ratio + = [..] number values + = 1

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(807) le programme calcul la moyenne rapport moy des valeurs de rapport obtenues depuis son lancement. When the set of indices i, j has been traveled, the program divides ratio by number values (806) which gives the desired ratio.

(807) The program calculates the average ratio of the ratio values obtained since its launch.

rapport moy. (808): the program displays the real and imaginary parts as well as the report module and

average ratio

 (809) The program continuously repeats this procedure to allow continuous adjustment. The program ends with instruction from the operator.

valeur moyenne complexe rapport moy est notée et servira de base dans la suite des opérations. The angular position of the polarization rotator must be adjusted so that the ratio module is approximately equal to 8. The program is then stopped and restarted, and after a sufficient number of iteration the

The average value of the average ratio is noted and will serve as a basis for subsequent operations.

5. obtaining the constant K and adjusting the diaphragm (114) and the mirror (116)
K is the maximum value in pixels corresponding to the maximum spatial frequency of the wave 1 / # v or #vest the wavelength in the observed medium, assumed to be index equal to the nominal index nv of the objective . The nominal index of the objective is the index for which it was designed and for which it does not create spherical aberration. This is also the index of the optical oil to be used with the lens.

 There are K pixels between the frequencies 0 and #. The frequency step along an axis is therefore 1 / K # v The frequencies vary in total from - 1 / # v to 1 / # v in steps of 1 / K # v.

#v #v @ K # v
If N is the total number of pixels along each axis taken into account for the Fourier transform, N frequency values are taken into account, ranging from - N to N.

2K # v 2K # v
After transformation, N position values are obtained with a step equal to half the inverse of the maximum frequency before transformation.

 The step in position is therefore 1 / @ = K # v.

Dreel' on a donc: D , N D p, d'ou K = bzz-. La longueur d'onde à considérer ici est la N @@ #v Dpix longueur d'onde dans le matériau, supposé être d'indice égal à l'indice nominal nv de l'objectif soit: #v = #. On a finalement: nv N 2K # v
If we consider two points between which the distance in pixels is Dpix and the actual distance is

So we have: D, ND p, where K = bzz-. The wavelength to be considered here is the N @@ #v Dpix wavelength in the material, supposed to be index equal to the nominal index nv of the objective is: #v = #. We finally have: nv

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To obtain the constant K, the image is made of an objective micrometer for which the real distances are known, then the formula above is applied.

 This is achieved by using a focus program that will be reused later whenever a focus on a sample is needed before three-dimensional image taking.

obtient donc un tableau d'entiers (type unsigned char pour 8 bits) 1[p, c, i, jl ou l'indice p variant de 0 à 2 correspond à l'état de phase, l'indice c variant de 0 à 1 correspond à l'état du commutateur (0=ouvert, 1=fermé) et les indices i et jvariant de 0 à hpix-1 et de 0 à vpix-1 correspondent aux coordonnées du pixel.

The algorithm of this program is in Figure 14. Its main steps are: (1000): The program acquires an image by the procedure acquires images of Fig.13. We

thus obtains an array of integers (type unsigned char for 8 bits) 1 [p, c, i, jl where the index p varying from 0 to 2 corresponds to the phase state, the index c varying from 0 to 1 corresponds to the state of the switch (0 = open, 1 = closed) and the indices i and jvariant from 0 to hpix-1 and from 0 to vpix-1 correspond to the coordinates of the pixel.

associée au pixel et à ses 8 voisins immédiats, et le tableau .1 î if Li, JI est mis à 1 pour ces 9 pixels. (1001): An array of BooleansFli, j] is generated: it is initialized to 0, then for each pixel, the maximum value reached by 7 [, 0, /, y] on the three images corresponding to the open position of the switch is calculated. If this value is equal to 255 (the highest value of the digitizer), the images corresponding to the closed position of the switch must be used in the calculation of the frequency

associated with the pixel and its 8 immediate neighbors, and the table .1 if Li, JI is set to 1 for these 9 pixels.

Si H[i,j] vaut 1, la valeur complexe ainsi obtenue est donc multipliée par le nombre complexe rapport moy obtenu lors de l'opération de calibration du commutateur pour donner la valeur finale de l'élément de tableau S[i,j], afin de tenir compte du décalage de phase et de l'absorption induits par le commutateur. (1002): the frequency representation S [i, j] of complex numbers is generated: for each pixel, the value is generated according to the following equations:

If H [i, j] is 1, the complex value thus obtained is thus multiplied by the complex ratio moy obtained during the calibration operation of the switch to give the final value of the array element S [i, j ], to account for phase shift and absorption induced by the switch.

 (1003): The program limits the array S to dimensions of 512x512. The program then optionally performs one or the other, or none, of the following two operations: - averaging over a width of 2, which brings the array S to a table S 'of dimensions 256x256 with S' [i, j ] = S [2i, 2d] + S [2i + 1,2d] + S [2i, 2d + 1] + S [2i + 1,2d + 1]. This averaging, coupled with a reduction in the opening of the diaphragm (114), makes it possible to reduce the diameter of the area observed and to reduce the calculation time. It is equivalent to low-pass filtering followed by subsampling.

S'[i,j] = S[128 + 1,128 + je . Ceci permet de diminuer le temps de calcul au prix d'une réduction de la résolution. a limitation of all the frequencies observed to a square of 256x256 pixels with

S '[i, j] = S [128 + 1,128 + I. This reduces the calculation time at the cost of a reduction of the resolution.

 However, in this case the program does not perform either of these two operations.

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 (1004): The program then performs the inverse Fourier transform of the resulting array.

 (1005): It displays the result on the screen, extracting the module, the real part or the imaginary part. In this case it will display the module. Whatever the displayed variable, the corresponding real number table is first normalized, either relative to the average value or to the maximum value. The program also writes the corresponding real file to disk. When the real part or the imaginary part are represented, it is essential that the point of impact of the direct beam be in (256,256) on the size image 512 x 512, otherwise a modulation becomes visible.

When the module is represented, the exact point of impact of the direct beam does not significantly influence the result.

 (1006): The program then starts the acquisition of a new image, thus operating continuously. It stops at the instruction of the operator.

 In order to obtain the image of the micrometer, the objective is first placed in a nearly focused position, the micrometer having been introduced as an object. In a first step, the reference wave is suppressed, the diaphragms are opened to the maximum, and the direct visualization program in real time of the image received on the sensor is launched, the filters in (103) and the polarization rotator being adjusted to allow enough current to pass through to sufficiently saturate the sensor at the point of direct impact of the beam.

The object is then moved to the horizontal plane using the corresponding positioner until the image consisting of many bright aligned points, characteristic of the micrometer, appears. The micrometer is then correctly positioned under the lens.

 The diaphragms at (107) and (114) are then adjusted for an aperture of about 8 mm. The filters at (103) are then set so that the maximum intensity on the CCD is at a level of about a quarter of the maximum value of the digitizer, ie 256/4 = 64. The reference wave is reintroduced. The focus program is then launched. The diaphragm (114) should be adjusted to be clearly visible on the displayed image, while being as open as possible. If the image is not well centered, the centering can be improved either by changing the orientation of the mirror (116), in which case it may be necessary to readjust the orientation of the mirror (121), or by changing the position of the diaphragm (114). The diaphragm at (107) should be adjusted so that the observed area appears uniformly illuminated. The focus program is then stopped, the reference wave is removed and the intensity of the beam is readjusted as before. The reference wave is then reintroduced and the focus program restarted.

deux graduations séparées par D,.eel micromètres est sur l'image ainsi obtenue de Dp,x pixels, si l'indice nominal de l'objectif est nv (en général, nv =1,5) et si la longueur d'onde du laser dans le vide est;' The microscope objective is then moved by the focusing device so as to obtain a good image of the micrometer. To facilitate focusing, it is advantageous to visualize a portion of the micrometer or lines of different lengths are present. This limits 'false focus' due to interference phenomena in front of the micrometer. Between two movements it is necessary to release the manual focusing device to obtain an image undisturbed by the vibrations. When a good image has been obtained, the program is stopped and the image obtained is used to obtain the distance in number of pixels between two lines, the metric distance between these lines being known. If the distance between

two graduations separated by D, .eel micrometers is on the image thus obtained of Dp, x pixels, if the nominal index of the objective is nv (in general, nv = 1.5) and if the wavelength the laser in the vacuum is;

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K N Diz, ou bien entendu Deel et IL sont dans la même unité. (# = 0.633 micrometers) and if the number of points of the Fourier transform is N (N = 512) then we have: n N dan

KN Diz, or of course Deel and IL are in the same unit.

# Dpix 5.15.adjustment of the diaphragms
The three-dimensional image that will be calculated has a size of 256 pixels, which limits the file sizes and calculation times. The iris adjustment is to reuse the focus program, this time with the intermediate averaging option, and adjust the iris (114) so that its image is clearly visible while being as large as possible. The diaphragm (107) is then set to be slightly more open than the minimum allowing regular illumination of the observed part of the sample.

5. 16. adjustment of the position of the condenser, obtaining the characteristics of the circle
During the acquisition procedure, the end of the light frequency vector must follow a circle (504), which is equivalent to the fact that the point of impact of the light beam on the sensor follows a corresponding circle. Here the impact point of the illumination beam is the dot illuminated on the sensor (118) when only the illumination beam is present (transparent plate), and which remains the point of maximum intensity when a sample susceptible of to be used by this microscope is present. For a given position of the condenser (111) and the microscope objective (113), the radius of the circle can not generally be chosen freely: this is a consequence of the strong aberrations induced by the condenser for the non-paraxial rays. On the other hand, if the position of the condenser is incorrectly adjusted transversely, the illumination beam leaves the observed area of the object and is intercepted by the diaphragm (114), and the circle can not be traveled. If it is wrongly set in the direction of the optical axis, the characteristics of the circle are not optimal. It is therefore generally necessary to adjust the position of the condenser and calculate the characteristics of the circle. These operations are however simplified if a condenser of very good quality is used, or if the condenser is replaced by a microscope objective. Indeed, in this case, the aberrations are small and the radius of the circle can be chosen freely, however less than a limit radius defined by the maximum opening of the system.

 An example of a program for adjusting the position of the condenser and obtaining the characteristics of the circle is detailed in FIG. 15. The principle of this program is to move the point illuminated by the direct beam (point of impact of the illumination beam) along concentric rays from the center of the sensor and to display the illuminance values at each point. successively illuminated by the direct beam, which forms on the screen a star-shaped figure shown diagrammatically in FIG. The position of the condenser can then be adjusted so that this star is as regular and wide as possible, and the program determines the characteristics of the circles (common center G and respective radii Rp and Rq) delimiting the outer part of the star, which allow to obtain the circle on which will move the point of direct impact of the lighting beam during the acquisition procedure. Before starting this program, the reference wave must be removed. The mirror (109) must be moved so that

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 the point of direct impact of the beam is at the center of the image. The filters at (103) must be adjusted to avoid saturation of the sensor and will have to be readjusted during the operation of the program to avoid saturation on the entire star. The main steps of this program are: (1100): the program calculates the radius values, indexed by k, and the angle, indexed by l, then the coordinates of the objective point. The x, y coordinates of this point are expressed in motor steps (not in pixels). x represents the number of steps taken by the motor (213) from its initial position (illuminated point in the center of the image). y represents the number of steps taken by the motor (208) from its initial position.

suffisamment proches les uns des autres, et l'incrément angulaire pas angle vaut 1-max . 1-max vaut par exemple 16, k-max est ajusté pour que le point éclairé pour l'indice k max sorte du domaine ou il est visible. * The step of moving along a radius, not radius, must be set so that the points of the star are

sufficiently close to each other, and the angle increment angle is 1-max. 1-max is for example 16, k-max is adjusted so that the illuminated point for the index k max is from the domain where it is visible.

 (1101): The program moves the motor to the objective point (1102): the point that was displayed on the screen in the previous step for the same indices k, l is cleared. The coordinates of this point were stored in Table V in V [k, l] (1103): an image is acquired from the sensor. This is a simple acquisition, the value of each pixel being read directly on the sensor.

 (1104): the maximum of illumination on the acquired image is calculated and recorded, its coordinates in pixels are recorded in table V containing pairs of integers, in V [k, l], and its value is stored in the table W containing reals, in W [k, l]. The point corresponding to the maximum illumination is displayed on the screen (the star is gradually formed by these points).

k min<p<k max sur la partie k bzz k-min du rayon. La valeur ww est une constante choisie de manière à ce que la partie centrale intense de l'étoile ne soit pas prise en compte. Le programme détermine ensuite les entiers: kp = max p E[k~min,k~max]1 W[p,l] 2 vmax. vcoefl kq = min{p E[k~min,k~max]1 W[p, 1] bzz vmax.veoef ou vcoef=0,5 par exemple. Il enregistre alors les coordonnées des points correspondants dans des tableaux P et Q:

P[l] = vlc/', l Q[l] = V[kq, 1] Le programme affiche les valeurs de l et de vmax dans une fenêtre de texte.

(1105): The program determines the maximum value vmax = max (W [p, l]) reached

k min <p <k max on the k bzz k-min part of the radius. The value ww is a constant chosen so that the intense central part of the star is not taken into account. The program then determines the integers: kp = max p E [k ~ min, k ~ max] 1 W [p, l] 2 vmax. vcoefl kq = min {p E [k ~ min, k ~ max] 1 W [p, 1] bzz vmax.veoef or vcoef = 0.5 for example. It then records the coordinates of the corresponding points in tables P and Q:

P [l] = vlc / ', l Q [l] = V [kq, 1] The program displays the values of l and vmax in a text window.

(1106): The program calculates an approximation of the center of the circle and ranks it in C [l]. C [I] is calculated as the intersection of the perpendicular bisector of P [4 and P [l + I maxl2] with the mediator of P [I + I maxl4] and P [l + l maxl4 + 1 maxl2]. Fig.17 illustrates the calculation principle on example l max = 8, for the point C [0]. The point C [0] is the intersection of two straight lines, one of which is the mediator of the P [0] P [4] segment and the other is the mediator of the P [2] P segment [6].

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 (1107): The program calculates the center G of the circle as the centroid of points C [l]. The coordinates of G will be denoted Gx, Gy (1108): It calculates the radius Rp of the outer circle as the average value of the distance between G and the points P [l], and the radius Rq of the inner circle as the mean value of the distance between G and points Q [l].

 (1109): It displays Gx, Gy, Rp, Rq in the text window.

 (1110): He repeats the whole operation. The program stops at the request of the operator.

(inférieure à 20 pixels par exemple), on prend R = R p 2 +R g . Si L est plus élevée, on peut prendre une valeur légèrement inférieure à Rp , par exemple R = Rp -10 . Si le condenseur est utilisé à une ouverture suffisamment inférieure à son ouverture maximale, la partie externe de l'étoile rejoint le centre, la largeur L va doncjusqu'au centre, et on peut là aussi utiliser R = Rp - 10 . For this adjustment operation, the micrometer must be slightly moved so as to be out of the field of view, the object then being equivalent to a transparent blade. The objective must be maintained in a focused position. At first, the program is used to refine the positioning of the condenser. This must be positioned transversely so that the points displayed form a 'star' whose branches all have a width (denoted L in Fig.16) and a near brightness, that is to say that the The values of the maximums displayed in step (1105) must be close for all branches. It must be positioned in the direction of the optical axis so that the radius Rp of the outer circle is as high as possible and that on each branch of the star, the outer zone corresponding to high intensities retains a sufficient width (for example greater than 10 pixels), denoted L in FIG. 16. The narrower the area, the more likely the image acquisition program, which uses the coordinates obtained for the circle, to diverge by trying to traverse this circle. For this first step, only a few angles # are needed, for example 8. Optionally the opening of the diaphragm (107) can be increased, which makes it possible to increase the width L. In a second step, the number angles taken into account is higher in order to obtain precise values of Gx, Gy, R p, Rq. Point G is the center of the circle that will be traveled during the acquisition step by the point of direct impact of the lighting beam. The radius R of this circle is determined from the Rpet Rq rays. If L = R p - Rq is low
Rp + Rq

(less than 20 pixels for example), we take R = R p 2 + R g. If L is higher, we can take a value slightly lower than Rp, for example R = Rp -10. If the condenser is used at an opening sufficiently smaller than its maximum opening, the outer part of the star joins the center, the width L goes to the center, and we can also use R = Rp - 10.

5. 17. recording of the reference wave
The knowledge of the reference wave is indispensable for the precise calculation of the complex values of the wave arriving at the sensor. This must therefore be recorded independently of the constant mean noise value that characterizes each pixel. For this purpose a specific program is used. As a first step, the illumination and reference waves are removed and the program records the resulting 'optical black' image on the CCD. It averages the intensity obtained on 100 images to have a

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enregistre l'image résultante dans un tableau 7/'e/'[] ou i varie de 0 à hpix-1 et j varie de 0 à vpix-l. black optical debris. In a second step, the reference wave is restored and the lighting wave remains suppressed. The program saves the resulting image, the average over 100 images to denoise. Then the program calculates the difference between the image of the reference wave alone and the optical black image, and

save the resulting image in an array 7 / 'e /' [] where i varies from 0 to hpix-1 and j varies from 0 to vpix-1.

5. 18. Focus on the object under study
This step must be repeated for each sample for which an image is desired. The lighting wave is restored. The sample to be studied is set up. The mirror (109) is set so that the point of direct impact of the illumination beam is at the center of the sensor. The filters at (103) are set so that, in the absence of a reference wave, the maximum intensity received on the CCD sensor is approximately 64. The reference wave is then reestablished. The focusing program is started with the intermediate averaging option, and the position of the lens is adjusted using the focusing device to obtain a clear image of the area of interest of the sample.

5. 19. Adjustment of radius R
After the focusing phase the condenser adjustment phase must be repeated, without changing the position of the objective and leaving the sample in place, and using the closed position of the optical switch. The position of the condenser is not necessarily modified but the new value of R is noted and the filters at (103) must be adjusted so that the maximum intensity received on each spoke (displayed in step (1104) of the focus program algorithm) is about a quarter of the maximum value of the digitizer, or 64. The reference wave, which must be suppressed during this step, is restored for the acquisition step.

un fichier frch acquis une représentation fréquentielle qui sera utilisée dans la phase de calcul tridimensionnel. La taille de l'image acquise depuis la caméra est hpix x vpix, mais cette taille est divisée par deux pour obtenir des représentations fréquentielles de dimension hel x vel, selon le principe de moyennage intermédiaire déjà utilisé dans le programme de focalisation. 5. 20. acquisition stage
This step makes it possible to acquire the two-dimensional frequency representations from which the three-dimensional representation will be calculated. The point of direct impact of the illumination beam is displaced in a circle of center G and radius R determined in the preceding adjustment step. The angular step is 2 or nbim is the number of two-dimensional frequency representations to nbim acquire and has the value of the integer part of 2nR. At each step, the program calculates and records in

a frch file acquired a frequency representation which will be used in the three-dimensional computation phase. The size of the image acquired from the camera is hpix x vpix, but this size is divided by two to obtain frequential representations of hel x vel dimension, according to the intermediate averaging principle already used in the focusing program.

 The acquisition program is detailed by the algorithm of Fig.18 whose steps are as follows: (1300): The basic data of the acquisition are recorded in the acquired file file: nbim: number of two-dimensional frequency representations

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 hel = hpix / 2: final number of points in the horizontal direction vel = vpixl2: final number of points in the vertical direction (1301): waiting time allowing absorption of the vibrations created by the movement of the positioner (110). A waiting time of about 2s may be appropriate.

obtient donc un tableau d'entiers (type unsigned char pour 8 bits) 1[p,c,i,jl ou l'indice/? variant de 0 à 2 correspond à l'état de phase, l'indice c variant de 0 à 1 correspond à l'état du commutateur (0=ouvert, 1=fermé) et les indices / et variant respectivement de 0 à hpix-1 et de 0 à vpix-1 correspondent aux coordonnées du pixel. (1302): The program acquires the images by the procedure acquires images of Fig.13. We

gets an array of integers (type unsigned char for 8 bits) 1 [p, c, i, jl or the index /? varying from 0 to 2 corresponds to the phase state, the index c varying from 0 to 1 corresponds to the state of the switch (0 = open, 1 = closed) and the indices / and varying respectively from 0 to hpix- 1 and from 0 to vpix-1 correspond to the coordinates of the pixel.

 (1303): An array of Booleans H [i, j] is generated: is initialized to 0, then for each pixel, the maximum value reached on the three images corresponding to the open position of the switch is calculated. If this value is equal to 255 (the highest value of the digitizer), the images corresponding to the closed position of the switch must be used in the calculation of the frequency associated with the pixel and its 8 immediate neighbors, and the array H is set to 1 for these 9 pixels.

Si H[i,j] vaut 1, la valeur complexe ainsi obtenue est donc multipliée par le nombre complexe rapport moy obtenu lors de l'opération de calibration du commutateur pour donner la valeur finale de l'élément de tableau S[i,j], afin de tenir compte du décalage de phase et de l'absorption induites par le commutateur.

(1304): the frequency representation S [i, j] of complex numbers is generated: for each pixel, the value is generated according to the following equations:

If H [i, j] is 1, the complex value thus obtained is thus multiplied by the complex ratio moy obtained during the calibration operation of the switch to give the final value of the array element S [i, j ], to account for phase shift and absorption induced by the switch.

(1305) -The maximum module point of Table S is determined. Its coordinates (/ yMax, y mox) are recorded.

Lobj = Gy + R sin(k. pas ou i obj et j obj sont les coordonnées de la position objectif en pixels. (1306) The position 'objective is calculated, the angle being k.pas: i ~ obj Gx + Rco k.pas)

Lobj = Gy + R sin (k) not or i obj and j obj are the coordinates of the objective position in pixels.

The displacement of the motors is calculated: not i = (i obj-i max) .pas ~ by ~ pixel a = (/ ~ o ~ / K) .6 ~ pa7 '~: <' e / or not ~ by ~ pixel is the number of steps of the motors per pixel of displacement, determined experimentally during the adjustments.

 (1307) - One of the motors makes it possible to move the point of direct impact of the beam in the direction of the axis i. It must perform a number of steps not i in the direction corresponding to an index i increasing for

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 the position of the direct impact point of the lighting beam (for step ~ i # 0, it must perform a number of steps-not in the opposite direction). The other motor moves the point of direct impact of the beam in the direction of the axis. Similarly, he must perform a number of steps not ~ j.

(1308) - An array of averaged frequencies is generated: Each dimension of the initial array S is divided by two to give an array Mk with

(i 3\jy)-L,e point ae moauie maximal au rameau ivk est ueiermme, ses uuufuuituecs IIItG.Gk , jmaxg et sa valeur max-moy = Mk imaxk , jmaxk = max 1 (Mk sont enregistrées.

The highest point at the branch ivk is the same, its values IIItG.Gk, jmaxg and its max-moy value = Mk imaxk, jmaxk = max 1 (Mk are recorded.

., r..1 [7'] Mk V'J ] = # max~ moy (1311)- imaxk , jmaxk et la représentation fréquentielle Mk sont enregistrés dans le fichier

fichacquis. 09 ::;. Hel-l 0 # j # vel-1 (1310) -The elements of table Mk are normalized by dividing them by max ~ moy:

., r..1 [7 '] Mk V'J] = # max ~ moy (1311) - imaxk, jmaxk and the frequency representation Mk are recorded in the file

fichacquis.

 (1312) - The algorithm ends when the angle is 2 #. The motor then returns to its initial position and the acquisition file ~ acquired file is closed.

La relation entre les coordonnées et la fréquence d'éclairage est:

La relation entre les coordonnées et la fréquence totale est donc:

5. 21. three-dimensional calculation
The acquisition procedure generated two-dimensional frequency representations Mk, where the index k represents the sequence number of each representation. Since these representations have been averaged over a width of 2, the values of Cx, Cy, and K must be divided by 2 to correspond to the new coordinate system. It is these divided values that are used in the following. The set of two-dimensional representations can be considered a three-dimensional representation (i, j, k) in which the index k represents the image index and the indices i and / represent the Cartesian coordinates of each representation. In the k-th two-dimensional frequency representation: the relation between the coordinates and the characteristic frequency is:

The relationship between the coordinates and the lighting frequency is:

The relation between the coordinates and the total frequency is therefore:

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par translation au point de coordonnées (fdiml2fdim/2fdiml2). On obtient donc, à partir de chaque point de coordonnées i,j d'une représentation bidimensionnelle Mk, un point de la représentation tridimensionnelle par:

The three-dimensional calculation procedure consists in principle in generating initially a three-dimensional representation in the form of an array F of dimensions fdim xfdim xfdim with fdim = 256, and then in performing the Fourier transform to obtain a table U of the same dimensions corresponding to the representation u (r), and in which the indices therefore correspond to the radius-vector. The representation F is a table whose indices represent the coordinates of K # ft, the zero being brought back

by translation at the coordinate point (fdiml2fdim / 2fdiml2). We thus obtain, from each point of coordinates i, j of a two-dimensional representation Mk, a point of the three-dimensional representation by:

When a point of the array F, with coordinates (m, nj, nk), is obtained successively from several distinct two-dimensional representations, the value of F retained at this point is the average of the values obtained from each of these two-dimensional representations. . When this point is never obtained, it is assigned a value of zero.

 When the array F has been generated, the array U can be obtained by inverse three-dimensional Fourier transform.

 This method can be applied directly if the program has sufficient RAM. The program whose algorithm is described FIG. 19, however, makes it possible to perform the calculations on a system whose RAM is limited, the files being stored on a sequential access support (hard disk).

 For practical reasons, part of the Fourier transformation will be carried out as Table F is generated, which will never be truly generated.

 The program operates in five stages. Each step uses an input file stored on the hard disk of the computer and generates an output file also stored on the hard disk, whose name is in italics in the figure. The program could theoretically perform more directly the operations necessary for the generation of the three-dimensional image, but the size of the files involved is too high so that they can be entirely contained in the memory of a computer. It is therefore necessary to manage their disk storage. Since reading / writing of disk file items is faster if the items are stored contiguously, the program must be designed to read and write to the disk only blocks of sufficient size. This is what the described algorithm allows, whereas a direct method would require reads / writes to non-contiguous addresses and would not be feasible due to the time lost in disk access. The steps of the algorithm are as follows:

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ni=i-imax+fdiml2,nj j jmax+fdiml2, les dimensions suivant ni et nj du tableau ainsi généré étant defdim x fdim. L'algorithme de cette partie est représenté figure 21. Les étapes sont les suivantes: (1600) : les valeurs de hel,vel,nbim sont lues dans le fichierfich~acquis. (1400) -centrage of two-dimensional frequency representations:
This procedure consists in translating the two-dimensional representations to move from a representation in the coordinate system (i, j, k) to a representation in the system (ni, nj, k) with

ni = i-imax + fdim12, nj jmax + fdim12, the following dimensions ni and nj of the array thus generated being defdim x fdim. The algorithm of this part is represented in FIG. 21. The steps are as follows: (1600): the values of hel, vel, nbim are read in the file fich ~ acquired.

 (1601): the frequency representation Mk corresponding to the index k is transferred in central memory with the corresponding values imaxk and jmaxk.

. Tk [ni, /] = Mk [ni - fdim l 2 + imaxk , nj - fdim l 2 + jmaxk lorsque 0 5 ni - fdim l 2 + imaxk <- hel -1 et 0 <- nj - fdim l 2 + Jmaxk 5 hel -1 . (1602): A translated frequency representation Tk of dimensions fdim xfdim is generated with:

. Tk [ni, /] = Mk [ni - fdim l 2 + imaxk, nj - fdim l 2 + jmaxk when 0 5 ni - fdim l 2 + imaxk <- hel -1 and 0 <- nj - fdim l 2 + Jmaxk 5 hel -1.

#Tk [ni, nj] = 0 in other cases
Fig. (20) shows an original image with its coordinate point (imaxk, jmaxk) and an arbitrary drawing around that point, and the new translated image.

imaxk , Jmaxk , Tk [0,0], Tk [1,0], ...... Tk fdim -1,0 , lmaxk, jmaxk, Tk [0,1], Tk [1,1],...... Tk fdim-1,1 , Imaxk, Jmaxk , Tk 0, fdtmTk 1, fdim, ...... Tk [fdim - 1, fdim - 1] , Notons que imaxk et jmaxk sont répétés à chaque ligne de Tk dans le fichier ftch centré. Ceci permet que ces données, indispensables au changement d'indice k # nk, restent disponible après l'opération d'échange des axes. (1603): The values of imaxk, jmaxk, and the Tk representation are stored in the centered file in the following order:

imaxk, Jmaxk, Tk [0,0], Tk [1,0], ...... Tk fdim -1,0, lmaxk, jmaxk, Tk [0,1], Tk [1,1] ,. ..... Tk fdim-1.1, Imaxk, Jmaxk, Tk 0, fdtmTk 1, fdim, ...... Tk [fdim-1, fdim-1], Note that imaxk and jmaxk are repeated at each Tk line in the centered ftch file. This allows these data, which are indispensable for the index change k # nk, to remain available after the axis exchange operation.

 (1604): the process is restarted as long as k is less than nbim.

Le changement d'indices /' -># ni et j xyz nj ayant été effectué, il reste à faire le changement d'indice k # nk . Pour effectuer ce changement d'indice en un temps raisonnable il est nécessaire de pouvoir charger en mémoire centrale, rapidement, un plan (ni,k). Pour que cette opération soit possible, il faut préalablement échanger les axes k et nj. C'est ce que fait cet algorithme.

(1401) -Exchange of the 'plan' and 'line' axes

The change of indices / '-># ni and j xyz nj having been carried out, it remains to make the index change k # nk. To make this change of index in a reasonable time it is necessary to be able to load in central memory, quickly, a plane (ni, k). For this operation to be possible, the axes k and nj must be exchanged beforehand. That's what this algorithm does.

The previously created centric file is re-read, the order of the data is changed, and an echl file is written in which the data is in the following order: imaxo, jmccco, To [0,0], To [1,01 , Fdim -1.0, imaxl, jmaxl, Tl [0,0], Tl [1,0], ...... Ii [fdim -1,0], imaxnbim-1 , iMaXnbim-1 Tnbrm-1 [0,0], Tb, ml [O], ...... Tnblm-1 [fdim-1,0],

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itnaxo , jmax0 , To 0,1, To 1,1], ...... To[fdim -1,1], imaxl , jmaxl , Tl [0,1], Tl [1,1],...... Tt [fdim -1,1], tmpnbtm-1, .lmnbrm-I , Tnb.-1[0,11, Tnbrm-t 1,1], ...... Tnbzm-l[fdim -1,1], imaxo , jmaxo , To 0, fdim -1, To 1, fdim -1, ...... To [fdim - 1, fdim - 1], imaxl, jmaxl,TlO, fdim-l,Ttl, fdim-1,......Tifdim-1, fdim-1, imaxnbim-1 jmaxnbrm-1, Tnbim-1 [0, fdim - 1], Tnbrm-1 1 fdim -1],...... Tn6rm-1 [Jdim -1, Jdim -1] C'est-à-dire que les axes nj et k sont échangés. Cette opération d'échange des axes est effectuée bloc par bloc. La Fig. (22) représente symboliquement (1700) le contenu d'un fichier tridimensionnel correspondant à des indices i,j, k, rangé en mémoire plan horizontal par plan horizontal et chaque plan étant rangé ligne par ligne, une ligne étant dans le sens de la profondeur sur le dessin. Les axes i,j,k et l'origine 0 du repère sont précisés sur le dessin. Le contenu du fichier obtenu par inversion des axes) et k est représenté en (1702). Le transfert des données d'un fichier à l'autre se fait bloc par bloc, le bloc (1701) étant copié en mémoire centrale puis transféré en (1703). La lecture et l'écriture des blocs se fait plan horizontal par plan horizontal, un plan horizontal dans le fichier lu ne correspondant pas à un plan horizontal dans le fichier écrit. La taille du bloc est la taille maximum qui puisse tenir dans la mémoire interne disponible de l'ordinateur. L'opération est répétée pour tous les blocs, les blocs situés 'au bord' n'ayant pas en général la même dimension que les autres. Cette manière d'opérer permet d'effectuer l'échange des axes avec un ordinateur dont la mémoire interne a une taille inférieure à celle des fichiers utilisés.

itnaxo, jmax0, To 0,1, To 1,1], ...... To [fdim -1,1], imax1, jmax1, Tl [0,1], Tl [1,1], .. .... Tt [fdim -1,1], tmpnbtm-1, .lmnbrm-I, Tnb.-1 [0,11, Tnbrm-t 1,1], ...... Tnbzm-l [fdim -1,1], imaxo, jmaxo, To 0, fdim -1, To 1, fdim -1, ...... To [fdim-1, fdim-1], imax1, jmax1, T10, fdim-1 , Ttl, fdim-1, ...... Tifdim-1, fdim-1, imaxnbim-1 jmaxnbrm-1, Tnbim-1 [0, fdim-1], Tnbrm-1 1 fdim -1], .. .... Tn6rm-1 [Jdim -1, Jdim -1] That is, the axes nj and k are exchanged. This axis exchange operation is performed block by block. Fig. (22) represents symbolically (1700) the contents of a three-dimensional file corresponding to indices i, j, k, stored in horizontal plane memory by horizontal plane and each plane being arranged line by line, a line being in the direction of the depth on the drawing. The axes i, j, k and the origin 0 of the reference are specified in the drawing. The contents of the file obtained by inverting the axes) and k is represented in (1702). The transfer of data from one file to another is block by block, the block (1701) being copied to the central memory and then transferred to (1703). The reading and writing of the blocks is horizontal plane by horizontal plane, a horizontal plane in the read file does not correspond to a horizontal plane in the written file. The size of the block is the maximum size that can fit in the available internal memory of the computer. The operation is repeated for all the blocks, the blocks at the edge not generally having the same dimension as the others. This way of operating makes it possible to exchange axes with a computer whose internal memory is smaller than the size of the files used.

void echange~axes(FILE* read~file,FILE* write~file,int ktot,int jtot,int itot,int memory-limit ) int knum,jnum,bknum,bjnum,keff,jeff,k,j,bk,bj; char* buff; knum=(int)sqrt(((double)memory~limit)/((double)itot)); jnum=knum;

buff=( char*)malloc(itot*knum *jnum); bknum=ktot/knum ; if(knum*bknum!=ktot) bknum+= 1 ; bjnum=jtot/jnum; if (jnum*bjnum!=jtot) bjnum+=1; The procedure in C language (Microsoft C / C ++ under Windows 95) that allows this operation is as follows:

void exchange ~ axes (FILE * read ~ file, FILE * write ~ file, int ktot, int jtot, int itot, int memory-limit) int knum, jnum, bknum, bjnum, keff, jeff, k, j, bk, bj; char * buff; knum = (int) sqrt (((double) memory limit ~) / ((double) itot)); Jnum = knum;

buff = (char *) malloc (itot * knum * jnum); bknum = ktot / knum; if (knum * bknum! = ktot) bknum + = 1; bjnum = Jtot / Jnum; if (jnum * bjnum! = jtot) bjnum + = 1;

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if (bk==(bknum-1)) kektot-knum*(bknum-1); else keff=knum; if (bj==(bjnum-1)) jejtot jnum*(bjnum-1); else jeff=jnum; for (k=O;k≤keff-1;k++) for (j=O;j≤jeff-lj++) fseek(read file,(bk*knum+k)*jtot*itot+(bj*jnum+j)*itot,SEEK SET); fread(buff+k*jeff*itot+j*itot, 1, itot, read~file); }

for (j=O;j< jeff 1 j++) for(k=0;k≤keff-l;k++) { fseek(write file,(bj*jnum+j)*ktot*itot+(bk*knum+k)*itot,SEEK SET); fwrite(buff+k*jeff*itot+j*itot, 1, itot, write file); free (buff);

Les paramètres à passer lors de l'appel de la procédure sont: read file: pointeur sur le fichier frch centré write-file: pointeur sur le fichier fich ech7 ktot : nombre total d'images nbim jtot: nombre total de lignes dans une représentation fréquentielle: fdim itot: taille en octets d'une ligne: fdim*sizeof(complexe)+2*sizeof(int), ou sizeof (complexe) la taille en octets d'un nombre complexe ( Tk [i,j] par exemple) et sizeof (int) taille en octets d'un nombre entier (imaxk par exemple). memory~limit: taille maximale en octets de la mémoire à accès aléatoire (RAM) dont dispose la procédure pour stocker les blocs. for (bk = O; bk≤bknum-l; bk ++) for (bj = O; bj≤bjnum-1; bj ++) {

if (bk == (bknum-1)) kektot-knum * (bknum-1); else keff = knum; if (bj == (bjnum-1)) ijtot jnum * (bjnum-1); else jeff = jnum; for (k = O; k≤keff-1; k ++) for (j = O; j≤jeff-lj ++) fseek (read file, (bk * knum + k) * jtot * itot + (bj * jnum + j) * itot, SEEK SET); fread (buff + k * jeff * itot + j * itot, 1, itot, read ~ file); }

for (j = O; j <jeff 1 j ++) for (k = 0; k≤keff-l; k ++) {fseek (write file, (bj * jnum + j) * ktot * itot + (bk * knum + k) * itot, SEEK SET); fwrite (buff + k * jeff * itot + j * itot, 1, itot, write file); free (buff);

The parameters to pass during the call of the procedure are: read file: pointer on the file frch centered write-file: pointer on the file file ech7 ktot: total number of images nbim jtot: total number of lines in a representation frequency: fdim itot: size in bytes of a line: fdim * sizeof (complex) + 2 * sizeof (int), or sizeof (complex) the size in bytes of a complex number (Tk [i, j] for example ) and sizeof (int) size in bytes of an integer (imaxk for example). memory ~ limit: The maximum size in bytes of random access memory (RAM) available to store blocks.

 The files must be open in commited mode, that is, the read / write operations are performed directly from or to the hard disk, without intermediate buffering in central memory.

 (1402) - calculation phase.

This calculation phase aims to replace the index 'image' k by the index nk given by the formula:

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ou i,j sont les coordonnées dans le repère d'origine (avant centrage). Dans le repère centré on a donc:

Lorsque les mêmes indices (i,j,k) sont obtenus plusieurs fois par remplacement de l'indice image, la valeur retenue pour l'élément correspondant de la représentation fréquentielle tridimensionnelle est la moyenne des valeurs pour lesquelles les indices (i,j,k) sont obtenus.

where i, j are the coordinates in the origin reference (before centering). In the centered coordinate system we have:

When the same indices (i, j, k) are obtained several times by replacing the image index, the value retained for the corresponding element of the three-dimensional frequency representation is the average of the values for which the indices (i, j, k) are obtained.

(1800) les éléments suivants sont lus dans le fichier fich echl et transférés en mémoire interne imax0 , jmax0 , 70 [0, nj], T0[l,nj], To [fdim - 1, nj], imax ,jmax, 7t [0, M/], Tl [l,nj], ...... Tl [fdim - 1, nj], lmaxnbim-1,.%m'nbm-1, Tnbm-1 [0, ni], Tnbm-1 1, n,l , ...... Tnbim-1 [fdim - 1, nj] (1801) les tableaux Dnj et Poids, de dimensions fdim xfdim, sont initialisés à 0. (1802) La condition suivante est testée:

ou o est l'ouverture du microscope, et n l'indice de l'huile optique et de la lamelle utilisés, soit à peu près: - 0 = 1,25 Si la condition est vraie, le point correspond à un vecteur fréquence ne sortant pas de n 1,51 l'ouverture de l'objectif et est donc dans la zone observable. A point of the three-dimensional frequency representation, of coordinates (ni, nj, nk), can be obtained by this change of coordinates only from a given plane (ni, k) and corresponding to its index nj. The planes (ni, k) can therefore be processed independently of each other. When in a plane (ni, k) the index k has been replaced by the index nk, it is therefore possible to directly perform the inverse two-dimensional Fourier transform of this plane before moving on to the next plane. This part of the program does this, the algorithm of which is detailed in FIG. 23. Its main stages are:

(1800) the following elements are read from the file echl file and transferred to internal memory imax0, jmax0, 70 [0, nj], T0 [l, nj], To [fdim-1, nj], imax, jmax, 7t [0, M /], Tl [1, nj], ...... Tl [fdim-1, nj], lmaxnbim-1,.% M'nbm-1, Tnbm-1 [0, ni], Tnbm-1 1, n, l, ...... Tnbim-1 [fdim-1, nj] (1801) arrays Dnj and Weight, of dimensions fdim xfdim, are initialized to 0. (1802) The following condition is tested:

where o is the opening of the microscope, and n is the index of the optical oil and lamella used, approximately: - 0 = 1.25 If the condition is true, the point corresponds to a frequency vector not going out no 1.51 aperture of the lens and so is in the observable area.

(1804) La valeur correspondante de fréquence est additionnée au tableau Dnj.L'élément correspondant du tableaux des poids, qui sera utilisé pour calculer la valeur moyenne, est incrémenté. (1803) The value nk is calculated by the formula:

(1804) The corresponding frequency value is added to the table Dnj.The corresponding element of the weight table, which will be used to calculate the average value, is incremented.

Dnj [ni, nk] + = Tk [ni, nj]

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Poids[ni,nk]+ =1 1 (1805) Lorsque l'ensemble des indices ni,nk a ainsi été parcouru, le programme parcourt l'ensemble des indices ni et nk en testant la condition Poids[ni,nk]# 0 et à chaque fois que cette condition est réalisée il effectue:

Dnj [ni, nk] ~ Dn,[ni,nk] D -' [M7,] Poid4ni,nk] (1806)le programme effectue une transformée de Fourier bidimensionnelle inverse du tableau Dnj.

Weight [ni, nk] + = 1 1 (1805) When the set of indices ni, nk has been traversed, the program traverses the set of indices ni and nk by testing the condition Weight [ni, nk] # 0 and whenever this condition is realized it performs:

Dnj [ni, nk] ~ Dn, [ni, nk] D - '[M7,] Poid4ni, nk] (1806) The program performs an inverse two-dimensional Fourier transform of array Dnj.

(1807) it stores the transformed array in the outputfich-Calc file in the following order: Dnj [0,0], Dani [1,0], ..... Dnj [fdim-1,0], Dnj [0,1], Dnj [1,1], ..... Dnj [fdim -1,1], Dnj [0, fdim -1], D "[1, fdim -1], .... D "[fdim - 1, fdim - 1] (1403) -2nd exchange of the axes: It remains at this level to perform a Fourier transform inverse to a dimension along the axis nj. In order to be able to perform this transformation in a reasonable time, it is necessary to exchange the axes nj and nk beforehand. The program can then load into the main memory complete plans (ni, nj) to process them.

In the file calc file the data are arranged in the following order: Do [0,0], Do [1,0], ..... Do [fdim -1,0], Do [0,1], Do [1,1], ..... Do fdim -1,1], Do [0, fdim - 1], Do [1, fdim - 1], ..... Do [fdim - 1, fdim - 1], Dl [0,0], Dt 1,0], ..... Dl [fdim - 1,0], Dt [0,1, Dt [1,1], ..... Dl fdim -1,1], Dl [0, fdim -1], Dl 1, fdim -1], ..... Dl fdim -1, fdim -1], Dfdim-1 [0,0], D fdrm -1 [10], ..... D fd, m-1 [fdim -1.0], D fdlm-1 [0,1], D fd, mt [1> 1, ..... D f.dm-1 [.dim -1,1], D fdrm-1 [0> .dim-1], D fd, mi [l, fdim -1], ..... D fd, m-1 fdlm -1, fdim - l

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Ce fichier est relu, et un fichier fich ech2 est généré, dans lequel les données sont réécrites dans l'ordre suivant: Do[O,O], Do[l,O],..... Dp[ fdim -1,0, Dl [0,0], Dl [1,0], ..... Dl [fdim -1,0], D fdim-1 [0,0], D fdm-1 [1>0 ..... D fdrm-1 [.%dim -1,0, D0[0,l],D0[U], Do [fdim -1,1], Dl [0,1], Dl [1,1],..... Dl [ fdim -1,1J, D fdem-i [0,1], Dfdrm-1 [hl, ..... D fd,m-1 [.Îdlm -1,1, Do [0, fdim - 1], Do [ 1, fdim -1, ..... Do [fdim - 1, fdim - 1], Dl [0, fdtm -1, Dl [1, ./w -1],..... Dl [ fdtm -1, fdim -1.

This file is read again, and a file file ech2 is generated, in which the data is rewritten in the following order: C [O, O], C [1, O], ..... Dp [fdim -1, 0, D1 [0.0], D1 [1.0], ..... D1 [fdim -1.0], D fdim-1 [0.0], D fdm-1 [1> 0 .. ... D fdrm-1 [.% Dim -1.0, D0 [0, 1], D0 [U], Do [fdim -1,1], D1 [0,1], D1 [1,1] , ..... Dl [fdim -1,1J, D fdem-i [0,1], Dfdrm-1 [hl, ..... D fd, m-1 [.Idlm -1,1, Do [0, fdim - 1], Do [1, fdim -1, ..... Cd [fdim - 1, fdim - 1], Dl [0, fdtm -1, D1 [1, ./w -1] , ..... Dl [fdtm -1, fdim -1.

read~file: pointeur sur le fichier fich calc write-file: pointeur sur le fichierfich ech2 ktot : fdim jtot : fdim

itot: taille en octets d'une ligne.fdim*sizeof(complexe) ou sizeof(complexe) désigne la taille en octets d'un nombre complexe. memory~limit: comme précédemment, la taille en octets de la mémoire disponible. D fdm-1 [0, fdim-1], D fd, m-1 [l, fdim -1, ..... D fd, m-1 [fdim -1, fdim -1 This exchange of the axes nj and nk is done in blocks like the previous axis exchange. The same procedure is used, the parameters to be passed are:

read ~ file: pointer to the file calc calc write-file: pointer to the file file ech2 ktot: fdim jtot: fdim

itot: size in bytes of a line.fdim * sizeof (complex) or sizeof (complex) is the size in bytes of a complex number. memory ~ limit: as before, the size in bytes of available memory.

Dp[0, nk, D0[l, nk], Do[ fdim -1, nk, Dl [0, nk , Dl [1, nk],..... Dl [fdim - 1, nk], D f'dm-1 [0, nul, D fdrm-1 [1, nk], D fdrm-1 [.Îdim -1, nk (1404) - Last Fourier Transformation This procedure consists of performing the inverse Fourier transform along the nj axis. It is an iterative treatment on the index nk. The algorithm of this part of the program is found in Fig. 24. Its essential steps are as follows: (1900): the program loads in internal memory the values:

Dp [0, nk, D0 [l, nk], Cd [fdim -1, nk, Dl [0, nk, D1 [1, nk], .....Dl [fdim-1, nk], D f 'dm-1 [0, zero, D fdrm-1 [1, nk], D fdrm-1 [.dim -1, nk

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Enk,ni [ni] = Dnj [ni,nk] Il effectue la transformée de Fourier inverse de ce tableau, générant le tableau #nk,ni (1902) : il enregistre les résultats dans le fichier fich~rep, dans l'ordre suivant:

Enk,O [0], Enk,l [0],.... Enk, fdm-1 0], Enk,O [1], Enk,l [1],.... Enk, fdm-1 [1], Enk,O fdm -1, Énk,1 .Îdim -1, .... Énk, f'dim-1 [fdim - 1] Le fichier ainsi généré contient alors la représentation tridimensionnelle de l'objet au format U[ni,nj,nk] ou

l'élément complexe U[ni,nj,nk] est rangé dans le fichier fich rep à l'addresse (nk*fdim*fdim+nj*fdim+nt) comptée à partir du début du fichier, l'addressage se faisant par éléments de type 'nombre complexe'. (1901): The program generates the Enk array, nor to one dimension:

Enk, ni [ni] = Dnj [ni, nk] It performs the inverse Fourier transform of this array, generating the array # nk, ni (1902): it records the results in the file file ~ rep, in the order following:

Enk, O [0], Enk, l [0], .... Enk, fdm-1 0], Enk, O [1], Enk, l [1], .... Enk, fdm-1 [ 1], Enk, O fdm -1, Enk, 1 .Idim -1, .... Enk, f'dim-1 [fdim - 1] The file thus generated then contains the three-dimensional representation of the object in U format. [ni, nj, nk] or

the complex element U [ni, nj, nk] is stored in the file rep file at the address (nk * fdim * fdim + nj * fdim + nt) counted from the beginning of the file, the address being done by elements of type 'complex number'.

V[ni,ni] = [ReU[nt,nj, nk)]2 , ou Re(x) désigne la partie réelle de x, la somme sur nk étant prise entre k deux plans 'limite' selon ce que l'on veut représenter. 5.22. visualization
The table U having been generated, we can visualize the contents. The simplest visualization consists of extracting a section, one of the indices being fixed at a constant value. On this section, we can visualize the real part, the imaginary part or the module. Another mode of visualization is to extract projections. For example, for a projection of the real part along the axis nk, we will represent the table V with

V [ni, ni] = [ReU [nt, nj, nk)] 2, where Re (x) denotes the real part of x, the sum over nk being taken between k two 'limit' planes according to what is wants to represent.

 6.Description of a second embodiment.

This embodiment is a simple variant of the first and is shown in FIG.

6. 1. Principle
In the first embodiment, the sensor (118) is in the image focal plane of the optical assembly consisting of the objective (113) and the lenses (115) and (117). The plane illumination wave therefore has a point image in this plane, and a spherical reference wave centered virtually on the object must be used to obtain uniform illumination on the sensor (118). In this second embodiment, the sensor (2018) is placed directly in the image plane of the objective. A flat lighting wave therefore no longer has a point image. The reference wave must be the image by the objective of a virtual plane wave passing through the object.

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An image in complex numbers is obtained on the CCD (2018) from three images differing by the phase of the reference wave, using as in the first embodiment the formula

The two-dimensional Fourier transform of this image gives an image in complex numbers equivalent to that which, in the first embodiment, was obtained directly in the plane of the CCD sensor. This image therefore replaces the image directly obtained on the sensor in the first embodiment. For the rest, this embodiment uses the same principles as the first.

 6. 2. Physical description.

 The system is shown in Fig.25. The elements of this figure, identical to those of FIG. 1, are numbered by replacing the first digit 1 of the elements of FIG. 1 by the number 20. For example (116) becomes (2016). This system is similar to that used in the first embodiment, except that: the controlled attenuation device of the beam consisting of the elements (104) and (105) is removed.

the CCD (2018) is placed in the plane where the diaphragm (114) was previously located. As a result, the elements (114) (117) (115) are deleted.

- The virtual image, after reflection on the semi-transparent mirror (2016), of the focusing point of the beam coming from the lens (2023), must be located on the optical axis and in the image focal plane of the objective (2013). The elements (2023) (2022) (2021) (2016) are thus moved to satisfy this condition.

On the CCD sensor (2018), the base cell size (distance between the center points of two neighboring pixels) must be less than # / 2 g / rev, or op denotes the numerical aperture of the lens,; , the length 2 wavelength in the vacuum of the laser used, g the magnification. For example, for an aperture x 100 aperture 1.25 we find 25 micrometers. A modified lens can be used to have x50 magnification, so as to obtain 12 micrometers, which makes it possible to use a current camera of 10 micrometer steps more optimally than with a x100 lens.

-The lens (2023) is mounted on a positioner allowing a translation along the axis of the beam entering the lens.

6. 3.settings: overview
In the previous embodiment, the image received on the sensor was in the frequency domain. An image in the spatial domain could if necessary be obtained from it by inverse two-dimensional Fourier transform, which was achieved by the focusing program described in FIG. 14. In this second embodiment, the image received on the sensor is in the spatial domain and an image in the frequency domain can be obtained by Fourier transform.

 Whenever the two-dimensional frequency image received directly on the CCD sensor (118) was used, it is now necessary to use the two-dimensional Fourier transform of the received image

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 on the CCD sensor (2018), which constitutes a frequency image which may for example have a dimension of 256x256 square pixels. Conversely, the focus program must be replaced by a program for directly viewing the image received on the CCD sensor.

 As the beam attenuation device is suppressed, only one image should be used instead of two in the steps where this device was used.

 The camera (2019) is fixed. The position adjustment of this camera along the optical axis is replaced by a position adjustment of the lens (2023) along the axis of the beam entering this lens. The position adjustment of the camera in the plane orthogonal to the optical axis is replaced by an angular adjustment of the mirror (2016).

For the rest, the operating mode is similar to the previous system. The adjustment steps and the programs used are detailed below:
6. 4. Program in common use:
In addition to the programs described in 5. 5. a program of visualization of the frequency image is used. This program generally replaces the direct visualization program used in the first embodiment, which made it possible to observe an image in the frequency domain. To use this program, a reference wave must be used, whereas in the direct visualization program used in the first embodiment, it was not necessary. When this program is used, it is necessary to avoid vibrations and thus release at least temporarily the focusing device if it is used, or to wait for the vibration absorption before each image when the stepper motors are used.

This program is similar to the focusing program described in 5.14 and whose algorithm is Fig.14. It is amended as follows:
The step (1000) of image acquisition, detailed FIG. 13, is modified as shown in Fig.26, in order to take into account the absence of the beam attenuation device.

 Step (1001) is deleted.

Step (1002) is modified to take into account the absence of table H. For each pixel, the value is generated according to the following equations:

In step (1002) the program limits the array S to dimensions hpix x hpix but does not perform averaging.

 Step (1004) is replaced by a direct Fourier transform.

 During step (1005), the program displays the intensity, corresponding to the square of the module of the elements of the transformed array S, as well as the maximum value of this intensity, the coordinates of the corresponding point and the ratio between the intensity of the this point and the sum of the intensities of its eight neighbors.

 This program makes it possible to appreciate the punctuality and the general appearance of a frequency image. On the other hand, to appreciate the unsaturation (which must be verified in almost all stages, which will not be

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 more reminded) we continue to use the programs described in 5. 5., the unsaturation to be verified directly on the CCD sensor (2018).

6. 5. adjustment of the position of the laser (2000) and the mirror (2021)
This step is similar to the step described in 5.6.

6.6. adjustment of the control voltages of the piezoelectric actuator
The process is identical to that described in 5.12. , except that there is no adjustment of the diaphragm (114) removed and the position of (2009) is set to maximize the intensity received on the sensor. The fact that the image received directly by the sensor is in the spatial domain does not affect the result.

 6.7. adjusting the level of the reference wave.

 This step is identical to that described in 5.11, the level of the reference wave being measured on the direct image.

6. 8. Position adjustment of (2023) (2002) (2016):
This setting is similar to that described in 5. 7. The direct visualization program is replaced by the visualization program of the frequency image described in 6. 4., for which the presence of the reference wave is necessary. The position adjustment of the camera along the optical axis is replaced by a position adjustment of the lens (2023) along the axis of the beam entering this lens. The position adjustment of the camera in the plane orthogonal to the optical axis is replaced by an angular adjustment of the mirror (2016).

 6. 9. setting the position of the condenser (2011).

 This setting is similar to that described in 5. 8. but it is the frequency image that must be observed and not the direct image.

 6. 10. adjusting the position of the lens (2006).

 It is similar to that described in 5. 9. but it is the image in frequency which makes it possible to appreciate the punctuality.

 6. 11. determining the number of steps per pixel.

 This step is similar to that described in 5.10, but the maximum intensity pixel is observed on the frequency image.

 6. 12. obtaining the constant K.

 This step is performed on the same principle as that described in 5.14. but it is modified to take into account the inversion between direct image and image in frequency.

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 In order to obtain the image of the micrometer, the objective is first placed in a nearly focused position, the micrometer having been introduced as an object. The program for direct viewing of the image received on the CCD is launched, in the absence of a reference wave. The diaphragm in (2007) must be adjusted so that the observed area appears uniformly illuminated. The micrometer is moved under the lens until you get an image of it.

 The microscope objective is then moved by the focusing device so as to obtain a properly focused image. To facilitate focusing, it is advantageous to visualize a portion of the micrometer or lines of different lengths are present. This limits 'false focus' due to interference phenomena in front of the micrometer.

 When a good image has been obtained, the program is stopped and the image obtained is used to obtain the distance in number of pixels between two lines, in the same way as in 5.14. If the distance between two graduations separated by Dreel micrometers is on the image thus obtained from pixels Dpix, if the nominal index of the objectives is nv (in general, nv is close to 1.5) and if the wavelength of the laser in the vacuum is; (# = 0.633 micrometers) and if the number of points of the Fourier transform that n, N will be used for image acquisition is N (N = 256) then we have: K = nv N Dreel, or heard # Dpix and Dreel, are in the same unit.

6. 13. diaphragm adjustment:
This step is similar to that described in 5.15. but the focusing program is replaced by a direct visualization of the image received on the sensor in the absence of a reference wave.

 6.14. adjustment of the position of the condenser, obtaining the characteristics of the circle This step is similar to that described in 5.16, but the step (1103) is modified: frequency image is acquired in the same way as in the visualization program of the frequency image described in 6.4. The square of the module of the elements of table S is taken as 'image' and replaces the direct image used in 5.16. To obtain this image in frequency, the reference wave must be used and a waiting time allowing the damping of the vibrations of the motors must be introduced before each acquisition, which makes this step particularly long. It is therefore important to use a good quality condenser to simplify this step.

6. 15. recording of the reference wave:
This step is similar to that described in 5.17. The reference wave only is recorded on the live image.

 6. 16. focus on the object studied.

 This step is simplified, the specific focusing program being replaced by a program for direct viewing of the image received on the CCD sensor in the absence of a reference wave.

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 6. 17. adjustment of radius R.

 This step is similar to that described in 5.19 but with the modifications specified in 6.14.

 6. 18. acquisition of the image.

 This step is similar to that described in 5. but the following modifications must be taken into account: step (1302): is replaced by the acquisition of images described in Fig.26-step (1303) removed.

puis en effectuant la transformée de Fourier du tableau S. step (1304) modified: the representation S [i, j] of complex numbers is generated by assigning each point the following value:

then performing the Fourier transform of Table S.

6.19. calculation step:
This step is identical to that described in 5.21.

6. 20. visualization: this step is identical to that described in 5.22
7. Description of a third embodiment.

This embodiment is more complex and more expensive than the previous ones but it allows superior performance in terms of definition and speed.

 7. 1. Principle.

This acquisition mode makes it possible to improve the performance of the mode 1 as follows: - increase in the image acquisition speed:
In the first embodiment, this speed is limited by the mechanical movement of the stepper motors and the need to wait until absorption of the vibrations induced after each movement. The present embodiment makes it possible to accelerate this image taking by replacing this mechanical system by an optical beam deflection system, based on liquid crystals and not inducing mechanical displacements in the system.

- improvement of accuracy:
In the first embodiment, the accuracy is limited by the impossibility of adopting all the possible directions for the lighting beam and by not taking into account the reflected wave. The present embodiment uses a dual purpose system. The lighting is then done through a

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 objective, which allows the frequency vector of the illumination wave to vary over all of the two sphere portions limited by the opening of each lens. In addition, the reflected wave crosses the lighting objective and can be taken into account.

 In the first embodiment, the intensity variations of the diffracted wave as a function of the polarization direction of the illumination wave are not taken into account, which leads to errors in the measurement of high frequencies. In the present embodiment, polarization rotators are used to vary the polarization direction of the illumination wave and the direction of analysis of the diffracted wave. An algorithm takes into account all the measurements thus obtained to obtain frequency representations in which the dependence of the diffracted wave with respect to the polarization of the illumination wave has been suppressed.

-compensation of spherical aberration:
In the foregoing embodiments the average index in the observed sample should be close to the nominal index of the objective. In the opposite case, the difference between the average index of the sample and the nominal index of the objective results in a spherical aberration which strongly limits the thickness of the observable sample. In this new embodiment, the hardware configuration and the algorithms used make it possible to compensate for the phase differences induced by the average index of the sample and to cancel this spherical aberration.

 Paragraph 7. 2. materially describes the microscope used.

 This microscope is the subject of a set of preliminary adjustments made in the abscence of the sample observed and which do not normally have to be repeated when the observed sample is modified: - The position adjustment of the various elements of the microscope system is performed as described in paragraph 7. 4.

 - The modulus of the reference wave is determined as described in paragraph 7.4.

 The parameters Kp, equivalent to the parameter K used in the first embodiment, are determined in the manner described in paragraph 7.6.

 - The characteristics of the lighting beams used are determined as described in paragraph 7.9.

 - The order index tables are determined as described in paragraph 7.13.

 After introducing the sample, the microscope is subject to a second set of adjustments: - The position of the objectives is set as described in paragraph 7.10.

 - The relative coordinates x, y, z of the reference beam reference points associated with each objective, as well as the average sample number and its thickness L, are determined as described in paragraph 7.11. This determination assumes the use of a specific algorithm described in paragraph 7. 8., using equations established in paragraph 7. 7. A simplified version of this algorithm is also used in clause 7.9.

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 - The value w0 characterizing the position of the sample is calculated as described in paragraph 7.15. The determination of this value uses an image acquisition procedure described in paragraph 7. 12. and equations established in paragraph 7. 14. Simultaneously, a first adjustment of the position of the sample is performed as indicated in paragraph 7.15.3.

 - The aberration compensation function, in the form of tables Dp, is obtained as described in paragraph 7.16.

 When these preliminary adjustments have been made, the procedure for obtaining three-dimensional representations can be started. This procedure is described in 7.17. It uses the image acquisition procedure described in 7.12. and uses the table Dp determined in 7.16. By indefinitely repeating this procedure, one can obtain a succession of three-dimensional representations characterizing the temporal evolution of the observed sample. It is necessary to adjust the position of the sample so that the representation obtained is that of an area of interest of the sample. This adjustment is made as indicated in 7. 17.3. and may involve a repetition of the preliminary steps of computing w0 and Dp described respectively in 7. and in 7.16.

 Various variants of the algorithms and settings made are described in 7. 18. Many settings can be removed if the conditions are favorable, for example if the index and the thickness of the sample are known in advance.

 A method of designing microscope objectives, specifically adapted to this microscope, is described in paragraph 7.19.

 7. 2. material description.

7. 2.1. overview
Figs. 27 and 28 provide an overview of the system. Most of the system, shown in Fig.27, is in a horizontal plane and is supported by an optical table.

However, the two microscope objectives used must be positioned on a vertical axis (2263) to be able to use a horizontally positioned sample (2218). The axis (2263) is at the intersection of two vertical planes defined further by their horizontal axes (2261) and (2262). These horizontal axes can make an angle between them of 0 degrees, 90 degrees or 180 degrees. Figure 28 shows in part a section along the vertical plane defined by (2261) and partly a section along the vertical plane defined by (2262).

 The beam from a laser (2200) vertically polarized will be derived into four beams feeding the right and left optical chains associated with the two objectives of the microscope. These four beams are indicated on the diagram and in the text by the following abbreviations: - FRD reference beam right.

 - FRG: left reference.

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 - EDF: straight lighting.

- FEG: left lighting.

 Each of these beams will subsequently be divided into a main beam, which will be noted as the original beam, and a reverse indicator beam. The reverse indicator beams will be denoted FRDI, FRGI, FEDI, FEGI.

 The beam is derived from the laser (2200) and has its vector electric field directed along an axis orthogonal to the plane of the figure. It passes through a beam expander (2201) and is separated into a lighting beam and a reference beam by a semi-transparent mirror (2202). The illumination beam passes through a diaphragm (2248), a filter (2203) and then a beam attenuation device (2204), a phase shift device (2205), a beam deflection device. (2206) which makes it possible to vary the direction of this parallel beam. It is then deflected by a semi-transparent mirror (2207) which separates a right light beam and a left light beam, intended to illuminate the sample in two opposite directions. The right illumination beam FED is deflected by a mirror (2208), passes through a beam deflection and switching device (2209), a phase rotator (2210), and is separated by a semi-transparent mirror (2211). in a main lighting beam and a reverse indicator beam. The main illumination beam then passes through an achromat (2212), a diaphragm (2213), is reflected on a mirror (2214) upwards, then on mirrors (2215) and (2216), and passes through the objective (2217) to illuminate the sample (2218). After crossing the sample, it passes through the objective (2219), is reflected by the mirrors (2220) (2221) (2222), then passes through the diaphragm (2223), the achromat (2224), the semi-circular mirror. transparent (2225), the phase rotator (2226), the achromat (2227), the semitransparent mirror (2228) and the polarizer (2253) and is received by the CCD sensor (2229).

 Both lenses (2217) and (2219) must have their optical axis (2263) vertical so that the optical oil needed to use them does not flow. The mirrors (2214) (2215) (2216) (2220) (2221) (2222) serve to deflect the beam so that it can pass through the lenses in a vertical direction. Fig. 28 shows a section along the axes (2262) and (2263) articulated around the optical axis (2263).

 Fig. 29 is a representation of the optical path of the light rays between the objective (2219) designated by 'OM' and the CCD sensor (2229) designated by 'CCD'. Mirrors, semi-transparent mirrors and phase rotators have been omitted from the figure but influence the position of the various elements. The rays propagate along an optical axis represented 'right', which actually stops being rectilinear between the planes P2 and P1, where it is deflected by mirrors (2220) (2221) (2222) to approach the goal in a vertical plane. The left part of the figure represents the optical path of rays which are parallel in the studied sample, and the right part opposite the optical path of rays coming from a point in the observed zone. The achromat (2224) is designated by 'L1', the diaphragm (2223) by 'D', the achromat (2227) by 'L2'. f1 is the focal length of L1, f2 is the focal length of L2. P1 is the plane in which focus parallel incoming rays into the lens (image focal plane). This plane must coincide with the focal plane object of the achromat (Ll) so that a parallel ray at the entrance of the lens is also parallel between the achromats L1 and L2. P2 is the plane in which the image of the observed sample is formed. It is in this plane that the diaphragm (D) must be positioned. P3 is the virtual image of plane P2 by the achromat Ll. P3 must

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 coincide with the object focal plane of L2 so that a ray from a central point of the object observed, forming a point image in P2, reaches the CCD in the form of a parallel ray. P6 is the image focal plane of L2. It is in this plane that the CCD must be placed, so that a parallel ray at the entrance of the lens forms a point image on the CCD.

 The optical path of the rays between the objective (2217) and the sensor (2239) is symmetrical with the preceding one.

 The reference beam separated by the mirror (2202) is reflected by (2233), passes through a filter (2234), and a semi-transparent mirror (2235) transforming it into a left part and a right part. The left part is reflected by the mirrors (2254) (2236), passes through the complementary filter (2255), the phase shift device (2251) and the diaphragm (2250) then reaches the semi-transparent mirror (2228) which separates into a main beam and a reverse indicator beam. The main beam is directed to the CCD (2229).

 Both the lighting beam and the reference beam have reverse indicator beams having the same characteristics as the main beam but pointing in the opposite direction. The FRGI inverse indicator of the reference beam FRG, resulting from the semi-transparent mirror (2228), passes through the achromat (2281) and is focused on a mirror (2282) which reflects it. It then crosses the achromat (2281) which makes it parallel again and is again reflected by the semi-transparent mirror (2228). It then has the same direction (but in the opposite direction) as the reference beam directed towards the CCD sensor (2229). Similarly. the FRDI reverse indicator of the FRD light beam, derived from the semi-transparent mirror (2211), is focused by the achromat (2231) on the mirror (2232). The latter reflects it, and after a new reflection on the semi-transparent mirror (2211) it has the opposite direction to that of the main light beam directed towards the objective (2217).

 The entire device is optically symmetrical with respect to the observed object. There is therefore a left lighting beam having a role symmetrical with respect to the right light beam, and a right reference beam having a role symmetrical to that of the left reference beam.

 The left illumination beam FEG, resulting from the semi-transparent mirror (2207), is reflected on the mirrors (2280) and (2283) then passes through the deflection and switching device (2240) equivalent to (2209). It then passes through the polarization rotator (2241) and is separated by the semitransparent mirror (2225) into a main beam that points to the microscope objective (2219), and a FEGI inverse indicator beam that passes through the achromat (2242), is focused on the mirror (2243) and finally reflected back on (2225).

 The right reference beam FRD, derived from the semi-transparent mirror (2235), is reflected by the mirror (2244) and passes through the complementary filter (2256). The semi-transparent mirror (2245) separates it into a main beam that passes through the polarizer (2252) and reaches the CCD (2239), and an FRDI reverse indicator beam that passes through the achromat (2246) and is focused on the mirror ( 2247), then returns to the semi-transparent mirror (2245) which reflects it towards the lens (2217).

 The polarizers (2252) and (2253) are thin plates consisting of a dichroic sheet held between two glass panes.

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 Zones (2274) (2275) (2276) (2277), delimited by dashed lines in the drawing, correspond to parts of the system fully immersed in optical oil. Such an area therefore constitutes a sealed container containing the optical elements visible in the drawing. The entry and the exit of the beam in this container are made by anti-reflective treated windows on their external face. This makes it possible to limit the defects related to the size of the glasses used in the various devices included therein.

 The CCDs (2239) and (2229) are integrated with cameras (2284) and (2230) themselves attached to three-axis positioners for adjusting their position along the axis (2264) and along the two orthogonal axes. to (2264), and in rotation about the axis (2264). The achromats (2227) (2224) (2212) (2237) (2246) (2231) (2242) (2281) are attached to positioners an axis allowing fine adjustment of the position in the direction of the axis (2264) . The mirrors (2282) (2243) (2232) (2247) are attached to positioners allowing adjustment of their orientation. The diaphragms (2213) and (2223) are adjustable and fixed to two-axis positioners to adjust their position in the plane orthogonal to (2264). The semi-transparent mirrors (2225) (2228) (2211) (2245) are attached to positioners to adjust their orientation. Mirrors (2214) and (2222) are attached to positioners to adjust their orientation. The microscope objective (2219) is attached to a 2-axis positioner for moving it in a plane orthogonal to the axis (2263). The objective (2217) is fixed to a focusing device for moving it along the axis (2263). The entire system is manufactured with the greatest precision possible in the positioning of the various elements.

 The mirrors (2247) (2232) (2243) (2282) are equipped with manual shutters (2257) (2258) (2259) (2260) for removing the beams reflected by these mirrors. FRD and FRG beams can be removed using completely opaque filters.

 The sample (2218) consists of two slats of stantard thickness (150 m) between which is in a thin layer (50 to 100 m) the substance to be observed. This sample is attached to a thicker blade so that it does not prevent the sample from being accessed by the lenses. The assembly is fixed to a positioner 3 axes in translation.

 The objectives used may be, for example, achromatic plan objectives of numerical aperture op = 1.25 and magnification g = 100 forming the image at 160mm from the neck of the objective. However, it is preferable to use specially designed lenses, described in paragraph 7.19.

pour longueur D = 2 f2 ouv , le nombre de pixels étant N plX x N pix avec par exemple N p,x =256
Les dispositifs de contrôle du faisceau (2204) (2205) (2206) (2209) (2240) (2251) (2210) (2241) (2226) (2238) sont tous pilotés par des rotateurs de phase commandés par des tensions bipolaires. La commande de ces dispositifs doit être synchronisée avec l'acquisition des images par la caméra. La caméra peut être une caméra rapide de type analyseur de mouvement, dotée d'une mémoire suffisante, disponible par exemple chez Kodak. Le système de calcul est un ordinateur doté d'une mémoire suffisante pour stocker The achromats (2212) (2237) (2224) (2227) (2246) (2231) (2242) (2281) can have for example the same focal length f = f1 = f2 = 200mm
The CCD sensors used must have square pixels and a square useful area whose side has

for length D = 2 f2 open, the number of pixels being N plX x N pix with for example N p, x = 256
The beam control devices (2204) (2205) (2206) (2209) (2240) (2251) (2210) (2241) (2226) (2238) are all driven by phase rotators controlled by bipolar voltages. The control of these devices must be synchronized with the acquisition of images by the camera. The camera can be a fast camera of the motion analyzer type, with sufficient memory, available for example from Kodak. The computing system is a computer with enough memory to store

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 the necessary three-dimensional arrays. Machines having for example 8GB of memory are available at Digital Equipment.

 The filters (2203) (2234) (2255) (2256) make it possible to adjust the intensity of the different beams.

As in the first embodiment, their values must be frequently adjusted during the various settings and during the use of the microscope. These adjustments are similar to what was done in the first embodiment and will not be recalled. They also have the role of limiting the intensity of the beams that are moving in the opposite direction to normal and tend to return to the laser (2200), during certain adjustment operations.

7.2.2.A beam attenuation device:
The attenuation device is shown in FIG. 30. It consists of a phase rotator (2501) designated 'RI' in the figure, a Glan-Thomson polarizer (2502) designated 'POLI', a second rotator (2503) designated 'R2', and a second polarizer (2504) designated 'POL2'. The beam entering the device is vertically polarized. The angle of the neutral axis of (2501) with the vertical is 0 for a bipolar voltage applied across the device of -5V and is rotated by an angle a by application of a voltage of + 5V, with a = About 22 degrees. The neutral axis of the rotator (2503) is characterized by the same angles, but with respect to the horizontal and not to the vertical. The polarizer (2502) selects the horizontal polarization direction. The polarizer (2504) selects the vertical polarization direction.

 Fig.31 illustrates the operation of the portion of the device consisting of (2501) and (2502) for an applied voltage of -5V. It represents in bold line the electric field vector (2505) of the input beam of the device, in a reference consisting of the vertical polarization axis (2506) and the horizontal polarization axis (2507). The passage by the rotator RI (2501) rotates this vector by an angle 2 # and is thus transformed into (2508). The passage through the polarizer POLI (2502) is a projection on the horizontal axis. At the output of this polarizer, the electric field vector (2509) of the beam is therefore horizontal and its amplitude has been multiplied by a factor sin (2 #).

 Figure 32 illustrates the operation of the portion of the device consisting of (2501) and (2502) for an applied voltage of + 5V. Since the neutral axis of RI has been rotated by an angle α, the electric field vector is rotated by a total angle 2 ([alpha] + #) and the amplitude of the output electric field is multiplied by sin (2 # 2 [alpha]).

si 20) sin2a + 26 expression qui s'inverse en:

The attenuation factor between the 'open' (+ 5V) and 'closed' (-5V) positions is therefore

if 20) sin2a + 26 expression that reverses in:

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For example for a = 1/16 eta = 22 we find 6 = 1.30
The second part of the device, consisting of (2503) and (2504), operates exactly like the first, except that it takes a horizontally polarized beam input and outputs a vertically polarized beam. The attenuation factor a2 of this second part is thus given by the same formula as a1 and the two parts of the device will be adjusted so as to have in each part the same attenuation (or approximately). Due to differences in adjustment between the two parts of the device, a2 and a, however, are not strictly equal in practice.

The attenuation command is made according to the table below, where V1 denotes the bipolar voltage applied to (2501) and V2 that applied to (2503).

<Tb>
<Tb>

VI <SEP> V2 <SEP> attenuation
<tb> -5V <SEP> -5V <SEP> a1 <SEP> a2
<tb> -5V <SEP> + 5V <SEP> a1
<tb> + 5V <SEP> -5V <SEP> a2
<tb> + 5V <SEP> + 5V <SEP> 1
<Tb>

7.2.3. Phase shift device:
This device consists of two identical units placed one after the other. A unit is constituted as shown in Fig.33.

 The vertically polarized beam at the input of the device first passes through a phase rotator (2601) designated by 'RI' and then a uniaxial birefringent plate (2602) designated by 'LP', then a second phase rotator (2603) designated by ' R2 'and a polarizer (2604) designated' POL '. The two positions of the neutral axis of each rotator are arranged symmetrically with respect to a vertical axis. The positions of the two rotators corresponding to the same control voltage are on the same side of the vertical axis: for a voltage of -5V they are represented in dotted lines, for a voltage of + 5V they are represented in solid lines. Similarly, the two axes of the birefringent plate are arranged symmetrically with respect to this vertical axis (the third axis being in the direction of propagation of the beam). Fig. 34 shows the state of the electric field vector of the beam at each step of the crossing of the device, for a voltage of -5V applied to each rotator.

 Fig. Fig. 34 by specifying the values of the angles between the different vectors and the phase shifts between these vectors and the input vector of the device. Fig. 36 shows FIG. 34 by specifying the values of the angles between the different vectors and the attenuation on each vector.

 The electric field vector (2605) at the input of the device is vertical. After crossing the rotator RI (2601) it is symmetrized with respect to the neutral axis (2606) of this rotator, which gives the vector (2607).

After crossing the birefringent plate, the vector (2607), shown in dashed lines, is decomposed into two components (2608) and (2609) corresponding to each neutral axis of the blade. The component (2609) is

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(2608) est affectée d'un décalage de phase - - et est réduite en amplitude d'un facteur sin 4 -aJ . Après traversée du rotateur (2603) l'ensemble est symétrisé par rapport à l'axe neutre (2612) de ce rotateur. (2608) est transformé en (2611), (2609) est transformé en (2610). Après traversée du polariseur (2604), ces deux composantes sont projetées sur un axe vertical. La composante (2610) est multipliée par un facteur cos # - [alpha]) et a donc été affectée globalement par un facteur cos2 (#/4- [alpha]). La composante (2611 ) est multipliée par un facteur Si{: - [alpha]) et a donc été affectée globalement par un facteur sin2 (#/4- a) . Les deux sont ensuite ajoutées pour donner une composante unique (2615) de valeur:

ou # est la pulsation de l'onde, t est le temps. On vérifie :

v = cos(w/) cos 2 +sin( wt) sin # sin(2a) 2 @ @ 2 soit en représentation complexe:

c = cos# + j sin sin( 2a ) Si # est l'argument de c alors on a:

On cherche a créer un décalage de phase de 9 = 60 dans une position des rotateurs et 0 = -60 dans la position symétrique, ce qui correspond à un décalage de phase total de 120 degrés. L'équation ci-dessus permet de déterminer la valeur du décalage de phase total # créé par la lame entre ses deux axes neutres. affected by a phase shift 2 and is reduced in amplitude by a cos factor 4 - [alpha]). The component

(2608) is affected by a phase shift - - and is reduced in amplitude by a factor sin 4 -aJ. After crossing the rotator (2603) the assembly is symmetrized relative to the neutral axis (2612) of this rotator. (2608) is converted to (2611), (2609) is converted to (2610). After traversing the polarizer (2604), these two components are projected on a vertical axis. The component (2610) is multiplied by a factor cos # - [alpha]) and has therefore been globally affected by a factor cos2 (# / 4- [alpha]). The component (2611) is multiplied by a factor Si {: - [alpha]) and has therefore been assigned globally by a factor sin2 (# / 4- a). Both are then added to give a single valued component (2615):

where # is the pulsation of the wave, t is the time. We check:

v = cos (w /) cos 2 + sin (wt) sin # sin (2a) 2 @ @ 2 be in complex representation:

c = cos # + j sin sin (2a) If # is the argument of c then we have:

It is sought to create a phase shift of 9 = 60 in a rotator position and 0 = -60 in the symmetrical position, which corresponds to a total phase shift of 120 degrees. The equation above allows to determine the value of the total phase shift # created by the blade between its two neutral axes.

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 With 9 = 60 and a = 40 degrees we get: rp = 120.7566 degrees. It is therefore necessary to use a uniaxial blade creating for the wavelength considered a phase difference of 120.75 degrees between its two axes.

 The two axes of the blade do not have a symmetrical role. If ## 1 is the phase shift at the crossing of the blade for a radius polarized along the axis i, there is only one choice of axes 1 and 2 such that ## l - ## 2 = + 120 degrees. The uniaxial blade should be oriented so that the rotator (2601) rotates the polarization of the incident ray towards the axis 2 when it is subjected to a bipolar voltage of -5V.

Vil vu V21 ''22 aecaiage -5V -5V -5V -5V 0 SV 5V -5V -5V + 120 -5V -5V 5V 5V + 120 1 5V 1 5V 1 5V 1 5V 1 les autres combinaisons étant inusitées. The phase shift device is constituted by two such units, ie Vy the voltage applied to the i-th rotator of the th-th device (i and j ranging from 1 to 2). The control of the phase shift system is done according to the following table:

Vil seen V21 ''22 aecaiage -5V -5V -5V -5V 0 SV 5V -5V -5V + 120 -5V -5V 5V 5V + 120 1 5V 1 5V 1 5V 1 5V 1 the other combinations being unusual.

7. 2.4. Beam diverter
The beam deflector is shown in Figs. 37 and 38. Its basic unit is an elementary block of variation consisting of elements (2801) to (2804).

 An elementary block of variation consists of a first rotator (2801) denoted 'RI' followed by a birefringent prism (2802) noted 'PD' (deviation prism) then a second rotator (2803) noted 'R2' and a Glan-Thomson polarizer (2804) denoted as 'POL'. The rotator (2801) has its neutral axis in the vertical direction for an applied voltage of -5V. For the same applied voltage, the rotator (2803) has its neutral axis in the horizontal direction. The prism (2802) consists of a birefringent, calcite or quartz material. The polarization direction of the extraordinary ray (first neutral axis) is for example in the vertical direction, and the polarization direction of the ordinary ray (second neutral axis) is in the horizontal direction.

An incident ray on this prism is therefore divided into an ordinary ray polarized in the vertical direction and an extraordinary ray polarized in the horizontal direction. The ordinary ray and the extraordinary ray have a different inclination at the exit of the prism (angle of their direction of propagation with that of the incoming beam).

 Figs. 39 and 40 illustrate the operation of this elementary block of variation. Fig. 3 corresponds to a deviation in one direction and Fig. 40 to a deviation in the other direction. The arrows in bold represent the electric field vectors of the beams considered.

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 In the case of FIG. 39, the voltages applied to the two rotators are respectively -5V for (2801) and + 5V for (2803). The electric field vector of the incoming beam is vertical (2901). After crossing the first rotator whose neutral axis (2902) is vertical, it remains vertical (2903). After crossing the deviation prism it is made up of the only extraordinary ray (2904). After crossing the second rotator it is symmetrical with respect to the axis (2906) of this rotator, which itself makes an angle of 40 degrees with the horizontal (it was assumed for the drawing that a = 40 but the result does not depend on the accuracy of this value). It is thus transformed into a vector (2905) making an angle of 10 degrees with the horizontal.

The polarizer projects this vector on the horizontal to obtain the vector (2907) whose deviation corresponds to the only extraordinary ray.

 In the case of FIG. 40, the voltages applied to the two rotators are respectively + 5V for (2801) and -5V for (2803). The field vector of the incoming beam is vertical (2911). After crossing the first rotator it is symmetrized with respect to the axis (2912) of this rotator, which itself makes an angle of 40 with the vertical. It is thus transformed into a vector (2913) making an angle of 10 degrees with the horizontal. After traversing the deflection prism, the beam is decomposed into an extraordinary field vector beam (2914) and an ordinary field vector beam (2915). After traversing the second rotator, with a horizontal axis, the field vector of the extraordinary beam is symmetrized with respect to the horizontal and becomes (2916). The polarizer then selects the only horizontal component and the outgoing vector (2917) thus corresponds to the single ordinary ray.

 A complete elementary block is represented by the rectangle (2805), the direction of the field of the incoming beam being represented by the arrow (2806). The block (2807) is identical but rotated 90 degrees to a horizontal axis so that the direction of the incoming beam field is horizontal (2808). The set of two blocks forms an elemental doublet (2809) allowing elementary beam deflection in the horizontal and vertical directions. As shown in Fig. 38, the set of deflector consists of eight successive elementary doublets. However, in order to have an efficient switching system, the last doublet (numbered 0) is placed on the part of the beam where the left and right lighting beams have already been separated. Two identical doublets (DO) and (DOb) are used, one on each branch of the beam. When a voltage of -5V is applied to both rotators, an elementary block acts as a closed switch. The last doublet can thus effectively switch the beam, a voltage of -5V to be applied to all its rotators to have a closed switch.

 Block (2209) in FIG. 27 therefore represents the doublet DOb. The block (2240) represents the doublet DO. The block (2206) represents the doublets D1 to D7.

 The type of crystal in which the prism is made and the angle between its two faces determine the angle of variation of the inclination of the beam between the two positions of an elemental doublet.

 The following notations are adopted: nl: index of the immersion liquid used for the beam deflection device. o: opening the lens

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 A: opening of the beam at the input of the deflection device, approximately equal to its value at the diaphragm where the image is formed. A is defined as the sine of the half-angle at the apex of the cone formed by the rays coming from the objective. g: magnification of the objective. d: distance between planes P2 and P4 of Fig.29. f1: focal length of the lens L1 in Fig.29.

The relation of Abbe and the resolution of the optical equations gives:
A = o / nlg (1-d / f1)
Fig. 41 shows the principle of calculating the deviation by the prism of ordinary radii. The ray (2922) enters the prism (2921) and comes out in (2923).

 #d is the angle at the top of the deviation prism.

 #e is the angle of the extraordinary beam coming out with the outer face of the prism.

#o is the angle of the ordinary beam coming out with the outer face of the prism. is the extraordinary index of the deviation prism. no is the ordinary index of the deviation prism.

( () e - () 0 ) cos() d = ne - no . sm() Le i-ième doublet doit créer une variation de l'inclinaison d'amplitude:

0, -0, = A = 2t Le demi-angle au sommet du i-ième prisme vaut donc:

=ArctanL-!##1 () d Arc -ne - no) soit avec la valeur de A précédemment obtenue:

9a d = ArctaJ J..! 0 (1- )) @ (2l g ne -no (@- f1) Dans cette équation il faut prendre en compte les valeurs suivantes: quartz : ne - no =0,009 calcite : ne - no =-0,172 We have: sin 0, 0 = sin () and likewise for the extraordinary radius: sin 9e = e sin 9d where: ni nor sin8e -sin9 = ne n sinBd nl is first order in (#e - #o ):

(() e - () 0) cos () d = ne - no. sm () The i-th doublet must create a variation of the amplitude tilt:

0, -0, = A = 2t The half-angle at the apex of the i-th prism is therefore:

= ArctanL -! ## 1 () d Arc -ne - no) with the value of A previously obtained:

9a d = ArctaJ J ..! 0 (1-)) @ (2l g ne -no (@ - f1) In this equation, the following values must be taken into account: quartz: ne - no = 0.009 calcite: ne - no = -0.172

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 For each prism: -inverting the ordinary and extraordinary axes makes it possible to reverse the direction in which the spokes are deflected when switching from a pair of voltages (-5V, 5V) to a voltage torque (5V, -5V) applied rotators of the elementary block concerned. Since this direction is reversed between quartz and calcite for the same choice of ordinary and extraordinary axes, these axes must be inverted in a calcite prism with respect to their position in a quartz prism.

-Inverting the orientation of the prism (top pointing down instead of top) also reverses the direction in which the spokes are deflected when we go from a couple of voltages (-5V, 5V) to a pair of voltage (5V, -5V) applied to the rotators of the elementary block concerned. But at the same time this operation reverses the direction of deviation of the spokes when a fixed voltage torque is applied. In order to have a minimum 'fixed' deflection of the rays the prism with stronger deviation of each series, calcite or quartz, must be reversed compared to the others. In order to maintain the deviation in the desired direction, its ordinary and extraordinary axes must be reversed.

For each prism one chooses the matter, quartz or calcite, which makes it possible to obtain this angle at the summit. The orientation of the prism is then selected so that at fixed voltage applied to the rotators. the induced variations of direction compensate at best between the prisms. We choose the position of the ordinary and extraordinary axes so that the spokes are always deflected in the same direction when we go from a couple of voltages (-5V, 5V) to a voltage torque (5V, -5V) applied to the rotators of the elementary block concerned. For each doublet, it is necessary to specify for the two prisms included in the doublet, which have the same characteristics: the angle at the vertex, the orientation of the vertex (normal or inverted with respect to FIG. 377, on which it is oriented towards the high), the position of the ordinary or extraordinary axes (normal or inverted with respect to figure 37 on which the extraordinary axis is vertical). For example, for a lens o = 1.25 g = 100 and with f1 = 200 mm, d = 20 mm, the following table is obtained or the angles are in degrees:

<Tb>
<tb> militia <SEP> at <SEP>#d<SEP> (self) <SEP>#d<SEP> (quartz) <SEP> cnoix <SEP> SEP orientation <SEP><SEP> position of <SEP> axes
<tb> prism <SEP> ordinary <SEP> summit <SEP> and
<tb> extraordinary
<tb> 0 <SEP> 3. <SEP> 742 <SEP> 51. <SEP> 340 <SEP> calcite <SEP> inverted <SEP> normal
<tb> 1 <SEP> 1. <SEP> 873 <SEP> 32. <SEP> 005 <SEP> calcite <SEP> normal <SEP> reversed
<tb> 2 <SEP> 0. <SEP> 937 <SEP> 17. <SEP> 354 <SEP> calcite <SEP> normal <SEP> reversed
<tb> 3 <SEP> 0.468 <SEP> 8. <SEP> 881 <SEP> inverse quartz <SEP> inverted <SEP>
<tb> 4 <SEP> 0.234 <SEQ> 4.467 <SEP> Normal <SEP> Quartz <SEP> Normal
<tb> 5 <SEP> 0. <SEP> 117 <SEP> 2. <SEP> 237 <SEP> Normal <SEP> Quartz <SEP> Normal
<tb> 6 <SEP> 0. <SEP> 058 <SEP> 1. <SEP> 119 <SEP> normal <SEP> normal <SEP> quartz
<tb> 7 <SEP> 0. <SEP> 029 <SEP> 0. <SEP> 559 <SEP> normal <SEP> normal <SEP> quartz
<Tb>

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 A deviation of the beam is a variation of its direction. But at great distance from the doublet creating the deviation it also translates into a spatial shift of the illuminated area. So that this phenomenon is not penalizing, the distances between the elements of the deflector must be reduced to the minimum and these elements must have a sufficient section so that, whatever is the chosen orientation, the beam 'fills completely' the zone delimited by the diaphragm. For example, this section may be 12 mm, the polarizers of Glan-Thomson then being of dimension 12 x 30 mm. All parts of the deflector that do not transmit the beam directly should be as absorbent as possible to minimize noise.

1 al. 1.658 + 1.486 ,.# Pour la calcite: ni z 1.486 = 1.572 . In order to suppress the constant deviations by the deflection prisms, the index of the optical liquid in which a prism is immersed must be equal to the average value of the ordinary and extraordinary indices of the prism, namely:

1 al. 1.658 + 1.486,. # For calcite: neither z 1.486 = 1.572.

, 1.544 + 1.553, ..., For quartz: ni - 1.544 1.553 = 1 ~ 5485
The portion of the beam deflector whose prisms are made of calcite must therefore be immersed in a liquid of index 1. 572, and the part whose prisms are made of quartz must therefore be immersed in a liquid of index 1. 5485. The The vessel containing the deflector and the optical liquid must therefore be separated into two parts, a glass window allowing the passage of the beam between these two parts which contain optical liquids of different indices.

 The control of the device is done by order of the 36 rotators. In each doublet the phase rotators are numbered from 0 to 3, the number 0 being the most 'left' rotator in FIG. 28. If i is the doublet index, varying from 0 to 7 and is the index of the rotator in a doublet, varying from 0 to 3, then we assign to the rotator the global index k = i + 1 + j * 9, except for the doublet numbered Ob for which we have ak = j * 9. A 36-bit control word is used in which the bit number k corresponds to the global index rotator k. For each bit, a value of 0 corresponds to an applied voltage of -5V and a value of 1 corresponds to a voltage of + 5V.

capteur coor- mot de commande COM[p,i,j] données (2239): (ij) (Oi80f8,Oljs>01>ja p=0 A lighting is characterized by the sensor on which the direct lighting beam arrives and by symbolic coordinates on this sensor. The sensor will be indexed by the integer p and the symbolic coordinates will be i, j or i and vary between 0 and 255. The symbolic coordinates do not necessarily correspond to pixel coordinates on the sensor. When it is desired to obtain a lighting characterized by the indices p, i, j, the control word is given by the table above:

co-control sensor COM [p, i, j] data (2239): (ij) (O180f8, Oljs>01> ja p = 0

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(2229): I M ((i%2,0,(i/2),(i%2),01,(i/2),(y%21,01,(j/2)7,(y%2),01,(y/2)7) p=l Dans ce tableau: a%b signifie a modulo b a/2 représente le produit de la division entière de a par 2, c'est-à-dire a décalé vers la droite (a,b,c..) représente a concaténé avec b puis avec c etc... a, représente a exprimé sur i bits.

(2229): IM ((i% 2.0, (i / 2), (i% 2), O1, (i / 2), (y% 21.01, (j / 2) 7, (y% 2), 01, (y / 2) 7) p = 1 In this table: a% b means a modulo ba / 2 represents the product of the integer division of a by 2, that is, shifted to the line (a, b, c ..) represents a concatenated with b and then with c etc ... a, represents expressed on i bits.

If a is an integer, its binary expression is a sequence of 0s and 1s. By transforming the 0s into 1 and vice versa, we obtain its complement that we write #. This rating will be maintained thereafter.

 When you want to remove both light beams, the command word to use is 0.

 7.3.Adjustment of the set.

7.3.1.First implementation of the system
The system, with the exception of elements (2204) (2205) (2206) (2209) (2240) (2210) (2241) (2238) (2226), is geometrically implemented with maximum accuracy. The path of the beam is controlled by using a piece of scattering paper interposed on its path. The position of the mirrors, semi-transparent mirrors, as well as (2200) and (2201) are adjusted thus controlling the trajectory of the beam.

 7. 3.2.Installation of beam control systems.

 For the implementation of beam control systems it is necessary to have a sufficient precision photometer, which will be used to measure attenuations or detect beam extinctions. These systems are composed of optical elements (prisms, rotators, polarizers, birefringent blades) which must be positioned accurately with respect to the optical axis and be mounted on positioners allowing a fine adjustment in rotation about this axis.

7.3.2.1. Rotator marking
The entire lighting beam modification system is based on the use of phase rotators. It is essential that the axis of each rotator rotates in the intended direction at the application of a voltage opposite to that used during its introduction. The position of the rotator must be defined when it is put in place and the setting is only a few degrees. To specify the position of the axes of the rotator before implementation is carried out a test between crossed polarizers, in two stages.

 Step 1, described in FIG. 42. the rotator (3001) is set up between the polarization direction input polarizer (3002) and the polarization direction output polarizer (3003). A voltage of + 5V is applied. The rotator is rotated to cancel the outgoing ray. The corresponding position, corresponding to the input polarizer, is marked with a red dot (3004).

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 Step 2: A -5V voltage is applied. The output polarizer is set to cancel the beam. We mark a green dot corresponding to the middle of the two polarizer positions, the side where the angle is the lowest. Figs. 44 and 44 describe this step in the two possible cases defined by the new position of the output polarizer, respectively (3005) and (3006). In the case of Fig.43 the green dot is marked in (3007) and in the case of Fig.44 it is marked in (3008).

 The red dot then marks the position of the axis for a voltage of + 5V and the green dot marks its position for a voltage of -5V. These points are used to preposition the elements correctly during the adjustment procedure.

7. 3.2.2.Installation of the beam attenuator
First of all, the polarizer (2502) is put in place and a fine adjustment is made in rotation so as to have the outgoing beam go out. The rotator (2501) is then put in place and a fine adjustment of its rotational position is made so as to have the attenuation a12 sought when the open position (voltage of + 5V applied to (2501)) is applied to the closed position (applied voltage of -5V).

Then (2501) is switched to the open position (voltage + 5V) and the polarizer (2504) is set up and rotated so that the outgoing beam is extinguished. The rotator (2503) is then put in place and a fine adjustment of its rotational position is made so as to have the desired attenuation a22 during the passage of the open position (voltage of + 5V applied to (2503)) to the closed position (applied voltage of -5V). For example we can use a1 = a2 = 1/16 which gives as attenuations
16 measurable by the photometer: a12 = a22 = @
256
The exact values obtained from the coefficients a12 and a22 are then measured. The coefficients a1 and a2 thus obtained will be used subsequently.

7. 3.2.3. Implementation of phase shift devices
These devices (2205) and (2251) are set up with the best possible accuracy taking into account the markings made previously.

 7. 3.2.4. Setting up the beam deflection and switching device.

 Each elementary block is set up successively starting from the block closest to the phase shifter. The beam attenuator must be in the open position. An elementary block is set up in the following order: - Placement of polarizer POL (2804). Fine adjustment in rotation to cancel the outgoing radius.

placing the rotator R2 (2803) in place. Fine adjustment in rotation to keep the outgoing beam at a zero value, a voltage of -5V being applied to R2.

placing the rotator R1 (2801) in place. Fine rotation adjustment to keep the outgoing radius at zero, with a voltage of -5V applied to R2 and RI.

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setting up of the deflection prism PD (2802). Fine adjustment in rotation to keep the outgoing beam at a zero value, a voltage of -5V being applied to RI and R2.

The DO and DOb blocks are set up in the same way as the others.

 7. 3.2.5.Installation of phase rotators (2210) (2241) (2238) (2226).

These rotators must have their neutral axis vertical for an applied voltage of -5V (green dot up). The axis of (2210) should turn to the right of FIG. 27 when a voltage of + 5V is applied (red dot on the right). The axis of (2241) should turn to the left of Fig.27 when a voltage of + 5V is applied (red dot on the left). The axis of (2238) and (2226) should turn upwards in Fig.27 when a voltage of + 5V is applied (red dot at the top).

 7. 3.2.6. Placing polarizers: The polarizers (2252) and (2253) are set up with their axis passing oriented vertically.

7. 3.3. Geometry adjustment
In a second step, a geometry adjustment is performed to correctly position the cameras, the achromatic lenses and certain mirrors. Some of these settings use an auxiliary CCD sensor, whose pitch (distance between the centers of two neighboring pixels) should be as small as possible.

From the image received either on one of the sensors of the system or on the auxiliary sensor, an algorithm is used to evaluate the punctuality of the image and the location of the maximum. The image received on a sensor is obtained by interfering on this sensor a reference wave and the wave whose punctuality must be evaluated.

t>J=C6(2lO,i,j-ll,ij-I21>J +J ZI1>t>>-IZtJJ 7.3.3.l.Obtaining a two-dimensional image and appreciation of punctuality:
In the first embodiment, we have seen how a two-dimensional image in complex numbers can be generated from three images differing from one another by the phase difference between the illumination wave and the reference wave. This image in the frequency domain can be transposed into the spatial domain by Fourier transform. In the adjustment phases that follow, we will be led to appreciate the punctuality and centering of such images, in the spatial or frequency domain. These images will either be received on one of the CCD sensors of the device, or received on an auxiliary sensor. The phase offsets will be made either with (2205) or with (2251). In some cases, the lighting wave will play the role of reference wave and vice versa. In all cases, the system thus realizes three successive images with successive offsets, indexed by the integer d, of +120 (d = 0), 0 (d = 1), -120 (d = 2) degrees. This gives an array of pixels I [d, i, j] where the subscript of 0 to 2 indexes the phase shift. The complex number image is deduced by:

t> J = C6 (2l0, i, j-11, ij-I21> J + J Zl1> t >> - IZtJJ

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 If one tries to evaluate the punctuality in the space domain, an inverse Fourier transformation is applied to this image.

 In both cases (whether or not there has been a Fourier transformation), from this image of dimensions Npix x Npix corresponding to the number of useful pixels of the sensor concerned (for example 256), the punctuality is evaluated by a program comprising the following steps: Step 1: the program calculates the maximum maximum of the module of S [i, j] and determines its coordinates (imaxljmaxl).

Etape 3: une transformée de Fourier directe est effectuée sur le tableau Sa Etape 4: le tableau Sa est complété par des zéros et on obtient un tableau Sb de dimensions Nb x Nb .

et Sb[i, j] = 0 sinon. Step 2: The part of the array S [i, j] located around (imaxl jmaxl) is extracted. We thus create a table Sa [i, j] of Na X Na dimensions with for example Na = 16:

Step 3: a direct Fourier transform is performed on the array Sa Step 4: the array Sa is completed by zeros and an array Sb of dimensions Nb x Nb is obtained.

and Sb [i, j] = 0 otherwise.

Step 5: The inverse Fourier transformation of Table Sb is performed. This gives an oversampled version of the initial part of the S-array located around the maximum module point.

Step 6: imax, jmax, max are calculated by the formulas:

The actual values max, imaxjmax thus obtained respectively characterize the value and the position of the maximum. Punctuality is better when the max value is higher. The

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 program also visualizes the module of the table S and the module of the table Sb to have a visual assessment of the punctuality.

7. 3.3.2. used devices
A diffuser is used, for example a piece of paper that makes it possible to visually follow the path of the beam.

 An auxiliary CCD is used for more accurate beam tracking than the diffuser. His step must be as weak as possible.

 A frequency meter is also used. This term will refer to the apparatus described in FIG. 71, which is intended for measuring the spatial frequencies of a paraxial beam. It consists of a mirror (5000) that reflects a parallel beam entering a lens (5001), which focuses the beam to a CCD (5002) mounted on a camera (5003). An optional polarizer (5004) can be inserted between the mirror and the lens. The use of the mirror (5000) allows the frequency meter to have a minimum size in the horizontal plane which is that of FIGS. 61 and 62. The optical axis of the lens and the CCD is always vertical during measurement operations.

* Given the sizing choices made, the maximum angle at which the beams enter the frequency meter is 0. If the total width of the CCD (5002) is 1, then the focal length of g (5001) is calculated so that rays arriving at angles between ~ !!. and o can be taken into account. It is therefore worth: f g l. A slightly lower value can be adopted to keep an o 2 safety margin.

 Before use of the frequency meter, the distance between the lens (5001) and the CCD (5002) must be adjusted so that the image of a parallel beam is as punctual as possible, which is done simply by sending to the frequency meter a beam whose parallelism was previously checked by an interferometric method and adjusting accordingly the distance between the lens and the CCD.

 The punctuality of the image obtained on the CCD (5002) makes it possible to check the parallelism of an incoming beam. The relative position of several points on this CCD characterizes the angle between the corresponding beams.

 In the absence of other precision in the description of a setting, the polarizer (5004) is not used.

 7. 3.3.3. Adjustment Cycle The adjustments are intended to ensure that: (1) the beams are following the intended path. This can usually be verified using a simple diffuser.

These beam trajectory checks are not described but must be done before the other adjustments. For example, the orientation of the mirror (2247) must be adjusted so that the reflected beam

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 is effectively superimposed on the incident beam, occupying the same area of space as the latter at the semi-transparent mirror (2245).

(2) the lighting beams and their inverse indicators have a point image on the CCD sensors.

(3) the reference beams have a point image in the plane of the diaphragms (2213) and (2223).

(4) a beam entering parallel to the objective (2217) and directed along the optical axis has a point image and centered on the sensor (2239).

(5) when a control word COM [1, i, j] is used, the coordinates of the point illuminated by the FED beam are deduced from those of the point illuminated by FEDI by a ratio homothety close to 1.

 The settings to be made are based on these conditions. The description of the adjustment steps is given for information only and constitutes an example of scheduling of the adjustment steps.

déviateur de faisceau est COM[ 1,128,128] , COM[0,128,128] ou 0 selon que l'on génère le faisceau d'éclairage droit FED, le faisceau d'éclairage gauche FEG ou aucun des deux. Les obturateurs (2257) (2258) (2259) (2260) et des obturateurs non représentés sur la trajectoire des faisceaux FRG et FRD permettent de choisir les faisceaux utilisés. During the entire setting except for step 14, the command word used for the

Beam deflector is COM [1,128,128], COM [0,128,128] or 0 depending on whether the right FED light beam, the left FEG light beam or neither are generated. The shutters (2257) (2258) (2259) (2260) and shutters not shown in the path of the beams FRG and FRD make it possible to choose the beams used.

 During certain adjustment phases, a given beam is measured on a sensor using a second beam serving as a reference. The program described in 7.3.3.1. is then used to evaluate the punctuality of the measured beam. The phase variations between the reference beam and the beam to be measured are obtained using (2205) or (2251). When no beam is used as a reference, for example if the CCD is that of the frequency meter, the image used is that directly received on the CCD.

étape 1 : en translation de la lentille (2231) Le fréquencemètre est positionné entre le miroir semi-transparent (2211) et le rotateur de polarisation (2238) . La lentille (2231) est réglée pour que l'image du faisceau FEDI sur le CCD du fréquencemètre soit ponctuelle. étape 2 : en translation de la lentille (2246) Le fréquencemètre est positionné entre le miroir semi-transparent (2245) et la lentille (2237). La lentille (2246) est réglée pour que l'image du faisceau FRDI sur le CCD du fréquencemètre soit ponctuelle. étape 3 : en translation de la lentille (2242) A point image is considered centered on a Npix x Npix size sensor if its coordinates

step 1: in translation of the lens (2231) The frequency meter is positioned between the semi-transparent mirror (2211) and the polarization rotator (2238). The lens (2231) is set so that the image of the FEDI beam on the CCD of the frequency meter is punctual. step 2: in translation of the lens (2246) The frequency meter is positioned between the semi-transparent mirror (2245) and the lens (2237). The lens (2246) is set so that the image of the FRDI beam on the CCD of the frequency meter is punctual. step 3: in translation of the lens (2242)

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The frequency meter is positioned between the semi-transparent mirror (2225) and the polarization rotator (2226). The lens (2242) is set so that the image of the FEGI beam on the CCD of the frequency meter is punctual. step 4: in translation of the lens (2281) The frequency meter is positioned between the semi-transparent mirror (2228) and the lens (2227). The lens (2281) is set so that the image of the FRGI beam on the CCD of the frequency meter is punctual. step 5: in translation of the lens (2212)
A temporary FEP lighting beam is introduced. This is derived directly from the output of the beam expander (2201) using a semi-transparent mirror and is redirected by a game of mirrors towards the objective (2217) in which it enters from the side where is normally the sample, and being directed along the optical axis of the lens. The objective (2217) should be approximately in the focused position, that is, in the position where it will be during normal use of the microscope. Objective (2219) must be temporarily removed in order to introduce FEP.

The frequency meter is positioned between the lens (2212) and the semi-transparent mirror (2211). The lens (2212) is set so that the image of the FEP beam on the CCD of the frequency meter is punctual. step 6: in translation of the lens (2237) and adjustment of the orientation of the semi-transparent mirror (2245):
An auxiliary CCD is placed at the location of the diaphragm (2213). The lens (2237) is set so that the image of the FRDI beam on this auxiliary CCD is punctual. The semi-transparent mirror (2245) is set so that the image of the FRDI beam on this auxiliary CCD is centered. step 7: CCD (2239) in translation.

The position of the CCD (2239) is adjusted so that the image of the FEP beam obtained by the procedure described in 7.3.3.1. from the CCD (2239) is punctual and centered. step 8: semi-transparent mirror (2211)
The position of this mirror is adjusted so that the image of the FEDI beam obtained by the procedure described in 7.3.3.1. from the CCD (2239) is punctual and centered. Step 9: Position goals.

 The FEP beam is removed and the lens (2219) is replaced. An auxiliary CCD is placed at the location of the diaphragm (2223). The sample is for example a transparent blade, optical oil being used on each side of the blade. The position of the lenses is set so that the image of the FRDI beam on this auxiliary CCD is punctual and centered.

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step 10: in translation of the lens (2224)
The frequency meter is positioned between the lens (2224) and the semi-transparent mirror (2225). The lens (2224) is set so that the image of the FED beam on the CCD of the frequency meter is punctual. step 11: translational adjustment of the lens (2227) and adjustment of the orientation of the semi-transparent mirror (2228):
An auxiliary CCD is placed at the location of (2223). The lens (2227) is set so that the image of the FRGI beam on this auxiliary CCD is punctual. The semi-transparent mirror (2228) is set so that the image of the FRGI beam on this auxiliary CCD is centered. step 12: the CCD (2229) in translation.

The position of the CCD (2229) is adjusted so that the image of the FED beam obtained by the procedure described in 7.3.3.1. from the CCD (2229) is punctual and centered. step 13: semi-transparent mirror (2225)
The position of this mirror is adjusted so that the image of the FEGI beam obtained by the procedure described in 7.3.3.1. from the CCD (2229) is punctual and centered. step 14: CCD (2229) and (2239) in rotation and translation
This step consists in adjusting in rotation the position of (2229) and (2239) so that their axis systems are merged. For this purpose, the command words COM [1,128,128], COM [1,250,128], COM [1,128,250] are used alternately. The two sensors are set in translation in a plane orthogonal to the axis (2264) and in rotation about this same axis. On each sensor we define a coordinate system (i, j) or the indexes pixels and / go from 0 to Npix - 1 with Npix = 256, and which marks the useful area of the sensor which will be used later. The origin point of the coordinate system, with coordinates (0,0), can be any of the four corners of the useful area of the sensor. At the same time as the adjustment is made, the origin point of the coordinate system is chosen. The criteria for setting and choosing the origin point are the same for both sensors and are as follows: - when COM [1,128,128] is used, the point of impact of the illumination beam, ie the direct light beam on (2229) or its reverse indicator on (2239), must be at the point of coordinates (128,128).

-When COM [1,250,128] is used, the point of impact of the illumination beam must be at a coordinate point (x, 128) where x is positive.

-When COM [1,128,6] is used, the point of impact of the illumination beam must be at a coordinate point (128, x) where x is positive.

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vecteurs de base unitaires 17 , c'est-à-dire par les repères (<9, /#, y'p ) ou p est l'indice du capteur (p=0 pour (2239) etp=l pour (2229)). The coordinate systems thus determined are defined by their origin point Op and their

unitary basic vectors 17, that is to say by the marks (<9, / #, y'p) where p is the index of the sensor (p = 0 for (2239) and p = 1 for (2229) ).

 These coordinate systems will be systematically used later.

 7. 4. Determination of the modulus of the reference wave.

 As in the first embodiment, the filters (2255) and (2256) are set so that the level of the reference wave is about a quarter of the maximum level allowed by the digitizer, a level of 256/4 = 64 in the case of 8-bit sampling of the video signal on both sensors.

 This reference wave is then determined as in the first embodiment, but because two sensors are present one obtains an array Iref [p, i, j] or i, j are the pixel indices as in the first embodiment. , and oup is the sensor index that is /? = 0 for (2239) andp = 1 for (2229).

 Iref [0, i, j] is the intensity received on the sensor (2239) when only the FRD beam is present and Iref [1, i, j] is the intensity received on the sensor (2229) when only the beam FRG is present.

 7. 5. Simple two-dimensional image pickup.

On obtient, à chaque acquisition, une image pour chaque capteur, et le tableau S[p,i,j] comporte donc un sous-tableau pour chaque capteur, l'indice p désignant le capteur. Toutefois dans la phase de réglage on n'utilisera en général qu'une seule de ces deux images. In the first embodiment, we have seen how a two-dimensional frequency representation in complex numbers can be generated from three images differing from one another by the phase difference between the illumination wave and the reference wave. In the adjustment phases that follow, we will have to generate this type of frequency representation. To generate such a representation, the system produces three successive images with successive offsets of +120, 0, -120 degrees applied to the illumination wave. The order of the phase shifts is reversed from that used in the first embodiment because they are applied to the illumination wave and not to the reference wave. This gives an array of pixels I [d, p, i, j] where the index d varying from 0 to 2 index the phase shift and where the index p denotes the sensor. The frequency representation is deduced by:

At each acquisition, an image is obtained for each sensor, and the array S [p, i, j] therefore comprises a sub-array for each sensor, the index p designating the sensor. However, in the adjustment phase, only one of these two images will generally be used.

 7.6.Objects of Kp parameters and adjustment of diaphragms.

 These parameters correspond to the parameter K of the first embodiment, but because of the dissymmetries of realization, the parameter is not necessarily the same for each sensor. So we define

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 two parameters K0 and K1 corresponding to the two sensors. These parameters are obtained as in the first embodiment, by taking a simple image using an objective micrometer. The objective micrometer used, however, must be designed for this purpose: marks must be made on a thin slide, a thick slide can not be used with this microscope.

 At first the objectives must be properly focused. For this purpose, parallel beams FED and FEG are suppressed. Only FRD and FRG reference waves are present. The mirrors (2282) and (2247) are used to obtain two-directional waves of propagation. The mirrors (2243) and (2232) are closed. The phase shifter (2251) is used to modify the phase of the waves. The micrometer is moved so that the marks are out of the scope of the objectives. The wave measured on one side of the objectives is the equivalent of the reference wave used on the other side. The program described in 7.3.3.1. with Fourier transformation to pass from the frequency domain to the spatial domain, is used to evaluate the punctuality of the image. The position of the lenses is adjusted to obtain a center point in the middle of the image.

de faisceau COM[0,128.128]. La position de l'échantillon dans le plan horizontal est modifiée jusqu'à ce que l'on obtienne une modification caractéristique de l'onde reçue sur les capteurs en l'abscence d'onde de référence, comme dans le premier mode de réalisation. In a second step, the sample must be correctly positioned. The mirrors (2282) (2247) (2243) (2232) are closed. Only the FEG beam is used, with a deviator command word

COM beam [0.128.128]. The position of the sample in the horizontal plane is modified until a characteristic change in the wave received on the sensors is obtained in the absence of a reference wave, as in the first embodiment.

 The reference wave FRD is then reintroduced and a focusing program similar to that used in the first embodiment, and using the image obtained on the sensor (2239), is launched. This program, however, differs from that used in the first embodiment in that the phase and amplitude changes of the illumination wave are now controlled by the devices (2204) and (2205) and that the value ratio ~ average characteristic of the attenuation is real and is that which has been measured in 7. 3.2.2. between two positions of the beam attenuator that are used alone here.

The position of the diaphragm (2213) is then adjusted in a plane perpendicular to (2264) so that its image is correctly centered. Its aperture is adjusted to be as high as possible, the diaphragm must however remain entirely visible on the image obtained. The position of the micrometer is then adjusted in the vertical direction so as to obtain a clear image. In this image, we measure the distance (Dpix) between two graduations separated by a real distance Dreel -
The FEG and FRD beams are then deleted. The FED beam is introduced with the command word of the beam deflector COM [1,128,128]. The FRG reference beam is also introduced.

The focus program is restarted, which this time uses the image received on the sensor (2229). The position of the diaphragm (2223) is then adjusted in a plane perpendicular to (2264) so that its image is correctly centered. Its aperture is adjusted to be as high as possible, the diaphragm must however remain entirely visible on the image obtained. On the image obtained, we measure the distance (Dpix) 1 between the same graduations as before.

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 (Dpix) is the distance in pixels measured on the image from the indexed sensor p, with p = 0 for (2239) and p = 1 for (2229) Dreel is the same for each measurement.

 Npix is the number of pixels of the useful sensor area and the Fourier transform used in the focusing program, for example Npix = 256.

 The openings of diaphragms obtained at the end of this procedure will be maintained thereafter.

 7.7.Difference of walking induced on a parallel beam.

 The sample observed does not necessarily have a mean index of the nominal index of objectives.

This index difference can lead to significant spherical abberration. In order to correct this aberration, it is necessary to take into account the average index no in the sample and the thickness L of the sample between two lamellae at the nominal index.

 Subsequent reconstruction of a three-dimensional image also requires knowledge of the relative position of the virtual origin points of the reference beams used on each side of the system. This relative position is defined by x, y, z which are the coordinates of the origin point of the reference beam used in the left part with respect to the origin point of the beam used in the right part.

 The parameters x, y, z, L, no cause phase shifts of a parallel wave crossing the sample.

parallèle à (2263) et ou â p, b se déduisent simplement des vecteurs i. 1 jp définis en 7.3.3.3.:

et il fait avec l'axe (2263) un angle de: sin [alpha]=1/@#i2 + j2
Kp Si le faisceau issu de l'objectif n'était pas dévié par les miroirs (2214) (2215) (2216) ou (2222) (2221) (2220) les vecteurs #p, #p seraient égaux aux vecteurs #p,#p. Bien que ce ne soit pas réellement le cas, les The calculation of these phase shifts is explained below: -correspondence between the direction of a parallel beam in the object and the coordinates of the corresponding point on the sensor: i and j are the coordinates of a pixel with respect to the optical center, expressed in pixels, on the sensor p, in the reference defined in step 14 of the control cycle described in 7. 3.3.2. A unit vector parallel to the frequency vector in the object has coordinates, in an orthonormal frame # p, bp, #p or #p is

parallel to (2263) and where p, b simply deduce vectors i. 1 jp defined in 7.3.3.3 .:

and it makes with the axis (2263) an angle of: sin [alpha] = 1 / @ # i2 + j2
Kp If the beam from the objective was not deflected by the mirrors (2214) (2215) (2216) or (2222) (2221) (2220) the vectors #p, #p would be equal to the vectors #p, #p. Although this is not really the case,

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vecteurs de base <?#,&#, c seront notés dans la suite de l'exposé 7p,jp,kp, sans différencier les vecteurs #p,bp des vecteurs correspondants #p,# définis en 7. 3.3.3. sur les capteurs.

base vectors <? #, &#, c will be noted in the following of the presentation 7p, jp, kp, without differentiating the vectors # p, bp from the corresponding vectors # p, # defined in 7. 3.3.3. on the sensors.

bzz = lono -lyny ou nv désigne l'indice nominal des objectifs, c'est-à-dire l'indice pour lequel ils ont été conçus et qui doit être celui de l'huile optique employée. # = Lno cosss- Lnv cosa

soit:

-Différence de marche induite par un déplacement du point éclairé: La grandeur accessible à la mesure est la différence de marche entre le faisceau inversé issu de FRG et le faisceau de référence FRD. Si ces deux faisceaux sont confondus et si le milieu séparant les objectifs a pour indice l'indice nominal des objectifs, la différence de marche est nulle. Cependant, si le point d'origine virtuel du faisceau de référence FRD a pour coordonnées (x,y,z) par rapport au point d'origine virtuel du faisceau de référence FRG, matérialisé par le point de focalisation de son faisceau inversé, alors cette différence de marche est calculée comme suit:
On utilise le vecteur v=(x,y,z) et le vecteur u défini plus haut. La Fig.46 montre le principe géométrique de calcul. La différence de marche induite est:

différence de marche totale: c'est la somme de la différence de marche dûe à la présence de l'objet et de celle dûe à la non-coincidence des points source.

-difference of walking induced by the presence of the object: Fig.45 shows the principle of calculation of this difference in operation. We have:

bzz = lono -lyny or nv denotes the nominal index of the objectives, that is to say the index for which they were designed and which must be that of the optical oil used. # = Lno cosss- Lnv cosa

is:

-Difference of step induced by a shift of the illuminated point: The magnitude accessible to the measurement is the difference in operation between the inverted beam resulting from FRG and the reference beam FRD. If these two beams are confused and if the medium separating the objectives is indexed to the nominal index of the objectives, the difference in path is zero. However, if the virtual origin point of the reference beam FRD has coordinates (x, y, z) with respect to the virtual origin point of the reference beam FRG, materialized by the focusing point of its inverted beam, then this difference in market is calculated as follows:
The vector v = (x, y, z) and the vector u defined above are used. Fig. 46 shows the geometric principle of computation. The induced difference in walking is:

total walking difference: this is the sum of the difference in walking due to the presence of the object and that due to the non-coincidence of the source points.

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In the absence of a diaphragm, the wave measured on the wave measured at the point of the coordinate sensor (i, j) is therefore:

7. 8. Maximization program.

 7. 8.1. Principle.

reçue est stockée dans un tableau Frec de dimensions N plX x N p,x . En pratique la méthode d'acquisition différera souvent du cas idéal mais permettra toujours

l'acquisition d'un tableau F,ec de dimensions N p,x x N p,x équivalent à celui qui serait obtenu dans le cas idéal. In the 'ideal' case where the sample is simply a lamina of thickness L and index no, a simple method can be used to determine the values of x, y, z, L, no. For this setting the FED and FEG light beams are removed and the FRD and FRG reference beams are introduced using the mirrors (2282) and (2247) to return symmetrical beams to the lenses. The FRG beam reflected by (2282) and heading toward the objective (2219) is centered on a central point of the diaphragm (2224). It is focused by the objective (2219) at a point of the object (2218). It then crosses the objective (2217) and reaches the CCD (2239) on which it is superimposed on the reference beam FRD reflected by the semi-transparent mirror (2245) towards the CCD (2239). The phase shifter (2251) is used to generate a phase shift between the two beams, which makes it possible to measure in a complex value the beam coming from FRG and received on (2239), by using the simple imaging procedure described in 7. 5. The wave thus

received is stored in a Frec array of dimensions N plX x N p, x. In practice, the acquisition method will often differ from the ideal case but will always

the acquisition of an array F, ec of dimensions N p, xx N p, x is equivalent to that which would be obtained in the ideal case.

La présence du diaphragme a en outre un effet de filtrage qui peut également être simulé. Because of the phase shifts induced by the sample, the value of the wave at a point in the absence of a diaphragm, and in a coordinate system centered on the optical center, is given by the formula established in 7.7 .: r # ########## @

The presence of the diaphragm also has a filtering effect which can also be simulated.

 The purpose of the program used is to calculate x, y, z, L, no by minimizing the difference between the wave thus simulated and the wave actually received.

l'onde reçue. L'onde reçue étant enregistrée dans un tableau F,ec de dimensions N p,x x N p,x , cet écart- type peut être calculé de la manière suivante, en 6 étapes, pour une valeur donnée du quintuplet

x Y z> L no : This difference can be characterized by the standard deviation # (x, y, z, L, no) between the simulated wave and

the received wave. The received wave being recorded in an array F, ec of dimensions N p, xx N p, x, this standard deviation can be calculated in the following manner, in 6 steps, for a given value of the quintuplet

x Y z> L no:

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Nc Nc Nc

avec e = bzz 0 et ou ic et jc sont les indices centres soit: ic = i - 2 , jc = j -
Npix 2 2 étape 2-la transformée de Fourier inverse de Fc est calculée. étape 3-Fc étant maintenant en représentation spatiale, la présence du diaphragme constitue une simple limitation dans ce domaine. Le programme calcule donc le tableau Fd de dimensions Npix x Npix en l'initialisant à 0 puis en effectuant:

pour tous les couples (i,j) tels que

étape 4- le programme effectue une transformation de Fourier du tableau Fd

E[M] étape 5- Le programme calcule la valeur rapport = i,J :IFd[i,j]1 2 qui permet de recaler en phase et i, j en intensité le tableau Fd avant de le comparer à Frec.

étape 6- Le programme calcule alors l'écart-type ()2 (x,y,z, L,no) = 1 IF,,, [i, j] - rapport. Fd[,@j,12 Ili
Le programme de calcul de x,y,z,L, no détermine la valeur de x,y,z,L, no qui permet de minimiser l'écart-type ainsi calculé. Tout programme de minimisation de la grandeur #2 (x,y,z, L,no) peut être utilisé de manière équivalente. L'algorithme décrit en 7. 8.2. constitue un exemple d'un tel programme mais peut être remplacé par tout programme de minimisation équivalent. step 1-the following frequency representation, of dimensions Nc × Nc with for example Nc = 4096, is calculated:

Nc Nc Nc

with e = bzz 0 and where ic and jc are the indices centers either: ic = i - 2, jc = j -
Npix 2 2 step 2-the inverse Fourier transform of Fc is calculated. step 3-Fc now being in spatial representation, the presence of the diaphragm constitutes a simple limitation in this field. The program therefore calculates the table Fd of dimensions Npix x Npix by initializing it to 0 then by carrying out:

for all couples (i, j) such as

step 4- the program performs a Fourier transformation of the Fd array

E [M] step 5- The program calculates the value ratio = i, J: IFd [i, j] 1 2 which makes it possible to recalibrate in phase and i, j in intensity the table Fd before comparing it with Frec.

step 6 The program then calculates the standard deviation () 2 (x, y, z, L, no) = 1 IF ,,, [i, j] - ratio. Fd [, @ j, 12 Ili
The program of calculation of x, y, z, L, no determines the value of x, y, z, L, no which makes it possible to minimize the thus calculated standard deviation. Any program for minimizing magnitude # 2 (x, y, z, L, no) can be used in an equivalent way. The algorithm described in 7. 8.2. is an example of such a program but can be replaced by any equivalent minimization program.

~ - j 2n 4 mode= 1: l'image réellement reçue est corrigée en phase par multiplication par e #. Une transformée de Fourier inverse permet d'obtenir une représentation spatiale. La grandeur choisie est le maximum du module sur l'ensemble de la représentation spatiale. To simplify calculations and facilitate convergence, the minimization of # 2 (x, y, z, L, no) is replaced in the algorithm described in 7. 8.2. by maximizing a characteristic quantity that varies according to a mode variable that increases as the algorithm converges to the solution. 3 mode values are used:

~ - j 2n 4 mode = 1: the image actually received is corrected in phase by multiplication by e #. An inverse Fourier transform makes it possible to obtain a spatial representation. The chosen size is the maximum of the module over the whole of the spatial representation.

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mode = 2: identical to the mode = 1 case, but the central part of the spatial representation is oversampled and the chosen size is the value of the module at the center of the points of the spatial representation. mode = 3: the wave to be received on the sensor for the considered values of x, y, z, L, no is calculated taking into account the filtering by the diaphragm. The magnitude chosen is the opposite of the standard deviation between the simulated wave and the actually received wave is - # 2 (x, y, z, L, no)
7. 8.2. Algorithm.

The algorithm of this program is described by Figs. 47 to 50 and Fig.60
Fig. 47 describes the highest level of the program. This level consists of a double loop of variation of the index no. The program calculates nopixels values of maxb, the largest value reached by the characteristic quantity for the index no, between nomin and nomax. This corresponds to the inner loop (3201). The program determines the new nocentre value, which must match the maximum value of maxb. It then starts a new iteration of the type (3201) where the values of no are centered around the new nocentre value and the width nolarg = nomax-nomin of the search interval has been divided by 2. This constitutes the loop external (3202) which is reiterated until the width of the search interval corresponds to the desired precision on the index no. This method avoids having to test too many values of no to arrive at a given precision result.

nomin ini, nomax ini (indice no ), Lmin,Lmax (largeur L), zmin,zmax (profondeur z). Le programme n'a pas besoin d'une valeur maximale et minimale des coordonnées x et y. The program must have as input the following values: - minimum and maximum values for each value sought based on available information.

nomin ini, nomax ini (index no), Lmin, Lmax (width L), zmin, zmax (depth z). The program does not need a maximum and minimum value of the x and y coordinates.

complexes F,ec [i, y] de dimensions NpixxNpix. - operating parameters, for example nopixels = 5 and pixels = 50 - image obtained for example in the manner described in 7.8.1., in the form of a table of numbers

complexes F, ec [i, y] of dimensions NpixxNpix.

 The main steps of the program are: - (3203): the current value of no is calculated.

- (3204): this procedure calculates the maximum value maxb reached by the characteristic quantity for the non current index, as well as the corresponding values of x, y, z, L. It is detailed Fig.48 - (3205): When the value maxb corresponding to the current iteration is greater than max ~ no, the current values of x, y, z, L, (calculated by the procedure (3204)), and no are stored and are the current approximation of the desired result.

- (3206): The width is compared to a certain limit to determine the convergence condition. For example, we can have lim = 0.05 # / L nopixels
The

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- (3207): Le programme se termine. Les valeurs x f , y f , z f , L f , nocentre correspondent à la meilleure approximation des valeurs réelles de x,y,z,L, no . Elles sont affichées et enregistrées pour être réutilisées ultérieurement.

- (3207): The program ends. The values xf, yf, zf, L f, nocenter correspond to the best approximation of the real values of x, y, z, L, no. They are displayed and saved for later use.

 For each index no the procedure (3204) computes a maximum value of the characteristic quantity and the associated values of x, y, z, L. However, a change of variables is performed and the variables actually used in the procedure are x, y, u, v with: u = cL + v = L-cz c = nv-1 no where nv is the nominal index of objectives.

 The procedure is to vary u etv and for each pair (u, v) to compute x, y, and the max value of the characteristic quantity.

ularg et vlarg des intervalles de recherche, ainsi que leurs centres ucentre-ini, vcentre ini et les valeurs de x et y, puis calcule la valeur #dif. Si la valeur obtenue est inférieure à une limite fixée comme critère de convergence, le programme calcule z et L par inversion du changement de variables, ce qui termine la procédure (3204). Sinon, il modifie éventuellement le choix de grandeur caractéristique (modification de mode), puis répète la procédure (3305). Ceci constitue la boucle (3301). L'ensemble de ces opérations constitue la procédure (3204) décrite Fig. 48
La Fig.48 décrit la procédure (3204). Ses étapes essentielles sont: - (3302): les intervalles de variation de u et v sont déterminés. The pair (u, v) varies firstly on a discrete set of upixel x vpixel size points, u and v varying respectively over intervals of width ularg and vlarg centered around the points ucentre ini and vcentre ~ inl. The program determines the new value of (ucentre, vcentre) which corresponds to the pair (u, v) for which the max value is the highest. It also determines xbar and ybar values that correspond to the difference between the values of x, y used for the calculation and the value of x, y refined at the end of the calculation. These operations constitute the procedure (3305) detailed in FIG. 49
When a new value of (ucentre, vcentre) has been obtained, the program decreases the width

ularg and vlarg search ranges, as well as their centers ucentre-ini, vcentre ini and the values of x and y, then computes the value #dif. If the value obtained is less than a limit set as a convergence criterion, the program calculates z and L by inverting the change of variables, which ends the procedure (3204). Otherwise, it optionally modifies the choice of characteristic quantity (mode modification), then repeats the procedure (3305). This constitutes the loop (3301). All of these operations constitute the procedure (3204) described in FIG. 48
Fig.48 describes the procedure (3204). Its essential stages are: - (3302): the intervals of variation of u and v are determined.

- (3303): The purpose of this procedure is to determine upixels and vpixels optimally. Its algorithm is described in Fig.60.

- (3304): The deviation of (phase / 27t) caused by traversing the blade and the following displacement z from the point of impact to a direction beam parallel to z is: dif = 1 / # ((no-nv ) L + nvz), We consider that the algorithm has converged as this quantity is known with sufficient precision. The uncertainty on this quantity is:

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Adif = 1 1 2 noc-n"c+n"u±no +n" +n"cw] # 1+c2 ou Au = ularg et #v = vlarg upixels vpixels Le programme modifie mode et détermine la fin de convergence en fonction la valeur obtenue de #dif . On

peut par exemple avoir liml=2, lim2=0.25,1im3=0.01 - (3305) : cette procédure calcule la grandeur caractéristique pour un ensemble de couples (u,v) et détermine le couple ucentre, vcentre correspondant à la plus grande valeur caractéristique, la valeur maxb de cette grandeur caractéristique, et les valeurs xbar,ybar qui représentent l'écart entre la nouvelle approximation de x,y et les valeurs courantes de x,y. Elle est détaillée Fig.49.

Adif = 1 1 2 noc-n "c + n" u ± no + n "+ n" cw] # 1 + c2 or Au = ularg and #v = vlarg upixels vpixels The program modifies mode and determines the end of convergence in function the value obtained from #dif. We

can for example have liml = 2, lim2 = 0.25,1im3 = 0.01 - (3305): this procedure calculates the characteristic quantity for a set of pairs (u, v) and determines the pair ucentre, vcentre corresponding to the highest characteristic value , the maxb value of this characteristic quantity, and the values xbar, ybar which represent the difference between the new approximation of x, y and the current values of x, y. It is detailed Fig.49.

si upixel. 5 alors: ucentre~Im=ucentre et ularg = ularg upixels si vpixels < 4 alors vcentre~ini, vlarg ne sont pas modifiés.

si pixels > 5 alors: vcentre ini=vcentre et vlarg = 4 vlarg vpixels
La Fig.49 décrit la procédure (3305). Ses étapes essentielles sont: - (3401): cette procédure calcule la grandeur caractéristique max pour les valeurs courantes de u,v, no . En mode 1 et 2 elle calcule également xbar et ybar qui représentent l'écart entre la nouvelle approximation de x,y et la valeur en entrée de la procédure. - (3306): modification of x, y, ularg, vlarg, ucentre ini, vcentre ini the program makes the following modifications: x = x + xbar y = y + ybar if upixels # 4 then ucentre ini, ularg are not modified .

if upixel. 5 then: ucentre ~ Im = ucentre and ularg = ularg upixels if vpixels <4 then vcentre ~ ini, vlarg are not modified.

if pixels> 5 then: vcentre ini = vcenter and vlarg = 4 vlarg vpixels
Fig.49 describes the procedure (3305). Its essential steps are: - (3401): this procedure calculates the max characteristic value for the current values of u, v, no. In mode 1 and 2 it also calculates xbar and ybar which represent the difference between the new approximation of x, y and the input value of the procedure.

- (3402): in the case of mode 3, the procedure (3401) did not calculate xbar and ybar. It is restarted in mode 2 to perform this calculation.

Fig. 50 describes the procedure (3401). Its essential steps are: - (3501): calculation of the corrected frequency representation. From the table Frec [i, j] the program calculates a corrected representation using:

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ou ic et jc sont les indices centrés soit: ic = /' # , je = j On vérifie alors, à une constante près indépendante de i etj:

n, ic jc A nv x-+y-i7C-J+a[i,j]u+b[i,j]v  0 0 Le programme génère la représentation fréquentielle corrigée de la manière suivante:

Npix $ Npix

where ic and jc are the indices centered either: ic = / '#, I = j One checks then, with a constant close independent of i andj:

n, ic jc A nv x- + y-i7C-J + a [i, j] u + b [i, j] v  0 0 The program generates the corrected frequency representation in the following way:

ou yx) = 0 quand Ixl : et y(x) = 1 quand Ixl z , et Au = # , Ou = vlag ' 2 2 upixels vpixels a[i,j] et b[i,j] représentent respectivement les fréquences suivant u et v de la fonction corrigée obtenue. On vérifie que ces fréquences ont toutes deux un signe constant. La multiplication par les fonctions y permet d'annuler les éléments pour lesquels ces fréquences sont trop élevées et d'éviter ainsi les repliements de spectre qui empêcheraient la convergence de l'algorithme.

or yx) = 0 when Ixl: and y (x) = 1 when Ixl z, and Au = #, where = vlag '2 2 upixels vpixels a [i, j] and b [i, j] represent respectively the following frequencies u and v of the corrected function obtained. It is verified that these frequencies both have a constant sign. The multiplication by the functions allows to cancel the elements for which these frequencies are too high and thus to avoid the folds of spectrum which would prevent the convergence of the algorithm.

- (3502): an inverse Fourier transformation of the Fcor array is performed.

- (3504): la partie centrale du tableau Fcor [i,j] est extraite. On crée ainsi un tableau Fa [i, j] de dimensions NaxNa avec par exemple Na =16:

- (3505): une transformée de Fourier directe est effectuée sur le tableau Fa - (3506) : le tableau Fa est complété par des zéros et on obtient un tableau Fb de dimensions Nb x Nb avec par exemple Nb =512.

et Fb[i,j]= 0 sinon. - (3503): max is the maximum value of the module on the array Fcor [l, j] The coordinates of the pixel in which the maximum is reached are denoted imax and jmax. We then have:

- (3504): the central part of the array Fcor [i, j] is extracted. One thus creates a table Fa [i, j] of dimensions NaxNa with for example Na = 16:

- (3505): a direct Fourier transform is carried out on the array Fa - (3506): the array Fa is completed by zeros and we obtain an array Fb of dimensions Nb x Nb with for example Nb = 512.

and Fb [i, j] = 0 otherwise.

- (3507): the inverse Fourier transformation of the table Fb is carried out.

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IFblll2i imax ="J lFb j]12 :IFb[i,j]12 IFbleI2j jmax I,J Jmax = :IFb[i,j]\2 max = Fb [imax, jmax]1 xbar n, N N Cimax- N61 pix Nb 2 ybar K0A Na jmoec - Nb ybar = nyN 0 plX Nb jmax- 2 - (3509):la représentation fréquentielle suivante, de dimensions Nc x Nc avec par exemple Nc =4096, est calculée :

- (3508): xbar, ybar, max are calculated by the formulas:

IFblll2i imax = "J lFb j] 12: IFb [i, j] 12 IFbleI2j jmax I, J Jmax =: IFb [i, j] \ 2 max = Fb [imax, jmax] 1 xbar n, NN Cimax-N61 pix Nb 2 ybar K0A Na jmoec - Nb ybar = nyN 0 plX Nb jmax- 2 - (3509): the following frequency representation, of dimensions Nc x Nc with for example Nc = 4096, is calculated:

avec Re = ## Ko et ou ic et jc sont les indices centrés soit: ic = i #- , jc = j - #A/ Npix - (3510): la transformée de Fourier inverse de Fc est calculée.

with Re = ## Ko and where ic and jc are the indices centered either: ic = i # -, jc = j - # A / Npix - (3510): the inverse Fourier transform of Fc is calculated.

pour tous les couples (i,j) tels que

- (3512) : le programme effectue une transformation de Fourier du tableau Fd

1 F,,, [i, j]Fd [', il (3513): Le programme calcule la valeur rapport = i,j :IFd[i,j]! 2 i, j (3511): Since Fc is now in spatial representation, the presence of the diaphragm constitutes a simple limitation in this field. The program therefore calculates the table Fd of dimensions Npix x Npix by initializing it to 0 then by carrying out:

for all couples (i, j) such as

- (3512): the program performs a Fourier transformation of the array Fd

1 F ,,, [i, j] Fd [', il (3513): The program calculates the value ratio = i, j: IFd [i, j]! 2 i, j

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max = ~l IF@ [,@ j, ~ rapport. Fi [,@ j,12
I, J
La Fig. 60 décrit la procédure (3303). Cette procédure vise à déterminer upixels et vpixels suivant les principes explicités ci-après: On peut exprimer la grandeur #/# calculée en 7. 7. , à une constante près, sous la forme:

avec :

s = #i2+j2/K02, i et j étant des indices centrés. - (3514): The program then calculates the max characteristic value:

max = ~ l IF @ [, @ j, ~ ratio. Fi [, @ j, 12
I, J
Fig. 60 describes the procedure (3303). This procedure aims to determine upixels and vpixels according to the principles explained below: We can express the magnitude # / # calculated in 7. 7., to a constant, in the form:

with:

s = # i2 + j2 / K02, where i and j are centered indices.

fonction fonc(u,v) de u et v. Si on fixe la valeur de v, elle devient simplement fonction de u. Si on limite la représentation Frec à un disque de rayon (en pixels) K0S0 cette fonction de u a comme fréquence maximale a(so) . a(so) est donc la fréquence maximale de fonc suivant u. De même, b(s0) est la fréquence maximale de fonc suivant v. upixels et vpixels doivent être déterminés de manière à ce que pour une valeur donnée de s0 aussi élevée que possible, les pas d'échantillonnage suivant u et v soient suffisamment précis pour éviter le repliement de spectre. Cette condition s'écrit:

Par ailleurs le nombre total de pixels est limité à une valeur pixels, ce qui s'écrit: upixels. vpixels = pixels En combinant ces équations on obtient l'équation El: The method of generating the characteristic quantity, in the mode = or mode = 2 case, consists of multiplying the frequency representation Frec by the phase correction factor e and then performing a Fourier transform. The representation thus obtained is in the spatial domain. The characteristic quantity is about the value of this representation at the point of origin. It is thus obtained as sum of elements of the form e -J2 # @ / #. This characteristic quantity can be considered as a

function fonc (u, v) of u and v. If we fix the value of v, it becomes simply a function of u. If we limit the Frec representation to a disc of radius (in pixels) K0S0 this function of ua as the maximum frequency a (so). a (so) is the maximum frequency of func following u. Similarly, b (s0) is the maximum frequency of func following v. upixels and vpixels must be determined so that for a given value of s0 as high as possible, the following sampling steps u and v are sufficiently accurate to avoid spectrum folding. This condition is written:

In addition, the total number of pixels is limited to a pixel value, which is written as: upixels. vpixels = pixels By combining these equations we obtain the equation El:

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Deux cas se présentent alors:

L'équation El a une solution s0 que le programme peut déterminer par dichotomie. Les valeurs de upixels et vpixels sont alors déterminées par: upixels = 2#a(s0)#ularg vpixels = 2#b(s0)#vlarg

L'équation El n'a pas de solution. Les valeurs de upixels et vpixels sont alors déterminées pour être proportionnelles à celles obtenues pour la valeur s0 = ouv soit : nv

Par ailleurs la condition upixels. vpixels = pixels doit toujours être vérifiée. La résolution de ces équations donne :

et on obtient donc finalement:

Two cases then arise:

Equation El has a solution s0 that the program can determine by dichotomy. The values of upixels and vpixels are then determined by: upixels = 2 # a (s0) #ularg vpixels = 2 # b (s0) #vlarg

The El equation has no solution. The values of upixels and vpixels are then determined to be proportional to those obtained for the value s0 = open either: nv

By the way the condition upixels. vpixels = pixels must always be checked. The resolution of these equations gives:

and we finally get:

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 In both cases, the values thus determined are real numbers which may be less than 1 or greater than pixels. A last step is therefore to translate them into integers in the interval [l, pixels].

The resulting algorithm, which makes it possible to determine upixels and vpixels, is shown in Fig.60.

(4201): so est la solution de l'équation la(so )b(so)1 = pixels Le programme résout cette équation 4. ularg. vlarg par dichotomie entre 0 et ouv. nv (4202):le programme prend pour upixels et vpixels le nombre entier le plus proche de la valeur réelle obtenue, puis il limite ces valeurs de la manière suivante: - si upixels<1 le programme effectue upixels=l - si vpixels<1 le programme effectue vpixels=1 - si upixels>pixels le programme effectue upixels=pixels -si vpixels>pixels le programme effectue vpixels=pixels
7. 9. Obtention des caractéristiques des faisceaux parallèles. The following steps should be detailed:

(4201): so is the solution of the equation la (so) b (so) 1 = pixels The program solves this equation 4. ularg. vlarg by dichotomy between 0 and op. nv (4202): the program takes for upixels and vpixels the integer closest to the actual value obtained, and then limits these values as follows: - if upixels <1 the program performs upixels = l - if vpixels <1 the program performs vpixels = 1 - if upixels> pixels the program performs upixels = pixels -if vpixels> pixels the program performs vpixels = pixels
7. 9. Obtaining the characteristics of parallel beams.

Each parallel beam generated by the lighting beam control system has an independent phase. The purpose of this procedure is to determine the phases and coordinates of these parallel beams. It is broken down into two parts:
7. 9.1. Adjusting the objectives and obtaining the relative position of the focusing points.

 The objective of this step is to determine the relative position of the reference points of the FRD and FRG reference beams. This objective can be achieved by adjusting the position of the lenses so that the image produced by the FRGI beam on the sensor (2239) is perfectly punctual.

 For this purpose, only the FRGI and FRD beams are used. The mirror (2282) is used to obtain a two-way directional wave. The mirrors (2243) (2232) (2247) are closed. The phase shifter (2251) is used to modify the phase of this wave. The space between the two lenses is occupied by optical oil at the nominal index of objectives. The measured wave on the right side of the objectives on the sensor (2239) indexed by p = 0 is the equivalent of the reference wave used on the other side. Its punctuality is evaluated by the procedure described in 7.3.3.1., Using a Fourier transform in said procedure. The position of the lenses is adjusted to obtain a center point in the middle of the image.

 If this position adjustment of the objectives is carried out with great care and with sufficiently precise positioners, of sub-micrometric precision, for example microscope focusing devices of sufficient quality, or positioners with piezoelectric control, then the points of origin of the images obtained from each side of the microscope are confused.

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 However, this requires an extremely precise positioning of the objectives. The adjustment procedure described in 7. 3.3.2. However, this quality of adjustment can be achieved by using medium precision positioners for lenses. Indeed, the fine adjustments are made, in this procedure, by moving cameras and not lenses. If the adjustment procedure described in 7. 3.3.2. is performed carefully, the points of origin of the frequency representations finally obtained are confused. Their relative coordinates are (x, y, z) = (0,0,0). It is better not to change the positions obtained for the objectives.

 However, the settings obtained by procedure 7. 3.3.2. or by a new setting of position of the objectives are in general imperfect. It is possible to use (x, y, z) = (0,0,0) but a better superposition of the images coming from each sensor will be obtained if a suitable algorithm is used to calculate a more precise value of these parameters.

nomax~~mi= nomin ~im= nv, nv étant l'indice nominal des objectifs. Lmn=Lmax=0 nopixels=1 pixels=20

zmrn = -20,1 et zmax = 20/L (par exemple)
7. 9.2. Obtention des valeurs complexes et des coordonnées des faisceaux d'éclairage. The wave measured on the sensor (2239), obtained according to the procedure described in 7.5. with p = O, is then recorded in a table Frec [i, j]. The x, y, z coordinates of the origin point of the reference wave from FRD relative to the origin point of the reference wave from FRG are then determined from Frec [i, j] using the program described in 7. 8. However, in order to take into account the absence of a sample, the procedure (3303) is replaced by the following two assignments: upixels = pixels vpixels = 1
In addition, the variables used are:

nomax ~~ mi = nomin ~ im = nv, where nv is the nominal index of objectives. Lmn = Lmax = 0 nopixels = 1 pixels = 20

zmrn = -20,1 and zmax = 20 / L (for example)
7. 9.2. Obtain complex values and coordinates of light beams.

stockées dans les tableaux la[p,0,i,j] , Ja[p,0,i,j]. - les coordonnées du point d'impact direct du faisceau d'éclairage sur le capteur p . Ces coordonnées seront stockées dans les tableaux la[p, l,i,j] , Ja[p, l,i,j]. The purpose of this procedure is to determine, for each parallel beam defined by the indices p, i, j of the control word COM [p, i, j] of the beam deflector: - the coordinates of the direct impact point of the beam d lighting on the sensor p. These coordinates will be

stored in the tables [p, 0, i, j], Ja [p, 0, i, j]. - the coordinates of the point of direct impact of the illumination beam on the sensor p. These coordinates will be stored in the tables [p, l, i, j], Ja [p, l, i, j].

the complex value of the corresponding illumination beam, its phase being measured at the origin point of the reference wave used on the sensor #. This convention of measurement of the phase ensures that the complex value thus obtained is independent of the position of the objectives, to a global factor of near phase affecting all the beams characterized by the same index p. This complex value will be stored in an array Ra [p, i, j]. Since the direct measurement of the beams gives relative coordinates

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 at the point of origin of the reference wave used on the p-sensor, this value shall be corrected according to the position values determined in 7.9.1.

 During this procedure, the reference beams FRD and FRG are used, as well as a lighting beam defined by a variable control word COM [p, i, j] of the beam deflector. The mirrors (2243) and (2232) are used to create a reverse indicator beam of the illumination beam that will strike the sensor opposite to the sensor normally illuminated by this beam. The mirrors (2247) and (2282) are closed.

The procedure described in 7. 5. is used to obtain on each sensor two-dimensional images in complex numbers. Phase offsets are performed using element (2205).

A program makes it possible to obtain these parameters in the form of tables la [p, q, i j], Ja [p, q, i j], Ra [p, i j]. By an oversampling method it determines the [p, q, ijl, Ja [p, q, i, j] with a precision less than the pixel. These tables are therefore tables of real numbers.

 The coordinate system used on the sensor /? is that determined in step 14 of the setting cycle 7. 3.3.2., defined by the leading vectors (# p, # p). This tracking convention will be maintained thereafter.

 The program consists of three loops traveled successively.

Loop 1: This is a loop on the index p, which successively takes the values 0 and 1.

For each of these indices the program uses the command word COMCp, ##, ##. It then determines the integer coordinates imaxOp, jmaxOp of the maximum of the resulting image on the sensor p.

programme génère les valeurs la po , q, i o , j0 ] o[o ' ,q,i0, j0 Ra po .'0 ' > Jo ] A chaque itération, correspondant à un triplet donné p0, io , joie programme effectue les 8 étapes suivantes: Etape 1: le mot de commande COM[p0,Npix/2, , ni est utilisé et les images résultantes sur chaque capteur sont enregistrée dans deux tableaux de nombres complexes M0q [i,j]ou q=0 pour l'image obtenue sur le capteur p0 et q=1pour l'image obtenue sur le capteur opposé. Loop 2: This is a loop on all triplets p0, i0, j0. For each of these triplets, the

The program generates the values la po, q, io, j0] o [o ', q, i0, j0 Ra po .'0'> Jo] At each iteration, corresponding to a given triplet p0, io, joy program performs the 8 following steps: Step 1: the control word COM [p0, Npix / 2,, n1 is used and the resulting images on each sensor are recorded in two arrays of complex numbers M0q [i, j] or q = 0 for the image obtained on the sensor p0 and q = 1for the image obtained on the opposite sensor.

Step 2: the command word COM [p0, i0, j0 is used and the resulting images are stored in the arrays M1q [i, j] Step 3: The program determines the coordinates imaxq, jmaxq of the maximum module point of the array M1q [/, y] for each value of q.

Step 4: The program extracts an image of size Nax Na, with for example Na = 16, around the point of coordinates imaxq jmaxq:

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et M2q[i,j] = 0 sinon.

and M2q [i, j] = 0 otherwise.

Step 5: The program performs a direct Fourier transform of the M2q arrays.

Etape 7 : le programme effectue la transformée de Fourier inverse du tableau M3. Step 6: the program completes the tables M2q by zeros, generating the tables M3q of dimensions Nb x Nb with for example Nb = 512. The array M3q is initialized to zero then the program performs for all the indices i, j each going from 0 to Na -1 and for the two indices q:

Step 7: The program performs the inverse Fourier transform of the M3 array.

ou x,y,z sont les coordonnées calculées en 7.9.1. Step 8: The program calculates the coordinates and the complex value at the center of the M3 array.

where x, y, z are the coordinates calculated in 7.9.1.

programme parcourt à nouveau les indices p p , io , j p , en testant à chaque fois la condition

afo,/o,yo1 1 Ra[po,io,jo] Il Lorsque cette condition est satisfaite, le programme effectue: 7o,127,127] 8 Lorsque cette condition est satisfaite, programme effectue: Loop 3: The program performs a final operation of canceling the values of Ra and assigning high values to Ja and la whenever the point of direct impact of the beam is outside the zone limited by the opening of the beam. objective, which results in a disappearance of this point. For this purpose

program goes through again the indices pp, io, jp, each time testing the condition

afo, / o, yo1 1 Ra [po, io, jo] When this condition is satisfied, the program performs: 7o, 127,127] 8 When this condition is satisfied, program performs:

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Iapo,0,io, jo=-1000 JaPo 0> io > jo ~ -1000
7. 10. Réglage de position des objectifs. Ra [p0, i0, j0] = 0

Iapo, 0, io, jo = -1000 JaPo 0>io> jo ~ -1000
7. 10. Adjusting the position of the lenses.

 The sample to be studied is set up. During this step, only the FRGI and FRD beams are used. The mirror (2282) is used to obtain a two-way directional wave. The mirrors (2243) (2232) (2247) are closed. The phase shifter (2251) is used to modify the phase of this wave. From optical oil to the nominal index of objectives is used. The wave measured on the right side of the objectives on the sensor (2239) indexed by /? = 0 is the equivalent of the reference wave used on the other side.

A program generates two images by the procedure described in 7.3.3.1 .: a spatial image obtained with Fourier transformation, and a frequency image obtained without Fourier transformation. The program extracts on each of these images the intensity (square of the complex number module constituting the image obtained in 7.3.3.1.). The program displays the resulting images.

 The spatial image must be centered.

 On the image in frequency, one must observe a clear disc. The adjustment must be made so that the intensity is as high as possible for the high frequencies (points far from the center). The disc observed must remain relatively homogeneous.

 If a dark ring appears between the outer edge and the central area, the sample is too thick and not all frequencies can be taken into account. The adjustment must then be made so as to have a relatively homogeneous disk, radius as high as possible. The disc does not reach its maximum size and high frequencies can not be taken into account. The resolution of the image, mainly in depth, is diminished. The only solution to this problem is to use a specially designed lens, described in paragraph 7.19.

 This method of adjusting the objectives is adapted to the case where the sample index differs significantly from the nominal index of the objectives. In the opposite case, and in particular if one wants to use a function Dp defined in 7.16 equal to 1, the adjustment must be made from the spatial image alone and so that this image is punctual and centered.

7.11. Determination of x, y, z, L, n0;
It is necessary to know these parameters to be able to compensate the spherical aberration and the effects of the non-coincidence of the points of origin of the reference waves. These parameters can be determined by not performing step 7.10. and thus leaving the objectives in the position where they were at the end of the step described in 7.9.1. The values x, y, z are then those which were determined in 7.9.1. The values of L and n0 may have been previously measured by means outside the microscope proper. However, this method has the disadvantage of not allowing a movement of the objectives during the setting up of the sample, and of requiring the use of a measuring system

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 expensive external. It is therefore better to re-determine all of these parameters. This second method allows for the shifting of objectives during sample placement and step 7.10. can be done.

 To apply this second method, one could in principle use the theoretical procedure described in 7.8.1. and using only one image acquisition, but local variations in sample characteristics near the focus point would distort the result. This is why a series of images is used and the variation of phase and intensity at the point of direct impact of the illumination beam is measured on each image. From this series of values, one can generate a table equivalent to the table Frec used in 7. 8. but in which one freed oneself from the local variations.

7. 11.1. Acquisition
The mirrors (2282) (2247) (2243) (2232) are closed to remove all reverse indicator beams, which will no longer be used later. The procedure described in 7. 9.2. is repeated, with the following modifications: - The sample is now present.

- Loop 1, which consists in determining imax0 p, jmaxo. , is deleted. The previously obtained values of imax0p, jmax0p are reused.

In loop 2, the indices p0 etq are set to 0. Steps 1 to 8 are therefore performed only for the set of indices io, where jo (p0 being set to 0). In each of these steps, only the elements corresponding to the index q = 0 are acquired or calculated.

Ia[po, q, io, j 0]' Ja[po, q ,io, jo], > Rapo 10 > j o ne sont pas recalculés et leurs valeurs précédemment obtenues sont maintenues. la quantité Rb po , i o , j o est calculée comme suit: -si Rapo,io, jo=0 alors Rb[p0 , ;0 , jo=0 0

- Step 8 of Loop 2 is modified as follows:

Ia [po, q, io, j 0] 'Ja [po, q, io, jo],> Rapo 10> jo are not recalculated and their previously obtained values are maintained. the quantity Rb po, io, jo is calculated as follows: -si Rapo, io, jo = 0 then Rb [p0,; 0, jo = 0 0

This quantity corresponds to the variation of the illumination beam due to the presence of the sample and the displacement of the objectives, on the sensor 0, for the illumination characterized by the indices i0, j0, with respect to a position of the objectives or the point of origin of the reference waves used on each objective would be confused.

- Loop 3 is deleted.

 7.11.2.generation of the frequency image.

 A second program is then launched. This one aims at generating, from the previous measurements, a table Frec usable in the algorithm described in 7. 8. As the coordinates

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IaPo q 10 j o Ja[Po A, h #> h des points échantillonnés par le tableau Rb ne correspondent pas à des pixels entiers, une méthode de suréchantillonnage et de filtrage est nécessaire pour générer le tableau Froc.

IaPo q 10 jo Ja [Po A, h #> h points sampled by the Rb array do not correspond to integer pixels, an oversampling and filtering method is needed to generate the Froc array.

ou E (x) le nombre entier le plus proche de x. This method is imperfect because the pitch (eg Ia [p, q, i, j1-p, q, i + 1, j]) separating two adjacent samples from the Rb array may vary. Nevertheless, for a quality realization, this variation is weak and the method of oversampling-filtering gives good results. This comprises the following successive steps: Step 1: generation of an oversampled frequency representation of dimensions Nc × Nc with for example Nc = 4096. The array Fs is initialized to 0 then the program traverses the set of indices i, j by testing the condition ra [0, i, j] # 0. When the condition is true, it performs:

or E (x) the integer closest to x.

pour tous les couples (i,j) tels que

ou ouv est l'ouverture des objectifs. Step 2: an inverse Fourier transform is applied to the table Fs Step 3: the central part of the array, of dimensions Npix x Npix. is extracted and the presence of the simulated diaphragm.

for all couples (i, j) such as

where open is the opening of the objectives.

Step 4: The Fourier transform of the Frec array obtained is carried out.

 7.11.3.calculating the parameters.

The Frec table obtained at the end of step 4 constitutes the frequency image, equivalent to the one whose acquisition is described in 7.8.1., But acquired in a manner less sensitive to local variations of the index. . It is possible to simulate this frequency image from a quintuplet (x, y, z, L, n0) and to calculate a max. This is what the program part described in FIG. 50 and comprising the steps (3509) to (3514), which finally calculates a characteristic magnitude max that will be noted max (x, y, z, L, no). The determination of the value of the quintuplet (x, y, z, L, no) consists in using a maximization program which varies (x, y, z, L, no) so as to determine the point corresponding to the value la higher of max (x, y, z, L, no). In principle, any maximization algorithm is suitable.

However, the number of variables and the complexity of the calculations are such that it is necessary to use a specific and optimized algorithm. The program described in 7. 8. is therefore used to calculate the parameters from the Frec table which constitutes the frequency image.

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 7. 12. Two-dimensional image capture.

7.12.1.Principe:
In the first embodiment, it has been seen how a two-dimensional frequency representation can be realized from several elementary images differing from one another by the phase difference between the lighting beam and the reference beam, as well as by the level of attenuation of the lighting beam. In this mode, phase rotators (2210) (2238) (2241) (2226) are added to vary the direction of polarization of the wave and the direction of analysis. Indeed, the diffraction of the illumination wave is not homogeneous in all directions. For a given direction, the diffracted wave strongly depends on the polarization of the incident beam.

 Remember that if a and b are two vectors, then: a # b is the vector product of a and b a. b is the scalar product of a and b Ilall is the norm of a.

We call: fc: characteristic frequency of a point fe: illumination frequency f0: frequency associated with the optical center of the sensor FIG. 51 shows the arrangement of these frequencies.

/ 3 is the angle between the vector fc ^ fe and the vector fc A f / I is the angle between the vector fe A fe and the vector fe ^ fo a is the angle between the vector ï and the vector f cAf (we omit the index p for the vectors i, j, k) ae is the angle between the vector # and the vector fe # f0 # is the angle between the vector fe and the vector fc
If the electric field vector of the illumination beam is parallel, in the object, to the vector fc #fe then the beam diffracted by the object in the direction fc is not attenuated. If it is orthogonal to this vector, the diffracted beam is attenuated by a factor cos #.

fe . Cette rotation conserve l'angle 3 . On note (Je a/6) le vecteur ainsi obtenu à partir du vecteur fe /\fe . Dans le cas de l'onde de fréquence fe polarisée parallèlement à fe AJe la rotation se fait autour de fe ^ fo et on note le vecteur résultant (/e A fe) re On note: The vector electric field of a beam, when it reaches the sensor, is in the plane of the sensor, which is a plane orthogonal to f0. The mode of transition from the electric field vector in the object to the electric field vector on the sensor is a rotation around the vector fc # f0 for the frequency wave

fe. This rotation keeps the angle 3. The vector thus obtained is denoted (I a / 6) from the vector fe / fef. In the case of the wave of frequency fe polarized parallel to fe AJe the rotation is around fe ^ fo and we note the resulting vector (/ e A fe) re Note:

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In the plane of the sensor, we have the configuration shown in Fig. 52, where the points O, E, C are respectively the optical center (frequency f0), the point of direct impact of the illumination wave (frequency f ), and the point where the diffracted wave (frequency fc) is measured.

champ électrique résultant au point C est (CooAo +COIAI)'17+(CIOAO +C4y . When the electric field vector of the lighting beam (at point E) is A0 # A1 # the vector

resulting electric field at point C is (CooAo + COIAI) '17 + (CIOAO + C4y.

During the measurements, we will use: - a lighting wave directed according to #. For this light wave, diffracted components polarized along the axes oriented by 1 and] will be measured, obtaining the Coo and C10 factors - a directional light directed at 7. For this illumination wave, polarized diffracted components will be measured. along the axes oriented by # and #, obtaining the factors C01 and C11
The factors Ckl are therefore the quantities measured.

 This is because the polarization and analysis directions obtained are not strictly orthogonal.

If the electric field vector of the illumination beam at the point E is parallel to the vector xe and the vector electric field of the beam received at the point C is parallel to the vector #c, there is no attenuation.

vaut: M = -cosqe cosç?cC00 -sine coscC0i -cosç?e sinç?cC10 -sinç9e sinqeCll' Afin de calculer cette valeur il est nécessaire de calculer préalablement les fonctions cos rp e , cos q e' sing, sin q e . Ceci se fait en utilisant d'une part les relations trigonométriques: cosrpe =cosae cos/3 -sina c sin,6, sin 9, = coso'e sin,6c + sinae cos,6, cosqe = cosae COSRe -sinae Sin/3e This case corresponds to an electric field vector at the point E of value Ax = AU cos qe + j sin 9,) and therefore a vector electric field resulting at the point C: A ((COO cosqe + COI sinqe) T + (Clo cos rp + Cn 1 sinço,) The projection of this vector on the axis oriented by -Xe has the value: - [(Coo cosrpe + Col sinq e) cosqe + (Clo cosço ,, + CI, sinrp sinrp]. one seeks to integrate in the calculations is the ratio of the algebraic value of the diffracted beam to that of the incident beam in the absence of attenuation due to the angle #, which corresponds to the case above and

is worth: M = -cosqe cosç? cC00 -sine coscC0i -cosç? e sinç? cC10 -sinç9e sinqeCll 'In order to compute this value it is necessary to calculate beforehand the functions cos rp e, cos qe' sing, sin qe. This is done using on the one hand the trigonometric relations: cosrpe = cosae cos / 3 -sina c sin, 6, sin 9, = coso'e sin, 6c + sinae cos, 6, cosqe = cosae COSRe -sinae Sin / 3rd

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sinue = cosae sin,6, -f-SlnGZe cos fl, et d'autre part les relations suivantes:

cos/3 ~ .fc ^fe le /\fo e Iife /\fell'ilfe /\foll Slric ~ f//. , .% ^.fe sin,6, = f, /, fe/\fe) "î/"!/' cosp = fe /\fe le /\fo cos,6, = cin/î ( fe*fo 1 /\10 fe ^fa fe sin,6, = f, If 7A; * fc ^ fo cosae=I'11 !!7c/o!! Il .f ^ Io sma;c=7..j-###j, smae cA! Je ^fo cosae 1. Ilfe I\f,11 fe f, Slriae =.l Ilfe ^,%II Si on utilise les valeurs normalisées des vecteurs fréquence:

on obtient: @

sin = cosae sin, 6, -f-SlnGZe cos fl, and on the other hand the following relations:

cos / 3 ~ .fc ^ fe / \ fhe Iife / \ fell'ilfe / \ foll Slic ~ f //. %. sin sin, 6 6,,,,,,,,,,,,,,,,,,,,,,,,, ## EQU1 ## where ## EQU1 ## where ## EQU1 ## j, smae cA! I ^ fo cosae 1. Ilfe I \ f, 11 ff, Slriae = .l Ilfe ^,% II If we use the normalized values of frequency vectors:

we obtain: @

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Vxy = -xcYe +Ycxe M2=x2+y2 Me 2 = xe 2 'F Ye 2 2
Toutefois, lorsque les dénominateurs sont nuls, les expressions ci-dessus doivent être remplacées par des valeurs limites.

Vxy = -xcYe + Ycxe M2 = x2 + y2 Me 2 = xe 2 'F Ye 2 2
However, when the denominators are zero, the above expressions must be replaced by limit values.

Une représentation fréquentielle bidimensionnelle est un tableau Mk, p,q i, j de nombres complexes, de dimensions N pIX x N pix 1 k est l'indice de l'image dans sa série, p est l'indice du capteur sur lequel parvient le faisceau d'éclairage direct (0 ou 1) et q a les valeurs suivantes: q=0: image reçue sur le capteur ou parvient l'éclairage direct q=1: image reçue sur l'autre capteur. 7. 12.2. Algorithm:

A two-dimensional frequency representation is a table Mk, p, qi, j of complex numbers, of dimensions N pIX x N pix k is the index of the image in its series, p is the index of the sensor on which the direct light beam (0 or 1) and q has the following values: q = 0: image received on the sensor or reaches the direct light q = 1: image received on the other sensor.

Hk, p,g i, j : image de référence, correspondant à une représentation fréquentielle bidimensionnelle obtenue pour une direction fixe du faisceau. Cette image de référence a pour objet de pouvoir ultérieurement compenser les modifications de trajet optique dûes aux vibrations des miroirs inclus dans le système. Si ces vibrations sont faibles, l'image de référence peut n'être acquise que périodiquement. In addition to the image itself, this program also generates the tables: Bk, p, q [i, j]: noise indicator

Hk, p, gi, j: reference image, corresponding to a two-dimensional frequency representation obtained for a fixed direction of the beam. The aim of this reference image is to be able to compensate for the optical path changes due to the vibrations of the mirrors included in the system. If these vibrations are weak, the reference image can be acquired only periodically.

The reference image can also be a simplified image, the accuracy criteria being lower than those of the useful image Mk, p, q [i, y]. To simplify the presentation, it is assumed that a reference image Hk, p, q [i, j] having the same characteristics as the useful image (except the direction of the illumination beam) is acquired for each useful image Mk, p , q [i, j].

 BHk, p, q [i, j]: noise indicator of the reference image.

 A series of two-dimensional frequency representations is obtained by calculation from a series of elementary images corresponding to interference patterns formed on the CCD sensors. The program of acquisition of the two-dimensional frequency representations is thus decomposed into a phase of acquisition of elementary images and a phase of calculation. These two phases can be separated, or each image can be computed as the acquisition progresses. We place ourselves here in the case where the two phases are separated.

 7. 12.2.1. acquisition of elementary images.

 The series of elementary images can be acquired at one time by the fast camera, without any calculations being carried out, the commands of the elements of modification of the beam before

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Ic[k, p], Jc[k, p] déterminant les indices 'symboliques' permettant de calculer pour chaque couple (k,p) le mot de commande du déviateur de faisceau CoA4p, ldk, p], Jc[k, pl]. Pendant cette procédure les faisceaux FRG et FRD sont présents en permanence, chaque image élémentaire étant formée sur un capteur par l'interférence de l'onde de référence et de l'onde diffractée par l'échantillon, lui-même éclairé par des ondes d'éclairage de caractéristiques variables. Les miroirs (2282) (2243) (2232) (2247) sont obturés. be synchronized with the acquisition of images. This is an iteration over the integer k and the integer p. The sequence of parallel lighting to be used must be specified in the tables

Ic [k, p], Jc [k, p] determining the 'symbolic' indices making it possible to calculate for each pair (k, p) the control word of the beam deflector CoA4p, ldk, p], Jc [k, p ]. During this procedure, the FRG and FRD beams are permanently present, each elementary image being formed on a sensor by the interference of the reference wave and of the wave diffracted by the sample, itself illuminated by waveforms. lighting of variable characteristics. The mirrors (2282) (2243) (2232) (2247) are closed.

rll0k, pc, d, r . r2 ]q, i, j , Avant chaque prise d'image élémentaire les rotateurs de phase permettant le contrôle du faisceau d'éclairage (atténuation, décalage de phase, déviation et polarisation) doivent être commandés de manière appropriée. For each pair (k, p), the taking of images is divided into two phases: phase 1: it consists of the acquisition of 36 pairs of elementary images, a pair of images comprising an image coming from each sensor, and the 36 pairs differing from each other by the state of all beam control systems except the beam deflector which keeps a constant state for a given torque (k, p). These 36 pairs of elementary images will be used later to generate a useful two-dimensional frequency representation Mk, p, q [i, j]. One of these elementary images is noted.

rll0k, pc, d, r. r2] q, i, j, Before each elementary image taking place, the phase rotators enabling control of the illumination beam (attenuation, phase shift, deflection and polarization) must be appropriately controlled.

The index c is determined by the following table, where att [c] constitutes an array containing the attenuation corresponding to the index, and where the values a1 and a2 are those explained in 7. 2.2. , measured in 7. 3.2.2., and where the beam attenuator is controlled as explained in 7.2.2.

<Tb>
<tb> index <SEP> c <SEP> attenuation <SEP> att [c]
<tb> 0 <SEP> 1
<tb> 1 <SEP> a1
<tb> 2 <SEP> a1 <SEP> a2
<Tb>
The indices d, r1, r2 are determined by the following tables:

<Tb>
<tb> index <SEP> d <SEP> shift <SEP> of <SEP> phase
<tb> (degrees)
<tb> 0 <SEP> +120 <SEP>
<tb> 1
<tb> 2 <SEP> -120
<tb> index <SEP> r2 <SEP> voltage <SEP> applied <SEP> to
<tb> rotators <SEP> (2210) <SEP> and <SEP> (2241)
<tb> 0 <SEP> 5V
<Tb>

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<Tb>
<tb> 1 <SEP> -5V
<tb> index <SEP> r1 <SEP> voltage <SEP> applied <SEP> to
<tb> rotators <SEP> (2238) <SEP> and <SEP> (2226)
<tb> 0 <SEP> 5V
<tb> 1 <SEP> -5V
<Tb>

A pair of elementary images (corresponding to the two values of the index q) is obtained for each combination of the indices c, d, r1, r2 and for each illumination direction defined by the indices (k, p).

MOk, pc, d, r , r2 q, i, j . For each lighting direction (k, p), we thus obtain 36 pairs of elementary images noted

MOk, pc, d, r, r2 q, i, j.

 The filter (2203) should be set so that the sensor is never saturated, but as close as possible to the saturation limit. Equivalently, it can be set in the absence of a reference wave so that the maximum intensity of the wave reaching the sensor in the absence of attenuation of the beam is one quarter of the maximum level allowed by the digitalization of the beam. video signal, ie 64 for an 8-bit digitizer.

- on notera MRO[, 1fc,J, ,r2 q,i, j une image élémentaire obtenue. -phase 2: It consists of the acquisition of 36 more elementary images, which will be used to generate the reference image. This phase is identical to phase 1 but:

- MRO [, 1fc, J,, r2 q, i, j, an elementary image obtained.

the command word used to obtain MRO [k, p] [c, d, r r2] [q, i, j] is C <3Mf /?, / ,,], J [,,] 1 or i, , j, are the coordinates of a constant point situated on the side of the sensor, for example the point (3905) in FIG. 56. representing a sensor and on which the outline (3902) represents the limit corresponding to the opening of the objective, which can not be exceeded by the illumination beams. This command word does not depend on k. The coordinates ir, jr can be chosen relatively arbitrarily. However, the choice of a point (3905) strongly eccentric allows points corresponding to vectors total frequency (ft following the notations used in 5. 3.) of comparable standard can be obtained from each sensor. For samples that do not have specific regular structures, such points correspond to comparable complex values on both sensors, which improves the reliability of the results.

 7. 12.2.2. Calculation of two-dimensional frequency representations.

M p,o[',./] et jt,/>,9 [' ./] le programme parcourt les indices (k,p) en effectuant pour chaque couple (k,p) les 3 étapes suivantes: After the acquisition phase, a specific program must be used to generate from these elementary images complex number images and the associated noise indicators. To generate

M p, o [',. /] And jt, />, 9 [' ./] the program traverses the indices (k, p) by performing for each pair (k, p) the following 3 steps:

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step 1: generating the mitigation scoreboard. this array is an array of integers M1 [q, i, j] generated in the following way: is initialized to 0, then the program traverses the set of indices q, i, j twice.

Mqq, +iadd, j + jadd] = 1 pour iadd et jadd variant de -1 à 1, et à condition de ne pas sortir des limites du tableau. - first run: the program calculates max ~ pix = max MOk, p0, d, rt, r2 q, i, j. If for a given value d, r1, r2 of q, i, j max ~ pix is equal to the maximum value of the digitizer, then the program sets to 1 this pixel and its immediate neighbors:

Mqq, + iadd, j + jadd] = 1 for iadd and jadd varying from -1 to 1, and provided you do not leave the limits of the table.

-second path: the program calculates max- pix = max MOk, pl, d, rt, r2 q, i, j. If for a given value d, r1, r2 of q, i, j max ~ pix is equal to the maximum value of the digitizer, then the program sets to 2 this pixel and its immediate neighbors: M1 [q, i + iadd, j + jadd] = 2 for iadd and jadd varying from -1 to 1, and provided you do not leave the limits of the table.

At the end of this step the array M1 [q, i, j] contains the index corresponding to the attenuation to be used to attenuate the image. step 2: generation of complex images corresponding to each rotator position.

L'objet de cette étape 3 est de calculer Mk, p,q i, j en fonction de M2rl,r2q,i, j . Ceci peut être réalisé simplement sans utiliser les variations de polarisation en effectuant Mk,p,q [i, j] = M2[1,1][q,i,j] le bruit étant alors donné par: jt,p,9[',y] = 1
La grandeur Mk,p,q[i,j] ainsi générée correspond à celle qui était utilisée dans le premier mode de réalisation. Néanmoins, cette méthode induit des imprécisions sur les fréquences élevées et il est

préférable d'utiliser le principe décrit en 7.12.1., ou M2rl,r2q,i, j correspond à la grandeur mesurée, qui était notée Cr1,r2 en 7.12.1. D'autres variantes de cette méthode seront décrites en 7.18.
L'étape 3 est donc içi réalisée comme suit : M2 [r, r2q, i> ≥ ']] [.J 1 2MOk, p] [M1 [qiJ] Or >> r29ij att M q, I, J 6 lref [pq + pq, I, J] -MO [k , p] [M1 [q, i, j]] h1> r2 [q, i, j - MO [k, p] M1 [q, i, j, 2, r1 r2] [q, i, j] ) 2 ~ 1 (MO [k, PeMlpq i>JI> rmrz [RiJyMOk> P [Ml9tJ] 2>ri>r29i> JJ step 3: combination of the images obtained for the various positions of the rotators.

The object of this step 3 is to calculate Mk, p, qi, j according to M2rl, r2q, i, j. This can be done simply without using the polarization variations by performing Mk, p, q [i, j] = M2 [1,1] [q, i, j] the noise being then given by: jt, p, 9 [ ', y] = 1
The magnitude Mk, p, q [i, j] thus generated corresponds to that used in the first embodiment. Nevertheless, this method induces inaccuracies on high frequencies and it is

it is preferable to use the principle described in 7.12.1., where M2rl, r2q, i, j corresponds to the measured quantity, which was denoted Cr1, r2 in 7.12.1. Other variants of this method will be described in 7.18.
Step 3 is thus performed as follows:

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i- Nprx Npix X, 2 Yc = 2 Zc = 1-xc -Yc n0 Kpo Kpo n" n" xe = IaqP>lk>PJk>P- N2rx ,7],,]]- Ze = 1-xe 2 -Ye xe- nOK , Ye- K ,ze - 1-xe -Ye no Kpo no Kpo VyZ YC2 - ZY. For each value of the indices q, i, j the program calculates: po = pq + pq

i-Nprx Npix X, 2 Yc = 2 Zc = 1-xc-Yc n0 Kpo Kpo n "n" xe = IaqP>lk>PJk> P-N2rx, 7] ,,]] - Ze = 1-xe 2 - Ye xe-OK, Ye-K, ze-1-xe-Ye no Kpo no Kpo VyZ YC2-ZY.

Les valeurs de sin q e cos q e sin q e cos q sont déterminées selon les tableaux d'affectation suivants:

Mce 0 autre M, 0 autre cosço, ~ Me Ye Mc 21 Mee (y2V^ ~ x@y@V^ + x@Vxy) sin ço, Me xe Mc 1 Mce e (~Xy@V + x2V +3'cvxyl ce autre Me 0 autre cosqe - Mc Ye Me 21 Mce (Yévyz-x'eYevxz'±xev.zyl sinqe 7t Me 1 Mce (-xeYevyz + xe Z vxz +Yexy) puis les coefficients sont calculés:

coef k, p, q, i, j 0,0 ~ - cos p COSq1e coef k, p,q,i, j0,1 ~ -sinpe cosrp V xz = -xeze e + zcx vxy = -xcYe + Ycxe Mc 2 = xc 2 + Yc Me 2 = xe 2 + Ye 2 2

The values of sin qe cos qe sin qe cos q are determined according to the following assignment tables:

Mce 0 other M, 0 other cosço, ~ Me Ye Mc 21 Mee (y2V ^ ~ x @ y @ V ^ + x @ Vxy) sin ço, Me xe Mc 1 Mce e (~ Xy @ V + x2V + 3'cvxyl this other Me 0 other cosqe - Mc Ye Me 21 Mce (Yevyz-x'eYevxz '± xev.zyl sinqe 7t Me 1 Mce (-xeYevyz + xe Z vxz + Yexy) then the coefficients are calculated:

coef k, p, q, i, j 0,0 ~ - cos p COSq1e coef k, p, q, i, j0,1 ~ -sinpe cosrp

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coef[k, p,q, i,j][l,O] = -COSq1e sin ço, coef[k,p,q,i,j][l,l] = -sinq1e sinq1e
Ces coefficients ne dépendent pas du résultat des prises d'images et dans le cas ou on répète toujours la même série ils peuvent être stockés dans un tableau plutôt que recalculés à chaque fois. C'est pourquoi on les a içi exprimé sous cette forme. Le programme utilise ensuite ces valeurs pour combiner les images obtenues avec les différentes positions des rotateurs de la manière suivante:

coef [k, p, q, i, j] [l, O] = -COSq1e sin ço, coef [k, p, q, i, j] [l, l] = -sinq1e sinq1e
These coefficients do not depend on the result of the taking of images and in the case where one repeats always the same series they can be stored in a table rather than recalculated each time. That is why they were expressed in this form. The program then uses these values to combine the images obtained with the different rotator positions as follows:

M2rl,r2q,i, j correspond à la grandeur mesurée, qui était notée Cr,r2 en 7.12.1 Mk,p,q [i,j] correspond à la grandeur qui était notée M en 7.12.1 Par ailleurs le programme calcule une amplitude de bruit:

Bk>P91>.I - attMlq,r,J Ce qui termine l'étape 3.

M2rl, r2q, i, j corresponds to the measured quantity, which was denoted Cr, r2 in 7.12.1 Mk, p, q [i, j] corresponds to the quantity which was denoted M in 7.12.1 Furthermore the program calculates a noise amplitude:

Bk>P91> .I - attMlq, r, J Which ends step 3.

. il - Npix remplaçées par - Jr #yremplacées par x,, # # # , ye = n 2- "0 0 nv nv
La procédure ci-dessus est celle qui permet le maximum de précision. Toutefois, en raison du nombre élevé d'images élémentaires requises, il peut être nécessaire d'utiliser une procédure plus rapide. Il est possible de ne pas utiliser les quatre images générées par la combinaison des indices r, , r2 ,comme dans le premier mode de réalisation dans lequel une seule image est générée. Il est également possible de ne pas utiliser l'atténuation de faisceau. La méthode la plus rapide consiste donc à n'utiliser que trois images élémentaires différant entre elles par leur phase. L'image de référence peut également être acquise seulement une fois sur dix (par exemple) de manière à limiter la perte de temps liée à son acquisition, et à condition que les vibrations ne soient pas trop importantes. L'image de référence peut être simplifiée de la même manière que l'image utile, mais cette simplification aura en général moins de conséquences sur la qualité des résultats. Il peut donc être utile de la simplifier d'avantage que l'image utile. When the program has calculated M k, p, q [1, j] and Bk, p, q ri, J] it also calculates H k, p, q [1, j] and BHk, p, q 1, j. This second calculation is done in the same way as the previous one, in three steps, but MOk, pc, d, r1, r2 q, i,, J], Mk, p, 9 [i, j) and Bk, p, 9 i, j are replaced respectively by MROk, pc, d, r1, r2q, i, j, Hk, p, qi, jet BI-Ik, p, q [i, it and in step 3 the assignments of x , and Ye are

. it - Npix replaced by - Jr # y replaced by x ,, # # #, ye = n 2- "0 0 nv nv
The above procedure is the one that allows maximum accuracy. However, because of the large number of basic images required, it may be necessary to use a faster procedure. It is possible not to use the four images generated by the combination of indices r 1, r 2, as in the first embodiment in which a single image is generated. It is also possible to not use beam attenuation. The fastest method is therefore to use only three elementary images differing in phase. The reference image can also be acquired only once in ten (for example) so as to limit the loss of time associated with its acquisition, and provided that the vibrations are not too great. The reference image can be simplified in the same way as the useful image, but this simplification will generally have less impact on the quality of the results. It may therefore be useful to simplify it further than the useful image.

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7. 13. Calculation of the order indices.

pixels (i, j) et à un capteur p des indices de commande virtuels (f, , y], Jdp,i, j tels que le mot de commande COMp,Idp,i, j,Jdp,i, j génère un éclairage éclairant un point aussi proche que possible du point de coordonnées (i,j) sur le capteur p. Ce tableau est généré par l'algorithme de la Fig.53. Dans cette algorithme, E(x) désigne l'entier le plus proche de x. Avant de lancer cet algorithme, le tableau D doit être initialisé à une valeur élevée, par exemple 100000. A l'issue de ce programme le tableau D contient pour chaque point la distance entre ce point et le point le plus proche obtenu pour le point d'impact direct

d'une onde d'éclairage. La double boucle de l'algorithme, (io,jo) et sur il, jl permet de définir des valeurs Id[p,i,j],Jd[p,i,j] y compris pour des points qui ne correspondent pas exactement au point d'impact du faisceau direct. The array of control indices is the table Id which allows to associate with coordinates in

pixels (i, j) and a sensor p virtual control indices (f,, y), Jdp, i, j such that the control word COMp, Idp, i, j, Jdp, i, j generates lighting illuminating a point as close as possible to the point of coordinates (i, j) on the sensor P. This array is generated by the algorithm of Fig. 5. In this algorithm, E (x) designates the nearest integer Before starting this algorithm, the array D must be initialized to a high value, for example 100000. At the end of this program, the table D contains for each point the distance between this point and the nearest point obtained. for the point of direct impact

a lighting wave. The double loop of the algorithm, (io, jo) and on it, jl makes it possible to define values Id [p, i, j], Jd [p, i, j] including for points which do not correspond exactly at the point of impact of the direct beam.

14k, p] = Jd[p,Jo[k], Jo[k]] et Jc[k, p] = Jd[p, Io[k], Jo[k]]
7. 14. Différence de marche induite sur les ondes issues de l'objet. A trajectory of the point of direct impact can be defined by the tables (I0 [k], Jo [k]) defining according to the index k the coordinates of the point of direct impact desired. For example if the trajectory is a circle of radius R pixels one can have: Io [k] = R cos R, J0 [k] = R sink / R for k ranging from 0 to 2 # R
The tables defining the control indices as a function of k and p are obtained from I0 [k] and Jo [k] by:

14k, p] = Jd [p, Jo [k], Jo [k]] and Jc [k, p] = Jd [p, Io [k], Jo [k]]
7. 14. Differential step induced on the waves coming from the object.

Fig. 54 illustrates the calculation of the difference in operation of a wave coming from a point 0 of the object with respect to the reference wave issuing virtually from a pointa of a medium of index nv (nominal index of the objectives ). We have: # = n0l0-nvlv A = nodo cosss-nvdv cosa with n0 sin ss = nv sina or finally:

xP , y p , z et la distance entre O et le bord de l'objet du coté du capteur/? est w p . Les vecteurs 1p, jp, p sont définis comme indiqué en 7. 7. On vérifie que conformément à l'orientation des axes sur la Fig. 55, les Fig. 55 illustrates the calculation of the difference in operation between a wave issuing from a point 0 of the object and the reference wave issuing virtually from the point A 0 where p is the index of the sensor considered. The coordinates of Appar relative to a reference centered in 0 and direction vectors #p, # p, # p are

xP, yp, z and the distance between O and the edge of the object on the side of the sensor /? is wp. The vectors 1p, jp, p are defined as indicated in 7. 7. It is verified that according to the orientation of the axes in FIG. 55, the

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Ta =-'lJo =-7l0 = -k1. Lorsque xp = yp = 0 on peut appliquer la formule précédente:

avec d0 = wp dv = wp - zp

1.2 1-2 sin a; = ### sinz =kp2 ou i,j sont des coordonnées en pixels prises à partir du centre optique du capteur. basic vectors of the marks used in each half-space identified by the sensor index p verify:

Ta = -Jo = -7l0 = -k1. When xp = yp = 0 we can apply the previous formula:

with d0 = wp dv = wp - zp

1.2 1-2 sin a; = ### sinz = kp2 where i, j are pixel coordinates taken from the optical center of the sensor.

et on obtient finalement pour la différence de marche totale:

En particulier on peut positionner le point 0 de manière à avoir

ou x,y,z sont les coordonnées déterminées en 7.11. On a alors:

Pour obtenir une représentation fréquentielle de l'objet, les représentations fréquentielles bidimensionnelles devront être corrigées pour compenser cette différence de marche. Dans cette expression, seules les valeurs de w n'ont pas encore été déterminées. If we also consider xp, yp we must add to this difference in the quantity:

and we finally get for the total walking difference:

In particular we can position the point 0 in order to have

or x, y, z are the coordinates determined in 7.11. We then have:

To obtain a frequency representation of the object, the two-dimensional frequency representations will have to be corrected to compensate for this difference of step. In this expression, only the values of w have not yet been determined.

7.15. Wp # calculation
7. 15.1. Principle:
To correct the two-dimensional frequency representations of the phase factor determined in 7. 14., it is necessary to determine previously the values wp, that is to say the only value w0 since w1 is deduced by w1 = L - wo.

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 If the average index of the object is close to the nominal index of objectives, the effect of wpsur value # p is negligible and we can for example adopt the value wp p = L 2 and position the sample between two objectives visually, adjusting this position later to obtain an image of the area of interest of this sample.

 It is also possible to add a reflective layer on the side of one of the slats which is in contact with the object, for example that which is located on the side of the objective (2217), on a small area. When the FRD beam and its inverse indicator are used alone and when the reflecting portion is positioned to reflect the RFD reverse indicator beam, then the interference pattern formed on the sensor (2239) must be a constant. The position of the sample must then be adjusted to actually obtain such a constant. When this adjustment has been made, we have w0 = z / 2.

If a sufficiently accurate positioner is used, the position of the sample can then be modified in the direction of the optical axis to obtain w0 = L / 2. The position of the sample must finally be modified in the direction orthogonal to the optical axis so that the reflective zone of the lamella is out of the field of view.

 However the two previous methods impose practical constraints that can be troublesome. One solution to avoid this difficulty is to make the determination of wp from measurements made on the sample in its final position.

 A frequency representation Fa can be obtained from the set of two-dimensional frequency representations from the sensor 0 (2239) when the point of direct impact of the illumination wave is on the same sensor, and travels on this sensor, for example, the trajectory shown in dashed lines. 56. This representation is obtained very similar to the method used in the first embodiment, with however the following differences: The two-dimensional frequency representation must be multiplied by the correction factor e-j2 # @ / # to cancel the phase shift produced by spherical aberration.

- the value of the coefficient K taken into account must be multiplied by a factor n0 to take into account nv the average index in the sample.

In order to limit the phenomena of folding of the correction function, the frequency representation is oversampled.

- When a point in the frequency space is obtained several times, the value used is one of the values obtained and not the average of the values obtained.

 In principle, the frequency representation thus obtained does not depend on the choice of the value chosen when a point in the frequency space is obtained several times. However, this is only true if the correction factor has a correct value.

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Fa[ni,nj,nk] = Fni,nj,nk\esç(-j27iG\ni,ni,nk\\v Lorsqu'un point de l'espace des fréquences est obtenu plusieurs fois, les valeurs Fsni,nj,nk et G[ ni, nj, nk] obtenues sont à chaque fois différentes. Pour chaque point, on définit Gmin[ ni, nj, nk] et Gmax[ ni, nj, nk], valeurs minimale et maximale obtenues pour G en ce point. Fsmin[ni, ni, nk] et 7M'x[,M/,] sont alors les valeurs obtenues pour F4ni, ni, nkl lorsque G[ ni, nj, nk] vaut respectivement Gmin[ni,nj,nk] et Gmax[ni,nj,nkl. -j2 ## w / @
Under these conditions, and taking into account the expression of the correction function e #, the value of the two-dimensional frequency representation Fa thus obtained, at a point in the space of the coordinate frequencies ni, nj, nk, can be write in the form:

Fa [ni, nj, nk] = Fni, nj, nk \ esc (-j27iG \ ni, ni, nk \\ v When a point in the frequency space is obtained several times, the values Fsni, nj, nk and G [ni, nj, nk] obtained are different each time For each point, we define Gmin [ni, nj, nk] and Gmax [ni, nj, nk], minimum and maximum values obtained for G at this point Fsmin [ni, ni, nk] and 7M'x [, M /,] are then the values obtained for F4ni, ni, nkl when G [ni, nj, nk] is respectively Gmin [ni, nj, nk] and Gmax [ni, nj, nkl.

The two frequency representations are then obtained: Famin [ni, nj, nk] = Fsminni, nj, nk exp_j2rGminni, nj, nkw p Famcrxm, n, nk = Fsmaxni, n, nk exp- j2rGmaxnr, n, nkw p
When the value of w0 is correct, these two representations are equal. The computation of w0 consists of minimizing the standard deviation between the two Famin and Famax frequency representations. The standard deviation to be minimized is in principle:

ou Btot[ni,nj,nk] est une amplitude de bruit définie en chaque point. However, since the noise is not constant over the whole of the frequency representation, each element of this sum must be weighted by the noise inverse at the point considered and we obtain:

or Btot [ni, nj, nk] is a noise amplitude defined at each point.

 By developing the expression of this standard deviation, a simplified expression is obtained which facilitates the minimization calculation.

7. 15. 2. Algorithm:
The calculation of wpse is done using a program whose algorithm is described Fig.57. This program must initially have the following information: - values established in 7.11: x, y, z, L, n0 - operating parameter wpixels, for example wpixels = 5.

 The essential steps of this program are the following: - (4001): image acquisition. A series of images is obtained by scanning at the point of direct impact of the illumination beam the trajectory shown in dashed lines in FIG. 56, or (3901) represents the

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programme calcule les indices de commande correspondants ldk, pl Jcf, p1. Le programme effectue alors l'acquisition de la série d'images selon la procédure indiquée en 7. 12. La procédure d'acquisition génère les

tableaux Mk, p,q [i, j . Toutefois, seuls les tableaux correspondant à des indices q,p nuls seront utilisés ici, soit Mk,0,0[i,j]. limit of the useful area of the sensor, (3902) represents the limit corresponding to the maximum opening of the objectives, (3903) represents a circular part of the trajectory and (3904) represents a rectilinear part of the trajectory. As indicated in 7. 13. we generate the folk paintings] Jo [k] according to this trajectory and the

program calculates the corresponding control indices ldk, pl Jcf, p1. The program then acquires the series of images according to the procedure indicated in 7. 12. The acquisition procedure generates the

tables Mk, p, q [i, j. However, only the tables corresponding to indices q, p void will be used here, ie Mk, 0,0 [i, j].

Etape 1.3.: une transformée de Fourier directe du tableau Msk est effectuée, ce qui termine la phase de suréchantillonnage. - (4002): calculation of Fsmin, Gmin, Fsmax, Gmax, Btot Step 1: Each table Mk, 0,0 [i, j] obtained during the acquisition phase is first oversampled as follows, in 3 steps: Step 1.1 .: the program performs the inverse two-dimensional Fourier transform of the table Mk, o, o Step 1.2 .: the program completes this array with zeros to obtain an Msk array of dimensions Nd x Nd (for example Nd = 512). Msk is initialized to 0 and then the program traverses the indices i, j of the table Mk, 0,0 by performing:

Step 1.3 .: a direct Fourier transform of the Msk array is performed, which completes the oversampling phase.

ou on note:

imaxk = tel Nd la[0,0, Ic[k,0], Jc[k,0] Npx li jmaxk = EC N Ja0,0, Ic[k,0], Jc[k,0]J y/Km-A. N pix ou E (x) l'entier le plus proche de x. Step 2: The elements of each Msk array are related to the value obtained at the point of direct impact of the illumination wave:

where we note:

imaxk = such Nd the [0,0, Ic [k, 0], Jc [k, 0] Npx li jmaxk = EC N Ja0,0, Ic [k, 0], Jc [k, 0] J y / Km -AT. N pix or E (x) the integer closest to x.

Step 3: When the program has thus generated the set of oversampled Msk tables it calculates an oversampled noise amplitude in the form of a set of tables of positive reals Bsk of dimensions Nd x Nd. For this purpose it goes through the indices i, j, k or i and / vary between 0 and Nd -1 by performing:

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Dans cette équation, lorsque le couple il, j1 est en dehors des limites du tableau Bk,0,0le coefficient Bk,0,0[i1,j1] est supposé égal à 0.

In this equation, when the pair il, j1 is outside the limits of the table Bk, 0.0the coefficient Bk, 0,0 [i1, j1] is assumed equal to 0.

Step 4: The program initializes the tables Fsmin, Fsmax at 0, it initialises the tables Gmin and Gmax respectively at 1020 and -1020, and sets the tables Bmin, Bmax at 1020. These tables each have dimensions of 2 Nd x 2 Nd x 2 Nd.

nJ = 1 Imaxk + Nd

Les valeurs m,nj,nk correspondent à des coordonnées dans un espace tridimensionnel de fréquences comme dans le premier mode de réalisation. Leur calcul menant à des valeurs non entières, on leur affecte l'entier le plus proche de la valeur obtenue. La valeur de K doit être corrigée pour tenir compte de l'indice de l'échantillon et on utilise donc n0 K0. Le coefficientr permet la prise en compte du suréchantillonnage. nv étape 4.2. : calcul des valeurs de G et Fs au point courant:

The program then traverses the indices i, j, k or i and j vary from 0 to Nd-1 by performing for each triplet (i, j, k) the following steps, numbered from 4.1 to 4.3: step 4. 1 .: calculation of the indices of the three-dimensional frequency representation. The program does the following: ni = i - imaxk + Nd

nJ = 1 Imaxk + Nd

The values m, nj, nk correspond to coordinates in a three-dimensional space of frequencies as in the first embodiment. Since their calculation leads to non-integer values, we assign them the integer closest to the value obtained. The value of K must be corrected to take into account the index of the sample and so we use n0 K0. The coefficientr allows the taking into account of the oversampling. Step 4.2. : calculation of the values of G and Fs at the current point:

avec: i.c=i.-Nd , j-c=j.- Nd , 1-Mc = 1.maxk -Nd z avec: !c = i - ##, jc = j - d , imc imaxk - d , c jmaxk - Dans les équations ci-dessus, ic,jc,imc,jmc correspondent à des coordonnées ramenées au centre optique et r a la même valeur que dans l'étape précédente.

with: ic = i.-Nd, jc = j.- Nd, 1-Mc = 1.maxk -Nd z with:! c = i - ##, jc = j - d, imc imaxk - d, c jmaxk - In the equations above, ic, jc, imc, jmc correspond to coordinates brought back to the optical center and ra the same value as in the previous step.

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Si Gval S; Gmin[ni, nj, nk] le programme effectue: Gmin[ni,nj,nk] = Gval Fsmin[ni,nj,nk] = Fsval

Bmin[ni,nj,nk] = Bsk [i, il Si Gva/GMc[M/,M/,MA:1 le programme effectue: G/Km'[M!,n/',MA'1 = Gval Fsma4ni,nj,nkl = Fsval Bmaxni, nj, nk = Bsk i, j Etape 5: Le programme génère une amplitude globale de bruit. A cet effet il parcourt les indices ni,nj,nk en effectuant pour chacun de ces triplets l'opération

(4003) : La fonction calculée est en principe égale à:

ou Es est l'ensemble des points en lesquels les valeurs de Gmin et Gmax diffèrent, soit:

Es tK:,M/,MGMtU:fM/,M/,K1 Gminnt,nj,nk} Soit en développant l'expression:

La première partie de l'expression ne dépend pas de w0. Minimiser l'écart-type revient donc à maximiser la fonction suivante ou ReO désigne la partie réelle:

Toutefois cette fonction présente des fréquences élevées causant des repliements de spectre qui perturbent la convergence de l'algorithme. Ceux-ci sont supprimés en utilisant la fonction: step 4.3 .: possible modification of the values of Gmin, Fsmin, Gmax, Fsmax.
The program tests the value of Gval.

If Gval S; Gmin [ni, nj, nk] the program performs: Gmin [ni, nj, nk] = Gval Fsmin [ni, nj, nk] = Fsval

Bmin [ni, nj, nk] = Bsk [i, it If Gva / GMc [M /, M /, MA: 1 the program performs: G / Km '[M1, n /', MA'1 = Gval Fsma4ni , nj, nkl = Fsval Bmaxni, nj, nk = Bsk i, j Step 5: The program generates an overall amplitude of noise. For this purpose it goes through the indices ni, nj, nk by performing for each of these triplets the operation

(4003): The calculated function is in principle equal to:

where Es is the set of points in which the values of Gmin and Gmax differ, namely:

Es tK:, M /, MGMtU: fM /, M /, K1 Gminnt, nj, nk} Either by developing the expression:

The first part of the expression does not depend on w0. Minimizing the standard deviation therefore amounts to maximizing the following function or ReO denotes the real part:

However, this function has high frequencies causing spectrum folds that disturb the convergence of the algorithm. These are removed using the function:

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(4004) : l'algorithme itère la boucle sur wlargjusqu'à ce qu'une précision suffisante soit atteinte. Par exemple on peut avoir lim =#/8 wpixels

(4005): La valeur w f affichée correspond à wo . On a: W) = L -w f et Wo = w f La valeur rapport affichée correspond à:

(4004): the algorithm iterates the loop on wlarg until sufficient precision is reached. For example we can have lim = # / 8 wpixels

(4005): The wf value displayed is wo. We have: W) = L -wf and Wo = wf The displayed report value corresponds to:

The displayed ratio value characterizes the quality of the overlap obtained between the images calculated from the Famin and Famax frequency representations. The closer it is to 1 better this crossover is. When the sample is out of the observation zone, this value is close to 0.

7. 15.3. focus
The focus setting is to correctly position the sample in the target viewing area. In this setting, the ratio values and wf must be recalculated continuously. The position of the sample must be adjusted along the axis (2263) so as to obtain a sufficiently high ratio value, then it can be adjusted more finely so as to obtain, for example
L wf = -.

2
This setting usually allows a first focus. However, if for example the index n0 is close to nv, this focus is very imprecise.

 In all cases, this adjustment must be completed by a more precise focus on the area of interest, as indicated in 7.17.3.

 7. 16. Obtaining the aberration compensation function.

-j2 ## / @
The function e # allowing in principle to correct the phase shifts introduced by the object and corresponding to the spherical aberration comprises high frequencies which are filtered by the diaphragm.

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It can not therefore be used directly and it is necessary to filter it to obtain in the form of an array of dimensions Npix x Npix a usable correction function.

le tableau Dsp correspond à la fonction e -j2##/# échantillonnée avec un pas suffisamment fin pour éviter le repliement de spectre. The aberration compensation function, which will be used in the imaging phase, is obtained in the following way: Step 1: generation of the Dspde tables dimension Ne x Ne with for example Ne = 4096:

the array Dsp corresponds to the function e -j2 ## / # sampled with a sufficiently fine pitch to avoid the aliasing of the spectrum.

pour tous les couples (ij) tels que

ou ouv est l'ouverture des objectifs. Step 2: inverse Fourier transformation of Tables Dsp 1 ,, 'Step 3: Extraction of the central part of the array, of Npix x Npix dimensions with simulation of the diaphragm. The program performs:

for all couples (ij) such as

where open is the opening of the objectives.

Step 4: Fourier transformation of the Dp array.

Then, in the form of Table D, the usable correction function is obtained.

 7. 17. Realization of three-dimensional images.

7. 17.1. principle
7. 17.1.1. Superposition of frequency representations.

 We have seen that for a given lighting beam (index k, p) we obtain two two-dimensional images corresponding to the two sensors and marked by the index q. When the trajectory of FIG. 56 on the sensor number 0, one can generate from the two-dimensional images obtained on the two sensors a frequency representation. Fig. 58 shows how a set of two-dimensional frequency representations generates a three-dimensional representation. A two-dimensional representation is composed of a sphere portion (4101) obtained on the sensor number 0 and a sphere portion (4102) obtained on the sensor number 1. When the point of direct impact moves on a transverse trajectory (3904) the movement of these portions of

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 spheres generates a volume. In Figure 58, there is shown a set of such portions of spheres, obtained for various positions of the point of direct impact on a transverse path. When the point of direct impact moves on the circle (3903) the volume (4104) delimited by (4105) is generated in addition.

When the direct impact point is on sensor number 1, a symmetrical volume is generated.

We distinguish four partial three-dimensional frequency representations that we will note
Fp, q where the pair (p, q) designates a pair (sensor receiving the direct light wave, a sensor whose two-dimensional representations make it possible to generate Fp, q are output) with p = 0 for the sensor (2239), p = 1 for (2229), q = 0 when it designates the same sensor asp and q = 1 when it designates the opposite sensor. The final three-dimensional representation is obtained by superposition of these partial three-dimensional representations.

 The complete frequency representation obtained is represented in section in Fig.59 It is composed of: - a part (4111) obtained by the sensor 0 or 1 receiving the point of direct impact of the beam, and corresponding to the representations F0,0and F1,0 that occupy the same part of the frequency space.

a part (4113) obtained by the sensor 1 when the point of direct impact of the beam is on the sensor 0, and thus corresponding to the representation F0,1.

a part (4112) obtained by the sensor 0 when the point of direct impact of the beam is on the sensor 1, and thus corresponding to the representation F1,1.

 To obtain exactly this volume it is necessary in principle to cover all the possible frequency values, ie Npix x Npix values on each sensor, minus the values being outside the zone limited by the opening of the objective. . Nevertheless, using the reduced trajectory of FIG. 56 we obtain a volume little different from that drawn.

 The trajectory of Fig. 56, however, is a simple example and various types of trajectory can be used in practice. Some examples are given below: A circle as in the first embodiment.

- The trajectory of FIG. 56, which allows to obtain better definition images.

- The trajectory of FIG. 56 made less dense. For example, one pixel out of two can be used along this path. This has the effect of limiting the thickness of the samples that can be observed under good conditions.

- A complete trajectory, that is to say defined by the tables I0 [k] and Jo [k] such that the point of coordinates (Io [k], Jo [k]) travels the whole of the disk limited by the opening of the lens. This means that each pixel included in the disk bounded by the circle (3902) of Fig. 56 must be reached once and only once. This trajectory brings only a slight improvement in the definition compared to that of FIG. 56 and significantly increases the acquisition time. On the other hand, the normal conditions of use of this microscope require that the diffracted beam remains of low intensity relative to the

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 lighting beam. The use of a complete trajectory makes the system more robust when one does not respect these conditions of use.

7. 17.1.2. Reference of uhase and intensity
In order to be able to combine the two-dimensional frequency representations to obtain partial three-dimensional frequency representations, it is necessary to establish a common reference of phase and intensity.

the complex values of the waves received on the directly illuminated sensor may be related to the value of the illumination wave at its point of direct impact, as in the first embodiment or in the calculation of w p.

- A more elaborate method is necessary for the waves received on the opposite sensor. The reference lights are used to establish a characteristic ratio of the phase variation on each sensor and this ratio is taken into account to cancel these variations before referring to the value of the lighting wave at its point of impact. direct. This makes it possible to render coherent all the two-dimensional representations corresponding to a pair p, qdonné, independently of the vibrations affecting the system, and thus to establish for each pair p, q a three-dimensional frequency representation.

 However, this does not make it possible to establish the phase relation between each of these three-dimensional frequency representations, which it is necessary to know to combine them into a single frequency representation. The phase relation between, for example, the three-dimensional frequency representations Fo, o and F0, which respectively correspond to the parts (4111) and (4113) of the three-dimensional representation of the set, can be established when these two parts have a common area (4114). It suffices to choose the phase difference that makes these two representations coincide on their common area. For there to be a common zone it is necessary that the opening of the objective is sufficient. The condition of existence of this common area is: no <2 / # 3 open or open is # 3 the opening of the objective. For example, for an aperture of 1.25, a maximum index of the sample of n0 = 1.44 is obtained.

 7. 17.1.2. Phase shift between two noisy tables.

x, et qui vaudrait en l'abscence de bruit x(sansbrUlt) - ## . A#i# Consider two two-dimensional arraysA [i] and B [i] where i varies from 0 to N-1. The elements of A (resp.B) are each affected by an independent Gaussian noise whose standard deviation is contained in an array GA [i] (or GB [i]). These tables, 4 and B being assumed equal to a constant ratio of phase and intensity and close to the noise, we seek to determine this ratio of phase and intensity, which we will note
B [i]

x, and which would be worth in the absence of noise x (sansbrUlt) - ##. Have#

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Dans les cas qui nous intéresseront par la suite #x# est toujours proche de 1. On a donc:

Maximiser cette quantité revient à minimiser la quantité:

The value sought for x is that which maximizes the quantity (px # A, B), representing the probability of a value of x knowing the arrays A and B. Maximizing this quantity amounts to maximizing p (B # A, x). For a given value of x, the law giving B [i] from A [it is composed of two Gaussian laws of respective standard deviations # x # GA [i] and GB [i]. So it's a Gaussian standard deviation law

In the cases that will interest us afterwards # x # is always close to 1. We have:

Maximizing this amount amounts to minimizing the amount:

qui vaut, après division par fa,oteur Ai indépendant qui vaut, après division par le facteur 1:[1 ]12 indépendant de x: (GA[il)2 +(GB[i])2

On vérifie que cette quantité est égale à:

La solution minimisant cette quantité est donc:

which is, after division by means of F, independent factor Ai which, after division by the factor 1, is equal to: [1] 12 independent of x: (GA [il] 2 + (GB [i]) 2

We check that this quantity is equal to:

The solution minimizing this quantity is therefore:

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 This result will be frequently used later, generalized to 2 or 3 dimensions, to determine the phase difference between two partially overlapping frequency representations.

* 7. 17.1.3. Combination of a series of noisy elements.

grandeur qui maximise PxI A . Maximiser cette quantité revient à maximiser 64|x) Or on a:

Maximiser cette quantité revient à minimiser la quantité suivante:

Qui vaut. après division par la quantité # 1 indépendante de x: i (GA[i])2

On vérifie que cette quantité est égale à:

La solution x qui la minimise est donc:

Le bruit sur x est alors donné par l'addition en valeur quadratique des bruits sur chaque A[i]:

One-dimensional arrays A [i] where i varies from 0 to N-1 are considered. The elements of A are each assigned by an independent Gaussian noise whose standard deviation is contained in an array GA [i]. In the absence of noise the elements of A are all equal to a value x that we want to determine. x is the

magnitude that maximizes PxI A. Maximizing this amount amounts to maximizing 64 | x) Or we have:

Maximizing this amount amounts to minimizing the following quantity:

Which is worth. after division by the quantity # 1 independent of x: i (GA [i]) 2

We check that this quantity is equal to:

The solution x which minimizes it is therefore:

The noise on x is then given by the quadratic addition of the noise on each A [i]:

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cri = i (GA[i])2 On fera également usage de ce résultat, pour déterminer une représentation fréquentielle à partir de plusieurs représentations partielles se recoupant en certains points. We check that this equates to: 1 / @ 2 = 1

cry = i (GA [i]) 2 This result will also be used to determine a frequency representation from several partial representations intersecting at certain points.

 7. 17.2 algorithm.

 A series of images is first acquired as indicated in 7. 12., the point of direct impact of the light beam traversing on each sensor a trajectory defined as indicated in 7.17.1.1. To simplify the presentation, we separate here the acquisition phase and the calculation phase. However, the three-dimensional frequency representations Fp, q can also be generated as the acquisition progresses.

For example, if a complete trajectory is used, the separation of the acquisition and calculation phases requires a very important memory and it is therefore preferable to perform the calculation as the acquisition progresses.

BHk, p,q [i, j] indicateur de bruit de l'image de référence k indiciant la prise de vue, p le capteur éclairé par le faisceau direct, q indiquant : q=0: capteur éclairé par le faisceau direct q=1: capteur opposé. The acquisition phase generates the following tables: Mk, p, q [i, j], corresponding to the principal shooting Bk, p, q [i, j] noise indicator Hk, p, q [i, j ] reference shooting for the k-th acquisition,

BHk, p, q [i, j] noise indicator of the reference image k indicating the shooting, p the sensor illuminated by the direct beam, q indicating: q = 0: sensor illuminated by the direct beam q = 1: opposite sensor.

imaxk, p,q = /a7, <?, /c[, /?], Vc), ]] .lmkP,9 = [, , 7c, p], .7c[, ]j
A partir de cet ensemble de données un programme génère une représentation tridimensionnelle spatiale de l'objet étudié. Ce programme comporte les étapes suivantes: Etape 1. Cette étape consiste à calculer le rapport caractéristique du décalage de phase et d'amplitude dû aux vibrations et aux fluctuations d'intensité du laser, entre une prise de vue de référence d'indice k=0 et la prise de vue de référence courante d'indice k. Ce décalage est caractérisé par les variations de la fonction
Hk,p,q[i,j] qui en l'abscence de vibrations devrait être constante. Pour tous les triplets (k,p,q) le programme calcule donc le rapport: The series of control indices used being defined by the tables Ic and Jc, the program also generates the series of coordinates of the points of direct and inverted impact of the light beams.

imaxk, p, q = / a7, <?, / c [, /?], Vc),]] .lmkP, 9 = [,, 7c, p], .7c [,] j
From this set of data a program generates a spatial three-dimensional representation of the object under study. This program consists of the following steps: Step 1. This step consists in calculating the characteristic ratio of phase shift and amplitude due to vibrations and intensity fluctuations of the laser, between an index reference shot k = 0 and the current reference shot of index k. This shift is characterized by variations in the function
Hk, p, q [i, j] which in the absence of vibrations should be constant. For all triplets (k, p, q) the program therefore calculates the ratio:

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Etape 2 : cette étape consiste à effectuer l'opération consistant à: - normaliser chaque représentation bidimensionnelle pour compenser les variations de décalages de phase et d'amplitude dûs aux vibrations, caractérisés par la quantité Rk,p,q - compenser l'aberration sphérique et le mauvais positionnement relatif des objectifs, caractérisés par Dp#+#q [i,j] - se ramener à la valeur de l'onde d'éclairage en son point d'impact direct.

Step 2: this step consists in performing the operation of: - normalizing each two-dimensional representation to compensate for the variations of phase and amplitude shifts due to the vibrations, characterized by the quantity Rk, p, q - to compensate for spherical aberration and the relative poor positioning of the objectives, characterized by Dp # + # q [i, j] - to be reduced to the value of the illumination wave at its point of direct impact.

The program thus traverses the indices k, p, q, i, j by performing:

The use of the Table Dp, which is the result of steps 7.11, 7. 15. and 7.16., Makes it possible to significantly improve the results when the average index of the object differs from the nominal index of the objectives. However, it is also possible not to perform steps 7.11, 7.15. and 7.16. The target position setting described in 7.10 must then be performed to obtain a centered and point spatial image.

Table D must then be set to 1.

 The use of the values Rk, p, q makes it possible to compensate for any vibrations of the optical table.

However, if the optical table is perfectly stable, this compensation is not necessary. The values Rk, p, q must then be set to 1.

bruit gaussien affectant chaque élément du tableau F p@q . Ces tableaux sont de dimensions 2 N pix x2N pix x 2 Npix.Chaque point d'une représentation fréquentielle bidimensionnelle correspond à un point de la représentation fréquentielle tridimensionnelle Fp,q, dont les coordonnées doivent être déterminées. Step 3: This step consists of calculating for each pair (p, q) a three-dimensional frequency representation Fp, q, accompanied by a table IBp, qde real, containing the inverse of the square of the standard deviation of

Gaussian noise affecting each element of the array F p @ q. These arrays are of 2 N pix x 2 N pix x 2 Npix dimensions. Each point of a two-dimensional frequency representation corresponds to a point of the three-dimensional frequency representation F p, q, whose coordinates must be determined.

When a point is obtained more than once, the most probable value is determined.

 The program initializes the arrays Fp, q, IBp, q to zero then traverses the set of indices p, q, k, i, j by carrying out for each quintuplet (p, q, k, i, j) the following operations, numbered from 1 to 3: operation 1: calculation of the indices of the three-dimensional frequency representation. The program performs:

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2Kp
La valeur de K devient alors commune aux deux capteurs et vaut Ka +K1/2. Elle doit être corrigée pour tenir compte de l'indice de l'échantillon et on obtient donc Km = n0 K0 + K1/@. nv 2 opération 2: modification des indices de la représentation fréquentielle tridimensionnelle dans le cas q=1.

A distance of one pixel, measured on the sensor p, corresponds to a real frequency deviation proportional to 1 / Kp. The pixels therefore do not represent the same frequency differences on the two
Kp sensors. It is reduced to a common unit and proportional to the frequency deviations by multiplying the distances obtained on the sensor p by the coefficient ap = K0 + K1 / 2Kp.

2KP
The value of K then becomes common to both sensors and is Ka + K1 / 2. It must be corrected to take into account the index of the sample and we thus obtain Km = n0 K0 + K1 / @. nv 2 operation 2: modification of the indices of the three-dimensional frequency representation in the case q = 1.

Le calcul des indices ni,nj,nk menant à des valeurs non entières, on leur affecte l'entier le plus proche de la valeur calculée. opération 3 : modification des éléments de tableaux. If = 1, the frequency corresponding to the coordinates </ M #, jmaxkpq is not the zero frequency. Indeed one has at this point, by taking again the notations used in 5.3. : f ~ - fe and therefore / t = / e "/ e = -2 fe The frequency obtained by the preceding method must be translated from a vector -2fe which results in the following additional operations, performed only in the case q = 1: ni + = 2apimaxk, p, 1 ni + = 2ap jmaxk, p, 1

The computation of the indices ni, nj, nk leading to non-integer values, we assign them the integer closest to the computed value. operation 3: Modify table elements.

The modified indices having been generated, the program modifies the elements of tables:

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programme parcourt donc les indices p,q,ni,nj,nk en effectuant, à chaque fois que IBp,q [m, nj, nk] 1= 0 . l'opération :

Etape 5: Les repères dans lesquels ont été évalués les indices i,j et donc ni,nj,nk sont inversés entre les deux capteurs. Il est donc nécessaire d'effectuer un changement de repère des représentations correspondant au capteur indicé 1 pour les exprimer dans le même repère que les représentations correspondant au capteur

indicé 0. Le programme effectue donc le changement de variables ni z 2 N p, - ni , nj 2 N p, - nj , nk -> 2Npix - nk dans les tableaux correspondant au capteur indicé 1 afin d'exprimer l'ensemble des fréquences dans le même repère. Les tableaux correspondant à une représentation fréquentielle issue du capteur 1 ont un indice p égal à 1 ou 0 et un indice q égal à #. Step 4: It remains an operation to carry out to obtain the most probable value on each frequency. The

The program thus traverses the indices p, q, ni, nj, nk by performing, each time that IBp, q [m, nj, nk] 1 = 0. the operation:

Step 5: The marks in which the indices i, j and therefore ni, nj, nk have been evaluated are inverted between the two sensors. It is therefore necessary to make a reference change of the representations corresponding to the sensor indexed 1 to express them in the same frame as the representations corresponding to the sensor

indexed 0. The program thus performs the change of variables ni z 2 N p, - n, nj 2 N p, - nj, nk -> 2Npix - nk in the tables corresponding to the sensor indexed 1 in order to express all the frequencies in the same frame. The tables corresponding to a frequency representation from the sensor 1 have an index p equal to 1 or 0 and an index q equal to #.

Etape 6: Le programme calcule le rapport caractéristique du décalage de phase et d'amplitude entre l'onde reçue sur le capteur éclairé directement et celle reçue sur le capteur non éclairé. Il parcourt donc les indices p=0, p=1en effectuant :

Dans cette expression les sommes sont restreintes à un ensemble E constitué des triplets

(ni, nj, nk) vérifiant 76 [ni, nj, nk]IBP,l [ni, nj, nk] # 0 Etape 7 : Le programme modifie les représentations tridimensionnelles obtenues à partir de capteurs non éclairés directement. Il parcourt les indices p, ni,nj,nk en effectuant:

Fp,l [ni, nj, nkl = Fp.I [ni, nl, nkl. Rb To make these changes of variable the program traverses the set of indices p, m, nj, nk by carrying out:

Step 6: The program calculates the characteristic ratio of phase shift and amplitude between the wave received on the illuminated sensor directly and that received on the unlit sensor. It thus traverses the indices p = 0, p = 1 by performing:

In this expression the sums are restricted to a set E consisting of triplets

(ni, nj, nk) satisfying 76 [ni, nj, nk] IBP, l [ni, nj, nk] # 0 Step 7: The program modifies the three-dimensional representations obtained from non-illuminated sensors directly. It goes through the indices p, ni, nj, nk by performing:

Fp, l [nl, nj, nkl = Fp.I [nl, nl, nkl. Rb

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LIBp,q[ni,nj,nk] *0 p, q Lorsque la condition est réalisée il effectue:

Etape 9 : Le programme effectue une transformation de Fourier tridimensionnelle inverse de la représentation fréquentielle ainsi obtenue pour obtenir une représentation spatiale. Step 8: The program calculates the final frequency representation, contained in an array F of dimensions 2Npix x Npix x 2 Npix - It initializes to 0 this array then traverses the indices ni, nj, nk by testing the condition:

LIBp, q [ni, nj, nk] * 0 p, q When the condition is realized it performs:

Step 9: The program performs a three-dimensional Fourier transformation inverse of the frequency representation thus obtained to obtain a spatial representation.

Step 10: As in the first embodiment, the program can then view the representation thus obtained in the form of sections or possibly stereoscopic projections.

7. 17.3. focus
The algorithm described in 7.17.2. allows obtaining three-dimensional representations of the sample. The focus adjustment is to adjust the position of the object such that these representations are those of an area of interest of the sample. This can be done by the operator who moves the sample while observing for example a plane projection or a section of this three-dimensional representation, and moves the object to obtain an image of the area of interest. If a displacement of the sample in the direction of the optical axis is made, this one modifies the values of wp, and the procedure described in 7.15.2. must be reiterated to obtain a correct value of wp.

 7. 18. Variants.

 The algorithms used in the present embodiment admit numerous variants, some of which are explained below.

l'ensemble des valeurs de k,p, imaxk,p,o, jmaxx,p,o

Cette valeur peut être introduite dans la formule utilisée à l'étape 2, qui est donc remplaçée par :

7. 18.1. Using the preset values of the direct light beam
This variant consists of modifying step 2 of the algorithm described in 7.17.2. to use the pre-recorded values of direct lighting. We have indeed, at a phase factor close that is constant on

the set of values of k, p, imaxk, p, o, jmaxx, p, o

This value can be entered in the formula used in step 2, which is replaced by:

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Rb[p, 14k, p], Jc[k, p]] est en principe égal à la fonction obtenue en 7.7. :

cette fonction étant toutefois filtrée par le diaphragme. Il est donc possible de remplacer

Rb\p, Ick, p\ Jc[k, /?]] par RBp\imaxkp0,jmaxkp()] ou la fonction RBp[i,j] est obtenue de la manière suivante (cette méthode d'obtention est similaire à celle utilisée pour Dp[i,j] en 7. 16.) Etape 1: génération des tableaux RBp de dimensions Ne x Ne avec par exemple Ne =4096:

Etape 2: transformation de Fourier inverse des tableaux RB Etape 3 : extraction de la partie centrale du tableau, de dimensions Npix x Npix avec simulation du diaphragme. Le programme effectue:

pour tous les couples (i,j) tels que

ou ouv est l'ouverture des objectifs. 7. 18.2. Using pre-calculated values of the direct light beam

Rb [p, 14k, p], Jc [k, p]] is in principle equal to the function obtained in 7.7. :

however, this function is filtered by the diaphragm. It is therefore possible to replace

Rb \ p, Ick, p \ Jc [k, /?]] By RBp \ imaxkp0, jmaxkp ()] or the function RBp [i, j] is obtained in the following manner (this method of obtaining is similar to that used for Dp [i, j] in 7. 16.) Step 1: Generation of RBp arrays of dimensions Ne x Ne with for example Ne = 4096:

Step 2: inverse Fourier transformation of the RB arrays Step 3: extraction of the central part of the array, of Npix x Npix dimensions with diaphragm simulation. The program performs:

for all couples (i, j) such as

where open is the opening of the objectives.

Step 4: Fourier transformation of the RBp array.

Ce remplacement est équivalent à un lissage de la fonction définie par le tableau Rb et peut dans certains cas améliorer les résultats, en particulier si l'onde diffractée est forte, sortant des conditions d'utilisation normales de ce microscope. Dans ce cas on combinera cette formule avec l'utilisation d'une trajectoire complète comme définie en 7.17.1.1. The function equivalent to the Rb array is then obtained in the form of the array RBp. Step 2 of the algorithm described in 7. 17.2. is then replaced by:

This replacement is equivalent to a smoothing of the function defined by Table Rb and may in some cases improve the results, especially if the diffracted wave is strong, coming out of the normal conditions of use of this microscope. In this case we will combine this formula with the use of a complete trajectory as defined in 7.17.1.1.

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7. 18.3. Obtaining confocal representations
A confocal microscope makes it possible to obtain three-dimensional spatial representations, which will be called confocal representations. The present microscope makes it possible to obtain a confocal representation strictly equivalent to that which would be obtained using a confocal microscope.

 In fact, the illumination wave used by a confocal microscope is the sum of the plane waves used in the case where a complete trajectory is used for the acquisition, each plane wave having to be assigned a phase depending on the illuminated point. The wave equivalent to the wave received by a confocal microscope of the same aperture as the present microscope, when the central point is illuminated, can therefore be generated by summing the two-dimensional representations of diffracted waves obtained for all the waves. lighting forming a complete trajectory.

 It can be shown that the confocal representation of the object is the inverse Fourier transform of a three-dimensional frequency representation obtained by summing the two-dimensional partial frequency representations obtained from each light wave, the whole of the light waves traversing a complete trajectory.

 In addition, a confocal microscope acquires images on only one lens and illuminates the sample only on one side. In addition, it generates a value that is the intensity of the wave that passed through the object and not its complex value. The confocal representation in intensity is thus obtained from the waves received by a single objective, and by extracting the square of the module from the previously obtained confocal representation. Finally, the confocal microscope does not correct the spherical aberration due to the index of the object.

ou les tableaux Dppeuvent être mis à 1 si on ne souhaite pas corriger l'aberration sphérique et ou RBp est défini comme en 7.17.3.2.

(2)- l'opération 3 de l'étape 3 est remplacée par Fa,, ni, nj, nk+ = Mk, p,9 [/, /] (3)- les étapes 4,5,6,7 ne sont pas effectuées.

(4)- l'étape 8 est remplaçée par F[ni,nj,nk] = Fpo,qo ni, nj, nk ou le choix des indices (po, qo) dépend du type de représentation confocale que l'on cherche à générer. A confocal representation can thus be obtained by the present microscope, using for the acquisition a complete trajectory as defined in 7.17.1.1. and by modifying the procedure described in paragraph 17. 2. as follows: (1) Step 2 is modified as follows:

or the arrays D can be set to 1 if it is not desired to correct the spherical aberration and where RBp is defined as in 7.17.3.2.

(2) - operation 3 of step 3 is replaced by Fa ,, ni, nj, nk + = Mk, p, 9 [/, /] (3) - steps 4,5,6,7 are not not done.

(4) - step 8 is replaced by F [ni, nj, nk] = Fpo, qo ni, nj, nk or the choice of indices (po, qo) depends on the type of confocal representation that one seeks to generate.

if (po, qo) = (0,0) or (po, qo) = (1,0), a representation corresponding to that which would be obtained by a reflection confocal microscope is generated.

- if (polo) = (0,1) or (polo) = (1,1) one generates a representation corresponding to that which would be obtained by a confocal microscope by transmission.

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(5) - the square of the spatial representation module obtained at the end of step 9 then corresponds to the confocal representation in intensity.

 Replacing the calculation of the most probable value of the frequency representation at each point has the consequence of an overvaluation of the low frequencies with respect to the high frequencies, which is equivalent to a filtering of the high frequencies and thus to a loss of definition.

 It is also possible to obtain a confocal representation from the three-dimensional frequency representation obtained in accordance with the unmodified paragraph 17: indeed, the three-dimensional representation of the object constitutes the most complete information possible that can be obtained with objectives of given aperture and can be used to simulate any type of image that could be generated from any type of microscope using the same lens and wavelength.

 However, using a complete path makes the system more robust, as described in 7.17.1.1. If a confocal representation is obtained using a trajectory like that of Fig. 56, it will be disturbed in the case where a large part of the illumination wave is diffracted, and more importantly than the confocal representation obtained at using a confocal microscope or using a full trajectory. It can not be considered as strictly equivalent to that generated by a confocal microscope.

 7. 18.4. Realization of three-dimensional images with control of the reference wave.

 In the methods described above, the phase shifter (2205) is controlled to generate phase shifts #d of the illumination wave dependent on the index d according to the table indicated in 7.12.2.1.

 To achieve the present variant, this discrete phase shifting device must be replaced by a device allowing a continuous phase shift. Such a device may be a liquid crystal device placed between two polarizers, marketed for example by the company Newport. By means of a modification of the trajectory of the beam, this device can also be a piezoelectric mirror as in the first embodiment.

phase par décalage phase Arg Ra 7c, 1, Jc[, p]]Rb\p, Idk, 1, Jc[k, ] phase Od par un décalage de phase 0 -Od - -Arg(Ra[p,IC[k,P], Jc[k, R p]]Rb[p, lc[k,p], Jc[k, P]]) ou Arg Rk,p,0 désigne l'argument d'un nombre complexe. Ceci permet d'annuler la phase de l'onde d'éclairage en son point d'impact direct et rend non nécessaire la compensation de cette phase. Pendant la phase de calcul décrite en 7. 17.2., dans l'étape 2, la formule utilisée peut alors être remplacée par:

The present variant consists, during the image acquisition provided for in 7.17.2. and performed as in 7.12.2.1., controlling the phase shift device to replace the offset of

phase shift phase Arg Ra 7c, 1, Jc [, p]] Rb \ p, Idk, 1, Jc [k,] phase Od by a phase shift 0 -Od - -Arg (Ra [p, IC [k , P], Jc [k, Rp]] Rb [p, lc [k, p], Jc [k, P]]) or Arg Rk, p, 0 denotes the argument of a complex number. This makes it possible to cancel the phase of the illumination wave at its point of direct impact and makes the compensation of this phase unnecessary. During the calculation phase described in 7. 17.2., In step 2, the formula used can then be replaced by:

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 This mode amounts to controlling the phase shift of the light beams by the phase shift device instead of compensating for it by calculation after the acquisition.

 7. 18.5. Obtaining frequency representations without calculating the received wave on the receiving surface.

If the optical table is of sufficient quality to suppress the vibrations, the formula used in 7.18.4. becomes:

To simplify the explanation, it can be assumed that the beam attenuator and the polarization rotators are not used. It is then verified that each frequency representation Fp, q obtained in the procedure described in 7.17. can express itself in the form:

ou Fp.q,d [ni, nJ, nk] est obtenu comme Fp,q dans la procédure 7.17. non modifiée, mais en remplaçant Mk, p,9 [i, j] par la valeur réelle MO[k, pu[0, d,0,0[q, /, y] obtenue dans la procédure décrite en 7.12. pour une valeur correspondante de l'indice d indiçant le décalage de phase. Il est donc possible de calculer pour chaque indice d une représentation fréquentielle séparée Fp,q,d , ces représentations étant ensuite superposées pour obtenir la représentation fréquentielle Fp,q, au lieu d'effectuer directement dans la procédure 7.12. la superposition des valeurs correspondant à chaque indice d.

or Fp.q, d [ni, nJ, nk] is obtained as Fp, q in procedure 7.17. unmodified, but replacing Mk, p, 9 [i, j] by the actual value MO [k, pu [0, d, 0,0 [q, /, y] obtained in the procedure described in 7.12. for a corresponding value of the index indicating the phase shift. It is therefore possible to calculate for each index of a separate frequency representation Fp, q, d, these representations being then superimposed to obtain the frequency representation Fp, q, instead of directly in the procedure 7.12. the superposition of the values corresponding to each index d.

 It is also possible to superimpose the tables corresponding to each index after passing through the spatial domain by inverse Fourier transformation.

et les tableaux Io[k],Jo[k] doivent être remplacés par des tableaux 10 [k,d],Jo[k,d]. On peut alors calculer comme précédement des tableaux Fp,q,d séparés avant de les superposer pour obtenir les tableaux Fp,q. Finally, it is possible not to use the same points of impact of the illumination wave as a function of the phase shift applied. In this case, at each phase shift corresponds a distinct trajectory

and the tables Io [k], Jo [k] must be replaced by tables 10 [k, d], Jo [k, d]. We can then calculate as previously separate tables Fp, q, d before superimposing them to obtain the tables Fp, q.

 This method of calculation is not particularly advantageous but shows that it is not essential to calculate in an intermediate phase complex two-dimensional representations, or even to perform data acquisition corresponding to these complex two-dimensional representations.

 7. 18.6. Realization of images with a single value of the phase shift.

 The present variant consists in modifying the procedure described in 7.12. so as to acquire only the real part of the complex number normally acquired as described in 7.12. This real part can be acquired in a single step, which makes it possible to use a single value of the index d characterizing the phase shift. Since only the real part is acquired, the frequency representation obtained, in

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 Assuming that the compensation table of the spherical aberration Dp is set to 1, is the real part of the complex representation. The spatial representation obtained by inverse Fourier transformation is then the superimposition of the normal image with a conjugate image symmetrical with respect to the point of origin of the reference wave. In order for the normal image not to be superimposed on its symmetrical one, the origin of the reference wave must be placed on the side of the diaphragm, slightly out of the aperture of the diaphragm, and not at the center of the diaphragm. this. The opening of the diaphragm must be halved so as to avoid the aliasing induced by this displacement of the origin point of the reference wave.

The image finally obtained then comprises the normal image and the symmetrical image, not superimposed and therefore usable. However, for the real part to be acquired in a single step, it is necessary that the intensity of the reference wave is sufficiently greater than the intensity of the diffracted wave, so as not to induce errors second order. The quality of the image finally obtained therefore depends on the intensity of the reference wave. Too low intensity induces second-order distortions and too much intensity increases Gaussian noise.

In order to better respect the condition of sufficient intensity of the reference wave, the intensity of the reference wave only must be adjusted not to one quarter of the maximum value of the digitizer as indicated in 7. 4. but for example at 80% of this value,
In order for the real part to be effectively acquired at each image acquisition, the single phase shift used must make it possible to directly obtain a constant phase reference. This shift will be, in a similar way to what was done in 7.18.4 .:

Despite the application of this phase shift, the phase reference may not be constant in the presence of vibrations of the optical table. This would destroy the image and it is therefore necessary to use a high quality optical table to remove these vibrations.

Comme en 7.18.4., mais en tenant compte de l'abscence de vibrations, l'étape 2 de la procédure décrite en 7.17.2. est remplacée par:

The index d therefore takes only one value instead of three and step 2 of the procedure described in 7.12.2.2. is replaced by:

As in 7.18.4., But taking into account the absence of vibrations, step 2 of the procedure described in 7.17.2. is replaced by:

This variant can be further simplified by using only one position of the phase rotators and only one position of the beam attenuator, whereby the 36 pairs of elementary images acquired in 7.12.2.1. can be reduced to one, at the cost of a sharp decrease in the quality of the image. In this case of extreme simplification, the indices c, d, r1, r2 take only one value and the whole of the procedure described in 7.12.2. is reduced to:

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7. 18.7. Simplified method for obtaining three-dimensional images.

 One can limit, to generate the three-dimensional image of the object, to the representation Fo, odéfinie in 7.17. This amounts, in the procedure described in 7.17.2., To adopt tables IBp, q void for any pair (p, q) # (0,0). This method is the method defined in 7.18.4. but simplified in this way, and adapted to the case where the average index of the sample is close to the nominal index of the objectives, and the table can be considered as perfectly stable.

Under these conditions, we have Rk, 0,0 = 1 and D0 [i, j] = 1.

M k,O,O[I, j] = Mk,0,0 [1, il c'est-à-dire que le tableau Mk,o,o n'est pas modifié avant d'être utilisé pour générer la représentation tridimensionnelle de l'objet. The formula: Mk P9 lt .1 = Mk (PP, R t J-Dpq + P9 .1 Rk, P, q DP Iimaxk>P0>,Imk.P> 0] Rk> P0 which was used in 7.18. 4. simplifies itself and we obtain:

M k, O, O [I, j] = Mk, 0,0 [1, that is, the array Mk, o, o is not modified before being used to generate the representation three-dimensional object.

 In this particular case, no algorithmic compensation of the phase shift of the reference beam is necessary, because the device used allows the generation of illumination beams having a constant phase shift with respect to the reference wave.

8 d = Od - Arg(Ra [p, I4k, p], Jc[k, pi]) c'est-à-dire qu'elle ne dépend pas de mesures effectuées préalablement sur l'objet lui-même. Si un objectif de microscope ayant pour indice nominal celui du vide est employé, les mesures préalables peuvent être effectuées en l'abscence de tout objet (en considérant comme un objet la lame transparente). In this particular case, steps 7.10, 7.11, 7.15, 7.16 can also be avoided. The position of the objectives can be adjusted as in 7.9.1, so as to have a point and centered image. The control of the phase shifter is then defined by:

D = Od - Arg (Ra [p, I4k, p], Jc [k, pi]) that is to say that it does not depend on measurements previously made on the object itself. If a microscope objective having the nominal index of the vacuum is used, the preliminary measures can be performed in the absence of any object (considering as an object the transparent blade).

 7. 18.8. Realization of an image with a single position of the polarizers.

 The present variant consists in not using the possibility of variation of the indices r1 and r2. If images according to the present variant are only generated, the polarization rotators (2210) (2241) (2238) (2226) can be deleted. The present variant involves a modification of step 3 of the loop on k, p described in 7.12.2.2., As well as a modification of step 8 of the algorithm described in 7.17.2.

 7.18.8.1. Modification of retape 3 of the loop on k, p described in 7.12.2.2.

 When the polarization rotators are not used, the direction of the electric field vector of the illumination beam and the direction of analysis of the received beam are oriented along the vector j of FIG. 52.

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- la composante suivant e est transmise, devenant la composante sur le vecteur - # e, mais est atténuée d'un facteur cos# ou 0 est l'angle entre le vecteur fe et le vecteur fc. We denote by e and # the vectors deduced respectively from the vectors 3ce and xc by rotation of in the plane of Fig.52 We have: j = ze sinue + e cosço,
During diffraction towards point C: - the following component #e is transmitted without attenuation, becoming the component on the vector - # c

the following component e is transmitted, becoming the component on the vector - # e, but is attenuated by a factor cos # where 0 is the angle between the vector fe and the vector fc.

reçue au point C est donc proportionnel à t = -xc sinq1e - #e costpe e cos 9 . On peut prendre en compte les relations xc = cosço, + j sinq1e ,#e = -T sinq1e + j COSq1e . La composante de suivant] est alors proportionnelle à Br = - cos q1 cos tp cos 0 - sin q1 sin q1 e . Ceci constitue un facteur d'atténuation qui affecte le faisceau diffracté mesuré au point C suivant une direction d'analyse orientée suivant] lorsque le faisceau d'éclairage est dirigé sur le point E et a son vecteur champ électrique orienté suivant] . Si la diffusion pouvait être considérée comme isotrope, ce coefficient serait constant. Pour compenser l'effet de l'anisotropie il suffit donc de diviser les valeurs mesurées par ce coefficient Br de manière à se ramener à un coefficient constant caractérisant la diffusion isotrope. La division par Br fait remonter le bruit affectant les points ou Br est faible, ce qui doit également être pris en compte.

For a vector electric field 7of the illumination wave, the vector electric field of the wave

received at point C is therefore proportional to t = -xc sinq1e - #e costpe e cos 9. We can take into account the relations xc = cosço, + j sinq1e, # e = -T sinq1e + j COSq1e. The next component] is then proportional to Br = - cos q1 cos tp cos 0 - sin q1 sin q1 e. This is an attenuation factor which affects the diffracted beam measured at point C in a direction of analysis oriented as the illumination beam is directed at the point E and has its vector electric field oriented next. If diffusion could be considered as isotropic, this coefficient would be constant. To compensate for the effect of anisotropy, it suffices to divide the values measured by this coefficient Br so as to reduce it to a constant coefficient characterizing the isotropic diffusion. The division by Br causes the noise affecting the points to rise or Br is low, which must also be taken into account.

- le programme calcule, en plus des valeurs déjà calculées en 7.12., cos6 = xcxe zaza te - le programme calcule le facteur compk, p, q] de compensation de l'atténuation : si - cos q1 e cos q1 e cos B - sin q1 sin (p, :9 lim alors cof,/?,1 = #, ou lim est une valeur très lim faible, par exemple lim = 10-10

sinon, com p k 'p'q q] -cosrp cosrpe cosB-sinrp 1 sinpe sinon, complu, p, #1 = -cosç?c cose cos#-sinç?c sin<pe Comme les valeurs coef k, p, q, /, /][/#], r2 utilisées en 7.12., les valeurs compk, p, q constituent un tableau qui peut être précalculé. - le programme calcule finalement:

The cos factor B is cos B = [fe II- '1 fc c || . This translates, using the normalized values of the frequency vectors, by: cos # = xcxe + Yc Ye + Zcze Step 3 of the procedure 7. 12.12. is modified as follows:

- the program calculates, in addition to the values already calculated in 7.12., cos6 = xcxe zaza te - the program calculates the compensation factor compk, p, q] of the attenuation: si-cos q1 cos q1 e cos B - sin q1 sin (p,: 9 lim then cof, / ?, 1 = #, where lim is a very low lim value, for example lim = 10-10

if not, com pk 'p'q q] -cosrp cosrpe cosB-sinrp 1 sinpe otherwise, complu, p, # 1 = -cosçc cose cos # -sinç? c sin <pe As the values coef k, p, q , /, /] [/ #], r2 used in 7.12., the compk, p, q values constitute a table that can be precalculated. - the program finally calculates:

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 where #acq is the standard deviation of the sensors noise. The sensors are usually designed so that #acq is ~ SNRdB in the order of 1. We have: #acq = 10 20 2 N where SNRdB is the signal-to-noise ratio in decibels and N is the number of sampling bits of the signal.

 5. 7. 18.8.2. Modification of step 8 of the algorithm described in 7.17.2.

 Multiplication by comp [k, p, q] can considerably increase the level of noise, which can distort the image obtained. To avoid this problem, step 8 of the procedure described in 7.17 is modified so as to cancel the components of the frequency representation which are smaller in modulus to the noise multiplied by a given const constant.

The cancellation of certain elements of the frequency representation is itself generating noise. To obtain a frequency representation of comparable quality to that obtained by the normal procedure, more precise sampling or an additional level of attenuation may be necessary.

de dimensions 2N pvc x2NP, x 2 N plX' Il initialise à 0 ce tableau puis parcourt les indices m,nj,nk en testant la condition: IBP,9 ni, nj, nk p, q 20 Lorsque la condition est réalisée il effectue:

L Fp,q [ni, "J> nk\1BVA [ni ,nj,nk] F[ni,nj,nk] = p,q IBP,9 ni, nj, nk P.q Il teste alors la condition F[ni, nj, nk] <~ const L IBp,q [ni, nj, nk] p.q Lorsque cette condition est réalisée il effectue: F[ni, nj, nk] = 0 const est une constante choisie pour qu'en l'abscence de signal (bruit seul) la condition soit 25 toujours vérifiée. On peut par exemple utiliser const=4
Une multiplication par une constante du niveau global de bruit modifie les résultats de cette étape 8 modifiée. C'est pourquoi en 7.18.8.1. on détermine un niveau de bruit absolu, alors qu'en 7.12 le niveau de bruit était défini à une constante près. Step 8 of the procedure described in 7.17 is modified as follows: step 8 modified: The program calculates the final frequency representation, contained in a table F

of dimension 2N pvc x2NP, x 2 N plX 'It initializes to 0 this array then traverses the indices m, nj, nk by testing the condition: IBP, 9 ni, nj, nk p, q 20 When the condition is realized it performs :

L Fp, q [ni, "J> nk \ 1BVA [ni, nj, nk] F [ni, nj, nk] = p, q IBP, 9 ni, nj, nk Pq It then tests the condition F [ni, nj, nk] <~ const L IBp, q [ni, nj, nk] pq When this condition is realized it performs: F [ni, nj, nk] = 0 const is a constant chosen so that in the absence of signal (noise only) the condition is always checked, for example const = 4
A multiplication by a constant of the overall noise level modifies the results of this modified step 8. This is why in 7.18.8.1. an absolute noise level is determined, whereas in 7.12 the noise level was set to a constant.

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 7. 18.9. Obtaining an image of a uniaxial birefringent crystal.

 An uniaxial crystal of ordinary index n0 cut to form a blade of reduced thickness is considered, the plane of the blade being orthogonal to the optical axis of the crystal. This blade constitutes the sample observed and is placed between the two lenses, optical oil being used between the objectives and the sample, the objective being designed to use lamellae of index equal to that of the optical oil. .

The optical axis of the crystal is thus confused with the optical axis of the objectives.

 This blade is supposed not to be perfect. It may be affected, for example, by occasional crystallization defects. The present procedure aims to obtain a three-dimensional image of these crystallization defects. It can also be an optical memory whose local index variations characterize the recorded bits. The present procedure allows obtaining a three-dimensional image characteristic of the variations of the ordinary index no of the sample.

 The average ordinary index no is assumed to be known, as is the thickness of the blade. The sample is introduced without moving the objectives, so that x, y, z are also known. It is also possible to obtain no, L, x, y, z by a modified version of the procedure described in 7.11. Such a modified version, applicable in the case of embodiment 4, will be described in 8.4.3.2.

 Obtaining the ordinary index image implies a modification of step 8 of procedure 7.17. , which is the one already described in 7.18.8.2. It also supposes a modification of the step 3 of the loop on k, p described in 7.12.2.2., Described hereafter by taking again the notations used in 7.12.

On note: üe = Je /\fo Ü - /cAfou Il.fe I\foll' -Ife ^.foll #e et #c sont donc définis d'après les vecteurs de la Fig.51. Ils sont tous deux dans le plan de la Fig. 52 (non représentés). ûe est orienté selon la direction de polarisation ordinaire de l'onde d'éclairage parvenant en E. #c est orienté selon la direction de polarisation ordinaire de l'onde diffractée parvenant au point C. 7. 18.9.1. Principle

Note that /e = / / fo / / / / / / / / et et et et et et et et et et et sont sont sont sont sont sont sont sont sont sont sont sont sont sont sont sont sont sont sont sont sont sont .5 .5 .5 .5. They are both in the plane of FIG. 52 (not shown). it is oriented in the direction of ordinary polarization of the light wave arriving at E. #c is oriented in the ordinary polarization direction of the diffracted wave arriving at point C.

i . On a typiquement 6:;:; 10 degrés. We denote #e and #c the vectors deduced respectively from the vectors #e and #c by rotation of # / 2 in the plane of Fig.52
We denote #e and #c the vectors deduced respectively from the vectors #e and #c by rotation of 2 in the plane of Fig.52
We note the angle between the vector # and the vector # obtained from 7 by a symmetry whose axis is the position of the neutral axis of the polarization rotators when this neutral axis is not parallel to

i. Typically 6:; 10 degrees.

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champ électrique mesuré au point C est (C,,A, + COI AI)T +(Cl0A0 +C,,4,)y . When the electric field vector of the lighting beam (at point E) is A0 # + A1 # the vector

electric field measured at the point C is (C ,, A, + COI AI) T + (Cl0A0 + C ,, 4,) y.

Aoâ+A1 j le vecteur champ électrique mesuré au point C est (QOOAO +6oit)+(6ioo +QiiAyJ avec # = # cos # + # sine. When an electric field vector ε = 1: cos a, e + j sin a is used for the illumination wave, the vector electric field measured at the point C is therefore: wm = (Coo cosae + Col sin ae) T + (ClO cosae + CI 1 sina ,,) J We can use: i = U. cos <Xe - v, sin <a; ej = sina + v, cosoe of or: wm = (Coo cosae cosac + Col sinae cos c + Clo cosae sina, + Ci 1 sina ,, sinc); + (- Coo cosae sinae -Col sinae sinac + CI () cosae cosa. + Cl, sinae cosae) Ve The value measured at point C along the direction of the vector ii, is therefore: Bm = Coo cos cosac + Col sinae cos c + CIO cosae sinac + CI sinae e sin a,
We denote by Qr1, r2 the value measured at point C for the combination r1, r2 of the control indices of the polarization rotators. When the electric field vector of the lighting beam (at point E) is

Aoâ + A1 j the vector electric field measured at point C is (QOOAO + 6oit) + (6ioo + QiiAyJ with # = # cos # + # sine.

le vecteur reçu au point C est donc:

soit:

(QOOAO +Qo(-Ao sine+Al coss))i

The relation defining # is reversed in: # = # 1 - # tan # cos When the electric field vector of the lighting beam is

the vector received at point C is therefore:

is:

(QOOAO + Qo (-Ao sine + Al coss)) i

Cette expression est l'équivalent de (CooAo +C0lAx)ï + {Cl0A0 +C1lAj , avec: Coo = Qoo - Q0 1 sin # C01 = Q01 cos #

This expression is the equivalent of (CooAo + C0lAx) ï + {Cl0A0 + C1lAj, with: Coo = Qoo - Q0 1 sin # C01 = Q01 cos #

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Cl =Qol sins+Qll L'expression de Bm se transforme donc comme suit: Bm=(Qoo -Q0, sine) cosa, cos a, +Q0, cosssinae cos a, +(Qol sins+QIl) sinae sina,

soit: Bm = (cosae cosac +cosae sinac tan #)Q00

±sinscosae cosac +cosssinae cosac +sinesinae sinac - sinstanscosa sinac)<201 +C cos 1 e cosae sinac,Qlo cos

+(sinae sinac -tanseosae sinac)Q Cette valeur Bm est la valeur mesurée au point C selon la direction du vecteur #c lorsque le vecteur champ électrique de l'onde d'éclairage est orienté selon #e Du fait de la définition des vecteurs ûe et #c, Bm est la valeur du rayon diffracté ordinaire pour un faisceau d'éclairage ordinaire. La mesure de Bm est indirecte au sens ou ce sont les valeurs Qij qui sont mesurées, la valeur de Bm en étant déduite.

Cl = Qol sins + Qll The expression of Bm is thus transformed as follows: Bm = (Qoo -Q0, sine) cosa, cos a, + Q0, cosssinae cos a, + (Qol sins + QIl) sinae sina,

either: Bm = (cosae cosac + cosae sinac tan #) Q00

± sinscosae cosac + cosssinae cosac + sinesinae sinac - sinstanscosa sinac) <201 + C cos 1 cosae sinac, Qlo cos

+ (sinae sinac -tanseosae sinac) Q This value Bm is the value measured at point C in the direction of vector #c when the electric field vector of the illumination wave is oriented according to #e Due to the definition of vectors and #c, Bm is the value of the ordinary diffracted ray for an ordinary light beam. The measure of Bm is indirect in the sense where the values Qij are measured, the value of Bm being deduced.

iie = x'e COS,l3e -Ye Sln3e Lors de la diffraction vers le point C, sur le même principe qu'en 7.18.8.1.: - la composante suivant #e est transmise sans atténuation, devenant la composante sur le vecteur -#c

- la composante suivant e est transmise, devenant la composante sur le vecteur - # e , mais est atténuée d'un facteur cos# ou # est l'angle entre le vecteur fe et le vecteur fc. Le vecteur reçu au point C est donc:

wr = -xyz cospe + #e sin/3e cos<9 On peut utiliser: Xc = ù, cos3c +vc sin,6, #e = -ûc sin,6, +vc cos,6, On en tire donc: Wr = (- cosfJ COsfle - sinj6, sin,6e COSe)2'lc + (- sin,6c cosfle +COSRc sin,6e COS 0), La valeur reçue au point C suivant la direction du vecteur ûeest donc: Br = - cosfJe cos,6,, - sin,6, sin/?g COS 0 Cette valeur Br est le coefficient d'atténuation qui affecte le faisceau diffracté ordinaire reçu au point C lorsque le faisceau d'éclairage est ordinaire. Dans un modèle de diffusion isotrope, le coefficient Br serait We can express the vector #e in the form:

iie = x'e COS, l3e -Ye Sln3e When diffracting towards the point C, on the same principle as in 7.18.8.1 .: - the next component #e is transmitted without attenuation, becoming the component on the vector - #c

the following component e is transmitted, becoming the component on the vector - # e, but is attenuated by a factor cos # where # is the angle between the vector fe and the vector fc. The vector received at point C is therefore:

wr = -xyz cospe + #e sin / 3e cos <9 We can use: Xc = ù, cos3c + vc sin, 6, #e = -c sin, 6, + vc cos, 6, so we draw: Wr = (- cosfJ COsfle - sinj6, sin, 6e COSe) 2'lc + (- sin, 6c cosfle + COSRc sin, 6e COS 0), The value received at point C along the direction of the vector ûe is: Br = - cosfJe cos, 6 ,, - sin, 6, sin /? g COS 0 This Br value is the attenuation coefficient that affects the ordinary diffracted beam received at point C when the illumination beam is ordinary. In an isotropic diffusion model, the Br coefficient would be

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 constant. As in 7.18.8.1., This attenuation can be compensated by dividing the measured value Bm by the coefficient Br.

cos(} = xexe + YeYe +zeze

sin,8, == 1 Vxy cos,6, = (YeVyz -XeVxz) MeMce MeMee 1 sinac = - 1xc cosae = 1Y, Mc Mc sin/3e = - 1 V xy cos,6, = 1 (-YeV yz +xeV xz) memce Memce 1 sina, =- 1Xe cosae = 1Ye Me Me Pour l'ensemble de ces valeurs, on utilise des valeurs limites appropriées lorsque les dénominateurs sont nuls :

si Mc = 0 on utilise ae = -a et /3 ~ ,13e = 0 si Me = 0 on utilise a = -ae et /9c = 3e = 0 si Mee = Oon utilise 8, = 3e = 0 si Mc = 0 et Me = 0 et M ce = 0 on utilise a = a = 8, = fle = 0 - le programme calcule le facteur comp[k, p, q] de compensation de l'atténuation : Si - COSÜ, cos/3e -sin/3 sin/3e cos 0:9 lim alors compk, p,q = # , ou //m est une valeur très lim faible, par exemple lim = 10-10

sinon, compk, p, q ~ -COS%j COSe -Sln 1 Slne COSe sinon, comp ,p,q - cos p c cos, pe-smpcsm fi ecos9 Le programme calcule les valeurs: coefk,p,q,i, j0,0=eosae cosac +cosae sina tan)co/K,,] coef[k, p,q,i, j0,li\ = -sinecosae cosae +cosesinae cosa +sinesinae sinac -sinetanscosae sinacompk, p, q]

7.18.9.2. Algorithm
Step 3 of the loop on k, p described in 7. 12.12. is therefore modified as follows: - the program calculates the following quantities, in addition to those calculated in 7.12.12 .:

cos (} = xexe + YeYe + zeze

sin, 8, == 1 Vxy cos, 6, = (YeVyz -XeVxz) MeMce MeMee 1 sinac = - 1xc cosae = 1Y, Mc Mc sin / 3e = - 1 V xy cos, 6, = 1 (-YeV yz + xeV xz) memce Memce 1 sina, = - 1Xe cosae = 1Ye Me Me For all these values, appropriate limit values are used when the denominators are zero:

if Mc = 0 we use ae = -a and / 3 ~, 13e = 0 if Me = 0 we use a = -ae and / 9c = 3e = 0 if Mee = Oon uses 8, = 3e = 0 if Mc = 0 and Me = 0 and M ce = 0 we use a = a = 8, = fle = 0 - the program calculates the compensation factor [k, p, q] of the attenuation: Si - COSÜ, cos / 3e - sin / 3 sin / 3rd cos 0: 9 lim then compk, p, q = #, where // m is a very low lim value, for example lim = 10-10

if not, compk, p, q ~ -COS% j COSe -Sln 1 Slne COSe else, comp, p, q - cos pc cos, pe-smpcsm fi ecos9 The program calculates the values: coefk, p, q, i, j0 , 0 = eosae cosac + cosae sina tan) co / K ,,] coef [k, p, q, i, j0, li \ = -sinecosae cosae + cosesinae cosa + sinesinae sinac -sinetanscosae sinacompk, p, q]

Comme en 7.12. les valeurs coef k, p, q, i, jrl , r2 et comp[k, p, q] constituent des tableaux qui peuvent être précalculés.

As in 7.12. the values coefk, p, q, i, jr1, r2 and comp [k, p, q] constitute tables that can be precalculated.

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ou #acq est l'écart-type du bruit des capteurs défini comme en 7.18.8.1.

M2r1, r2 ][ q, i, il correspond à la valeur mesurée qui était notée (3,.,. en 7.18.9.1. le calcul de Mk,p,q[i,j] équivaut au calcul du rapport Bm défini en 7.18.9.1. - the program finally calculates:

where #acq is the standard deviation of the sensor noise defined in 7.18.8.1.

M2r1, r2] [q, i, it corresponds to the measured value which was noted (3, ..., in 7.18.9.1, the calculation of Mk, p, q [i, j] is equivalent to the calculation of the ratio Bm defined in 7.18.9.1.

Br
7. 19. Adapted microscope objectives.

 In all embodiments it is possible to use standard microscope objectives. These objectives have a nominal index nv close to that of glass. They are designed to work with an immersion liquid and a coverslip of nv index. These objectives will give good results if the observed sample has an average index close to nv or is not thick. If the sample observed consists essentially of water, with a 1.33 index, and if the aperture of the objective is 1.25, then the total thickness of the sample must be sufficiently smaller than the width total of the generated image. If it is too high, the three-dimensional representation obtained may be distorted. Indeed, the spherical aberration caused by the thickness of the sample can then become such that the wave coming from a lens can be received by the objective vis-à-vis only for a small part of the frequencies used.

 A microscope objective is designed to use an optical liquid of given index, the index of the optical liquid having been called the nominal index of the objective. It is also designed to use a slide cover of given index and thickness, the index of the blade is not necessarily equal to the nominal index of the objective. If we assume the average index of the object equal to the nominal index of the objective, the objective allows a compensation of the spherical aberration due to the cover glass, which is independent of the position of the object.

 If, on the other hand, the nominal index of the objective differs from the average index of the object, the variations of position of the object cause a variation in the thickness of the layers respectively corresponding to the object and the optical liquid. Induced spherical aberration therefore depends on the position of the object and can not be compensated by the objective, a valid compensation for a position of the object being no longer for another position. This problem has no effect on obtaining two-dimensional images, which is usual with conventional microscopes, and in which the index of the sample does not intervene. On the other hand, it is awkward for the observation of three-dimensional images of a thick sample.

 One solution to this problem is to use a goal whose nominal index is close to the average index of the observed sample.

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 If the sample observed consists essentially of water, the optical liquid may be water or a liquid of stabilized index close to that of water. The objective can be designed by usual methods of optical calculation, taking into account the index of the optical liquid and the need to compensate for the aberration due to the blade. This design can be facilitated by the use of a Teflon blade (polymer manufactured by DuPont), whose index is close to that of water and which therefore induces a low aberration.

 If the observed sample is a high index birefringent crystal as in the case of optical memories, the nominal index of the objective should be close to that of the crystal, which implies the use of an optical liquid of high index, the coverslip to be index close to that of the observed crystal or may possibly be deleted.

8. Fourth embodiment (preferred mode)
This embodiment is considered the best embodiment because in the field of visible is that which allows the best performance in terms of speed and image quality.

8.1. Principles
The fourth embodiment differs from the third embodiment - by the use of a different beam deflection device - by the introduction of an additional device for suppressing the direct wave coming on the CCDs to avoid or limit the effect. saturation.

- by the fact that the sampling is "regular", that is to say that the point image of a lighting beam on the CCD coincides with the center of a pixel of the CCD.

 The beam deflection and direct wave suppression devices are based on the use of a spatial light modulator (SLM) marketed by the Displaytech company. This consists of a matrix of 256x256 elements each functioning as an independent polarization rotator. It operates in reflection, that is to say that the light incident on the SLM is reflected with a modified polarization, said polarization modification being different at each point of the matrix.

 It exists in two versions: intended for amplitude modulation, in which for one of the control voltages, the neutral axis of the ferroelectric liquid crystal (FLC) is oriented in the direction defined by one of the axes of the matrix, and another for phase modulation, in which the two possible positions of the neutral axis of the FLC are symmetrical with respect to one of the axes of the matrix.

 Regular sampling and good control of the beam path also imply proper use of the lenses.

 8. 1.1. Control of the trajectory of the beam.

 When a plane beam but not directed along the optical axis away from its point of origin, it moves away from the optical axis and can become unusable. Fig. 67 illustrates a method for controlling the position of such a beam with respect to the optical axis. A parallel beam (4800) from a

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 plan (4801) must be used in a plan (4804) distant from (4801). If it spreads in a straight line, it moves away from the optical axis and becomes inoperable (4805).

 The lenses (4802) and (4803) have the same focal length / The plane (4801) is the object focal plane of (4802). (4804) is the image focal plane of (4803). The object focal plane of (4803) is merged with the image focal plane of (4802) and represented by the dotted lines (4806).

 In the plane (4801) the beam (4800) is parallel and centered on the optical axis, that is to say that its intersection with this plane forms a disc centered on the optical axis. Such a plan will be called space plan and noted by the letter E.

 In the plane (4806) the beam is punctual, that is to say that its intersection with the plane is practically reduced to a point. Such a plan will be called frequency plan and noted by the letter F.

 In the plan (4804) the beam is again centered and parallel. This plan is therefore a new space plan. It is the image of the plane (4801) by the optical system consisting of lenses (4802) and (4803).

 The device allows to reform in the plane (4804) a beam equivalent to that present in the plane (4801), but symmetrical with respect to the optical axis.

By changing the focal length of the second lens as in FIG. 68, it is possible to modify the angle of the beam with respect to the optical axis and its section. The focal length of the first lens is f1, that of the second lens is f2, the distance between the two lenses is f1 + f2. The angle of the beam with respect to the optical axis is multiplied by f1 and the beam section is multiplied by f2 f2 f1
8. 1.2. Beam deflection device
A direction at the exit of the deflection device is equivalent to a given spatial frequency and the terms 'frequency' or 'angle' will be used in the following to define a deviation.

de ps, sina varie de 0 à 2ps par pas de soit au total # - 2 valeurs possibles en excluant le zéro. Ce
2ps NsPs 2 principe est appliqué pour générer un faisceau de direction donnée. Cependant ce dispositif simple n'est pas suffisant pour les raisons suivantes: - On cherche a générer une seule fréquence et il faut donc ensuite supprimer un des deux faisceaux générés, par exemple (4602) - Le faisceau issu de ce système de modulation simple est bruité, en ce sens qu'en plus de la fréquence correspondant au maximum d'éclairement de nombreuses fréquences parasites sont présentes. The beam deflection device uses a phase SLM whose entire surface is illuminated by a plane beam. When a phase profile (4601) in crenals like that shown in FIG. 64 is applied on such a surface, the long distance diffracted intensity is maximal for the angles a and -a where a is such that h = # / 2 is d sin a = # / 2 These two angles define two symmetric diffracted beams (4602) and (4603) from the SLM. The number of pixels of the SLM used being Ns and the pitch (distance between two pixels)

ps, sina varies from 0 to 2ps in steps of either total # - 2 possible values excluding zero. This
2ps NsPs 2 principle is applied to generate a given direction beam. However this simple device is not sufficient for the following reasons: - We try to generate a single frequency and we must then remove one of the two generated beams, for example (4602) - The beam from this simple modulation system is noisy, in that in addition to the frequency corresponding to the maximum illumination of many parasitic frequencies are present.

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 To suppress the parasitic frequencies and the symmetrical beam, a system whose schematic diagram is used is used. 65. In this diagram, the SLMs are represented as if they function by transmission, and the polarizers associated with these SLMs have not been represented. A plane beam (4611) incident on a phase SLM (4612) operating as indicated above is diffracted in two directions shown in solid and dashed lines. (4612) is in the object focal plane of a lens (4613). In the image focal plane of (4613), a given angle beam at the output of (4612) gives a point image. The object focal plane of the lens (4612) is a space plane, and the image focal plane of (4612) is a frequency plane. In the frequency plan, we place: - a diaphragm (4615) whose function is to stop the symmetrical beam (dashed).

 an SLM (4614) whose function is to suppress parasitic frequencies. When the SLM (4612) is controlled to generate a given frequency, this frequency corresponds to a point in the SLM (4614). This point is controlled to let the beam pass, and the other points of the SLM (4614) are controlled to stop the beam. The parasitic frequencies are thus suppressed.

 A second lens (4616) then again transforms the point obtained in the frequency plane into a corresponding direction at the output of the device.

 8. 1.3. Device for suppressing the direct wave.

 The wave that has crossed the objective and reaches the CCD has high intensity frequencies around the point of direct impact of the beam. In the previous embodiment, this resulted in saturation of the CCD when low beam attenuation was used.

 To suppress or attenuate this saturation effect, a device whose principle is indicated in FIG. 66, on which the SLM is represented as if it were operating in transmission, and on which the polarizer associated with the SLM is not represented.

 The wave coming from the object and having crossed the objective is filtered in an image plane by the diaphragm (4700). A lens (4703) makes it possible to form, in its image focal plane, which constitutes a frequency plane, a frequency image of this wave. In the previous embodiment, a CCD was directly placed in this frequency plane. In the present embodiment, an SLM (4704) is placed therein. The direct beam (4702), not deviated by the sample, is shown in dashed lines. His image on the SLM is punctual. By obscuring the corresponding pixel, and possibly a few pixels close, we remove this point of intense lighting. The other pixels of the SLM are left in the traveling position, which allows a ray (4701) of other frequency to cross the SLM.

 However, the SLM is not a 'perfect' system in that in the area where it is left transparent, it is in fact a 'grid', with each pixel passing but a certain obscured space being left between two pixels. This grid diffracts the rays passing through it, generating unwanted diffracted rays that are superimposed on the useful beam. Dotted (4710) is a possible direction of this beam at the output of the SLM (4704). A lens (4705) allows from the beam passed through (4704) to reform a space plane identical to that in which is placed (4700). In this space plane the unwanted rays diffracted by (4704) are outside the image of the diaphragm (4700). A

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 diaphragm (4706) placed in a plane of space and whose opening coincides with the image of the aperture of the diaphragm (4700) thus makes it possible to suppress these diffracted rays.

 A last lens (4708) makes it possible to reform a frequency plane in which the CCD (4709) is placed.

 8. 1.4. Obtaining a regular sampling.

 In the third embodiment, the values of ni, nj, nk obtained at the end of step 1 of step 3 of the imaging procedure described in 7.17.2 are not integer. Since integers are necessary in the rest of the algorithm, we take for each of these values the nearest integer. Nevertheless, this is an approximation that can result in disturbances on the generated three-dimensional image. In the present embodiment, the optical system is provided so that said values of ni and nj are substantially integral, that is, for there to be regular sampling along the axes ni and nj. The following sampling nk remains non-regular, nevertheless this method strongly reduces the disturbances.

 A given light wave produced by the beam deflection system produces on the one hand a direct beam to hit one of the sensors and on the other hand a reverse indicator beam to hit the other sensor. Conversely, a given pixel of a sensor can be reached by a direct beam produced by a light wave or by an inverse indicator beam produced by another light wave.

 For regular sampling, each light wave used must produce a direct beam and an inverse beam each arriving at the center of a corresponding pixel of the corresponding CCD, the coordinates of the pixel reached by the direct beam on a CCD being the same as those of the pixel reached by the reverse indicator beam on the other CCD. At each pixel of the CCD which is in the area delimited by the aperture of the lenses must correspond two lighting beams for which the pixel is reached respectively by the direct beam and the reverse indicator beam.

 The frequency representation obtained on the CCD can be transformed in various ways due to inaccuracies in the characteristics of the system.

- by translation. This translation can be compensated by corresponding displacements of mirrors.

- by homothety. A change in the focal length of the lens forming the image on the CCD results in a homothety on this image - by rotation. The portion of the system comprising the two lenses, consisting of the assembly (4460) of FIG. 62, detailed in FIG. 63, if it is not perfectly constructed, causes a rotation of the image produced on the CCD.

 A homothety applied to the image produced on the CCD invalidates the exact correspondence between a pixel of the CCD, which is fixed, and the points of impact of the direct or inverted beam, which are modified by the homothety. To avoid such a homothety, it is necessary to precisely control the focal length of the lens forming the image. An appropriate system allows the adjustment of this focal length.

 The rotation produced by (4460) is applied only to the direct beam. It can be compensated by a corresponding rotation of the CCD. But this operation shifts the pixels of the CCD by

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 relation to the points of impact of the reverse beam. It is therefore necessary to perform a corresponding rotation of the reverse indicator beam to cancel this gap. An appropriate system allows this rotation.

 8. 1.4.1. Adjusting the focal length.

To obtain an optical element whose focal length is precisely adjusted around a central value fc, two lenses of focal length / separated by a distance d are associated.

La valeur de f est alors f = /e + '\//e (/cl) Une ensemble de focale fc réglable à ±r est donc constitué de deux lentilles de focale/séparées par une distance d avec : d = 4fcr

La distance focale de l'ensemble est ajustée en faisant varier la distance d. The focal length of the set is then f, = f 2 1 - 1 d 2f If we want to set fc to a width of ± 1%, ie r = 0.01, then we must have # = r with approximately fc = f / 2. The adopted value of d is: d = 4fcr

The value of f is then f = / e + '\ // e (/ cl). A set of focal length fc adjustable to ± r is therefore composed of two focal lenses / separated by a distance d with: d = 4fcr

The focal length of the set is adjusted by varying the distance d.

Such doublets are used at various points of the device for similar reasons.

 8.1.4.2. Rotation resetting.

 To adjust in rotation a lighting beam is used a device described in FIG. 69, inserted on the path of the lighting beam in an area where this beam is parallel and therefore defined by its wave vector.

This device consists of a set of mirrors (4901) to (4906). Mirrors (4901) (4902) are fixed.

The mirrors (4903) (4904) (4905) (4906) are integral with each other and the assembly (4910) constituted by these mirrors is rotatable about an axis (4909). The arrows shown in the plane of the figure represent the wave vectors of the beam at each point of the device.

 The transformation of a wave vector by a mirror comprises a vector symmetry with respect to an axis orthogonal to the plane of the mirror and an inversion of the direction of the vector. The number of mirrors being even inversions cancel each other out and we are interested in the symmetrization part. The pair of mirrors (4901) (4902) performs two successive symmetrizations of orthogonal axes between them, which is equivalent to a single axis symmetry (4907). In the same way, the pair of mirrors (4903) (4904) performs a symmetry

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 of axis (4908). Mirrors (4905) (4906) perform two vector symmetries of the same axis, which cancel each other. The operation performed by the entire device is therefore composed of a vector symmetry axis (4907) and a vector symmetry axis (4908). Fig.70 shows, in a view along A, the axes (4907) and (4908). When no rotation of (4910) has been performed, these axes are merged and the compound of the two symmetries is the identity. The wave vector of the beam is not modified by the device.

 When a rotation of angle α is applied to the assembly (4910), the two axes are shifted by an angle α as shown in FIG. 70. The composition of the two symmetries is then a vector rotation of angle 2a.

 The system therefore makes it possible to apply to a lighting wave a vector rotation compensating for that due to the set (4460).

 8. 2. Physical description.

 An overall scheme of the system is constituted by Figs. 61,62,63. In these figures, the elements directly equivalent to corresponding elements of Figures 27 and 28 are numbered by taking the number of the corresponding element in Figures 27 and 28 and replacing the first two digits by 43. For example 2204 gives 4304. The elements having no direct equivalents in FIGS. 27 and 28 have numbers beginning with 44. The plane of FIGS. 61 and 62 is a horizontal plane, the figures constituting a view from above. The elements of the system are fixed on an optical table suitably isolated from the vibrations. Fig. 63 shows in several views the portion of the microscope containing the objectives, which constitutes a three-dimensional structure.

 A laser (4300) polarized in the vertical direction generates a beam whose vector electric field is thus directed along an axis orthogonal to the plane of the figure. This beam passes through a beam expander (4301). The beam from the expander is then divided into a reference beam and illumination beam by a semi-transparent mirror (4302).

 The illumination beam passes through a diaphragm (4348), a filter (4303) for adjusting its intensity, and then a phase shift device (4304) and a beam attenuator (4305).

 It then passes through a lens (4401). This lens focuses the beam in a plane or is placed a hole (4402) (pinhole in English) large enough not to disturb the beam, whose function is to partially stop the reflected beams returning in the opposite direction on the laser. The beam is then reflected on one side of a double mirror (4403). The two reflective sides of (4403) form a right angle. The beam then passes through a lens (4404) whose object focal plane coincides with the image focal plane of (4401), then moves towards a phase SLM (4405). The phase SLM (4405) is placed at the image focus of (4404). The beam reflected by (4405) crosses (4404) and is reflected by the second face of the double mirror (4403). The beam then passes through a diaphragm (4406) placed at the image focus of (4404) for the beam reflected by (4405), which will be called the second image focus of (4404). It then passes through a lens (4407) whose object focus coincides with the image focus of (4404). The beam then passes through a polarizer (4408). It is then reflected on a mirror (4409) placed a little behind the image focal plane of (4407). It then passes through a doublet of lenses (4411) (4410) of the type described in 8.1.4.1. The object focal plane

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 of this doublet coincides with the image focal plane of (4407). The amplitude SLM (4412) is placed in the image focal plane of this doublet. The beam passed through this doublet goes towards (4412) which reflects it. It then crosses the doublet, then crosses a polarizer (4413) and a diaphragm (4414) placed in the second image focal plane of the doublet (4410) (4411). It then crosses a doublet formed of (4415) and (4416). The object focal plane of the doublet (4415) (4416) coincides with the image focal plane of the doublet (4410) (4411). It is then directed to the amplitude SLM (4417) which reflects it. He then crosses the doublet (4415) (4416). It is reflected by a mirror (4418), passes through a diaphragm (4419) placed at the second image center of the doublet (4415) (4416), then passes through a polarizer (4420) and a lens (4421) whose object focal plane coincides with the second image focal plane of the doublet (4415) (4416). He then achieves a semi-reflective mirror (4307) which separates it into a right-hand FED light beam and a left FEG light beam.

 The beam FEG is then reflected by a mirror (4432) and passes through a doublet of lenses (4433) (4434) which can, depending on the congestion conditions, be before or after the mirror (4432). The object focal plane of the doublet (4433) (4434) coincides with the image focal plane of (4421). The beam is then reflected by a mirror (4435) and an assembly (4436) equivalent to the assembly (4910) of FIG. 69, movable about an axis (4450) and constituted mirrors (4446) (4447) (4448) (4449). The beam then passes through a beam extinguisher (4437). This beam extinguisher is constructed as the beam attenuator described in 7.2.2. but with a # null angle. The beam then passes through a polarization rotator (4341) and is separated by the semitransparent mirror (4325) into a main illumination beam directed toward (4324), which will still be noted FEG, and a directed reverse indicator beam. to (4342), which will be noted FEGI. The doublet (4433) (4434) thus has two image focal planes, one in the direction of the main beam and the other in the direction of the reverse indicator beam.

 The lens (4324) is placed in front of the image focal plane of the doublet (4433) (4434) so that the image focal plane of this doublet in the direction of the main beam remains virtual. The lens (4324) forms an image of this focal plane, and this image must be in the plane of the diaphragm (4323).

 The image focal plane of this doublet in the FEGI beam direction coincides with the object focal plane of a lens (4342). The beam FEGI passes through this lens which focuses it on a mirror (4343) which can optionally be closed by a shutter (4359). The beam reflected by this mirror crosses the lens (4342) and is reflected again by (4325). The beam FEGI then crosses a polarization rotator (4326) then a polarizer (4438). It is then reflected by one side of the double mirror (4439). It then crosses the doublet (4440) (4441) and moves towards the amplitude SLM (4442). The object focal plane of the doublet (4440) (4441) must be confused with an image focal plane of the doublet (4433) (4434). The amplitude SLM (4442) is placed in the image focal plane of the doublet (4440) (4441). The beam reflected by the SLM (4442) crosses the doublet (4440) (4441), is reflected by the second face of (4439), and points to a diaphragm (4443) placed in the second image focal plane of the doublet (4440). ) (4441). The beam passes through (4443) then a doublet (4444) (4445), a polarizer (4353), and reaches the CCD (4329) mounted on the camera (4330). The object focal plane of (4444) (4445) coincides with the second image focal plane of the doublet (4440) (4441). The CCD (4329) is placed in the image focal plane of (4444) (4445).

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 The FEG beam passes through the lens (4324) and the diaphragm (4323). It is then successively reflected by the mirrors (4322) (4451) (4452) (4453). It crosses the objective (4319) then the sample (4318), then the objective (4317). It is then successively reflected by the mirrors (4454) (4455) (4456) (4314) and reaches the diaphragm (4313). The diaphragm (4323) must be placed in the plane, or the objective (4319) normally forms the image of the sample, ie 160 mm from the neck of the lens for a standard lens.

The diaphragm (4313) must be placed in the plane or the objective (4317) normally forms the image of the sample.

 The beam FEG then passes through the lens (4312) which is placed in such a way that, in the case where a transparent plate is used (absence of disturbances by the object), and at the exit of this lens, the beam is parallel. The beam then passes through the polarization rotator (4338), the polarizer (4423) is reflected on a face of (4424), passes through the doublet (4425) (4426), is reflected on the amplitude SLM (4427), crosses the doublet (4425) (4426), is reflected on the second face of (4424), crosses the diaphragm (4428), the doublet (4429) (4430), the polarizer (4352), and reaches the CCD (4339) mounted on the camera (4384). The image of the diaphragm (4313) by the lens (4312) coincides with the object focal plane of the doublet (4425) (4426). The SLM (4427) is in the image focal plane of the doublet (4425) (4426). The diaphragm (4428) is in the second image focal plane of the doublet (4425) (4426). The object focal plane of the doublet (4430) (4429) coincides with the second image focal plane of the doublet (4425) (4426). The CCD (4339) is placed in the image focal plane of the doublet (4430) (4429).

 The right illumination beam FED passes through a lens (4431) and is reflected by a mirror (4308).

Depending on the congestion conditions, the position of the lens and the mirror can be reversed. The FED beam then passes through the beam extinguisher (4422) identical to (4437) and then the polarization rotator (4310). It is separated by a semi-transparent mirror (4311) into a main lighting beam that will still be noted FED and a reverse indicator beam that will be noted FEDI.

 The FEDI beam then passes through the lens (4331), is reflected by the mirror (4332), crosses (4331), is reflected in the direction of (4338) by the semi-transparent mirror (4311). (4332) can optionally be closed by the shutter (4358). (4332) is in a focal plane of (4331), and the other focal plane of (4331) coincides with the image of (4313) by (4312). The FEDI beam then follows (4311) and (4339) a path symmetrical to that followed by the FEGI beam between (4325) and (4329).

 The main illumination beam FED follows (4311) to (4329) a path symmetrical to that followed by the main illumination beam FEG between (4325) and (4339).

 The reference beam, separated from the illumination beam by the partially transparent mirror (4302), is separated into a right reference beam FRD and a left reference beam FRG by the semi-transparent mirror (4335).

 The right reference beam FRD is then reflected by the mirror (4344), then passes through the filter (4356) and the diaphragm (4349). It is then separated by the semi-transparent mirror (4345) into a reference beam directed towards the CCD (4339), which will still be noted FRD, and a reverse indicator beam that will be noted FRDI. The FRDI beam passes through the lens (4346), is focused on the mirror (4347) which reflects it,

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 crosses the lens (4346) and is partially reflected back to (4430). The shutter (4357) optionally allows the removal of this reverse indicator beam.

 The left reference beam FRG is reflected by the mirrors (4354) (4336) and then passes through a filter (4355), a phase shifter (4351), a diaphragm (4350). It is then separated by the semi-transparent mirror (4328) and a reference beam directed towards (4329), which will still be noted FRG, and a reverse indicator beam that will be noted FRGI. The FRGI beam passes through the lens (4381), is focused on the mirror (4382) which reflects it, crosses in the opposite direction (4381), and is partially reflected by (4328). The shutter (4360) optionally allows the removal of this reverse indicator beam.

 To help understanding the scheme the lighting beam has been shown in solid lines. It alternates between frequency planes and space planes, as defined in 8.1.1. In a frequency plane, the beam is focused at one point. In a space plane, it is parallel and 'centered', in the sense it illuminates a circular area symmetrical with respect to the optical axis, not depending on its orientation. The letter (E) associated with the number of an element means that this element is in a space plane. In the absence of an optical element, the letter (E) alone can also designate a space plane. Similarly, the letter (F) designates a frequency plan. A letter (E) has been placed on the diaphragm (4313), although this diaphragm is not exactly a plane of space: the image of this diaphragm by the lens (4312) which is a virtual space plane and which must be understood as designated by the letter E. Similarly. the diaphragm (4323) does not exactly correspond to a space plane.

 Conversely, the reference beam has been shown in dashed lines. The reference beam is concentrated at one point in the space planes. It is parallel and centered in the frequency planes.

 The space and frequency planes alternate on the path of the beam. A space plane and a successive frequency plan are always separated by a lens or a doublet. Their succession follows the logic outlined in 8.1. A space plane and a frequency plane separated by a lens (or a doublet) always occupy two focal planes of this lens (or doublet).

 The beam deflection device whose principle has been described in 8. 1.2. is implemented by elements corresponding to those of FIG. 65. The SLMs (4612) and (4614) are respectively materialized by the SLMs (4405) and (4412). The diaphragm (4615) is materialized by (4406). The device has been adapted to take into account that the SLMs operate in reflection, to include the polarizers, and to position the diaphragm (4406) in a different plane of the SLM (4412). The SLM (4417) has been added to further filter the illumination wave, improving the suppression of spurious frequencies.

 The direct wave suppressor described in 8.1.3. is implemented by elements corresponding to those of FIG. 66. The SLM (4704) corresponds to the SLM (4427). The diaphragms (4700) and (4706) correspond respectively to (4313) and (4428). The CCD (4709) corresponds to (4339). The lens (4703) corresponds to the doublet (4425) (4426). The lens (4705) corresponds to the same doublet crossed in the opposite direction. The lens (4708) corresponds to the doublet (4430) (4429). Symmetrical correspondences are valid for the symmetrical part of the microscope.

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 The doublets used allow an application of the principle described in 8.1.4.1. They consist of two lenses that can be moved together, one of the lenses can also be moved relative to each other.

 The system constituted by (4436) realizes the principle described in 8.1.4.2.

 On each polarizer, the passing axis is indicated by a line, representing an axis in the plane of the figure, or a circle, representing an axis in a plane orthogonal to the plane of the figure.

 On each SLM, a mark is represented which constitutes the one in which the coordinates of the pixels are evaluated. On each amplitude SLM, the position of the neutral axis corresponding to an extinction of the beam is also represented, with the same convention as for the passing axis of the polarizers.

The other possible position of the neutral axis is obtained from the extinction position by a rotation of about 40 degrees in one direction or another. On the SLM phase (4405) the two positions of the neutral axis are symmetrical with respect to a vertical axis.

 On the polarization rotators, a marker has been indicated. A position of the neutral axis, corresponding to an applied voltage of -5V, is the horizontal axis of the marker. In the other position, the neutral axis is approximately directed along a vector of equal coordinates on both axes.

 The polarizers (4408) (4413) (4420) may be Glan-Thomson prisms, which have the advantage of low absorption. They cause however a spherical aberration too important to be used on the path of the wave coming from the object. The polarizers (4423) (4352) (4438) (4353) are preferably dichroic polarizers consisting of a dichroic film held between two sufficiently thin glass plates.

 All lenses used in the system are achromats or compound lenses, minimizing spherical aberration.

 Most elements are mounted on positioners allowing a precise adjustment of their position. The characteristics of these positioners will be indicated in 8.5. at the same time as the setting procedure. The sample, whose positioning characteristics are not explained in 8. 5., is mounted on a three-axis positioner in translation.

8. 3. Dimensioning
It is necessary to specify the focal length of each lens and the aperture of each diaphragm to size the system. For doublets we will specify the focal length of the doublet. f, denotes the focal length of the lens (or doublet) number i, the lenses being numbered as follows:

<Tb>
<tb> index <SEP> i <SEP> number <SEP> of <SEP> the <SEP> lens <SEP> on <SEP> the <SEP> scheme, <SEP> or <SEP>, <SEP> between
<tb> parentheses, <SEP> of <SEP> two <SEP> lenses <SEP> constituting <SEP> a <SEP> doublet
<tb> 1 <SEP> 4401 <SEP>
<tb> 2 <SEP> 4404 <SEP>
<tb> 3 <SEP> 4407 <SEP>
<Tb>

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<Tb>
<tb> 4 <SEP> (4410,4411)
<tb> 5 <SEP> (4415,4416) <SEP>
<tb> 6 <SEP> 4421 <SEP>
<tb> 7 <SEP> 4431 <SEP> or <SEP> (4433,4434)
<tb> 8 <SEP> (4425,4426) <SEP> or <SEP> (4440,4441)
<tb> 9 <SEP> (4430,4429) <SEP> or <SEP> (4444,4445)
<tb> 10 <SEP> 4312 <SEP> or <SEP> 4324
<tb> 11 <SEP> 4331 <SEP> or <SEP> 4342
<tb> 12 <SEP> 4346 <SEP> or <SEP> 4381
<Tb>
li is the width of the diaphragm number i, the diaphragms being numbered as follows:

<Tb>
<tb> index <SEP> / <SEP> number <SEP> of the <SEP> diaphragm <SEP> on <SEP> the <SEP> schema
<tb> 0 <SEP> 4349 <SEP> or <SEP> 4350
<tb> 1 <SEP> 4348 <SEP>
<tb> 2 <SEP> 4406 <SEP>
<tb> 3 <SEP> 4414 <SEP>
<tb> 4 <SEP> 4419 <SEP>
<tb> 5 <SEP> 4313 <SEP> or <SEP> 4323
<tb> 6 <SEP> 4428 <SEP> or <SEP> 4443
<Tb>
In addition we adopt the following notations: pc distance between the centers of two adjacent pixels, on the CCD sensors pc distance between the centers of two adjacent pixels, on the SLM phase pf distance between the centers of two adjacent pixels, on the SLM amplitude
Npix number of pixels on a CCD sensor or an amplitude SLM (these numbers are equal).

 Ns number of pixels on the phase SLM. Ideally we should have Ns = 2Npix but the SLM are not available in any size and we can also be satisfied with Ns = Npix with additional attenuation of the lighting beam. o: numerical aperture of a microscope objective g: magnification of a microscope objective f0: focal length of a microscope objective. d0: distance between the lens (4312) and the diaphragm (4313).

The width of the reference beam must be at least: l0 = pcNpix

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La largeur d'illumination sur (4405) est: psNs = 'f-2 l1, d'ou on tire: 'f2 ~ ## f1 f1 l1 f2~psNs Pour éviter une perte de puissance inutile il est préférable d'avoir l0 = l1 et donc f2 = psNs f1 pcNpix La largeur du diaphragme (4406), qui laisse passer la moitié des fréquences provenant du SLM (4405) sous

un angle a max est : l2 = f2 sin max soit avec la valeur de sin max qui résulte de 8.1.2. , l2 = f2 - La partie utile du SLM (4412) doit être l'image du diaphragme (4406) ce qui implique: f4/f3l2 = pf Npix

A partir des deux équations précédentes on obtient: f3 f2 = 2S p f Np, L'onde issue de (4412) présente un angle maximal sin,l3m = 2 . Le diaphragme (4414) doit laisser 2p passer la totalité de ces ondes et vérifie donc : 13 = 2 sin/?max/4 soit 13 = f4 -
Pf La largeur du diaphragme (4419) est égale à celle du diaphragme (4413) Soit 14 = l3 Sa largeur est transformée en la largeur du diaphragme objet (4312) par : l5 = f7/f@ l3 f6 La largeur du diaphragme objet (4312) vaut: l5 #/2 g/0 N pix

Des équations précédentes on tire: f4 L7 = 2 ô p f N p f6 2 0 La taille d'image sur le SLM (4427) doit être la même que sur le SLM (4417) d'ou: f6/f f8/f = 1 f5 f7

La taille d'image sur la caméra est liée à celle sur le SLM (4427) par: PeN plX = f9 PIN plX soit: f9 = -f~ f8 f8 pf Les SLM (4412 et (4417) étant de mêmes caractéristiques, on a: f4 = f5 La lentille (4312) doit avoir son plan focal objet confondu avec le plan focal image de l'objectif de microscope, et se trouve à une distance do de l'image de l'objectif. On vérifie que ceci implique: f10 = gf0 + d0 La distance focale de (4331) ou de (4346) doit être suffisante pour éviter l'aberration sphérique. f2 f2 ~ PsNs

The illumination width on (4405) is: psNs = 'f-2 l1, from which one draws:' f2 ~ ## f1 f1 l1 f2 ~ psNs To avoid a loss of unnecessary power it is better to have l0 = l1 and thus f2 = psNs f1 pcNpix The width of the diaphragm (4406), which lets half of the frequencies coming from the SLM (4405) under

an angle a max is: l2 = f2 sin max or with the value of sin max which results from 8.1.2. , l2 = f2 - The useful part of the SLM (4412) must be the image of the diaphragm (4406) which implies: f4 / f3l2 = pf Npix

From the two previous equations we obtain: f3 f2 = 2S pf Np, The wave resulting from (4412) has a maximum angle sin, l3m = 2. The diaphragm (4414) must let 2p pass all of these waves and thus check: 13 = 2 sin /? Max / 4 = 13 = f4 -
Pf The width of the diaphragm (4419) is equal to that of the diaphragm (4413) Either 14 = 13 Its width is transformed into the width of the object diaphragm (4312) by: 15 = f7 / f @ l3 f6 The width of the diaphragm object ( 4312) is worth: l5 # / 2 g / 0 N pix

From the previous equations we draw: f4 L7 = 2 pf N p f6 2 0 The image size on the SLM (4427) should be the same as on the SLM (4417) of where: f6 / f f8 / f = 1 f5 f7

The image size on the camera is linked to that on the SLM (4427) by: PeN plX = f9 PIN plX ie: f9 = -f ~ f8 f8 pf The SLMs (4412 and (4417) having the same characteristics, a: f4 = f5 The lens (4312) must have its object focal plane coincident with the image focal plane of the microscope objective, and is at a distance do from the image of the objective. : f10 = gf0 + d0 The focal length of (4331) or (4346) must be sufficient to avoid spherical aberration.

f2 - f4 = /5 = f6 = f7 = f8 - fli = f12 - f Any set of values satisfying the above equations may in principle be suitable. A particularly simple solution is to ask: f = pfNpix g
2 o and to impose:

f2 - f4 = / 5 = f6 = f7 = f8 - fli = f12 - f

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13 = K 1 O 1PS f1 = pcNpixf

PS NS f9 = pcf
Pf f10 = gf0 + d0 et les ouvertures de diaphragmes:

10 =15 =13 =14 =2-;;NpIX 12 = f - l0 = l1 = pcNpix La largeur du faisceau en sortie de l'élargisseur de faisceau (4301) doit être légèrement supérieure à l0, la limitation étant effectuée plus loin par les diaphragmes. The other focal lengths are then easily obtained:

13 = K 1 O 1 PS f1 = pcNpixf

PS NS f9 = pcf
Pf f10 = gf0 + d0 and the openings of diaphragms:

10 = 15 = 13 = 14 = 2 - ;; NpIX 12 = f - l0 = l1 = pcNpix The width of the beam at the output of the beam expander (4301) should be slightly greater than 10, the limitation being carried out further by the diaphragms.

8. 4. Operating mode
The mode of operation is essentially the same as in the third embodiment.

à Ns -1, l'élément 4[,/] correspondant au pixel de coordonnées k, et ayant la valeur 0 pour un pixel de phase négative et la valeur 1 pour un pixel de phase positive. L'état des SLM (4412) et (4417) est donné par un tableau de commande B[k, l] dans lequel k et 1 varient de 0 à Npix - 1 , l'élément B[k,l] correspondant au pixel de coordonnées k, l et ayant la valeur 0 pour un pixel éteint et la valeur 1 pour un pixel allumé. It is therefore described by paragraphs 7.4. at 7.17. and by the variants exposed in 7. 18. A certain number of differences must however be noted:
8. 4.1. Beam Diverter Control
The state of the SLM (4405) is given by a control panel A [k, l] where k and l vary from 0

at Ns -1, the element 4 [, /] corresponding to the coordinate pixel k, and having the value 0 for a negative phase pixel and the value 1 for a positive phase pixel. The state of the SLMs (4412) and (4417) is given by a control panel B [k, l] in which k and 1 vary from 0 to Npix-1, the element B [k, l] corresponding to the pixel of coordinates k, l and having the value 0 for a pixel off and the value 1 for a pixel lit.

avec B,) [k, 1] = 0 en tout point sauf en i,j ou on a BI) [i, j] = 1 - on applique au SLM (4405) un tableau A, approprié, soit : A, [k, 1] = E 1 ki + 1)+1(1 + 1 I-/.2j
Npix ou E désigne la partie entière et %2 signifie modulo 2. To obtain a frequency characterized by the indices (i, j): - the pixel of coordinates i, j is illuminated on the SLMs (4412) and (4417) that is to say that a table is used

with B,) [k, 1] = 0 at all points except i, j where we have BI) [i, j] = 1 - we apply to SLM (4405) an appropriate array A, namely: A, [ k, 1] = E 1 ki + 1) +1 (1 + 1 I - / 2j
Npix or E denotes the integer part and% 2 means modulo 2.

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tableau de commande du SLM (4405) fl, [k,1] = E 1 {ki + 1 +l j + 1) %2 Npx tableau de commande du SLM (4412) BI] [i, j] = 1 B,}[k,l] = 0 si (k, 1) mot de commande tableau de commande du SLM (4417) B [i, j] = 1 COM[p, i, j] B, [k,l] = 0 si (k, l (i, j bits de commande des rotateurs de (4422) p, p bits de commande des rotateurs de (4437) p,p
Le mot de commande ainsi constitué se substitue dans l'ensemble des procédures 7. 4. à 7.17. à celui qui était constitué comme indiqué en 7.2.4. The 'control word' used in the third embodiment is therefore constituted by the concatenation of the control panels of the SLMs (4405) (4412) (4417) and the control bits of the phase rotators of (4422) and ( 4437). As before, the directly illuminated sensor is designated by the index p with p = 0 for (4339) and p = 1 for (4329). For control of the phase rotators included in the beam extinguishers (4422) and (4437) a null control bit corresponds to an applied voltage of 5V (open position) and a control bit to 1 corresponds to an applied voltage of - 5V (closed position).

SLM control panel (4405) fl, [k, 1] = E 1 {ki + 1 + lj + 1)% 2 Npx control board of the SLM (4412) BI] [i, j] = 1 B,} [k, l] = 0 if (k, 1) SLM control panel command word (4417) B [i, j] = 1 COM [p, i, j] B, [k, l] = 0 (k, l (i, j rotator control bits of (4422) p, p rotator control bits of (4437) p, p
The control word thus constituted is substituted in the set of procedures 7. 4. to 7.17. to the one who was constituted as indicated in 7.2.4.

 8. 4.2. Use of the direct wave suppression system.

par le faisceau d'éclairage soit i=la[q,p,lc[k,p],Jc[k,p]], j=Ja[q,p,lc[k,p],Jc[k,p]]. Il est donné par le tableau suivant, ou r désigne un 'rayon d'extinction' que l'on peut par exemple prendre égal à 2.

indice c 2 autre (atténuation non maximale) indice du SLM p p indices*.' (k -i)2 +(1- j)2 >rZ (k ~i)2 +tl- j2 <r2 valeur de l'élément du tableau C[k,l] 1 1 1 0 The SLMs (4427) and (4442) are respectively associated with the sensors (4339) and (4329) and indexed by the same indices /? = 0 and p = 1. In the procedure described in 7.12.2.1., Phase 1, during the acquisition of a pair of elementary images, it is necessary to also control these SLMs. The value of an element C [k, l] of the control panel used for such an SLM depends on the index of the SLM, the indices c and p of the image being acquired, and the indices i and j corresponding to the point of the illuminated sensor directly

by the light beam i = [q, p, lc [k, p], Jc [k, p]], j = Ja [q, p, lc [k, p], Jc [k, p ]]. It is given by the following table, where r denotes an 'extinction radius' which can for example be equal to 2.

index c 2 other (non-maximal attenuation) index of SLM pp indices *. ' (k -i) 2 + (1- j) 2> rZ (k ~ i) 2 + tl-j2 <r2 value of the element of the array C [k, l] 1 1 1 0

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 8. 4.3. Using regular sampling.

la[q, p, t , j = ip + (N p. - i -1) p Ja [q,p,i,j]=j
Il suffit donc de déterminer le tableau Ra[p,i,j]
On utilise les tableaux Io et Jo caractérisant une trajectoire parcourant l'ensemble des points accessibles, c'est-à-dire que (lo[k], Jo[k]) doit parcourir l'ensemble des valeurs telles que
Npix) 2 Npix)2

Io[k] - -J + (JO[k]- N ' l2 J 5.R;uv ou Rou,, est le rayon du disque limité par l'ouverture de l'objectif sur un capteur, et correspond par exemple au rayon de la zone illuminée sur (4339) lorsque le faisceau FRGI est utilisé seul. Cette trajectoire sera nommée par la suite trajectoire complète . 8.4.3.1.Modification of the procedure 7. 9.2. the coordinates of the light beams are known in advance and are:

the [q, p, t, j = ip + (N p - -1 -1) p Ja [q, p, i, j] = j
It is therefore sufficient to determine the array Ra [p, i, j]
We use the tables Io and Jo characterizing a trajectory traversing the set of accessible points, that is to say that (lo [k], Jo [k]) must traverse all the values such that
Npix) 2 Npix) 2

Io [k] -J + (OJ [k] - N '12 J 5.R; uv or Rou ,, is the radius of the disk limited by the opening of the objective on a sensor, and corresponds for example to the radius of the illuminated area on (4339) when the FRGI beam is used alone This trajectory will be named after the complete trajectory.

 A program performs the acquisition defined by these tables, according to the procedure described in 7.12.

acquisition, il suffit d'enregistrer les valeurs M f/o[1,Jo[/c]1 et H k,p,q [1 r ,) r ] . The index n0 is not known, it is taken equal to n @ in the procedure 7.12, However, during this

acquisition, just record the values M f / o [1, Jo [/ c] 1 and H k, p, q [1 r,) r].

ou ir, jr sont les coordonnées du maximum de l'image de référence, comme définies en 7.12. et ou x,y,z sont les coordonnées déterminées en 7.9.1. The program initializes the array Ra to 0, then it traverses the series of indices k, p by performing for each pair k, p:

where ir, jr are the coordinates of the maximum of the reference image, as defined in 7.12. and where x, y, z are the coordinates determined in 7.9.1.

 8.4.3.2. Modification of the procedure 7. 11.

d'images Mk.p.q [<,y] et Hk,P.9 [',7]. Toutefois, lors de cette acquisition, il suffit d'enregistrer les valeurs MkP,9Ll Lk''I Lk,et Hk>P>9Ltr>Jr. Le programme parcourt alors la série des indices k. Pour chaque valeur k il effectue :

The program performs the series of acquisitions defined by the tables Io and Jo defining a complete trajectory, already used in 8.4.3.1., According to the procedure described in 7.12. It thus generates the series

of images Mk.pq [<, y] and Hk, P.9 [', 7]. However, during this acquisition, it is sufficient to record the values MkP, 9Ll Lk''I Lk, and Hk>P>9Ltr> Jr. The program then goes through the series of indices k. For each value k it performs:

The program described in 7. 8. is then used to calculate the parameters x, y, z, L, n0 from the table Frec thus constituted.

 The procedure 7. 11. thus reformulated can be used directly to calculate x, y, z, L, no in the case of the uniaxial crystal described in 7. 18.9., Thus avoiding having to carry out preliminary measurements and making

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 possible movement of objectives. In this case, the acquisition mode of the series of images allowing the calculation of x, y, z, L, no corresponds to the procedure described in 7.12 and modified as indicated in 7.18.9.

 8. 4.3.3. Modification of the procedure 7. 13.

Idp,i, j=ip+NP, -i-1)p Jd[p.iJ]=j I4k, p] plok+(Np. -Iok-1)p
Jc[k,p] = Jo[k]
8. 4.3.4. modification de la procédure 7. 6. In 7. 13, we obtain directly without using the program of fig. 53:

Idp, i, j = ip + NP, -i-1) p Jd [p.iJ] = j I4k, p] plok + (Np-Iok-1) p
Jc [k, p] = Jo [k]
8. 4.3.4. modification of the procedure 7. 6.

The values of the coefficients K1, K2 determined in 7.6. check: K1 = K2
8. 5. Setting:
The position of each element of the system must be precisely set before use.

8. 5.1. used devices
Devices already described in 7. 3.3.2. are used.

8. 5.2. Types of images used
During the adjustment, various types of images may be used: - images obtained on an auxiliary CCD: auxiliary CCD placed for example in a space plane may make it possible to determine the center of a lighting beam in this plane, or the punctuality in this plane of a reference beam.

 - images obtained on one of the microscope CCDs: these images can be obtained and analyzed as indicated in 7.3.3.1. in the presence of a reference beam. One can also directly observe the received images in the absence of reference beam.

 - images obtained on the CCD of the frequency meter: directly, they make it possible to check the flatness of a wave or the angle separating two plane waves.

 - images of the surface of an SLM: placing the frequency meter behind the lens which transforms the wave coming from a given point of the SLM into a plane wave, an image of the surface of the SLM is formed on the CCD of the frequency meter, which can be used for example to check that the SLM is lit properly. To view figures formed by controlling the SLM, a polarizer must also be present between the SLM and the CCD of the frequency meter. If it is not already present in the system, it is possible to use the polarizer of the frequency meter.

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 pixel-by-pixel images of the surface of an SLM: such an image consists of a two-dimensional array containing the illumination of each pixel. To obtain it, the frequency meter is placed as before, in the presence of a polarizer. The entire SLM is placed in an absorbing position ('black' image). Then we turn on each pixel one by one, each time recording the intensity of the corresponding point on the frequency meter. The intensities thus measured for each pixel of the SLM are stored in a table, which constitutes the pixel-by-pixel image of the SLM. This type of image can be used for example to check the point-by-point correspondence between the various SLMs, necessary to obtain a correct lighting and a regular sampling.

 8. 5.3. Setting criteria.

 The adjustments are to ensure that: (1) the beams follow the intended path. This can usually be verified using a simple diffuser.

(2) the lighting beams are parallel in the space planes. This is verified using the frequency meter.

(3) the reference beams are punctual in the space planes and the illumination beams are punctual in the frequency planes. This is true for example using an auxiliary CCD.

(4) the polarizers are well adjusted. The beam extinctions can for example be observed on the frequency meter.

(5) a beam entering parallel to the objective (4317) and directed along the optical axis has a point image and centered on the sensor (4339).

(4442) et sur les capteurs (4339) et (4329) doivent avoir pour coordonnées (N,,x - 1 - i,i) Cette condition (6) peut se vérifier à l'aide d'images obtenues sur les capteurs ou à l'aide d'images pixel par pixel obtenues sur les CCD. (6) when the control word Al, j is used for the SLM (4405) and when the control word B1, j is used for the SLMs (4412) and (4417), the following conditions are met: (i) the point of coordinates l, j must be effectively illuminated on the SLMs (4412) and (4417) (ii) when the FEG and FEGI beams are used, the illuminated points on the SLMs (4427) and (4442) and on the sensors (4339) and (4329) must have the coordinates (i, j) (iii) when the FED and FEDI beams are used, the illuminated points on the SLMs (4427) and

(4442) and on the sensors (4339) and (4329) must have the following coordinates (N ,, x - 1 - i, i). This condition (6) can be verified by means of images obtained from the sensors or using pixel-by-pixel images obtained on the CCDs.

 The settings to be made are based on these conditions. The description of the adjustment steps is given for information only and constitutes an example of scheduling of the adjustment steps.

8. 5.4. Setting steps
In the description of the adjustment steps, reference will frequently be made to the optical axis. Due to the many reflections, the optical axis can only be defined locally. It is therefore to this optical axis defined locally that reference will be made.

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 Prior to any fine tuning, the whole system is set up with all the precision possible by geometric methods, with the exception of the elements (4304) (4305) (4422) (4437) (4351) which will be put in place. place during adjustment.

Throughout the adjustment, the position of the neutral axis of the polarization rotators (4310) (4338) (4341) (4326) is maintained in the plane of FIG. 62. A point will be said centered on one of the sensors (4339) or (4329) if its coordinates are (Npix / 2, Npix / 2
In the first step of setting a given element, the type of positioner on which this element is mounted is indicated.

Step 1. Laser beam (4300) beam angle adjustment (4301)
This assembly is mounted on an angular positioner for adjusting the direction of the beam.

A diffuser is used to check the beam path. The position of the set (4300,4301) is adjusted so that the beam follows the intended path.

Step 2. Implementation of the phase shift device (4304).

 This phase shift device is identical to that described in 7. 2.3. and set up as described in 7.3.2.3.

Step 3. Implementation of the beam attenuation device (4305).

 This beam attenuation device is identical to that described in 7. 2.2. and is implemented as described in 7.3.2.2.

Step 4 .: 2-axis translation adjustment of the 'hole' (4402)
This hole is mounted on a two-dimensional positioner allowing displacement in the plane orthogonal to the optical axis.

 It is set to maximize the intensity of the beam that has passed through the 'hole'.

Step 5. Adjusting the orientation of the two-sided mirror (4403)
This mirror is mounted on an angular positioner to adjust the orientation. A diffuser is used to check the beam path and the position of the mirror is set so that the incident beam on the SLM (4405) occupies the entire usable area of this SLM.

Step 6. Setting the orientation of the SLM (4405)
This SLM is mounted on an angular positioner to adjust its orientation, coupled with a positioner two axes in translation allowing adjustment of its position in a plane orthogonal to the optical axis.

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 The SLM is put in a totally reflective position. A diffuser is used to verify that the reflected wave on the SLM reaches the intended point on the mirror (4403) and is moving in the intended direction.

Step 7. Fine adjustment of the orientation of the two-sided mirror (4403), translation adjustment of the SLM (4405), adjustment of the aperture of the diaphragm (4348), and translational adjustment of the lens (4404).

 The lens (4404) is mounted on a positioner a translational axis allowing adjustment in translation in the direction of its optical axis.

* This step aims to: - adjust the position of the lens (4404) so that the SLM (4405) is in a space plane.

adjusting the orientation of the two-sided mirror (4403) and the translational position of (4405) so that the beam arriving at (4405) is centered.

- adjust the opening of (4348) so that the beam incident on (4405) is as wide as possible, without overflowing the active surface of the SLM.

 It is possible on an SLM to independently control the active zone and a peripheral zone called 'apron'. The entire active area is controlled to perform a polarization rotation in a given direction, and the apron is controlled to perform a polarization rotation in the opposite direction. The active zone is then modified so that a cross centered in the middle of the active zone is put in the same state as the apron.

 The frequency meter is positioned behind (4406), which is wide open.

 The opening of the diaphragm (4348) is slightly greater (by 20% for example) than its nominal opening calculated in 8.4.

 The frequency meter is first positioned in the absence of its polarizer so that an image of the illuminated area of (4405) is formed on its CCD.

 The polarizer of the frequency meter is then introduced and set in rotation so as to show on the image a maximum contrast between the peripheral zone ('apron') and the active central zone of the SLM.

 The position of (4403) is then adjusted so that the whole of the active zone and the border with the apron is visible on the image. We must see an illuminated square active area surrounded by a dark area (the apron) and crossed with a centered cross.

 The position of (4404) is set to have the best possible contrast.

 The diaphragm (4348) is then reduced in opening. We must see on the image an illuminated disc of reduced diameter, intercepting the dark cross. The position of (4403) and that of (4405) in translation are adjusted so that the center of the disc and the center of the cross coincide.

 The position of (4404) is adjusted again to have the best possible contrast.

 The opening of the diaphragm (4348) is then enlarged to the maximum without however that the illuminated disk reaches the zone of apron.

Step 8. Translational adjustment of the lens (4407)

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This lens is mounted on a positioner in translation an axis in the direction of the optical axis.

 This adjustment is intended to ensure that a parallel beam from the laser and fully reflected by (4405) is again parallel after passage of (4407).

 The frequency meter is positioned behind (4407). (4406) is widely open. The control panel of (4405) is fully set to 0. The position of (4407) is adjusted to have an image as punctual as possible on the frequency meter.

Step 9. Rotational adjustment of the polarizer (4408).

 The polarizer (4408) is attached to a positioner allowing adjustment in rotation about the optical axis.

 When the command word Aoo is used, the SLM (4405) reflects the beam in a direction DO. When ANpix -1.0 is used, the direction of the beam is changed and the component on the frequency corresponding to the direction DO must be canceled. The polarizer (4408) is set to effectively cancel this component.

 The frequency meter is positioned behind (4408). The diaphragm (4406) is widely open. Table Aoo is first applied to (4405). The illuminated point P on the frequency meter's CCD is located. The ANpix-1.0 array is then used and the position of (4408) is adjusted to cancel the intensity received at point P.

Step 10. Adjustment in 2-axis translation and opening of the diaphragm (4406)
The diaphragm (4406) has an adjustable opening and is adjustable in translation along two axes orthogonal to the optical axis.

 Its position and its aperture must be adjusted so that it passes the useful frequencies and stops the symmetrical frequencies, its role being that of the diaphragm (4615) described in 8.1.2.

 The frequency meter is used and positioned behind (4408). The CCD axes of the frequency counter must be oriented as indicated by the mark (4470). A specific program is used.

Le programme somme les intensités obtenues dans chaque cas par le capteur CCD et affiche l'image correspondante. Il superpose sur cette image des symboles indiquant le maximum obtenu dans chacun de ces cas. Il itère indéfiniment cette procédure pour que cette image soit mise à jour en permanence pendant le réglage du diaphragme. This program successively applies to the SLM (4405) the tables:

The program summarizes the intensities obtained in each case by the CCD sensor and displays the corresponding image. It superimposes on this image symbols indicating the maximum obtained in each of these cases. It iterates indefinitely this procedure so that this image is constantly updated during the adjustment of the diaphragm.

 The diaphragm must be adjusted in position and opening so that the point obtained for the indices (0,0) is not visible (closed by the diaphragm) and so that the other four points are visible (at the limit of diaphragm), positions shown in Fig. 72 or (5010) represents the limit of the diaphragm.

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Step 11. Adjusting the orientation of the mirror (4409)
The mirror (4409) is fixed on a positioner to adjust its orientation.

It is applied to (4405) the table ANpix NpixUn diffuser is used to control the trajectory of the
2 '2 beam. The angular position of (4409) is adjusted so that the beam reaches the center of (4412).

Step 12. Adjusting the orientation of the SLM (4412)
The SLM (4412) is attached to a three-axis positioner in rotation to adjust the orientation (axes in the plane of the sensor) and the rotational position (axis orthogonal to the plane of the sensor), coupled with a two-axis positioner in translation allowing displacement in a plane orthogonal to the optical axis.

 The ANpix Npix array remains applied to (4405). The control panel of (4412) is set to 1. A 2 'diffuser is used to control the path of the beam. (4412) is adjusted so that the wave is reflected to (4414) and is centered in the middle of this diaphragm.

Step 13. Rotating the polarizer (4413)
The control panel of (4412) is set to 1. The frequency meter is positioned behind (4413) so that the image of (4412) is formed on its CCD. The control panel of (4412) is then set to 0. (4413) is then set in rotation so as to cancel the intensity received on the CCD of the frequency meter.

Step 14. Fine adjustment of the mirror orientation (4409), adjustment of the position and focal length of the doublet (4410) (4411), and adjustment in rotation and translation of the SLM (4412).

 The lens (4410) is mounted on a positioner an axis in the direction of the optical axis. This positioner and the lens (4411) are themselves mounted on a second positioner an axis in the direction of the optical axis. It is therefore possible either to move together (4410) (4411) or move (4410) alone to vary the distance between the two lenses of the doublet (4410) (4411).

 The SLM (4405) makes it possible to control the direction in which the wave coming from this SLM is diffracted.

At a direction of the beam at the output of the SLM (4405) corresponds a point in a frequency plane and in particular a point in the plane of the SLM (4412).

est appliqué à (4405) corresponde à un point de coordonnées C Np'x 2 ' Nprx 2 sur le SLM (4412). La position de (4410)(4411)(4412) doit en outre être réglée pour qu'il y ait une correspondance point à point entre les The position of (4410) (4411) should be adjusted so that the beam image from the SLM (4405) is actually punctual in the frequency plane or is (4412). The position of (4409) and (4412) must be set so that the frequency generated when the control panel ANpix Npix 2 '2

is applied to (4405) corresponds to a coordinate point C Np'x 2 'Nprx 2 on the SLM (4412). The position of (4410) (4411) (4412) shall further be set to have a point-to-point correspondence between

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 frequencies generated by the arrays A1, j applied to (4405) and the pixels of (4412), that is to say that when the control panel A1, j is applied to (4405) the coordinate pixel (i , j) be illuminated on the SLM (4412), regardless of the integers i and j.

 The series of operations ol to o3 is repeated a sufficient number of times, so as to converge to the correct position of each element. ol. Setting the joint position of (4410) and (4411) to obtain a point-in-time image.

The frequency meter is positioned behind (4414). The diaphragm (4414) is widely open. The ANpix Npix array is applied to (4405) and the control array applied to (4412) is set to 1. The position
2.2 joint of the set (4410) (4411) is adjusted to have on the CCD sensor of the frequency meter an image as punctual as possible.

02. Angular adjustment of (4409) and translation adjustment of (4412) to obtain a centered frequency image.

 ANpix Npixreste applied to (4405). (4409) and (4412) are then set so that the generated center frequency 2 '2 is in the middle of the SLM (4412). This adjustment is done with the frequency meter and a program of localization of the maximum, which one will call program PA.

 The PA program turns on each pixel of the SLM (4412) and measures the corresponding intensity on the frequency meter. The pixel generating the highest intensity corresponds to the maximum.

coordonnées (i,j) des pixels sur le SLM (4412), i et variant de 0 à Noix - 1. Pour chaque couple (i,j) cette procédure effectue les étapes suivantes: - elle applique le tableau de commande Blj défini comme en 8.4.1. au SLM (4412). The basic procedure of the PA program, which will be called PB, runs through all the

coordinates (i, j) pixels on the SLM (4412), i and ranging from 0 to Nuts - 1. For each pair (i, j) this procedure performs the following steps: - it applies the control panel Blj defined as in 8.4.1. at the SLM (4412).

- It then acquires an image on the CCD of the frequency meter.

it determines the maximum value of the intensity measured over all the points of this image.

que les valeurs de io, jo et la valeur Ao ' 7o ] '
Le programme PA consiste à itérer indéfiniment la procédure PB de manière à pouvoir effectuer le réglage correspondant. - it saves this value in a table M in M [i, j]
When it has thus traversed the set of indices i, the procedure determines the point of maximum intensity of the array M and its indices i0, j0 which correspond to the maximum. It displays on the screen the two-dimensional image corresponding to the array M, possibly enlarged around the maximum, as well as

that the values of io, jo and the value Ao '7o]'
The program PA is to iterate indefinitely PB procedure so as to make the corresponding setting.

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La position de (4409) doit être ajustée pour avoir (i 0' j 0) = # # , # # et pour maximiser M [i0,j0]. o3. Réglage de focale du doublet (4410)(4411) et réglage de (4412) en rotation.

The position of (4409) must be adjusted to have (i 0 'j 0) = # #, # # and to maximize M [i0, j0]. o3. Focal length adjustment of the doublet (4410) (4411) and adjustment of (4412) in rotation.

The frequency meter, set as before, is used. A program for displaying the characteristics of the system is used, which will be called a PC program.

A N AN Bzz AN-1-,N? appliqués à (4405). Ces tableaux de commande sont - -Ic -,Npi -1-C c.# 2 2 2 2 2 numérotés dans cet ordre. c est une constante, par exemple c=20, introduite pour éviter que les points illuminés sortent de la zone active du SLM en cas de mauvais réglage initial. The PC program successively uses four control panels

AN AN Bzz AN-1-, N? applied to (4405). These control boards are - -Ic -, Npi -1-C c # 2 2 2 2 2 numbered in this order. c is a constant, for example c = 20, introduced to prevent illuminated points from coming out of the active area of the SLM in the event of a bad initial setting.

For the nth command word, the program uses the PB procedure already described and stores the coordinates of the maximum obtained in X [n] and Y [n]. When this operation was performed for the four command words, the program thus obtained four-element X and Y arrays, corresponding to the pixel coordinates of the successive maximums. When the system is well tuned, one must have:

The purpose of the adjustment is therefore to obtain these equalities effectively. Adjusting the focal length of the doublet (4410) (4411) adjusts the scale and the rotation setting of (4412) adjusts the rotational position.

Si/est la distance focale de chaque lentille et si dl est la distance entre ces lentilles avant réglage,

distance focale effective l'ensemble deux lentilles avant réglage est: fI distance focale effective l'ensemble deux lentilles avant réglage est; f, - - 2 1 - dl 1---L 2f de même la distance focale de l'ensemble après réglage est: f2 = f 2 1 ~ 1 dz 2f The program calculates the ratio of the actual distances to the distances that should be obtained with a correct setting:

If / is the focal length of each lens and if dl is the distance between these lenses before adjustment,

effective focal length the whole two lenses before adjustment is: fI effective focal length the whole two lenses before adjustment is; f, - - 2 1 - dl 1 --- L 2f likewise the focal length of the assembly after adjustment is: f2 = f 2 1 ~ 1 dz 2f

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Dans cette équation/et dl sont mal connus mais on peut utiliser la distance focale 'de conception' du doublet (4410)(4411) . Cette distance est celle pour laquelle le doublet a été prévue. On la notera fc et elle vaut à peu près f/2. On obtient alors:

d2 -dl =4fc(1-r) Le programme PC affiche:

- la valeur d2 - dl , qui permet de corriger en conséquence la distance entre lentilles. The magnification being proportional to the focal length, it must be adjusted so that: f2 / f1 = 1 / r which leads, by developing the calculations, to:

In this equation / and dl are poorly known but one can use the 'design' focal length of the doublet (4410) (4411). This distance is the one for which the doublet has been predicted. It will be noted fc and it is worth about f / 2. We then obtain:

d2 -dl = 4fc (1-r) The PC program displays:

- The value d2 - dl, which allows to correct accordingly the distance between lenses.

the straight lines respectively connecting the points 1 and 4 and the points 2 and 3 X [1] -X [4] - the difference X [1] -X [4] / N-2c, which gives approximately the angle in radians whose rotation position must be corrected.

-le rapport 1'(2] - r[ 3] , qui doit être égal à 1. Npix-2c
X [1] -X [4]

the ratio 1 '(2) - r [3], which must be equal to 1.

X [1] -X [4]
The SLM (4412) is rotated to cancel the displayed deviation X [1] -X [4] / Npix-2c, and the
Npix-2c distance between the lenses of the doublet (4410) (4411) is changed according to the displayed value of d2-d1.

Step 15. Adjustment of the diaphragm (4414) in translation.

 The diaphragm (4414) is mounted on a positioner 2 axes in translation to move in a plane orthogonal to the optical axis.

 The opening of (4414) is known. It must be set in translation. An auxiliary CCD is placed just behind (4414). The BNpix Npix control panel is used for the SLM (4405), i.e. 2 '2 only one center point of this SLM is turned on, the direct reflected beam being stopped by (4406). The SLM control panel (4412) is set to 1 (pass position). The image of the lit point of (4405) is then formed in the plane of the diaphragm (4414). (4414) is then set in translation so that its center coincides with the image of the lit point of (4405).

Step 16. Adjustment in 2-axis translation of the SLM (4417)

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This SLM is mounted on a positioner two axes in translation in the plane of the SLM, coupled with a positioner three axes in rotation to adjust the orientation (axes in the plane of the sensor) and the position in rotation (axis in a orthogonal plane to the sensor).

Control panels, 4 NN and BN N are used respectively for SLMs
2 '2' 2 (4405) and (4412). A diffuser is used to track the beam arriving at (4417) and (4417) is set in translation so that the beam reaches its center.

Step 17. Setting the orientation of the SLM (4417).

 The same control boards as before are used for SLMs (4405) (4412). The control panel of the SLM (4417) is set to 1. (4417) is set so that the reflected beam reaches the intended point on (4419), which is verified by means of a diffuser.

Step 18. Adjusting the orientation of the mirror (4418)
The mirror (4418) is mounted on an angular positioner to adjust its orientation.

 (4418) is set to effectively return the beam in the intended direction, which is verified with a diffuser.

Step 19. Translational adjustment of the diaphragm (4419)
The diaphragm (4419) is mounted on a two-axis positioner in translation allowing displacement in a plane orthogonal to the optical axis.

The opening of (4419) is known. It must be set in translation. The BNpix Npix control panel is used for the SLM (4405), ie only one center point of this SLM is turned on,
2.2 the direct reflected beam being stopped by (4406). SLM (4412) and (4417) control panels are set to 1 (pass position). The image of the lit point of (4405) is then formed in the plane of the diaphragm (4419). (4419) is then set in translation so that its center coincides with the image of the lit point of (4405).

Step 20. Rotating the polarizer (4420)
The polarizer (4420) is mounted on a positioner allowing its adjustment in rotation with respect to the optical axis.

The command boards ANpix Npix and BNpix Npix are respectively applied to (4405) and
2,2 2 '2 (4412). The control panel of (4417) is set to 1. The frequency meter is placed just behind (4420).

The image on his CCD is pretty punctual. The control board of (4417) is then set to 0. The position of (4420) is adjusted to cancel the intensity received on the frequency meter.

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Step 21. Adjustment in 2-axis translation and rotation of the SLM (4417), adjusting the position and the focal length of the doublet (4415) (4416).

 The lenses (4415) (4416) are mounted on a translational positioner allowing either their simultaneous displacement in the direction of the optical axis or the displacement of (4415) alone.

SLM (4412) lorsque les tableaux de commande A Ne N pu et BN N sont appliqués respectivement à 2 ' 2 2,2 (4405) et (4412) soit effectivement ponctuelle dans le plan de fréquence ou se trouve (4417). La position de (4417) doit être réglée pour que dans ces conditions le point illuminé sur le SLM (4417) ait pour (N pix N

coordonnées C N2'x , N'x J . La position de (4415)(4416)(4417) doit en outre être réglée pour qu'il y ait une correspondance point à point entre les pixels de (4412) et ceux de (4417), c'est-à-dire pour que lorsque les tableaux de commande Al,j et Bl,j sont appliqués respectivement à (4405) et (4412) le point éclairé sur (4417) soit le pixel de coordonnées (i, j) , quels que soient les entiers i etj. The position of (4415) (4416) shall be adjusted so that the beam image from the

SLM (4412) when the control boards A Ne N pu and BN N are respectively applied to 2 '2, 2.2 (4405) and (4412) is actually punctual in the frequency plane or is (4417). The position of (4417) must be set so that under these conditions the illuminated dot on the SLM (4417) has (N pix N

coordinates C N2'x, N'x J. The position of (4415) (4416) (4417) shall further be adjusted so that there is a point-to-point correspondence between the pixels of (4412) and those of (4417), i.e. when the control boards A1, j and B1, j are respectively applied to (4405) and (4412) the illuminated point on (4417) is the coordinate pixel (i, j), irrespective of the integers i andj.

Les tableaux de commande A N N et B N pu N pl:< sont appliqués respectivement aux SLM
2,2 2,2 (4405) et (4412). Le tableau de commande appliqué à (4417) est mis à 1. La position de l'ensemble (4415) (4416) est ajustée pour avoir sur le capteur CCD du fréquencemètre une image aussi ponctuelle que possible. The frequency meter is positioned behind (4420). The series of operations ol 1 to ol3 is repeated a sufficient number of times. oll. Setting the joint position of (4415) and (4416) to obtain a spot frequency image.

The control panels ANN and BN pu N pl: <are respectively applied to the SLMs
2,2 2,2 (4405) and (4412). The control panel applied to (4417) is set to 1. The position of the set (4415) (4416) is adjusted to have on the CCD sensor of the frequency meter an image as punctual as possible.

012. Translation setting of (4417) to obtain a centered frequency image.

A NIN and B remain applied respectively to the SLMs (4405) and (4412). (4417) is
2,2 2,2 then set so that the generated center frequency is in the middle of the SLM (4417). This adjustment is made with the frequency meter and the PA program for locating the maximum defined above. However, in this maximum location program, the SLM (4412) is replaced by the SLM (4417).

013. Adjustment of (4415) to obtain the correct frequency increase and rotation setting of (4417).

The PC program is used. However, in this program: - the SLM (4412) is replaced by the SLM (4417) - when a command word Al, j is applied to the SLM (4405), the corresponding command word B1 is applied to the SLM (4412) ).

 The inter-lens distance correction obtained is applied to the distance between (4415) and (4416) and the rotational adjustment is made on (4417) in rotation with respect to an axis orthogonal to the plane of the sensor.

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Step 22. Adjusting the orientation of the semi-transparent mirror (4307)
The semi-transparent mirror (4307) is mounted on an angular positioner to adjust its orientation.

The SLMs (4405) (4412) (4417) are controlled to generate a center frequency: control board of (4405) is ANpix Npix and the control board of (5512) and (4417) is BN N. The
2,2 2,2 position of (4407) is adjusted using a diffuser so as to return the beam in the intended direction.

Step 23. Adjusting the orientation of the mirror (4308)
The mirror (4308) is mounted on an angular positioner to adjust its orientation.

 The SLM control is unchanged. The position of (4308) is adjusted using a diffuser to return the beam in the intended direction.

Step 24. Placing the beam extinguisher (4422)
The SLM control is unchanged. This beam extinguisher is set up according to the procedure given in 7.3.2.2.

Step 25. Translational adjustment of the lens (4431)
The SLM control is unchanged. The frequency meter is positioned behind (4431). The position of (4431) is adjusted to obtain a point image.

Step 26. Adjusting mirror orientation (4332)
This mirror is mounted on a two-axis positioner to adjust the orientation.

 The SLM control is unchanged. Between (4311) and (4331), two beams propagating in opposite directions are superimposed. A diffuser introduced on the side of the beam will be illuminated on both sides. The illuminated parts on each side of the diffuser must be the same: the two beams are then exactly superimposed. A wrong setting of (4332) results in a shift between the position of these two beams. (4332) is set so that between (4311) and (4331) the beams propagating in both directions are exactly superimposed.

Step 27. Translational adjustment of the lens (4331)
The lens (4331) is mounted on a positioner a translational axis allowing movement in the direction of the optical axis.

The frequency meter is positioned between (4311) and (4338). The control of the SLMs (4405) (4412) (4417) is defined by the tables AN N and BN N. The position of (4332) is set from
2 '2' so that FEDI has an image as punctual as possible on the frequency meter.

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Step 28. Adjusting the orientation of the semitransparent mirror (4311).

 This semi-transparent mirror is mounted on a positioner two axes in rotation (the two axes being in the plane of the semi-transparent mirror) to adjust the orientation.

 The SLM setting is not changed. A diffuser is used to control the path of the beam. (4311) is set so that the FEDI beam follows the intended path.

Step 29. Adjusting the orientation of the two-sided mirror (4424)
The double mirror (4424) is mounted on a two-axis rotational positioner, the two axes being in the plane of the non-reflecting face.

 (4424) is set so that FEDI reaches the center of (4427), which is verified using a diffuser.

Step 30. Setting the orientation of the SLM (4427).

 This SLM is mounted on a positioner two axes in translation in the plane of the SLM, coupled with a positioner three axes in rotation to adjust the orientation (axes in the plane of the sensor) and the position in rotation (axis in a orthogonal plane to the sensor).

 SLM (4405) (4412) (4417) control panels are not modified. The SLM control panel (4427) is set to 1.

 The beam path being controlled by a diffuser, the angular position of (4427) is adjusted so that the FEDI beam is aimed at the point provided on (4424).

Step 31. Fine adjustment of the orientation of the two-sided mirror (4424), rotation and translation adjustment of (4427) and adjustment of the focal length and position of the doublet (4425) (4426).

(4427) ait pour coordonnées C N2'x , ## . La position de (4425)(4426)(4427) doit en outre être réglée pour qu'il y ait une correspondance point à point entre les pixels de (4417) et ceux de (4427), c'est-à-dire

pour que, lorsque les tableaux de commande A,,, et B,, sont appliqués respectivement au SLM (4405) et aux SLM (4412) et (4417), le point éclairé sur (4427) soit le pixel de coordonnées (i,j), quels que soient les entiers i et j. The position of (4425) (4426) shall be adjusted so that the FEDI beam image, when the ANpix Npix and BNpix Npix control panels are applied to the SLM (4405) and
2 '2 2' 2 SLM (4412) and (4417), or actually punctual in the frequency plane where is (4427). The position of (4424) and (4427) must be adjusted so that under these conditions the point illuminated on the SLM

(4427) has for coordinates C N2'x, ##. The position of (4425) (4426) (4427) shall further be adjusted so that there is a point-to-point correspondence between the pixels of (4417) and those of (4427), i.e.

so that when the control boards A ,,, and B ,, are respectively applied to the SLM (4405) and the SLMs (4412) and (4417), the illuminated point on (4427) is the coordinate pixel (i, j), whatever the integers i and j.

 The frequency meter is positioned between (4424) and (4428). Its polarizer is set up. The FEDI beam is used. The control board of (4427) is set to 0 and the polarizer of the frequency meter

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 is set to cancel the intensity received on the frequency meter's CCD. The series of operations o21 to o23 is then repeated a sufficient number of times, to converge to a correct setting.

021. Adjusts the joint position of (4425) and (4426) to obtain a point-in-time image.

The ANpix Npix control panel is applied to the SLM (4405) and the
2 1,2 BNpix Npix command is applied to the SLM (4412) and (4417). The control board applied to (4427)
2 '2 is set to 1. The position of the set (4425) (4426) is adjusted to have on the CCD sensor of the frequency meter an image as punctual as possible.

022. Setting the (4424) orientation and translational setting of (4427) to obtain a centered frequency image.

 (4424) and (4427) are set so that the generated center frequency is in the middle of the SLM. This adjustment is made with the frequency meter and the PA program for locating the maximum defined above.

However, in this maximum location program, the SLM (4412) is hereby replaced by the SLM (4427).

023. Adjustment of (4425) to obtain the correct frequency increase and rotation setting of (4427).

The PC program is used. However, in this program: - the SLM (4412) is replaced by the SLM (4427) - when a command word Al, j is applied to the SLM (4405), the corresponding command word B1 is applied in addition to the SLMs (4412) and (4417).

 The inter-lens distance correction obtained is applied to the distance between (4425) and (4426) and the rotation setting is made to (4427).

Step 32. Adjustment in 2-axis translation of the diaphragm (4428) (4428) is mounted on a two-axis translational positioner allowing displacements in a plane orthogonal to the optical axis.

 The opening of (4428) is known. It must be set in translation.

FEDI is used. (4428) is provisionally deleted. An auxiliary CCD is placed just behind (4428). The ANpix Npix control panel is applied to the SLM (4405) and the
2 '2 BNpix Npix command is applied to the SLM (4412) and (4417). The control board of (4427) is 1. The
2 '2 center of the illuminated area is marked on the auxiliary CCD. (4428) is then set up so that its center coincides with the center of the illuminated area.

Step 33. Rotating the polarizer (4352)

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This polarizer is mounted on a positioner a rotating axis for adjusting the rotational position about its optical axis.

 FEDI is used. The (4427) control panel is set to 0. The SLM (4405) (4412) (4417) control panels are not modified. The rotational position of (4352) is adjusted to cancel the intensity received on the CCD (4339).

Step 34. Adjusting the orientation of the mirror (4344)
This mirror is mounted on a positioner allowing an adjustment of its orientation. The diaphragm (4349) is wide open. A diffuser is used to verify that the FRD beam reaches the CCD (4339) and is centered on this CCD.

Step 35. Adjusting the position and opening of the diaphragm (4349)
This diaphragm is mounted on a positioner two axes in translation allowing movement in the plane of the optical axis, and has an adjustable opening.

 Its position is adjusted in the presence of FRD so that the image of the diaphragm is centered on the CCD and its aperture is set so that this image covers the entire CCD.

Step 36. Adjusting the focal length and position of the doublet (4430) (4429) and setting in translation and rotation of the sensor (4339)
The lenses (4430) (4429) are mounted on a translational positioner allowing one hand to move the two lenses together and to move (4429) relative to (4430).

 The CCD (4339), integral with the camera (4384) is mounted on a three-axis rotational positioner allowing on the one hand a rotation around the optical axis, on the other hand a setting of the orientation of the sensor, coupled with a three-axis positioner in translation.

 The positioners of the lenses (4430) (4429) and the camera (4384) are themselves mounted on a positioner allowing a displacement of the assembly in the direction of the optical axis.

 The position of (4430) (4429) shall be adjusted so that the FEDI beam image, when the ANpix Npix and BNpix Npix control panels are applied respectively to the SLM (4405) and the 2 '2 2.2 SLM (4412) and (4417) and when the control board of (4427) is set to 1, is actually punctual in the frequency plane or is (4339). The position of (4339) must be set so that (Npix Npix) under these conditions the point illuminated on the CCD (4339) has coordinates Npix / 2, Npix / 2). The position of (4339) (4429) (4430) must further be set so that there is a point-to-point correspondence between the pixels of (4417) and those of (4339), i.e. that when the control boards Al, j and B1, j are respectively applied to the SLM (4405) and the SLMs (4412) and (4417) and when the

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 control of (4427) is at 1, the illuminated point on (4339) is the coordinate pixel (i, j), irrespective of the integers i and}.

 The FEDI and FRD bundles are used.

 Table C applied to (4427) is set to 1.

 The series of operations o31 to o33 is repeated a sufficient number of times.

031. Adjusts the joint position of (4429) and (4430) to obtain a point-in-time image.

The ANpix @ Npix control panel is applied to the SLM (4405) and the
2 2 BNpix @ Npix command is applied to SLMs (4412) and (4417). The punctuality of the image generated on the
CCD (4339) is evaluated according to the procedure described in 7.3.3.1. The position of the set (4429) (4430) is adjusted to have an image as punctual as possible.

032. Translation setting of (4339) to obtain a centered frequency image.

calculées selon la procédure indiquée en 7.3.3.1., soient ##, Nprx1 033. Réglage de (4429) pour obtenir le bon grandissement en fréquence et réglage en rotation de (4339). The translational position of (4339) is adjusted so that the coordinates of the point image,

calculated using the procedure given in 7.3.3.1., to be ##, Nprx1 033. Adjustment of (4429) to obtain the correct frequency increase and rotation setting of (4339).

The PC program is used. However, in this program: when a control word A1, j is applied to the SLM (4405), the corresponding control word B1, j is additionally applied to the SLMs (4412) and (4417).

the tables X [i] and Y [i] are not obtained by the procedure PB. They correspond to the coordinates of the maximum determined by the procedure described in 7.3.3.1., Without specific action on an SLM.

 The inter-lens distance correction obtained is applied to the distance between (4429) and (4430).

 The rotation setting is made on (4339) (4384), rotated about the optical axis.

L'orientation du CCD est réglée pour avoir y2i -Y3, ~ 1 Etape 37. Réglage de la position en translation de l'ensemble constitué du CCD (4339) et du doublet (4430) (4429). X [1] -X [4]

The orientation of the CCD is set to have y2i -Y3, ~ 1 Step 37. Setting the translational position of the set consisting of the CCD (4339) and the doublet (4430) (4429).

 The FRDI beam is used. An auxiliary CCD is set up at the location of the diaphragm (4313). The position of said set is adjusted so that the FRDI image on the auxiliary CCD is punctual.

Step 38. Adjusting the orientation of the mirror (4347)
This mirror is mounted on a two-axis positioner to adjust the orientation.

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 The SLM control is unchanged. Between (4345) and (4346), two beams propagating in opposite directions are superimposed. A diffuser introduced on the side of the beam will be illuminated on both sides. The illuminated parts on each side of the diffuser must be the same: two beams are then exactly superimposed. (4347) is set so that between (4345) and (4346) the beams propagating in both directions are exactly superimposed.

Step 39. Translational adjustment of the lens (4346)
The lens (4346) is mounted on a positioner a translational axis to adjust the position in the direction of the optical axis.

 FRDI is used. The frequency meter is positioned on the FRDI path between (4345) and (4430).

The position of the lens (4346) is adjusted so that the image on the CCD of the frequency meter is punctual.

Step 40. Setting the orientation of the semi-transparent mirror (4345)
The semi-transparent mirror (4345) is mounted on a two-axis positioner to adjust the orientation.

 An auxiliary sensor is provisionally put in place behind (4313). The semi-transparent mirror (4313) is set so that the image on this temporary sensor is centered relative to the diaphragm (4313).

Step 41. position adjustment of the objectives (4317) and (4319) in translation.

 The objective (4319) is mounted on a focusing device. The objective (4317) is mounted on a positioner two axes in translation allowing movement in a plane orthogonal to the optical axis.

 The FRDI beam is used. A temporary CCD sensor is positioned just behind (4323) on the FRDI path. The position of the lenses is set to obtain a focused spot image.

Step 42. Introduction of a provisional lighting beam.

 This beam, which will be called 'FEP', is derived from the laser by a semi-transparent mirror placed between (4304) and (4305) and is brought by a set of mirrors towards the entrance of the microscope objective ( 4317), on the side of the sample. Objective (4319) must be provisionally removed for this purpose. At the entrance to the lens, this beam is directed along the optical axis of the lens.

Step 43. adjusting the orientation of the mirror (4314) and translational adjustment of the lens (4312).

 The mirror (4314) is mounted on an angular positioner to adjust its orientation. The lens (4312) is mounted on a positioner an axis in translation in the direction of the optical axis.

 FEP and FRD are used. An image is obtained from the sensor (4339). The punctuality and the coordinates of the FEP image point are evaluated by the procedure described in 7.3.3.1.

 The lens (4312) is set so that the image is punctual.

 The mirror (4314) is set so that the image is centered.

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Step 44. Adjusting the position of the lenses.

 The FEP beam is removed and the objective (4317) is replaced. The FRDI beam is used.

A temporary CCD sensor is set up behind (4323) on the FRDI path. The objectives are set so that the image is punctual and centered with respect to the diapham (4323).

Step 45. Translational adjustment of the lens (4324).

 EDF is used. It crosses successively the objectives (4317) and (4319), then the lens (4324) and reaches the frequency meter, which is positioned behind (4324). The position of (4324) is set to obtain as accurate an image as possible on the frequency meter's CCD.

Step 46. Mirror Orientation Adjustment (4432) (4435), First Rotation Adjustment of (4436) and First Orientation Adjustment of Semi-Transparent Mirror (4325)
SLMs (4405) (4412) (4417) are controlled to generate a center frequency. The FEG beam is used. (4325) is in the normal position. The path of the beam is controlled with a diffuser.

Each mirror is adjusted to have the intended trajectory. In particular, the beam must occupy the entire opening of (4323).

Step 47. Installation of the beam extinguisher (4437)
This beam extinguisher is put in place as described in 7.3.2.2.

Step 48. Adjusting the position and the focal length of the doublet (4433) (4434), adjusting the rotation of the assembly (4436), and adjusting the orientation of the semi-transparent mirror (4325).

 The lens (4434) is mounted on a positioner in translation along the optical axis. This positioner and the lens (4433) are themselves mounted on a second positioner in translation an axis along the optical axis.

The position of (4433) (4434) shall be adjusted so that the FEG beam image, when the ANpix Npix and BNpix Npix control panels are applied to the SLM (4405) and
2 '2 2' 2 SLM (4412) and (4417) and when the control board of (4427) is set to 1, is actually punctual in the frequency plane or is (4339). The position of (4325) must be set so that under these conditions the illuminated point on the CCD (4339) has coordinates (Npix / 2, Npix / 2). The position of (4433) (4434) (4436) (4325) shall further be set so that there is a point-to-point correspondence between the pixels of (4417) and those of (4339), that is, ie, when the control boards A1, jet B1, j are applied respectively to the SLM (4405) and the SLMs (4412) and (4417) and when the control board of (4427) is 1, the point illuminated on (4339) is the pixel of coordinates (i, j), whatever are the integers i and}.

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 The FRD and FEG beams are used. The control board applied to (4427) is set to 1.

 This adjustment is made by performing steps o41 to o43 041 a sufficient number of times. Setting the joint position of (4433) and (4434) to obtain a spot frequency image.

The ANpix Npix control panel is applied to the SLM (4405) and the
2.2 BNpix Npix command is applied to SLM (4412) and (4417). Punctuality of the image generated on the CCD
2.2 (4339) is evaluated according to the procedure described in 7.3.3.1. The position of the set (4433) (4434) is adjusted to have an image as punctual as possible.

042. Angular adjustment of (4325) to obtain a centered frequency image.

 The angular position of (4325) is adjusted so that the coordinates of the point image, calculated according to the procedure indicated in 7.3.3.1., Are (Npix / 2, Npix 2 2 043. Setting of (4433) to obtain the correct frequency increase and rotation setting of (4436).

The PC program is used. However, in this program: when a control word A1, j is applied to the SLM (4405), the corresponding control word B1 is applied to the SLMs (4412) and (4417).

the values X [i] and Y [i] are not obtained by the procedure PB. They correspond to the coordinates of the maximum determined by the procedure described in 7.3.3.1., Without specific action on an SLM.

 The inter-lens distance correction obtained is applied to the distance between (4433) and (4434) and the rotation setting is made on (4436).

AN pb N pb et BN pb N pb des SLM (4405),(4412),(4417) et avec le faisceau FEG. Il peut être également 2 ' 2 2 2

obtenu avec les tableaux de commande A NN BN M et avec le faisceau FEDI. 2 ' 2 ' Step 49. Adjusting the rest of the 'left' part of the microscope
Each element still not regulated corresponds to a symmetrical element in the right part of the microscope. The adjustment of the elements that are still not adjusted is 'symmetrical' to the setting of the corresponding elements of the right part of the microscope. It is performed symmetrically, with the FEGI beam replacing the FEDI beam. However, the following fact must be taken into account: - a point centered in (Npix / 2, Npix / 2) on the sensor (4339) can be obtained with control panels

AN pb N pb and BN pb N pb of the SLMs (4405), (4412), (4417) and with the FEG beam. It can also be 2 '2 2 2

obtained with control panels A NN BN M and with the FEDI beam. 2 '2'

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 (Npix pix Npix) - a center point in (Npix / 2, Npix / 2) on the sensor (4329) can be obtained with ANpix @ N and BN control panels of the SLMs (4405), (4412), (4417) ) and with the FED beam. It can also be 2 '2 2 obtained with the ANpix Npix BNpix Npix control panels and with the FEGI beam.

Etape 50. Mise en place de (4351)
Ce dispositif de décalage de phase est identique à celui décrit en 7. 2.3. et mis en place comme indiqué en 7.3.2.3. 2,2 2,2 The control words of the SLM are therefore not perfectly equivalent during the two settings. The adjustment of the left part of the microscope comprises in particular steps equivalent to steps 31 and 36. In these steps, the control panels AN N and BNpix N must be replaced by 2 2 2 2

Step 50. Establishment of (4351)
This phase shift device is identical to that described in 7. 2.3. and set up as described in 7.3.2.3.

At the end of this set of settings the system is ready to be used.

 8. 6. Variation of the mode of use.

One can limit oneself, to generate the three-dimensional image of the object, to the representation
Fo, as defined in 7.17. This amounts, in the procedure described in 7.17.2., To adopt tables IBp, q void for any pair (p, q) # (0,0).

 It is also assumed that the object has an average index close to the nominal index of the object observed and that the optical table is totally free of vibrations.

 Steps 7.9, 7.10, 7.11, 7.13, 7.15, 7.16 can then be deleted. The present method also differs from the previous method by the method used to adjust the position of the lenses before use, by the control boards applied to the beam deflector during the imaging, and by the image overlay algorithm.

 8. 6.1. Goal setting.

 This setting can be made in the presence of the object. It can also be done with a transparent blade provided you do not move the lens when you introduce the object. If objectives intended to operate without immersion liquid or slide are provided (nominal index equal to 1) and if the sample is thin or of average index close to 1, it can also be done in the same way. object abscence. During this adjustment, the FEG and FRD beams are used and the following operations are performed: - the control panel of the SLM (4405) is set to 0 - the control panels of the other SLMs are set to 1.

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the polarizer (4408) is rotated so as to cancel the received FEG beam on (4339).

the control panel BNpix Npix is applied to the SLM (4405) which is zero in all respects except at the point of 2 '2 coordinates (Npix / 2, Npix / 2).

the punctuality of the image received on the sensor (4339) is evaluated using the procedure described in 7.3.3.1. with Fourier transformation.

- The position of the lenses is adjusted so that the image is perfectly punctual and centered.

the polarizer (4408) is then returned to its initial position.

8. 6.2. beam deflector control
The Alj control panel used in 8.4.1. for the SLM (4405) is replaced

8.6.3.algorhhme de calcul de la représentation tridimensionnelle
Les étapes 1 et 2 de l'algoritlune décrit en 7. 17.2. peuvent être supprimées. En effet, le réglage supplémentaire effectué, le tableau de commande du déviateur de faisceau utilisé, et l'abscence de vibrations permettent d'éviter tout décalage de phase du faisceau d'éclairage. En particulier, si la variante décrite en 7.18.5. est utilisée, le dispositif de décalage de phase (4304) n'est pas utilisé, le déphasage # d étant constant et pouvant être choisi comme nul.

8.6.3.calgorithm for calculating the three-dimensional representation
Steps 1 and 2 of the algorithm described in 7. 17.2. can be deleted. In fact, the additional adjustment made, the control panel of the beam deflector used, and the absence of vibrations make it possible to avoid any phase shift of the lighting beam. In particular, if the variant described in 7.18.5. is used, the phase shifter (4304) is not used, the phase shift # d being constant and can be selected as zero.

9. Fifth embodiment
This embodiment does not allow image acquisition as fast as the previous mode and is not, for this reason, the preferred embodiment in the general case. Nevertheless, in the particular field of UV radiation, it is the preferred embodiment. Indeed, in this field, embodiments 3 and 4 are not feasible due to the unavailability of liquid crystals and polarizers. Considering that it can operate with short wavelength UV radiation, this embodiment is also the one that makes it possible to obtain the best definition on the image generated.

 9. 1. Principles.

 This fifth embodiment is similar to the second embodiment in that the image is captured in a space plane and in that the beam direction variations are made using a movable mirror. It is similar to the third embodiment in that two microscope objectives are used, and in that most of the algorithms are modified forms of those used in the third embodiment. It differs from all previous embodiments in that the wave of

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 reference is not fixed but is modified at the same time as the illumination wave. It is described by Fig.73 and 74.

 The objective of this fifth embodiment is to improve the resolution using an ultraviolet laser. There is no ferroelectric liquid crystal working in ultraviolet, and therefore it is necessary to adopt solutions based on more traditional optical components. In particular, the beam deflection device is a moving mirror (5113).

 However, the use of a moving mirror in a system close to the first or second embodiment generates vibrations. After each movement of the mirror, it is necessary to wait for the stabilization of the system before proceeding with the acquisition. In order to overcome the vibrations caused by the moving mirror, it is necessary to position it outside the optical table and separate the light beams and reference on the optical table after passing the mirror. It follows that the movements of the mirror result in a simultaneous movement of the reference beams and lighting.

 In order to take full advantage of the possible ultraviolet resolution, it is necessary to be able to effect, as in the third and fourth embodiments, changes of orientation of the electric field vector of the illumination beam. These changes are made by separating the wave, by a semi-transparent mirror (5102), into two paths, a polarization-modifying phase plate (5111) being inserted on one of the paths and shutters (5104) and (5109) to choose the path used. The two waves are then superimposed again by a mirror (5112). The shutters are placed at a point where the light wave occupies only a small spatial extension and can therefore be opened or closed rapidly.

 For the same reason it is necessary to have several directions of analysis. On each side of the microscope, two CCD sensors are used, one for each direction of analysis. Since it is difficult to have good polarizers in the UV range, the analysis direction will be modified only by a modification of the direction of polarization of the reference wave, for example by means of wave plates ( 5238) (5239) which modify this polarization differently before each sensor.

 The reference wave is mobile and can in particular traverse the object with an angle close to the maximum aperture of the objective. It follows that the spatial frequency received on the sensor may be twice as high as with a system where the reference wave is centered with respect to the optical axis as in the second embodiment. At equal image size, a sensor with twice the pixel dimensions is therefore necessary, compared with the other embodiments.

 To suppress the direct light wave, a window (5165) or (5191) is used, on which is fixed a black point, placed in a frequency plane. By moving this black point, the deleted frequency is changed. On the other hand, this method does not make it possible to obtain the value of the wave at the point of direct impact of the illumination wave on which the three-dimensional reconstructions practiced in the other embodiments are based. Moreover, the mobile mirror is not suitable for rapid changes of the light wave between very different frequencies. However, these changes were necessary in the third embodiment to obtain the reference images which allowed to phase in the

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 two-dimensional representations obtained on the sensor opposite to the point of direct impact of the illumination wave. Therefore, a phase registration method that does not require a reference image or acquisition of the point corresponding to direct lighting must be provided in this embodiment.

 Section 9. 2. materially describes the microscope used and paragraph 9. 3. gives the applicable design principles. As the microscope is of a material design substantially different from Embodiment 3, its setting and use also greatly differs from the setting and use of the microscope according to Embodiment 3.

 The microscope is subject to a set of adjustments made in the abscence of the sample: - The position adjustment of the various elements is performed as described in paragraph 9. 5. This setting uses an acquisition procedure of images described in paragraph 9.4.

 - The tables allowing the control of the beam deflection mirror are determined as described in paragraph 9.6.

 - The tables to control the windows (5165) and (5191) used to suppress the direct light beam are determined as described in paragraph 9.7.

 The constant K, equivalent to that used in the first embodiment, is determined as described in 9.8.

 - The position of the CCD sensors must be fine-tuned as described in section 9.10.

 - The table characterizing the frequency response of the sensors is determined as described in section 9.11.

 - The relative coordinates of the center points of the images obtained on each side of the microscope are determined as described in paragraph 9.12.

 - The phases of each lighting beam are determined as described in paragraph 9.13.

 After placing the sample the microscope is subject to a set of additional adjustments: - The position of the objectives is set as described in paragraph 9.14.

 - The relative x, y, z coordinates of the reference beam reference points associated with each lens, as well as the sample average no and the L thickness, are determined as described in paragraph 9.15.

 - The value w0 characterizing the position of the sample is calculated as described in paragraph 9.16. The procedure described in paragraph 9.16. is essentially similar to that described in paragraph 7.15. and in particular comprises a first focus adjustment.

 - The aberration compensation function Dp is obtained as described in section 9.17.

 When these settings have been made, the procedure for obtaining three-dimensional images is started. A version of this procedure, similar to that described for the third embodiment, is

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 described in 9.18. A specifically adapted version of this procedure is described in 9.19. In all cases, the two-dimensional frequency representations are acquired using a procedure described in section 9. 9., which is also used in some adjustment steps.

 Although not recalled, a focus setting similar to that described in 7.17.3. is performed, which may involve a recalculation of w0 and Dp.

 A very simplified version of the operation of this microscope is described in 9.20.

 9. 2. Physical description.

 An overall scheme of the system is constituted by Figures 73,74,63. The plane of Figs. 73 and 74 is horizontal. The assembly (5176), surrounded in dashed lines in FIG. 74, is identical to the corresponding set in the fourth embodiment and is shown in Fig.63.

 A vertically polarized laser (5100) produces a beam whose vector electric field is thus directed along an axis orthogonal to the plane of the figure. This beam then passes through a beam expander (5101).

 The beam is then separated in two by a semi-transparent mirror (5102). One of the beams from (5102) passes through a lens (5103) then a shutter (5104) placed in the focal plane of this lens. It then passes through a second lens (5105) whose object focal plane coincides with the image focal plane of (5103), then is reflected by a mirror (5106) and a semi-transparent mirror (5112). The portion of the beam that is not reflected by (5112) will strike an absorbent surface (5253). The second beam from (5102) is reflected by a mirror (5107), passes through a lens (5108) and then a shutter (5109) placed in the focal plane of this lens. It then passes through a second lens (5110) whose object focal plane coincides with the image focal plane of (5108). It then crosses a waveguide (5111) and then passes through the mirror (5112).

At the output of the mirror (5112) the two beams from the semi-transparent mirror (5102) are again superimposed. The focal lengths of the lenses (5103) (5105) (5108) (5110) are equal. The waveguide (5111) introduces an optical path difference of half a wavelength between its two neutral axes.

It is positioned to transform the vertically polarized incoming beam into a polarized beam in the horizontal direction. The small spatial extension of the beam passing through the shutters (5104) (5109) allows the use of fast mechanical shutters, a small displacement being sufficient to close the beam.

 The beam coming from (5112) goes towards the mirror (5113) which reflects it. This mirror is mounted on a two-axis positioner (5114) similar to that shown in Figures 2 and 3, which allows to control its orientation. It is placed at the focal point of the lenses (5110) and (5105). The beam from (5113) then passes through the lens (5250) whose object focus is on (5113), then the lens (5251) whose object focus coincides with the image focus of (5250). It is then reflected by a partially transparent mirror (5115) that produces a reference beam directed to (5117). The semitransparent mirror (5117) then separates the reference beam into a right reference beam FRD and a left reference beam FRG. The beam having passed through (5115) then passes through a partially transparent mirror (5116) which separates a specific beam FS. The beam having crossed (5116) is then

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 separated by a semi-transparent mirror (5118) into a right illumination beam FED and a left illumination beam FEG.

 The FRD beam first passes through a lens (5120) whose object focus coincides with the image focus of (5251), then a second lens (5121) whose object focus coincides with the image focus of (5120).

It is then reflected by a mirror (5122) placed at the image focus of (5121) and mounted on a piezoelectric 'stack' (5123) producing wavelength displacements, which is the shifter. phase, on the same principle as the element (122) of FIG. It then passes through a filter (5124) making it possible to adjust its intensity, then a lens (5125) whose object focus is on the mirror (5122). It then passes through a doublet of lenses (5127) (5126) operating according to the principle explained in 8.1.4.1. the object focus of the doublet (5127) (5126) coinciding with the image focus of (5125). It is then separated into two beams by a partially transparent mirror (5234). One of these beams is then reflected by the mirror (5235), passes through a wave plate (5239), and is reflected in part to the CCD (5174) by the partially transparent mirror (5236), the unreflected portion being stopped by an absorbent surface (5237). The other beam passes through a wave plate (5238), and is then partially reflected to the CCD (5171) by the partially transparent mirror (5232), the non-reflected portion being stopped by an absorbent surface (5233). The CCDs (5174) and (5171) are respectively mounted on the cameras (5175) and (5172). They are each in an image focal plane of the doublet (5126) (5127).

 The FRG beam is reflected by a mirror (5252). It crosses a lens (5145) whose object focus coincides with the image focus of (5251), then a second lens (5146) whose object focus coincides with the image focus of (5145). It is then reflected by a mirror (5147) placed at the image focus of (5146) and mounted on a piezoelectric 'stack' (5148) which constitutes the phase shifter. It then passes through a filter (5149) to adjust its intensity, then a lens (5150) whose object focus is on the mirror (5147). It then passes through a doublet of lenses (5151) (5152) operating according to the principle explained in 8.1.4.1. the object focus of the doublet (5151) (5152) coinciding with the image focus of (5150). It then passes through a rotating adjustment device of the type described in 8.1.4.2. , consisting of the mirrors (5219) (5220) and the assembly (5221) consisting of the mirrors (5214) (5215) (5216) (5217), and movable in rotation about an axis passing through the center of the mirrors ( 5220) (5214) (5217). It is then separated into two beams by a partially transparent mirror (5244). One of these beams is then reflected by the mirror (5245), passes through a wave plate (5249), and is then reflected in part to the CCD (5198) by the partially transparent mirror (5246), the unreflected portion being stopped by an absorbent surface (5247). The other beam passes through a waveguide (5248) and is reflected in part to the CCD (5201) by the partially transparent mirror (5242), the nonreflected portion being stopped by an absorbent surface (5243). The CCDs (5198) and (5201) are respectively mounted on the cameras (5199) and (5202). They are each in an image focal plane of the doublet (5151) (5152).

 The FED beam is reflected by a mirror (5141), passes through a filter (5142) to adjust its intensity, a lens (5143) whose object focus coincides with the image focus of (5251), a shutter (5144) ), and a lens (5154) whose object focal plane coincides with the image focal plane of (5143) and whose image focal plane coincides with the image of the diaphragm (5158) by the lens (5157). It is reflected by

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 mirrors (5153) and (5155), and is separated into two beams by a partially transparent mirror (5156). One of the beams, directed to (5157), is the main beam and will be denoted FED. The other beam, directed to (5159), is the inverse indicator of FED and will be noted FEDI.

 The FED beam passes through the lens (5157), the diaphragm (5158), the device (5176) shown in FIG. 63, passes through the diaphragm (5184) and the lens (5183). A focal plane of the lens (5157) coincides with the image focal plane of the microscope objective (4317) [in the conventional sense of use of the lens, opposite to the direction of the rays]. A focal plane of the lens (5183) coincides with the focal plane image of the microscope objective (4319). The diaphragms (5158) and (5184) are placed in the planes where the lenses normally form the images of the sample. The beam from (5183) passes through the semitransparent mirror (5182). It passes through the lens (5188) whose object focal plane coincides with the image of the diaphragm (5184) by the lens (5183). It then crosses a glass (5191) of small thickness, on which is a black point absorbing a few tens of micrometers in diameter. This window is positioned in the image focal plane of the lens (5188) and has the function of stopping the direct light beam. A diaphragm (5190) placed approximately in the same plane makes it possible to improve the spatial frequency filtering performed by the microscope objective. The beam then passes through a doublet (5192) (5193) whose object focal plane coincides with the window (5191). It is then separated into two beams by a semi-transparent mirror (5240). One of the beams from (5240) reaches the CCD (5198) after passing through the partially transparent mirror (5246). The other beam is reflected by the mirror (5241) and reaches the CCD (5201) after passing through the partially transparent mirror (5242). The CCDs (5198) and (5201) are each in an image focal plane of the doublet (5192) (5193).

 The FEDI beam passes through the lens (5159), a focal plane of which coincides with the image focal plane of the lens (5154). It reaches the mirror (5160), optionally shut off by the shutter (5161), which reflects it. It then crosses the lens (5159) and is reflected by the semi-transparent mirror (5156) to the lens (5162). It passes through the lens (5162) whose object focal plane coincides with the image of the diaphragm (5158) by the lens (5157). He then goes through the partially transparent mirror (5163). It then passes through a glass (5165) of small thickness, on which is a black point absorbing a few tens of micrometers in diameter. This window is positioned in the image focal plane of the lens (5162) and has the function of stopping the direct light beam. An optional diaphragm (5164) placed approximately in the same plane makes it possible to improve the spatial frequency filtering performed by the microscope objective. The beam then passes through a lens (5166) whose object focal plane coincides with the image focal plane of (5162). It is then separated into two beams by a semi-transparent mirror (5230). One of the beams from (5230) reaches the CCD (5174) after passing through the partially transparent mirror (5236). The other beam is reflected by the mirror (5231) and reaches the CCD (5171) after passing through the partially transparent mirror (5232). The CCDs (5174) and (5171) are each in an image focal plane of the lens (5166).

 The beam FEG is reflected by the mirrors (5119) (5204), passes through a filter (5205) to adjust its intensity, a lens (5206) whose object focus coincides with the image focus of (5251), a shutter (5207), a doublet (5179) (5178) whose object focal plane coincides with the image focal plane of

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 (5206) and whose image focal plane coincides with the image of the diaphragm (5184) by the lens (5183). It then passes through a rotary adjustment device of the type described in 8.1.4.2., Consisting of the mirrors (5177) (5180) and the assembly (5181) consisting of the mirrors (5210) (5211) (5212) (5213). ), and mobile in rotation about an axis passing through the center of the mirrors (5180) (5210) (5213). It is then separated into two beams by a partially transparent mirror (5182). One of the beams, directed to (5183), is the main beam and will be denoted FEG. The other beam, directed to (5185), constitutes the opposite indicator of FEG and will be denoted FEGI.

 The FEGI beam passes through the lens (5185) whose focal plane coincides with the image focal plane of the doublet (5178) (5179). It reaches the mirror (5187), optionally shut off by the shutter (5186), which reflects it. It then crosses the lens (5185) and is reflected by the semi-transparent mirror (5182) to the lens (5188).

 The beam FS first passes through a filter (5128) and then a lens (5129) and is reflected by a mirror (5130). It then crosses a shutter (5254) then a lens (5140) whose object focus is confused with the image focus of (5129). It is then separated by a semi-transparent mirror (5163) into a main beam FS directed to (5162) and a reverse indicator beam directed to (5189), which will be noted FSI. The FSI beam passes through a lens (5189), is reflected on a mirror placed at the object focus of (5189) and can be closed by a shutter (5209), crosses the lens (5189) and is reflected again by the semitransparent mirror ( 5163) to (5164).

 Each lens used is an achromat or composite lens that minimizes optical aberrations.

 The beam control principles given in 8.1.1. and 8. 1.4. remain valid and it is indicated in the same manner as for the fourth embodiment the space planes (E) and frequency (F).

The reference wave is here parallel, as the light wave and as in the second embodiment. This is why it is punctual in the frequency planes and parallel in the space planes as the lighting wave. The special beam FS is on the other hand punctual in the space planes and parallel in the frequency planes, as was the reference wave in the fourth embodiment.

 Many elements are mounted on positioners to adjust the position in a setting phase.

 The assemblies (5181) and (5221) are mounted on rotational positioners, according to their operating mode explained in 8.1.4.2.

 The other mirrors, partially transparent mirrors and piezoelectric mirrors are mounted on angular positioners to adjust their orientation.

 The lenses which will be adjusted in 9. 5. are mounted on positioners a dimension allowing a displacement in the direction of the optical axis.

 Each doublet consists of two lenses. It transforms a frequency plan located on one side of the doublet into a plane of space located on the other side of the doublet. The lens located on the side of the space plane is mounted on a positioner allowing a translation in the direction of the optical axis. This positioner is

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 itself mounted on a second positioner also allowing a translation in the direction of the optical axis. The second lens is mounted directly on this second positioner.

 The objective (4317) is mounted on a two-dimensional positioner for positioning in a plane orthogonal to the optical axis. The objective (4319) is mounted on a focusing device.

* The sample (4318) is mounted on a three-axis positioner in translation.

 The CCDs are mounted on positioners an axis in rotation and three axes in translation, allowing rotation around the optical axis and three degrees of freedom in translation.

 The dashed line (5203) separates two areas. The elements to the left of this line are mounted on a table directly linked to the ground, without damping. The elements to the right of this line or in FIG. 74 are mounted on an optical table suitably isolated from vibrations. Both tables are at the same level. The windows (5165) and (5191), the diaphragms (5164) and (5190), and the shutters (5144) (5207) are the only exceptions to this rule. Each of the windows (5165) and (5191) is mounted on a two-axis positioner in motorized translation allowing a displacement in a plane orthogonal to the optical axis, itself mounted on a manual positioner allowing a translation in the direction of the optical axis, itself directly related to the ground. The positioning system with two axes in translation must be precise and not cause parasitic movements in rotation of the window. Indeed, such displacements would result in phase variations that may in certain cases be detrimental to the quality of the images produced.

 Each of the shutters (5144) (5207) is directly connected to the ground. Each of the diaphragms (5164) (5190) is connected to the ground by means of a positioner 3 axes in translation and 1 axis in rotation about the optical axis.

 In order to be able to bond to the floor windows and shutters, a rigid mechanical construction is used to obtain a stable support located above the optical table, linked to the ground and not to the optical table, and to which the shutters can be fixed as well as the windows, through their positioners.

 The diaphragms (5164) and (5190) are constituted as shown in FIG. 82. The diaphragm (5710) has a circular opening (5711), a part (5712) for concealing an additional surface portion in this opening.

des axes neutres dirigés selon 1.cors 8 + sin g . On each camera is indicated the reference which is used to express the coordinates of the pixels of the corresponding CCD. On each wave plate, a marker is indicated. The direction vector of this reference in the plane of the figure is denoted by # and the direction vector of this coordinate system in the plane orthogonal to that of the figure is denoted 7. The wave plate (5111) has a neutral axis directed along # + j. The other waveboards have

neutral axes directed according to 1.cors 8 + sin g.

 In the case where this microscope operates in the ultraviolet range: - The set of non-polarizing components traversed by the light, that is to say the lenses, including those of the lenses, the windows, and the mirror substrates semi-transparent, can be made of a silica.

Silica or quartz lenses are available from various manufacturers.

- Mirrors and semi-transparent mirrors must be specially designed for UV.

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- The wave plates are for example in quarz.

The laser is for example an excimer laser. In pulsed mode, the pulses must be synchronized with the acquisition of images, for example at 1 image per pulse.

 9. 3. Dimensioning.

Le rapport f1 doit donc être égal ou légèrement inférieur à # g, chacune des valeurs f1 et f2 étant f2 4pc o par ailleurs suffisante pour éviter l'aberration sphérique. We denote: f1: focal length of the lens (5162) or of the lens (5188) f2: focal length of the lens (5166) or doublet (5192.5193) f3: focal length of the lens (5157) or the lens (5183) pc distance between the centers of two adjacent pixels, on the CCD 2 Npix sensors: lateral dimension in pixels of a CCD sensor. o: numerical aperture of a microscope objective g: magnification of a microscope objective fo: focal length of a microscope objective. do: distance between the lens (5157) and the diaphragm (5158). l1: width of the diaphragm (5164) or (5190) The lens (5157) must have its object focal plane coincident with the image focal plane of the microscope objective, and is at a distance do from the image of the goal. It is checked that this implies: f3 = gfo + do The opening of the beam on arrival on the CCD is: a = f1 o f2 g The sampling period required on the CCD must be greater than pc and is worth by application of the Nyquist criterion: # 1
2 2a We thus obtain:

The ratio f1 must therefore be equal to or slightly less than # g, each of the values f1 and f2 being f2 4pc o otherwise sufficient to avoid spherical aberration.

 The width l1 of the diaphragm (5164) must filter only the frequencies higher than the nominal aperture of the objective. We must have l1 = 2f1 o g

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The diameter of the incident beam on the mirror (5113) must be such that the necessary directional variations can actually be reproducibly performed using the positioning system of this mirror. We denote p [alpha] the angular step of displacement of the mirror, that is to say the smallest variation of the orientation angle of this mirror that can be reproducibly performed by the positioning system of the mirror. this mirror. Diaph is the aperture diameter of the diaphragm (5158) and Dmir the diameter of the incident beam on the mirror (5113). We then check that the present condition is expressed by: p [alpha] # o Ddiaph or the sign means very inferior, ie for example gNpix Dmir 1 0 Ddiaph
10 gNpix Dmir
Apart from the above criteria, there is a great deal of freedom in choosing the focal lengths of the other lenses. The design criteria applied to the beam paths FEG, FED, FRG, FRD are as follows: (1). The succession of the space and frequency planes must be as specified in the diagram. This succession of space and frequency planes is the method used to control the trajectory and the opening of the beam as specified in 8.1.1.

 (2). The lighting and reference beams, in the absence of diaphragm used between the mirror (5113) and the CCD sensors, must have the same diameter on their arrival on the sensors. Equivalently, they must have the same aperture, the aperture here being the angle between the parallel beams arriving on the CCDs for two different positions of the mirror (5113).

 (3). The focal lengths of the lenses should be sufficient to avoid spherical aberration.

 (4). The focal lengths of the different lenses are adapted to meet the constraints of space.

critère (4) se traduit par 2 fa +2 fb = L , d'ou on tire fa = L 2 Dl DI + D2 et fb L 2 L)] #+# LJ2 # . For example, if the diameter of the beam is D1 at (5122) and must be D2 upon arrival on the CCD, and if the distance between (5122) and (5174), following the path planned for the beam, is L, then if fa and fb are respectively the focal lengths of the lens (5125) and the doublet (5126) (5127), and taking into account the principles outlined in 8.1.1., the criterion (1) results in D2 = fb and the
D1 fa

Criterion (4) results in 2 fa + 2 fb = L, from which we draw fa = L 2 D1 DI + D2 and fb L 2 L)] # + # LJ2 #.

 The entire system will be adjusted so that when the beam FEG enters the objective (4317) while being directed along the optical axis, its direction on arrival at (5174) or (5171) is confused with that of the reference wave. When the mirror (5113) is moved from this central position, the direction of the reference beam will be changed in one direction and the direction of the illumination beam will be changed in the opposite direction, that is, in one direction. frequency plan, the points corresponding to the FEG and FRD beams will remain symmetrical with respect to the point corresponding to the

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 lighting beam when it enters the objective along the direction of the optical axis. Maintaining this symmetry is made possible by: - the general configuration of the device. Indeed, by repeating the diagram of FIG. 67, when the beam passes from a space plane (4801) to a second space plane (4804), its direction is reversed. In the adopted configuration, the difference between the number of space planes traversed by the lighting beam and the number of space planes traversed by the reference beam is an odd number, and the lighting beam is therefore reversed. relative to the reference beam.

 - the respect of the condition (3), which means that the displacement of the reference beam and the displacement of the lighting beam are of the same amplitude.

 This symmetry of displacement makes it possible to simplify the algorithms and the adjustment procedure.

The design criteria applied to the path of the FS beam are as follows: - the beam FS must be parallel to its arrival on (5163) - its width at its arrival on (5163) must be equal to that of a beam which would be punctual in the plane (5158) and whose opening would be limited by the opening of the lens. This width, at the arrival of the beam on (5163), is about f1 og
9. 4. Obtaining a simple two-dimensional frequency representation and determining the maximum
The term simple two-dimensional frequency representation is understood to mean a representation for which polarizations have not been taken into account, which can be obtained without knowing the values of K and the point of direct impact of the illumination wave, from of a single sensor. The steps for producing such a representation, for a given illumination wave, are as follows: Step 1 - acquisition: (5104) is open and (5109) is closed, so that the polarization of the wave of lighting is fixed. d is defined as follows, the phase shift being performed with the previously calibrated piezoelectric actuators (5123) (5148): phase shift index (degrees) 0 +120 1 0 2 -120
The image is obtained from any of the CCD sensors. When obtained using (5171) or (5201) the phase plates (5238) and (5248) must be deleted.

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On obtient ainsi le tableaux MF[<V)[!j] ou i et; varient de 0 à 2NP, -1 . Etape 2- Calcul des représentation spatiales bidimensionnelles. Le programme effectue:

Etape 3- transformation de Fourier .

This gives the tables MF [<V] [! J] or i and; range from 0 to 2NP, -1. Step 2- Calculation of two-dimensional spatial representations. The program performs:

Step 3- Fourier transformation.

représentation fréquentielle MH[ij] oup prend les valeurs 0 ou 1 et ou i et j varient de 0 à 2NP, -1. The Fourier transform of the MG array according to the indices i and j is performed. This generates the

frequency representation MH [ij] oup takes the values 0 or 1 and where i and j vary from 0 to 2NP, -1.

 In some cases, this Fourier transformation may not be performed: it then obtains a spatial representation instead of a frequency representation.

 When the image is approximately punctual and the coordinates and the value of the maximum must be known, the maximum calculation program proceeds as indicated in 7.3.3.1., Except that the table S now has dimensions 2 Npix x 2 Npix and is the MH array calculated as above. It thus obtains the coordinates imax, jmax of the maximum on the sensor concerned. The image is considered centered if (imax, jmax) = (Npix, Npix) and is considered perfectly pointwise when the maximum value obtained is the highest possible.

9. 5. Adjusting the manual positioners
9. 5.1. Setting criteria:
FEP designates a plane lighting beam entering the objective (4317) while being directed along the optical axis and reaching the sensors (5174) (5171).

 The adjustments are to ensure that: (1) the beams follow the intended path.

(2) the lighting and reference beams are punctual in the frequency planes and parallel in the space planes.

(3) the FS and FSI beams are punctual in the space planes (4) the FS and FSI beams have point images centered on the sensors (5171) (5174) (5201) (5198).

(5) a FEP parallel beam entering a microscope objective (4317) and directed along the optical axis has a point image and centered on the two-dimensional frequency representations obtained by the procedure 9.4. from the images received on the sensors (5174) or (5171).

(6) When the image of the FEG beam on the two-dimensional frequency representations obtained by the procedure 9.4. from the images received on the sensors (5174) or (5171) is punctual and centered, then

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 the image of the FEGI beam on the two-dimensional frequency representations obtained by the procedure 9.4. from the images received on the sensors (5198) or (5201) is punctual and centered.

(7) Whatever the position of the mirror (5113): - the points corresponding to the beams FRD, FEDI, FEG, FEP on the two-dimensional frequency representations obtained by the procedure 9. 4. from the images received on the sensors (5174 ) or (5171) are arranged as shown in Fig.78 - the points corresponding to the beams FRG, FEGI, FED on the two-dimensional frequency representations obtained by the procedure 9. 4. from the images received on the sensors (5198) or (5201) are arranged as shown in Fig.79.

 To further explain this condition we will similarly note a beam and the corresponding point on one of the sensors and note (A, B) the vector connecting points A and B. This condition means that: (i) FRD and FEDI are on the same vertical line.

(ii) FEDI and FEG are on the same horizontal line.

(iii) FEP is the middle of FRD and FEG (iv) (FRG, FEGI) = (FRD, FEDI) (v) (FEGI, FED) = (FEG, FEDI)
The settings naturally follow from the conditions (1) to (7). The following detailed set of steps is an example of scheduling these settings.

 9. 5.2. Steps of adjustment.

 In some tuning phases, a temporary parallel beam marked FEP will be used. This beam is derived directly from the laser (5100) by means of a semi-transparent mirror and directed towards the entrance of the objective (4317), to which it manages to be directed along the optical axis, and that it crosses before heading towards the sensors (5171) and (5174).

 The introduction of VET requires the temporary abolition of the objective (4319). The so-called ground-related parts of the system are actually connected to a plane support ordinarily placed on the ground or on a table without any particular precaution, the optical table itself being placed, via dampers, on this flat support . During all the adjustments described in this paragraph, the optical table will be secured to the flat support, that is to say fixed without damping and without freedom of movement to the plane support, in a position as close as possible to the position of the optical table when it is free on its shock absorbers. The plane support itself will be fixed on a second optical table. This device makes it possible to generate interference patterns using the FEP beam, which would be impossible because of the vibrations if said flat support was fixed directly to the ground as in the normal operating phase of the microscope.

 The use of the FEG, FED, FEGI, FEDI, FS, FSI beams is controlled by the shutters (5144) (5207) (5218) (5209) (5161) (5186) (5254). Unrepresented shutters also make it possible to remove the FRD and FRG beams.

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N p, , NP, ) . On an image of dimensions 2Npix2Npix a point will be said centered if its coordinates are

N p,, NP,).

The following steps are an example of scheduling the settings: Step 1: Preset
A preset is made during which the mirror is positioned at a central position and the beam path is controlled with a diffuser. During this preset, the position of all elements is adjusted so that the beam follows approximately the intended path. For example, at the output of (5112) one checks the good spatial superposition of the beams. Between (5156) and (5159) it is verified that the reflected beam has the same spatial extent as the arriving beam.

 During the entire setting that follows, this preset can be constantly checked or cleared, still using the diffuser, without this being recalled. If you work in the UV field, it is dangerous to visualize the light directly. We then replace the diffuser with an auxiliary CCD, and we observe on a screen the illuminated area on this CCD instead of observing it directly.

Step 2: Adjustment in translation of the lens (5105)
The frequency meter is positioned behind the lens (5105) and the position thereof is set to have a point image on the frequency meter.

Step 3: Adjustment in translation of the lens (5110)
The frequency meter is positioned behind the lens (5110) and the position thereof is set to have a spot image on the frequency meter.

Step 4: Adjust the orientation of the semi-transparent mirror (5112).

 The frequency meter is used and positioned behind (5112). Since the shutters (5104) and (5106) are open and closed alternately, the integrated image produced on the frequency meter sensor consists of two points from each of the superposed beams. The angular position of (5112) is adjusted so as to superimpose these two points.

Step 5: Adjustment in translation of the lens (5251)
The frequency meter is positioned behind the lens (5251) and the position thereof is set to have a spot image on the frequency meter.

Step 6: translational adjustment of the lens (5121)
The frequency meter is positioned behind the lens (5251) and the position thereof is set to have a spot image on the frequency meter.

Step 7-Translation Adjustment of the Duplicate (5127) (5126)

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The frequency meter is placed behind (5127) on the beam path and the doublet is moved so that the image on the CCD of the frequency meter is punctual.

Step 8-Adjustment in translation of the lens (5146).

 This adjustment is made using the frequency counter, placed behind (5146). The image on the CCD of the frequency meter should be as punctual as possible.

Step 9-Translation Adjustment of the Duplicate (5151) (5152):
The frequency meter is placed behind (5152) in the beam path and the adjustment is made so that the image on the CCD of the frequency meter is punctual.

Step 10-Translation Adjustment of the Lens (5140)
The setting is made using the frequency counter behind (5140). The image on the CCD of the frequency meter must be punctual.

Step 11-Translation Adjustment of the Lens (5154)
The frequency meter is placed behind (5154). The image on the CCD of the frequency meter must be punctual.

Step 12-Translation Adjustment of the Duplicate (5178) (5179)
The frequency meter is placed for example behind (5213). The image on the CCD of the frequency meter must be punctual.

Step 13-Translation Adjustment of the Lens (5159)
The frequency meter is placed between (5156) and (5162). The position of (5159) is set so that the FEDI image on the frequency meter's CCD is punctual.

Step 14-Introduction of a FEP parallel temporary lighting beam.

 This beam has the characteristics explained at the beginning of this paragraph.

Step 15-Translation Adjustment of the Lens (5157)
The frequency meter is placed between (5156) and (5162). The position of (5157) is set so that the FEP image on the frequency meter's CCD is punctual.

Step 16-Setting the orientation of the semi-transparent mirror (5156)
The position of (5156) is set so that FEP and FEDI have coincident point images on the frequency meter.

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Step 17-Translational adjustment of the lens (5162).

 A CCD is provisionally set up at the site of (5158). FS is used. (5162) is set so that the FS image on this temporary CCD is punctual.

Step 18: Adjusting the orientation of the partially transparent mirror (5163)
The CCD remains used with the FS beam. (5163) is set so that the FS image on this temporary CCD is centered with respect to the location of the diaphragm.

Step 19-Translation Adjustment of the Lens (5189)
The frequency meter is positioned between (5163) and (5164). (5189) is set to obtain a point image of FSI on the frequency meter.

Step 20-Translation Adjustment of the Lens (5166)
FEDI is used. The frequency meter is positioned on the path of the behind beam (5166) and the position of (5166) is adjusted so that the FEDI image on the frequency meter is punctual.

Step 21-Adjustment in 3-axis translation of the sensors (5174) and (5171).

 We use FSI and FRD. A program calculates the two-dimensional frequency representation received on each CCD (5174) or (5171) according to the procedure described in 9.4, but not performing the Fourier transform step 3. The position of the CCDs is adjusted to obtain from each CCD a point-centered image.

Step 22-Adjusting the Orientation of the Partially Transparent Mirror (5236)
We use FRD and FEDI. A program calculates the two-dimensional frequency representation received on the CCD (5174) according to the procedure described in 9.4.

 The position of (5236) is adjusted so that the two-dimensional frequency representation obtained on each CCD is centered.

Step 23-Setting the orientation of the partially transparent mirror (5232)
We use FRD and FEDI. A program calculates the two-dimensional frequency representation received on the CCD (5171) according to the procedure described in 9.4.

 The position of (5232) is set so that the two-dimensional frequency representation obtained on each CCD is centered.

Step 24-Setting the focal length of the doublet (5126) (5127) and adjusting in rotation about the optical axis of the sensors (5174) (5171).

 The FRD, FEP beams are used. A program calculates the two-dimensional frequency representation received on each CCD (5174) or (5171) according to the procedure described in 9.4.

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 The initial position of the mirror (5113), in which the previous settings were made, is the centered position. It must be registered. It will be called position C.

 The mirror (5113) is moved such that, on the two-dimensional frequency representation obtained on each CCD (5174) or (5171), the point corresponding to FEP is eccentric to the maximum. This position of the mirror is recorded and will be reused later. It will be called position E.

The FEDI beam is introduced
The positions of the different elements are adjusted so that on each of the two representations obtained: the coordinates of the points associated with FRD (central point) and FEDI are correct compared to those of the point associated with FEP, that is to say symmetrical relative to the horizontal axis passing through the point associated with FEP, as shown in FIG. 78 or (5501) represents the contour of the two-dimensional zone obtained after the procedure described in 9. 4. and or (5502) represents the limit defined by the opening of the objective.

 - the images of FEP and FEDI remain punctual More precisely: - the focal length of the set (5126) (5127) is set so that the distance between the point associated with FEP and the point associated with FRD is equal to the distance between the point associated with FEP and the point associated with FEDI.

Since changes in position of the doublet lenses may result in defocusing, the positions of the doublet lenses are also adjusted so that the FEP and FEDI image remains punctual.

 - The rotational position of the sensors is adjusted so that the line passing through the points associated respectively with FRD and FEDI is vertical.

 Due to the non-coincidence of the axis of rotation of the CCDs with the central point of these sensors, this rotation setting can cause a loss of the translation setting of the CCDs. Therefore, at the end of this operation, the mirror is returned to position C and step 21 is performed again. Steps 21 and 24 can thus be repeated in sequence a certain number of times so as to converge towards correct adjustment of the transducers in translation and in rotation.

Step 25-Translation Adjustment of the Position of the Objectives (4319) and (4317)
The mirror (5113) is returned to its original position (position C), the beam FEP is removed, the objectives are put back in place. A temporary CCD is positioned at the location of (5184). The FS beam is used alone. A transparent slide is used as an object.

 The position of the lenses is adjusted to obtain a point and centered image.

Step 26-Translation Adjustment of the Lens (5183)
The FED beam is used. The frequency meter is positioned behind (5183) on the FED path. (5183) is set for FED to have a spot image on the frequency meter.

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Step 27-Translation Adjustment of the Duplicate (5178) (5179) and Adjustment of the Orientation of the Semitransparent Mirror (5182)
The FEG and FRD beams are used. A two-dimensional frequency representation is obtained from the CCDs (5174) or (5171) by the procedure 9.4.

 The joint position of the doublet (5178) (5179) is adjusted so that the representation obtained is punctual. The semi-transparent mirror (5182) is set so that this image is centered.

Step 28-Focal length adjustment of the doublet (5178) (5179), rotational adjustment of the assembly (5181), and adjustment of the orientation of the semi-transparent mirror (5182).

 The FRD, FEG beams are used. A two-dimensional frequency representation is obtained from the CCDs (5174) or (5171) by the procedure 9.4. Operations ol and o2 above must be repeated in this order a number of times to converge to a proper setting. ol: The mirror (5113) is set in position C and the semi-transparent mirror (5182) is set so that the point of the frequency representation corresponding to FEG is centered. o2: The mirror (5113) is set to the E (eccentric) position.

 The different elements are set so that the point corresponding to the FEG obtained on the image is correctly positioned relative to the others. The point corresponding to FEP is known from the setting made in step 24. The point corresponding to FEG must be symmetrical with the point corresponding to FRD with respect to the point corresponding to FEP as indicated in FIG. 78.

 More precisely: - The focal point of the doublet (5178) (5179) is set so that the distance between the points corresponding to FRD and FEP is equal to the distance between the points corresponding to FEP and FEG. Since the positional changes of the doublet lenses may result in defocusing, the lens positions of the doublet are also adjusted so that the FEG image remains punctual.

 - The rotating position of the assembly (5181) is set so that the points FRD, FEP and FEG are aligned.

Step 29-Translation Adjustment of the Lens (5185)
The mirror (5113) is returned to position C. The frequency meter is positioned between (5182) and (5188). The position of (5185) is set so that the FEGI image on the frequency meter is punctual.

Step 30-Translation Adjustment of the Lens (5188)
The FS beam is used. The frequency meter is positioned behind (5188). The position of (5188) is set so that FS has a spot image on the frequency meter's CCD.

Step 31-Translation Adjustment of the Duplicate (5192) (5193)

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FEGI is used. The frequency meter is positioned behind (5193). The joint position of (5192) (5193) is set so that FEGI has a point image on the frequency meter's CCD.

Step 32-3-axis translation adjustment of the sensors (5198) and (5201).

 FS and FRG are used. A program calculates the two-dimensional frequency representation received on each CCD (5198) or (5201) according to procedure 9.4. but not performing step 3 of Fourier transformation. The position of the CCDs is adjusted to obtain from each CCD a point-centered image.

Step 33-Adjusting the Partially Transparent Mirror Orientation (5246)
FRG and FEGI are used. A program calculates the two-dimensional frequency representation received on the CCD (5198) according to 9.3.1.

 The position of (5246) is adjusted so that the two-dimensional frequency representation obtained is centered.

Step 34-Adjusting the Orientation of the Partially Transparent Mirror (5242)
FRG and FEGI are used. A program calculates the two-dimensional frequency representation received on the CCD (5201) according to 9.3.1.

 The position of (5242) is adjusted so that the two-dimensional frequency representation obtained is centered.

Step 35-Setting - of the doublet focal length (5151) (5152) - of the focal length of the doublet (5192) (5193) - of the set (5212) in rotation - of the CCDs (5198) and (5201) in rotation around the optical axis
The FRG, FED, FEGI beams are used. The mirror (5113) is returned to the E (eccentric) position.

 A program calculates the two-dimensional frequency representation received on the CCDs (5198) (5201) according to the procedure 9.3.1.

 The positions of all the elements are adjusted in such a way that: - the coordinates of the points associated with FRG, FED, FEGI are correct, or with the notation used in 9.5.1. : (FRG, FEGI) = (FRD, FEDI) and (FEGI, FED) = (FEG, FEDI) where the positions of the FRD, FEG, FEDI points are those obtained in steps 24 and 28, the whole of these points being shown in Figs. 78 and 79.

 - images of FEP and FEG remain punctual More precisely:

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The focal length of the doublet (5192) (5193) is adjusted so that the distance between the points corresponding to FEGI and FED is correct. Since the positional changes of the doublet lenses may result in defocusing, the lens positions of the doublet are also adjusted so that the FED and FEGI image remains punctual.

 The rotational position of the CCDs (5198) and (5201) is set so that the FEGI-FED segment is horizontal.

 The focal length of the doublet (5151) (5152) and the position of the assembly (5151) (5152) are adjusted so that the distance between FRG and FEGI is correct and that the straight line linking these points is vertical. Since the positional changes of the doublet lenses may result in defocusing, the lens positions of the doublet are also adjusted so that the FEGI image remains punctual.

 At the end of this adjustment the mirror (5113) is brought back to position C.

Steps 32 to 35 can be repeated in this order a number of times to converge to the correct positions. Indeed, step 35 causes a disturbance of the central position of the CCDs and the orientation of the reference beams used in position C.

Step 36: Adjust the position of the window (5165) in the direction of the optical axis.

 FSI and FRD beams are used. A frequency image is obtained by procedure 9.4.1. from the sensors (5171) (5174). On this frequency image, the black point of the glass is visible in dark on a light background. The position of the glass is adjusted so that the black dot is detached from the background with the best possible contrast.

Step 37: Adjust the position of the window (5191) in the direction of the optical axis.

 The beams FS and FRG are used. A frequency image is obtained by the procedure 9. 4. from the sensors (5201) (5198). On this frequency image, the black point of the glass is visible in dark on a light background. The position of the glass is adjusted so that the black dot is detached from the background with the best possible contrast.

Step 38: in rotation about the optical axis and 2-axis translation of the diaphragms (5164) and (5190)
Prior to this adjustment, the mirror (5113) is brought back to the central position.

 These diaphragms have the form shown in Fig.82. They are adjustable in translation on 3 axes and in rotation around the optical axis. The beams FS, FSI, FRG, FRGI are used for their adjustment. A frequency image is obtained by procedure 9. 4. from each of the sensors (5174) (5198).

 They are set in translation to have an image centered on each sensor and as clean as possible without however impeding the movement of the moving window (5165) or (5191) associated with them. They are set in rotation so that the coordinates of the point obscured by the moving part (5712) are the same on the image obtained from each sensor. These coordinates will subsequently be noted (io, jo). At the end of this adjustment, the program also determines the radius Rouv of the image obtained on each sensor, which

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 characterizes the area accessible by the beams not stopped by the opening of the objective.It is better to underestimate slightly Rouv.

As a result of this adjustment procedure, the lenses are positioned so that FS has a point image centered on each sensor. This setting will not be changed until the sample is inserted.

 9. 6. Control of the beam deflector.

 At each position of the mirror corresponds a maximum (point FE in Fig. 75) of the frequency image obtained by procedure 9. 4. The point FR corresponding to the reference wave is at the center of the image. The point FO corresponding to the optical center is the middle of FR and FE. The coordinates of the point FE in a coordinate system centered on FO are the equivalent of the coordinates of the point of direct impact of the reference wave with respect to the optical center in the third embodiment.

 The index p will characterize the right or left side of the microscope with p = 0 for the sensors (5171) (5174) and p = 1 for the sensors (5198) (5201).

 The positioning system of the beam deflection mirror consists of two actuators that do not exhibit hysteresis. For example, stepper motor positioning can be used as described in the first embodiment. If the assembly is performed with sufficient care, such a system may have a very low hysteresis. The position of the mirror is then characterized by the number of steps performed by each motor from a central point. It is also possible to use piezoelectric positioners equipped with a feedback loop allowing precise control of their elongation, in which case the number of steps of each motor is replaced by the elongation of each actuator. It is also possible to use piezoelectric positioners without a feedback loop, however these have a high hysteresis which makes it necessary to determine the voltages used on a given trajectory, a point-to-point determination of the position values of the mirror, as performed here. below, not being possible.

 The control of the motors is defined by two boards tab2 or tabl [p, i, j] (resp.tab2 [p, i, j]) is the number of steps that the actuator 1 (resp. that the point FE has the coordinates (i, j) on the image obtained by the procedure 9. 4. from a sensor indexed by p, in a coordinate system in which FO has for coordinates (Npix / 2, Npix / 2). The actuators are numbered so that the actuator 1 determines a movement along the axis i and the actuator 2 determines a movement along the axis j.

 The determination of tables tabl and tab2 is done in the absence of object (transparent blade), by a specific program. The program then determines, for each objective point, the corresponding number of steps of each motor from an origin point. Fig. 77 represents an example of an algorithm of such a program. The main steps are:

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 (5407): Changing the shutter control. When p = 0, the beam used must be FEG and when p = 1 the beam used must be FED.

(5401): imax etjmax correspond to the coordinates of the maximum obtained by procedure 9.4. from the sensor receiving the point of direct impact of the illumination wave. We then have: imax x =
2 jmax y = 2 (5402): the lim value used depends on the precision of the actuators. For example, we can have lim = 0.25.

pasl=(i-x),pas~par~pixel/2 pas2=(i-y).pas~par~pixeII2 La valeur de position courante est modifiée: posl + =pasl pos2+=pas2 pas~~par pixel est le rapport (nombre de pas de déplacement du moteur)/ (nombre pixels de déplacement de FE sur l'image obtenue en 9.4.). Il doit avoir été préalablement déterminé, de manière similaire à ce qui est fait dans le premier mode de réalisation, mais avec les images maintenant calculées selon la procédure 9.4. et non pas obtenues directement sur le CCD. (5403): the displacement of the motors is worth, in a similar way to what was done in 5.20 .:

pasl = (ix), not ~ by ~ pixel / 2 pas2 = (iy) .not ~ by ~ pixeII2 The current position value is modified: posl + = pasl pos2 + = pas2 not ~~ per pixel is the ratio (number of no displacement of the motor) / (number of moving pixels of FE on the image obtained in 9.4.). It must have been previously determined, similar to what is done in the first embodiment, but with the images now calculated according to the procedure 9.4. and not obtained directly on the CCD.

(5404): the displacement of the motors is carried out, for a number of pas pas, not 2 of each motor.

tab 1 [p, i,j]=pos tab2[p,i,j]=pos2 Toutefois, dans le cas - #- 2+ N 2' 2 > R;uv les valeurs affectées sont par exemple des valeurs négatives signalant une erreur, comme tabl [p,i,j]=-10000, tab2[p,i,j]= -10000 (5406) : les moteurs sont déplacés de -posl, -pos2 de manière à retourner au point d'origine, qui doit rester constant pour éviter de fausser la trajectoire. (5405): The current values of the coordinates in motor steps are stored in a table:

tab 1 [p, i, j] = pos tab2 [p, i, j] = pos2 However, in the case - # - 2+ N 2 '2>R; uv the assigned values are for example negative values signaling a error, as tabl [p, i, j] = - 10000, tab2 [p, i, j] = -10000 (5406): the motors are moved from -posl, -pos2 so as to return to the point of origin, which must remain constant to avoid distorting the trajectory.

In order to obtain a light wave on the sensor p, at the point of coordinates i, j, the two motors will be moved to their positions characterized respectively by tab1 [p, i, j] and tab2 [p, i, j] , and the shutters (5144) and (5207) will be operated according to the following table:

<Tb>
<tb> index <SEP> p <SEP> position <SEP> of <SEP> (5144) <SEP> position <SEP> of <SEP> (5207)
<tb> 0 <SEP> closed <SEP> open
<tb> 1 <SEP> open <SEP> closed
<Tb>

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9. 7. Glass control (5165) and (5191)
Each of these panes is for example mounted on a two-axis positioner in translation controlled by stepper motors and for moving the window in a plane orthogonal to the optical axis. For each position of the illumination wave, characterized by indices p, i, j, it is necessary to position the window so as to cancel the direct illumination. This is done by controlling the stepper motors to move the window to a position characterized by the number of steps of each motor by the coordinates tab1 [p, i, j], tab2 [p, i, j].

 Prior to this use of windows, a program is used to determine tabv1 [p, i, j], tabv2 [p, i, j] tables. An example of such a program is described in FIG. 77.

 To use the program of FIG. 77 the FS, FSI, FRD and FRG beams are needed and the object used is a transparent slide. The filter (5128) used on the path of the beam FS is set so that the sensors are saturated on a few pixels around the impact points of the beams FS and FSI.

 The main steps of this program are: (5107): The position of the mirror (5113) is controlled by the tables tab1 [p, 0, 0], tab2 [p, 0, 0].

(5401): An image is obtained by the procedure described in 9. 4. with Fourier transformation from a sensor located on the side characterized by the index p. The module of the elements of this image is extracted to obtain an image in real numbers on which the point obscured by the 'black point' of the glass appears in clear on a black background. The image thus obtained constitutes the table S of dimensions 2Npix x 2Npix from which the coordinates imax and ymax of the maximum are calculated, by the procedure described in 7.3.3.1. We then have: x = imax y = jmax (5402): the value lim used depends on the accuracy of the positioner. For example, we can have lim = 0.25.

pasl=(i-x).pas~parixell2 pas2=(i-y).pas~par~pixell2 La valeur de position courante est modifiée: posl +=pasl pos2+=pas2 pas-par-pixel est le rapport (nombre de pas de déplacement du moteur)/ (nombre pixels de déplacement du point de coordonnées imax,jmax sur l'image obtenue en 9.4.). Il doit avoir été préalablement déterminé, par exemple en déplaçant la vitre selon une des directions et en mesurant le nombre de pixels de déplacement du point de coordonnées (imax,jmax). (5403): the displacement of the motors is worth, in a similar way to what was done in 5.20 .:

pasl = (ix) .pas ~ parixell2 pas2 = (iy) .pas ~ by ~ pixell2 The current position value is modified: posl + = pasl pos2 + = step2 step-by-pixel is the ratio (number of steps of motor) / (number of pixels of displacement of the point of coordinates imax, jmax on the image obtained in 9.4.). It must have been previously determined, for example by moving the window in one of the directions and measuring the number of moving pixels of the coordinate point (imax, jmax).

(5404): the displacement of the motors is carried out, for a number of pas pas, not 2 of each motor.

tabv][p,i,jl=posl tabv2[p,i,j] pos2 (5405): The current values of the coordinates in motor steps are stored in a table:

tabv] [p, i, jl = posl tabv2 [p, i, j] pos2

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Toutefois, dans le cas cri - N;IX) 2 + (j - N r ) 2 > R;uv les valeurs affectées sont par exemple des valeurs négatives signalant une erreur, comme tabJ[p,i,j]=-10000. tab2[p,i,j]= -10000 (5406) : les moteurs sont déplacés de -posl, -pos2 de manière à retourner au point d'origine, qui doit rester constant pour éviter de fausser la trajectoire.

However, in the case C 1 - N; IX) 2 + (j - N r) 2>R; uv the assigned values are, for example, negative values signaling an error, such as tabJ [p, i, j] = - 10000. tab2 [p, i, j] = -10000 (5406): the motors are moved from -posl, -pos2 so as to return to the point of origin, which must remain constant to avoid distorting the trajectory.

 9. 8. Obtaining the constant K.

 The micrometer is introduced as a sample. An image is obtained in the presence of the FED and FRG beams by the procedure described in 9.4. in which the step of Fourier transformation is not performed. The complex value module of this image is used to obtain a true image of the intensity. The position of the sample is adjusted so that this image is correctly focused. The distance in pixels Dpix between two graduations separated by a real distance Dreel is measured. The value of the constant K is then K = nv 2Npix Dreel.

# Dpix
9.9. Obtain a complete two-dimensional frequency representation.

 In the third embodiment, a two-dimensional frequency representation was obtained by the procedure described in 7.12. In the present embodiment, the mode of obtaining this representation must be modified.

9. 9.1. Principle
9. 9.1.1. Acquisition.

During the acquisition, the index r will designate the open switch, according to the following table:

<Tb>
<tb> index <SEP> r <SEP> shutter <SEP> (5109) <SEP> shutter <SEP> (5104)
<tb> 0 <SEP> open <SEP> closed
<tb> 1 <SEP> closed <SEP> open
<Tb>
The index p will designate the right (p = 0) or left (p = 1) side of the microscope or will reach the direct illumination wave and consequently the position of the shutters (5144) and (5207), according to the following table :

<Tb>
<tb> index <SEP> p <SEP> shutter <SEP> (5207) <SEP> shutter <SEP> (5144) <SEP>
<tb> 0 <SEP> open <SEP> closed
<tb> 1 <SEP> closed <SEP> open
<Tb>

The index q will designate the side of the microscope from which the acquired data originates, with q = 0 for data coming from the side where the direct light wave arrives and q = 1 for data coming from the opposite side.

<Desc / Clms Page number 218>

 We put s = pq + pq .s means the side of the microscope from where the acquired data come from, with s = 0 for the right side and s-- 1 for the left side.

The subscript (s, t) is indexed in the following manner.

<Tb>
<tb> index <SEP> s <SEP> 0 <SEP> 1
<tb> index <SEP> t <SEP> 0 <SEP> 1 <SEP> 0 <SEP> 1
<tb> sensor <SEP> (5174) <SEP> (5171) <SEP> (5198) <SEP> (5201)
<Tb>
the data MA [k, p] [d, r, t] [q, i, j] come from the sensor indexed by (p # + pq, t) For each quintuplet (k, p, q, r, t) we obtains, from a corresponding sensor, and from three acquisitions corresponding to different phases of the reference wave, an image in the form of a two - dimensional array of complex numbers of dimensions 2 Npix x 2 Npix.

9. 9.1.2. Frequency crossing
The image thus obtained is in spatial representation. Fourier transform is performed to obtain an image in frequency representation. The representation thus obtained is centered around a point FR corresponding to the reference beam. It must be translated and limited to obtain a representation of Npix x Npix dimensions centered around the FO point corresponding to the optical center.

coordonnées (N pzx , N p,x ) , correspondant à la fréquence de l'onde de référence. Le point noté FE correspond à la fréquence de l'onde d'éclairage (q=O) ou de son onde inverse (q=l). Le point noté FO correspond au centre optique du système, c'est-à-dire à la fréquence d'une onde traversant l'objet observé dans le sends de l'axe optique. Les contours (5301) et (5303) délimitent la représentation. Fig.75 and 76 represent the representations respectively obtained, for a given index p, on the sensors indexed by q = 0 and q = 1. In these figures, the point noted FR is the central point,

coordinates (N pzx, N p, x), corresponding to the frequency of the reference wave. The point noted FE corresponds to the frequency of the illumination wave (q = 0) or its inverse wave (q = 1). The point noted FO corresponds to the optical center of the system, that is to say to the frequency of a wave passing through the object observed in the sends of the optical axis. Contours (5301) and (5303) delimit the representation.

 In the case q = 0, FR and FE are symmetrical with respect to FO. In the case q = 1, FR and FE are symmetrical with respect to a horizontal line passing through FO.

 The limited and centered frequency representation is obtained from these figures by extracting the area of dimensions Npix x Npix centered around the point FO, limited by (5302) or (5304) in the figures.

 9. 9.1.3. Combination of the different polarizations.

 We denote Dp, s, r, t the complex value measured at a point C of a frequency representation obtained at the end of the procedure described in 9.9.1.2., From the sensor indexed by s, r and t when the direction of the lighting wave is characterized parp.

 We write # s, r, t the electric field vector of the reference wave on the sensor characterized by the indices s, r and t.

 In FIG. 80, the different combinations of the indices s, r, ts are represented in tabular form. In each box of the table:

<Desc / Clms Page number 219>

 the neutral axis of the phase plate located in front of the sensor in question is shown in dotted lines.

the electric field vector of the reference wave before passage of the phase plate, directed along / or #, is represented in solid lines.

the vector electric field # s, r, t of the reference wave after passage of the phase plate and reflection on the semi-transparent mirror which superimposes it on the beam coming from the object, directed according to ~ # or v, is also represented in solid lines. If s = 0, this vector is deduced from the vector electric field of the wave before passage of the blade by a symmetry whose axis is the neutral axis of the blade. If s = 1, additional symmetry of vertical axis must be made.

obtenues est, à une constante près: ws,,,r - (-1)STr+s(rr)l 1 + - )
La phase de l'onde de référence diffère entre les capteurs (5171) et (5174). On note [alpha]s le rapport caractéristique du décalage de phase et d'intensité entre les capteurs indicés respectivement par (s, t=0) et (s, t=1). The values of # s, r, t are deduced from this figure. A formula gathering all the values

obtained is, to a constant: ws ,,, r - (-1) STr + s (rr) l 1 + -)
The phase of the reference wave differs between the sensors (5171) and (5174). Note [alpha] s the characteristic ratio of phase shift and intensity between the sensors respectively indexed by (s, t = 0) and (s, t = 1).

 The wave detected on a given sensor constitutes a projection of the wave reaching this sensor on an oriented axis as the electric field vector of the reference wave. The unit vector orienting this axis will be noted as the electric field vector of the reference wave.

les composantes de l'onde diffractée polarisées selon les axes orientés par v,,O,o et ws,o,l, obtenant respectivement les facteurs Dp,s,o,o et Dp,s,o,\ - une onde d'éclairage dirigée selon j . Pour cette onde d'éclairage, on mesurera les composantes de l'onde diffractée polarisées selon les axes orientés par #s,1,0 et #s,1,1, obtenant respectivement les facteurs

,1,0 et Dp,s,l,1
Lorsque le vecteur champ électrique du faisceau d'éclairage (au point E) est Ao (- 1) p + A1# le vecteur champ électrique résultant au point C, sur le cotés du microscope, est donc:

1 Ar DP,s,r,t (i + ta s)w s,r,t r, t
Lorsque le vecteur champ électrique au point E est A0# + A1# le vecteur champ électrique résultant au point C, sur le cotés du microscope, est donc:

For the measurements we use: - a directed light wave according to (-1) '# where p is the index of the sensor towards which the direct light wave is directed. The factor (-1) is due to the fact that the horizontal component of the illumination wave, symmetrized by the mirrors which direct it in two opposite directions as a function of the index p, is reversed when the direction of the wave lighting is itself reversed. For this light wave, we will measure

the components of the diffracted wave polarized along the axes oriented by v ,, O, o and ws, o, 1, respectively obtaining the factors Dp, s, o, o and Dp, s, o, \ - a wave of directed lighting according to j. For this light wave, we will measure the components of the diffracted wave polarized along the axes oriented by # s, 1.0 and # s, 1.1, respectively obtaining the factors

, 1.0 and Dp, s, l, 1
When the electric field vector of the illumination beam (at point E) is Ao (-1) p + A1 #, the resulting electric field vector at point C, on the side of the microscope, is therefore:

1 Ar DP, s, r, t (i + ta s) ws, r, tr, t
When the electric field vector at point E is A0 # + A1 #, the resulting electric field vector at point C, on the side of the microscope, is:

<Desc / Clms Page number 220>

Ce qui correspond à l'expression

La même expression qu'en 7. 12 peut être utilisée à partir de ces valeurs de Cp,s,d,r pour obtenir la grandeur recherchée Mp,s,les indices p,s qui étaient inutile en 7.12. étant rajoutés:

Mp,s = - cosq cos<Co,o -sin e coslpcC p,s,O,1 - cosq sinpcCp,s,,,o - sin9e sinrpcCp,s,l,l

avec :

Which corresponds to the expression

The same expression as in 7. 12 can be used from these values of Cp, s, d, r to obtain the desired quantity Mp, s, the indices p, s which were useless in 7.12. being added:

Mp, s = - cosq cos <Co, o -sin e coslpcC p, s, O, 1 - cosq sinpcCp, s ,,, - sin9e sinrpcCp, s, l, l

with:

adopter pour ce coefficient la valeur 1 DP,S,r,o Dpz>r>1 ou les sommes sont sur les indices et sur un nombre de points réduit autour du point d'impact direct de l'onde d'éclairage. Previously it is necessary to determine the coefficient as. Around the point of impact of the illumination wave a comparable value is obtained on each sensor for a given index r. So we can

adopt for this coefficient the value 1 DP, S, r, o Dpz>r> 1 where the sums are on the indices and on a reduced number of points around the point of direct impact of the illumination wave.

9. 9.2. Acquisition
As in the third embodiment, the point of direct impact of the illumination wave travels a trajectory indexed by k and characterized by the tables Io [k], Jo [k].

<Desc / Clms Page number 221>

 As in 7.12.2.1., The acquisition of the elementary images is an iteration on the integers p and k respectively denoting the sensor to which the direct lighting beam arrives and the sequence number of the elementary image in the series of the images. corresponding to a given index p.

( Io[k] N 2 2 + (JO[k] - N # V < Rom le programme commande le déplacement du miroir par les

tableaux tabl [p,lo[k],Jo[k]] , tab2[p,Jo[k],Jo[k]] et les obturateurs (5144) et (5207) comme indiquée en 9.6. Il déplace la vitre située du coté opposé au point d'impact direct de l'onde d'éclairage de manière à ce que son point noir soit hors du champ de fréquences utilisée. There is no beam attenuation here. For each couple (k, p) checking

(Io [k] N 2 2 + (OJ [k] - N # V <Rom the program controls the movement of the mirror by

tables tabl [p, lo [k], Jo [k]], tab2 [p, Jo [k], Jo [k]] and the shutters (5144) and (5207) as indicated in 9.6. It moves the window on the opposite side to the point of direct impact of the light wave so that its black point is outside the frequency field used.

l'onde d'éclairage de la manière indiquée en 9.7., par les tableaux tabv][P,Io[k],Jo[k]] , tabv2[p,lo[k],Jo[k]]. It controls the movement of the window on the side where the point of direct impact of

the illumination wave in the manner indicated in 9.7., by the tables tab] [P, Io [k], Jo [k]], tabv2 [p, lo [k], Jo [k]].

 However, according to a variant that will be called variant 2, it does not use this window and moves so that its black point is outside the frequency field used.

 To increase the speed, it is necessary to limit as much as possible the number of changes in the index p, which involve a manipulation of the shutters (5144) and (5207) which are slower for example than (5104) and (5109). The program then performs a first iteration over k, at p = 0, followed by a second iteration over k, at p = 1.

 At each value of (k, p) the program acquires 12 pairs of elementary images.

A couple of elementary images is as in 7.12.2.1. a table indexed on the one hand by the index q with q = 0 if the image is detected on the same side as the point of direct impact of the reference wave, and q = 1 if it is detected on the opposite side .

 on the other hand by the indices i and / characterizing the position of the pixel on the sensor concerned.

L'acquisition d'une série d'images correspondant aux indices k,p,q,d,r,tgénère ainsi la série des

couples d'images élémentaires MA[k,p][d,r,t][q,i j] The indices p, q, r, ts are defined as indicated in 9.9.1.1. The index d determines the phase shift of the reference wave and is defined by the following table:

The acquisition of a series of images corresponding to the indices k, p, q, d, r, thus generates the series of

elementary image pairs MA [k, p] [d, r, t] [q, ij]

<Desc / Clms Page number 222>

référence. Il déplace les moteurs jusqu'aux positions posl[p, i,. , j, pos2[p, ir , jr] ou (i r,j r) sont normalement, les coordonnées (io, jo) du point fixe occulté par les diaphragmes, déterminées dans l'étape 38 de la procédure de réglage 9. 5. Toutefois, si la variante 2 est utilisée, (ir,jr) sont les coordonnées d'un autre point fixe, fortement excentré mais non occulté. Le programme effectue alors l'acquisition d'une série

de 6 couples d'images élémentaires, obtenant un tableau MA2 [kpl [dr, t] [q, ijl
Toutefois, selon une variante, que l'on appellera la variante 1, le programme n'effectue pas l'acquisition de cette image de référence. The program additionally performs the acquisition of a series of images corresponding to the image of

reference. It moves the motors to posl [p, i ,. , j, pos2 [p, ir, jr] or (ir, jr) are normally the coordinates (io, jo) of the fixed point obscured by the diaphragms determined in step 38 of the adjustment procedure 9. 5. However, if variant 2 is used, (ir, jr) are the coordinates of another fixed point, strongly eccentric but not obscured. The program then acquires a series

of 6 pairs of elementary images, obtaining an array MA2 [kpl [dr, t] [q, ijl
However, according to a variant, which will be called variant 1, the program does not perform the acquisition of this reference image.

 9. 9.3. Calculations.

 The computation of the two-dimensional frequency representation, of the reference image, and the characteristic tables of the noise on these two images is carried out by the following steps 1 to 8: Step 1-Calculation of the two-dimensional spatial representations.

Etape 2- Passage en représentation fréquentielle. The program performs on all the data obtained:

Step 2- Passage in frequency representation.

Mk pY t9 l j Etape 3: compensation de la réponse fréquentielle des capteurs. The indices i and vary from 0 to 2 Npix -1. The program performs the Fourier transform according to these two indices of each of the spatial representations previously obtained. This leads to transformed representations:

Mk pY t9 lj Step 3: compensation of the frequency response of the sensors.

 This compensation is not essential but it significantly improves the accuracy of the microscope.

Le tableau RI représente la réponse fréquentielle inversée des capteurs. Il est déterminé en 9.11. Toutefois, selon une variante que l'on appellera variante 3, utilisée pour certains réglages, le tableau RI est mis à 1. The program calculates the MD array:

Table RI represents the inverse frequency response of the sensors. It is determined in 9.11. However, according to a variant that will be called variant 3, used for certain settings, the RI array is set to 1.

Step 4-Translation and limitation of the two-dimensional frequency representation.

<Desc / Clms Page number 223>

ou i et j varient maintenant de 0 à Npix -1. The position of the FO point indicated in 9.9.1.2. is stored as tables Io [k] Jo [k]. The considerations in 9.9.1.2. then result in the following operations performed by the program:

where i and j now vary from 0 to Npix -1.

Step 5: Calculation of the [alpha] coefficients.

alphak, p, q . Le programme parcourt l'ensemble des triplet (k,p,q). Pour chaque triplet - il initialise à 0 les nombres nom et denom. A coefficient [alpha] s is determined for each triplet (k, p, q). It is stored in an array of complexes

alphak, p, q. The program traverses the set of triplets (k, p, q). For each triplet - it initializes to 0 the numbers name and denomination.

(i -lok)Z + -.Iok) < lrm2 avec par exemple lim=20. it traverses the set of triplets r, i, j by testing the condition:

(i-lok) Z + -.Iok) <lrm2 with for example lim = 20.

- Lorsque la boucle sur r,i,j est terminée il effectue: nom

alphak, p,q nom denom Etape 6- Combinaison des valeurs correspondant aux indices r et t

Cette étape a pour objet de calculer Mk, p,q i, j en fonction de ME[k, pr, tq, i, j . Ceci peut être réalisé très simplement en effectuant l'opération suivante: Mk, p,q !/\ Y] = ME[k, p][l,l][<7, /, y] , la valeur affectée au bruit étant alors constante et l'étape 5 étant rendue inutile. Si cette méthode doit être utilisée, il est cependant préférable de supprimer les lames de phase (5111) (5238) (5239) (5248) (5249). When the condition is true it performs:

- When the loop on r, i, j is complete it performs: name

alphak, p, q noun Step 6- Combination of the values corresponding to the indices r and t

This step aims to calculate Mk, p, qi, j according to ME [k, pr, tq, i, j. This can be done very simply by performing the following operation: Mk, p, q! / \ Y] = ME [k, p] [l, l] [<7, /, y], the value assigned to the noise being then constant and step 5 is rendered useless. If this method is to be used, it is however preferable to delete the phase slides (5111) (5238) (5239) (5248) (5249).

principe a été indiqué en 9.9.1.3., la quantité ME[k, p][r, t][q, i, jl étant la valeur mesurée notée Dp,s,r,t en 9. 9.1.3. L'étape 6 est alors effectuée comme suit:
Pour chaque valeur des indices k,p,q,i,j le programme calcule: In all cases, this method, similar to that used in the second embodiment, induces imperfections in high frequencies. It is therefore preferable to use the method whose

The principle has been given in 9.9.1.3., the quantity ME [k, p] [r, t] [q, i, jl being the measured value denoted Dp, s, r, t in 9. 9.1.3. Step 6 is then performed as follows:
For each value of the indices k, p, q, i, j the program calculates:

<Desc / Clms Page number 224>

Les valeurs de sinpc COSq1c sinpe cos o, sont déterminées selon les tableaux d'affectation suivants:

The values of sinpc COSq1c sinpe cos o, are determined according to the following allocation tables:

<Tb>
<tb> Mce <SEP> other <SEP> ~~~~~~~
<Tb>

Mc autre COSq1e 1 Me Ye Mc 2 Mc \e ' / y# - xcycvxz + xcvxy) M2cMcey sin<D,. 0 / y ,Y2r/ i v i/ sinq1e Me xe / 1 Me -xcYcvyz +xcvxz +Ycvxyl

Mc other COSq1e 1 Me Ye Mc 2 Mc \ e '/ y # - xcycvxz + xcvxy) M2cMcey sin <D ,. 0 / y, Y2r / ivi / sinq1e Me xe / 1 Me -xcYcvyz + xcvxz + Ycvxyl

<Tb>
<tb> Me <SEP> Mc2Mce
<tb> Mce <SEP> 0 <SEP> other
<tb> Me <SEP> 0 <SEP> other
<Tb>

cos '1 - Mc Ye ~ Me 2 1 Mce (yeVJ'z -xeYexz 'xevxyl sino,, 0 Xç~ J~LXeyeV 4-yv +v sinq1e ## -#####)'-<'e''±'''exz'e e ce puis les coefficients sont calculés:

cos '1 - Mc Ye ~ Me 2 1 Mce (yeVJ'z -xeYexz' xevxyl sino ,, 0 Xc ~ J ~ LXeyeV 4-yv + v sinq1e ## - #####) '- <' e '' ± '''exz'e e then the coefficients are calculated:

<Desc / Clms Page number 225>

These coefficients do not depend on the result of the taking of images and in the case where one repeats always the same series they can be stored in a table rather than recalculated each time. The program then uses these values to combine the images obtained with the different rotator positions as follows:

coef[k, p, q, i, jr, t correspond à la quantité notée Epsrt en 9.9.1.3. avec s = pq + pq .

coef [k, p, q, i, jr, t corresponds to the quantity noted Epsrt in 9.9.1.3. with s = pq + pq.

ME [k, pr, t] [q, i, j] corresponds to the quantity denoted Dp., R in 9.9.1.3.

- sinon: Bk,p,0[i, j] = MAX ou MAX est une valeur élevée, par exemple 1010 Bk,p,1[l,j] vaut:

Etape 8-Calcul de l'image de référence. Mk, p, q, j corresponds to the quantity noted Mp, s in 9.9.1.3. Step 7: The noise amplitude is calculated as follows:

otherwise: Bk, p, 0 [i, j] = MAX or MAX is a high value, for example 1010 Bk, p, 1 [l, j] is:

Step 8-Calculation of the reference image.

notera Hk,P,9i, j] le tableau ainsi généré et BH k,p,q[i, j] l'amplitude de bruit correspondante. Toutefois, dans le cas de la variante 1, cette image de référence n'est pas calculée. The reference image is calculated in exactly the same way as the main image, but using the MA2 array instead of the MA array and replacing the lo [k], Jo [k] values by (ir, jr) . We

note Hk, P, 9i, j] the table thus generated and BH k, p, q [i, j] the corresponding noise amplitude. However, in the case of variant 1, this reference image is not calculated.

 9. 10. Fine adjustment of the position of the sensors.

 This operation is intended to ensure a precise adjustment with respect to each other of the two sensors corresponding to the same side of the microscope, in particular in the direction of the optical axis. In the absence of such a setting, the origin point of the frequency representations generated from each sensor may differ slightly, which subsequently compromises the good superposition of the portions of the frequency representations from each side of the microscope. The fact of not making this adjustment does not prevent the generation of three-dimensional representations of the sample but limits the precision of these representations.

<Desc / Clms Page number 226>

 A displacement in translation of a sensor causes a modulation in the frequency domain and therefore a phase shift of the values of the plane waves obtained from this sensor. The adjustment consists of checking that the plane waves received on each sensor for various directions of the illumination beam are in phase.

initialise à 0 les tableaux MFs,t de dimensions N p/X x N p, . Il effectue une boucle sur les indices s, i et j. The indices are indexed by the indices s, t with the same convention as in 9.9.1.3. The program

initializes to 0 the tables MFs, t of dimensions N p / X x N p,. It makes a loop on the indices s, i and j.

For each triplet s, ij satisfying <- N 2 J 1z + C j - N 2 '1z J <~ R 2 it performs the following operations: - it actuates the shutters so as to use the beam FEG for s = 0 and the EDF beam for s = 1.

it moves the mirror to the point corresponding to tab 1 [s, i, j], tab 2s, i, j - it generates from each sensor indexed by s a two-dimensional image according to the method described in 9. 4., thus obtaining two images MHs, t [k, l] or indices s ett were added to characterize the sensor, with the same convention as in 9.9.

- It moves the mirror to a fixed point of coordinates (ir, jr) - it generates from each sensor indexed by s a two-dimensional image according to the method described in 9. 4., obtaining two images MHRs, t [k, l ].

It performs for the pair of integers (ii): rj - MHs, 2i, 2 j It performs for couple of integers (i, j): MFS t [i, j \ MHf2s, t [2i, 2j] After completed this loop on s, i, j, the program calculates the following deviations:

The translational position of the sensor (5171) should be adjusted to minimize # 0 and the position of the sensor (5201) should be adjusted to minimize # 1. The program must therefore loop on the calculation of these deviations until the adjustment is completed. #s represents the mean square deviation due to phase errors between the frequencies received on the two sensors located on the same side of the microscope.

9. 11. Determination of the frequency response of the sensors
The sensors perform a filtering of the spatial frequencies that reach them. This filtering is in the best case equivalent to an averaging on the surface of the pixel, however in general it is more important because of the defects of the CCDs and the cameras. In embodiments based on reception in a frequency plane, this filtering simply induces a darkening of the portion of the generated image that is remote from the center. In this embodiment, this filtering is performed in the space plane and poses more important problems. It is better to use good quality cameras and compensate for this filtering. This space plane filtering is equivalent to a frequency multiplication by an RF array whose inverse RI is used in procedure 9. 9. to perform the compensation. To limit the

<Desc / Clms Page number 227>

 noise on the frequency response, it is acquired using plane waves rather than from a single spherical wave.

7o[j - N 2 l2 J +CJok- N;/X r 5, R;uv ou Rouv est le rayon limité par l'ouverture des objectifs, qui a été obtenu à l'étape 37 de la procédure de réglage 9. 5. Cette trajectoire sera nommée par la suite trajectoire complète . 9. 11.1. Acquisition
We use tables Io and Jo characterizing a trajectory traversing the set of accessible points, that is to say that (Io [k], Jo [k]) must traverse all the points such as

Wherein R is the radius limited by the aperture of the lenses, which was obtained in step 37 of the tuning procedure 9. 5. This trajectory will be named after the complete trajectory.

(injr) non occulté. Il génère ainsi les séries d'images Mk.p.q[i,J] et Hk, p,q i, j . L'indice no n'étant pas connu, il est pris égal à nv dans la procédure 9.9. Toutefois, lors de cette acquisition, il suffit d'enregistrer les valeurs M., p,9 lok, .Iok et Hk.p,q [1,. y, j. 9.11.2. calcul

Le programme initialise à 0 le tableau RFl de dimensions N plX x NFIX - Il parcourt alors la série des indices k. Pour chaque indice k il effectue :

ou ir,jr sont les coordonnées du maximum de l'image de référence, comme définies en 9.9. A program performs the acquisition defined by these tables, according to the procedure described in 9.9. with variants 2 and 3, that is without using the windows (5165) (5191) and with a coordinate point

(injr) not occulted. It thus generates the series of images Mk.pq [i, J] and Hk, p, qi, j. Since the index no is not known, it is taken equal to nv in procedure 9.9. However, during this acquisition, it is sufficient to record the values M., p, 9 lok, .Iok and Hk.p, q [1 ,. y, j. 9.11.2. calculation

The program initializes to 0 the RFl array of dimensions N plX x NFIX - It then goes through the series of indices k. For each index k it performs:

where ir, jr are the coordinates of the maximum of the reference image, as defined in 9.9.

x2Npix puis en effectuant pour i et j variant de 0 à N pix - 1 :

It then performs the inverse two-dimensional Fourier transform of array RF1, obtaining an array RF2. It completes this array with zeros by initializing the array RF3 of size 2Npix to 0

x2Npix then doing for i and j varying from 0 to N pix - 1:

It then performs the inverse two-dimensional Fourier transform of the RF3 array, obtaining the RF array corresponding to the frequency response of the sensors.

-sinon : RI[i,j] = 0
Le tableau RI ainsi déterminé est en particulier utilisé en 9.9. The program then calculates the inverse frequency response of the sensors as follows:

-Not: RI [i, j] = 0
The table RI thus determined is used in particular in 9.9.

<Desc / Clms Page number 228>

 9. 12. Determination of the relative coordinates of the points of origin of the images obtained on each side of the microscope.

 The frequency images obtained on each side of the microscope by the procedure 9. 9. are equivalent to the frequency images that were obtained in the previous embodiments. They are, in the same way, relative to a point of origin, which no longer depends on the origin point of the reference wave, but on the position of the sensor. To be able to superimpose these representations it is necessary to know the relative position of the points of origin of the representations obtained on each side of the microscope.

 This is achieved by using FS and FSI spherical waves. The spherical wave FS or FSI received on each side of the microscope must in principle be punctual and centered on each receiving surface. The position of the objectives can therefore be adjusted in the presence of the beams FS, FSI, FRG, FRD so that the image obtained on each sensor by the procedure 9. 4. used without Fourier transform, is perfectly punctual and centered. If this position adjustment of the lenses is carried out with the utmost care and with sufficiently precise positioners, of sub-micrometric precision, for example microscope focusing devices of sufficient quality, or positioners with piezoelectric control, then the points of origin of the images obtained from each side of the microscope are confused.

 The adjustment procedure described in 9.5. However, this quality of adjustment can be achieved by using medium precision positioners for lenses. Indeed, fine adjustments are made. in this procedure, by moving cameras and not lenses. If the adjustment procedure described in 9. 5. is carried out carefully, the origin points of the finally obtained frequency representations are merged. Their relative coordinates are (x, y, z) = (0,0,0).

 However, the settings obtained by the 9. 5. procedure or by a new position setting of the lenses are generally imperfect. In particular, they can be influenced by local imperfections of the sensors. It is possible to use (x, y, z) = (0,0,0) but a better superposition of the images coming from each sensor will be obtained if a suitable algorithm is used to calculate a more precise value of these parameters. An accurate determination of the relative positions of the points of origin can be obtained by a method similar to that used in 7.9.1. However: - The image of the FS or FSI beam in the reception plane is punctual and not distributed over the entire receiving surface as in 7.9.1. The consequences are that the image obtained is sensitive to local defects of the sensors and that it is strongly noisy.

- The focal point of FS or FSI does not correspond to the characteristic point (with the terminology used in 3.16.) Of one of the objectives, whereas in 7.9.1. the focal point of the reference beam corresponded to the characteristic point of a corresponding objective.

 The method used is therefore modified to overcome, as far as possible, these disadvantages.

The beams used are FS, FSI, FRD, FRG and the object used is a transparent blade. The method used breaks down into two phases:

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Acquisition phase: It consists of an iteration on the indices k, l traversing the set EO of the points

dimensions N pix x N p,x est initialisé à 0 puis le programme effectue, pour chaque couple (k, P de l'ensemble EO , les étapes 1 à 7 suivantes: étape 1: positionnement du miroir de déviation du faisceau au point déterminé par tabl[O, k, l], tab2[0, k, l] étape 2: Une image est acquise de chaque coté du microscope selon la procédure décrite en 9.4. sans

effectuer la transformée de Fourier. On notera ces images MO, [/, y] au lieu de MH[i, j , l'indice s caractérisant le capteur avec s=0 pour (5174) et 5=1 pour (5198). étape 3 : le programme détermine les coordonnées imaxs,jmaxs de la valeur maximale de chaque tableau

M0j,y]. Il calcule alors les tableaux MIs[i,j] avec:

dimensions N pix x N p, x is initialized to 0 then the program carries out, for each pair (k, P of the set EO, the following steps 1 to 7: step 1: positioning of the deflection mirror of the beam at the determined point by tabl [O, k, l], tab2 [0, k, l] step 2: An image is acquired on each side of the microscope according to the procedure described in 9.4.

perform the Fourier transform. Note these images MO, [/, y] instead of MH [i, j, the index s characterizing the sensor with s = 0 for (5174) and 5 = 1 for (5198). step 3: the program determines the coordinates imaxs, jmaxs of the maximum value of each array

M0j, y]. It then calculates the tables MIs [i, j] with:

ou Rmv est déterminé pour que le disque de rayon Rmv centré sur imax s' jmax contienne tous les points dont les valeurs hors bruit sont supérieures au niveau de bruit, tout en étant aussi réduit que possible. En pratique, Rniv peut être déterminé empiriquement et valoir une dizaine de pixels. étape 4: le programme effectue la transformée de Fourier bidimensionnelle de chaque tableau Mls [l, j], obtenant les tableaux M2s[i,j]. étape 4 : programme applique le filtre RI aux tableaux ainsi obtenus:

M3Si>J=M2slJlj étape 5: Le programme calcule le tableau M4 de dimensions Npix x Npix de la manière suivante:

-sinon, M4[i,j] = 0 Le tableau M4 représente le décalage de phase entre les deux capteurs dû à la non-coïncidence des points d'origine, partiellement débruité. étape 6 : le programme effectue la transformée de Fourier inverse du tableau M4, obtenant un tableau M5. étape 7 : le programme modifie le tableau M6 de la manière suivante:

Phase de calcul: Le programme calcule le tableau M7 qui est la tranformée de Fourier du tableau M6. Le programme calcule les coordonnées x,y,zobtenues par la procédure décrite en 7. 8. à partir du tableau M7,

or Rmv is determined so that the disk of radius Rmv centered on imax s' jmax contains all the points whose noise-free values are higher than the noise level, while being as small as possible. In practice, Rniv can be determined empirically and worth ten pixels. step 4: the program performs the two-dimensional Fourier transform of each array Mls [l, j], obtaining the arrays M2s [i, j]. step 4: program applies the IN filter to the tables thus obtained:

M3Si> J = M2slJlj step 5: The program calculates the array M4 of dimensions Npix x Npix as follows:

[0101] M4 [i, j] = 0 Table M4 represents the phase shift between the two sensors due to the non-coincidence of the points of origin, partially denoised. step 6: the program performs the inverse Fourier transform of array M4, obtaining an array M5. Step 7: The program modifies the M6 array as follows:

Calculation phase: The program calculates the array M7 which is the Fourier transform of the array M6. The program calculates the x, y, z coordinates obtained by the procedure described in 7. 8. from Table M7,

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maximale de I M6i, jl . Il calcule alors rapport = M6jimax, jmax
Fd [imax,jmax] étape 2 : le programme calcule la grandeur caractéristique max:

ou la somme est sur l'ensemble des couples (i,j) inclus dans le disque de centre (imax,jmax) et de rayon
Rniv
2
9.13.Détermination des phases des faisceaux
Cette procédure est similaire à la procédure 7. 9.2. La position des objectifs est celle qui a été utilisée en 9.12. pour obtenir les coordonnées x,y,z et ne doit pas être modifiée au cours de la présente procédure. which replaces the table marked Frec in 7. 8. However, for this step, the procedure described in 7. 8. must be modified as indicated in 7.9.1. to account for the fact that the index of the object is known. It must also be modified in a second way to take into account that the acquisition mode is different and that the standard deviation # 2 must be calculated in the spatial domain and not in the frequency domain as in 7.8.1. . This second modification consists in replacing the steps (3512) to (3514) of FIG. 50 by the following steps, which are performed in spatial representation and where M6 (and not M7) is used: step 1: the program determines the coordinates (imax jmax) of the point corresponding to the value
M6 [imax, jmax]

maximum of I M6i, jl. It then calculates ratio = M6jimax, jmax
Fd [imax, jmax] step 2: the program calculates the max characteristic value:

where the sum is on all couples (i, j) included in the center (imax, jmax) and radius disc
Rniv
2
9.13.Determination of the phases of the beams
This procedure is similar to procedure 7. 9.2. The position of the objectives is the one used in 9.12. to obtain the x, y, z coordinates and must not be modified during this procedure.

 We use the tables Io and Jo already used in 9.11 and characterizing a complete trajectory.

Mk,p,q i, j et Hk,p,q i, j . L'indice no n'étant pas connu, il est pris égal à n, dans la procédure 9.9. Lors de cette acquisition, il suffit d'enregistrer les valeurs Mk, p,q [Io[k], Jok et Hk, p,q i,. , j, 1 -
Le programme initialise à 0 le tableau Ra puis il parcourt la série des indices k,p en effectuant pour chaque couple k,p:

ou ir,jr sont les coordonnées du maximum de l'image de référence, comme définies en 9. 9. et ou x,y,z sont les coordonnées déterminées en 9.12. A program performs the acquisition defined by these tables, according to the procedure described in 9.9. with the variants 2 and 3, that is to say without using the windows (5165) (5191), with a point of coordinates (ir, jr) not occulted, and without compensation of the filtering of the sensors. It thus generates the series of images

Mk, p, qi, j and Hk, p, qi, j. The index no not being known, it is taken equal to n, in the procedure 9.9. During this acquisition, it is sufficient to record the values Mk, p, q [Io [k], Jok and Hk, p, qi ,. , j, 1 -
The program initializes the array Ra to 0, then it traverses the series of indices k, p by performing for each pair k, p:

or ir, jr are the coordinates of the maximum of the reference image, as defined in 9. 9. and where x, y, z are the coordinates determined in 9.12.

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 9. 14. Adjusting the position of the lenses in the presence of the sample.

images par la procédure décrite en 9.4.: une image spatiale obtenue sans effectuer l'étape 3 et une image fréquentielle obtenue en effectuant l'étape 3. Le module des valeurs complexes est extrait sur chaque image. The sample to be observed is put in place. The beams FS and FRG are used. The FRG beam used is in the direction of the optical axis, so the deflection mirror is in central poition, defined by

images by the procedure described in 9.4 .: a spatial image obtained without performing step 3 and a frequency image obtained by performing step 3. The complex values module is extracted on each image.

The position of the objectives is adjusted on the same principle as in 7.10 .:
The spatial image must be centered.

 On the image in frequency, one must observe a clear disc. The adjustment must be made so that the intensity is as high as possible for the high frequencies (points far from the center). The disc observed must remain relatively homogeneous.

 If a dark ring appears between the outer edge and the central area, the sample is too thick and not all frequencies can be taken into account. The adjustment must then be made so as to have a relatively homogeneous disk, radius as high as possible. The disc does not reach its maximum size and high frequencies can not be taken into account. The resolution of the image, mainly in depth, is diminished. The only solution to this problem is to use a specially designed lens, described in paragraph 7.19.

9. 15. Determination of x, y, z, L, n0
This step is similar to that described in procedure 7.11. As in the procedure described in 7.11., This step can be avoided by performing a prior measurement of the quantities L and no and introducing the sample without moving the objectives, and therefore without performing step 9. 14., of so as not to modify the values of x, y, z obtained in 9.12.

3. Il génère ainsi les séries d'images Mk, p,9 [i, 7] et Hk, p,q [i, 7]. Toutefois, lors de cette acquisition, il suffit d'enregistrer les valeurs n,o 41. -o[]1 et Hk, p,q [4 ' 7r j Le programme parcourt alors la série des indices k. Pour chaque valeur k il effectue:

The program carries out the series of acquisitions defined by the tables Io and Jo defining a complete trajectory, already used in 9.11.2, according to the procedure described in 9. 9. used with the variants 2 and

3. It thus generates the series of images Mk, p, 9 [i, 7] and Hk, p, q [i, 7]. However, during this acquisition, it suffices to record the values n, o 41. -o [] 1 and Hk, p, q [4 '7r j The program then traverses the series of indices k. For each value k it performs:

The program described in 7. 8. is then used to calculate the parameters x, y, z, L, n0 from the table Frec thus constituted.

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 9. 16. W calculation and focus adjustment.

 This step is performed as described in 7.15. However, it can be avoided if the sample index is close to the nominal index of objectives, in which case we can choose for example wp = L / 2.

the tables Mk, p, q [i, j] obtained by the procedure 9. 9. used without variant are substituted for those previously obtained by the procedure 7.12.

- les valeurs imaxk , jmcrxk sont maintenant données par: imaxk =#"-7o)/r1, jmaxk =##Jo[A:]. 'p!X noix - L'étape 2 de la procédure (4002) de la Fig. 57 nécessite l'acquisition de la valeur de l'onde au point

('MaXk, jmaxk . Les vitres étant utilisées pour arrêter l'onde d'éclairage directe, cette valeur n'est pas disponible. Cette étape est donc remplaçée par les étapes 2.1et 2. 2. suivantes : étape 2,1. Pour chaque valeur de k, le programme calcule:

étape 2. 2. Pour chaque valeur de k,l,j le programme effectue:

ou Frec est le tableau déterminé en 9.15. - because the sampling is regular, we use Ko = K1 = K

the values imaxk, jmcrxk are now given by: imaxk = # "- 7o) / r1, jmaxk = ## Jo [A:]. 'p! X nuts - Step 2 of the procedure (4002) of FIG. 57 requires the acquisition of the value of the wave at the point

Since the windows are used to stop the direct light wave, this value is not available, this step is therefore replaced by the following steps 2.1 and 2. 2. Step 2.1. each value of k, the program calculates:

step 2. 2. For each value of k, l, j the program performs:

or Frec is the table determined in 9.15.

 9. 17. Obtaining the aberration compensation function.

This step is performed as described in 7.16. with Ko = K1 = K
9. 18. Realization of three-dimensional images by the method described in the third embodiment.

9. 18.1. without direct wave suppression This step is performed as described in 7.17.2.

the tables Mk, p, 9 i, j Hk, P, 9 i, j Bk, P, 9 i, j BH kp, q [i, j] obtained by the procedure 9.9 used with variant 2 are substituted for those previously obtained by the procedure 7.12 - because the sampling is regular, we use Ko = K1 K, ao = a1 = 1.

- the values imaxk, p, q, jmaxk, P, 9 are now given by: imaxk, p, q = lok, jmaxk, p, q = Jo [k].

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 9. 18.2. with suppression of the direct wave.

l'algorithme décrit en 7.17.2. nécessite l'acquisition de la valeur de l'onde au point imaxk, p,o , jmaxk, p,o Les vitres étant utilisées pour arrêter l'onde d'éclairage directe, cette valeur n'est pas disponible. Cette étape est donc remplaçée par l'étape 2 suivante, équivalente à celle indiquée en 7.18.1. étape 2 : Pour chaque valeur de k,p,q,i,j le programme effectue:

The principle is the same as above but the 9. 9. procedure is used without variant. In addition, step 2 of

the algorithm described in 7.17.2. requires the acquisition of the value of the wave at the point imaxk, p, o, jmaxk, p, o The windows being used to stop the direct light wave, this value is not available. This step is therefore replaced by the following step 2, equivalent to that indicated in 7.18.1. Step 2: For each value of k, p, q, i, j the program performs:

9. 19. Realization of three-dimensional images in a fast method with suppression of direct lighting.

 The use of the method described above has the disadvantage of requiring the acquisition of reference images. At each acquisition of reference image, it is necessary to make a significant displacement of the mirror (5113). It is possible to use a reference image to phase in several successive useful images, and thus not to acquire a reference image at each acquisition of elementary image. Nevertheless, if the system is not perfectly stable on a time scale comparable to the acquisition time of a complete three-dimensional frequency representation, the acquisitions of reference images must be numerous. Due to the large displacement of the mirror that they require, these acquisitions constitute a significant loss of time. To avoid acquisition of reference images, steps 1 and 2 of 7.17.2. , which aim to perform phase registration of two-dimensional frequency representations, can be replaced by the method described below. This method can also be used with the other embodiments but is then of limited interest.

 This method includes a preliminary phase, which is performed before any calculation requiring phase registration (before the actual imaging phase), and a modification of the steps used in the imaging phase. The acquisition of an image to be processed by this method can be done according to the procedure 9. 9. used with the variant 1, that is to say without acquisition of reference image and with use of the glass for cancel the direct lighting.

* 9. 19.1. Preliminary phase.

fréquentielles bidimensionnelles indicées par l'indice l, les tableaux Kn p,q [wu, /] Fh p,9 ni, nj, l . Dans ces tableaux: p indice le coté (gauche ou droit) vers lequel parvient l'onde d'éclairage direct q indice le coté d'ou provient la représentation fréquentielle (opposé ou non à celui ou parvient l'onde d'éclairage directe) The preliminary phase consists of determining, from a limited number of representations

two-dimensional frequency indexed by the index l, the tables Kn p, q [wu, /] Fh p, 9 ni, nj, l. In these tables: p index the side (left or right) to which the direct light wave arrives q index the side from which the frequency representation comes (opposite or not to that where the direct lighting wave arrives)

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 l index the position of the point corresponding to the direct light wave, on the image generated by the method described in 9. 9., from the side indexed by q = 0.

 The indices (l, p) therefore characterize a light wave and the indices (l, p, q) characterize a two-dimensional frequency representation corresponding to this light wave and to the sensor indexed by q.

 The indices n1, nj are the coordinates on two axes of this frequency representation, after centering with respect to the point of direct impact of the illumination wave.

The table Knp, q [ni, nj, l] contains the third coordinate nk of the frequency representation considered, for each pair ni, nj.

The table Fhp.q [ni, nj, 1] contains the value of this representation at the point of coordinates ni, nj, nk after phase registration with respect to the representation defined by / = 0.

The table Bh p, q [ni, nj, 1] contains the noise on the corresponding elements of Fh p, q [ni, nj, 1].

 These tables thus characterize the values of the three-dimensional frequency representation of the object in a certain number of points. The table Knp, q characterizes the points in which values are available, and the table Fhp, characterizes these values themselves. The positions of the direct light wave corresponding to the indices l are chosen so that any two-dimensional frequency representation, after refocusing, has a non-empty intersection with the part of the three-dimensional frequency representation of the object constituted by the superposition of the representations corresponding to the different indices l. and characterized by the tables Kn p, q and Fhp, q.

 The preliminary phase is broken down into three steps: Step 1: FIG. 81 represents the points corresponding to the direct illumination wave, the image generated by the procedure 9. 9. from the sensors or reaches this direct illumination wave, for several values of l.

We denote IL [l], JL [l] the coordinates of the point indexed by l, with for example:

<Tb>
<tb> 1 <SEP>#IL [l] <SEP>#JL [l]
<tb> 0 <SEP> Npix <SEP> Npix
<tb> 2 <SEP> 2 <SEP>
<tb> 1 <SEP> Npix-1- <SEP> margin <SEP> Npix
<tb> 2
<Tb>

2 N po: Npix - 1 -marge

2 N in: Npix - 1 -marge

<Tb>
<tb> 2
<tb> 3 <SEP> margin <SEP> Npix
<tb> 2
<tb> 4 <SEP> Npix <SEP> margin
<tb> 2
<Tb>

<Desc / Clms Page number 235>

 or margin = 10 for example.

programme détermine alors, pour chaque valeur de l, la valeur de k telle que IL[l] = lo[k et JL[l = Jok . The points indexed by l must be part of the trajectory defined by Tables Io and Jo. The

The program then determines, for each value of l, the value of k such that IL [l] = lo [k and JL [l = Jok.

He puts this value in the table TK in TK [l].

Step 2: The second step is to determine the arrays Kn p, q and Fhp, q The program initializes these arrays first, for example to a value of-10000.

ni = i -lmcpck, p,q + NP, nj = j - jmaxk,p,q + Nn

Il prend pour chacun de ces nombres l'entier le plus proche puis il effectue:

Etape 3 : cette étape consiste en une modification du tableau Fhp,q. Le programme parcourt l'ensemble des (l,p,q). Pour chaque valeur de ce triplet, le programme effectue les opérations 1 à 3 suivantes: opération 1: le programme initialise à 0 les nombres nom et denom opération 2 : le programme parcourt l'ensemble des valeurs de (ni,nj) en testant la condition

Kn p.q ni,nj,1-KnP,9ni,nj,0I2 2 <- lim avec par exemple lim= 1. Lorsque cette condition est réalisée il effectue :

opération 3 : le programme effectue:

The program then goes through all the quintuplets (l, p, q, i, j). It calculates for each of them k = TK [l]

ni = i -lmcpck, p, q + NP, nj = j-jmaxk, p, q + Nn

He takes for each of these numbers the nearest integer then he performs:

Step 3: This step consists of a modification of the table Fhp, q. The program goes through all (l, p, q). For each value of this triplet, the program performs the following operations 1 to 3: operation 1: the program initializes to 0 the numbers name and denom operation 2: the program traverses the set of values of (ni, nj) by testing the condition

Kn pq ni, nj, 1-KnP, 9ni, nj, 0I2 2 <- lim with for example lim = 1. When this condition is realized it performs:

operation 3: the program performs:

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9. 19.2. Imaging phase
The imaging phase differs from that used in 7.17.2. by the phase registration method. The phase registration is performed with respect to the part of the frequency representation of the object characterized by the tables calculated in the preliminary phase, and not with respect to the image point of the illumination wave, at pre-recorded values of the illumination wave or reference images.

 The following steps 1,2,3 replace steps 1 and 2 defined in 7.17.2.

Etape 2 : étape consiste à établir le coefficient complexe caractérisant, pour chaque représentation bidimensionnelle, le décalage de phase et d'intensité entre cette représentation bidimensionnelle et la portion de représentation tridimensionnelle caractérisée par les tableaux Knp,q et Fhp,q.Ce coefficient complexe, pour la représentation caractérisée par les indices k,p,q, s'exprime sous la forme nomk,p,q Il denomk, p,q

est obtenu en effectuant une boucle sur l'ensemble des indices (kp, q, ij, 1). Pour chaque (kp, q, ij, 1) : -le programme calcule: ni = i - tmaxk, p,q + Nt"x nj = j-jmaxkpq + N plX

-Il teste la condition:

IKn p,q [ni,nj, 1]- nkl2 lim avec par exemple lim=1. -Si la condition est vraie, le programme effectue alors les opérations

Etape 3 : cette étape constitue le recalage en phase proprement dit. Le programme effectue:

Step 1: The program performs, for all the values of k, p, q, i, j:

Stage 2: step consists in establishing the complex coefficient characterizing, for each two-dimensional representation, the phase and intensity shift between this two-dimensional representation and the three-dimensional representation portion characterized by the tables Knp, q and Fhp, q. , for the representation characterized by the indices k, p, q, is expressed in the form nomk, p, q Il denomk, p, q

is obtained by performing a loop on the set of indices (kp, q, ij, 1). For each (kp, q, ij, 1): -the program calculates: ni = i - tmaxk, p, q + Nt "x nj = j-jmaxkpq + N plX

-It tests the condition:

IKn p, q [nl, nj, 1] - nkl2 lim with for example lim = 1. -If the condition is true, then the program performs the operations

Step 3: This step constitutes the actual phase registration. The program performs:

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 9.20. Realization of three-dimensional images according to a simplified method.

One can limit oneself, to generate the three-dimensional image of the object, to the representation
Fo, as defined in 7. 17. This amounts, in the procedure described in 7. 17.2., To adopt tables IBp, q void for any pair (p, q) # (0,0).

 It is also assumed that the object has an average index close to the nominal index of the object observed and that the optical table is totally free of vibrations.

 Steps 9.11. at 9.17 can then be deleted. The present method also differs from the previous one by the method used to adjust the position of the objectives before use and by the image overlay algorithm.

 9. 20.1. Lens and mirror adjustment (5113).

 This adjustment can be made with a transparent blade provided you do not move the lenses after adjustment, when you introduce the object. If objectives intended to operate without immersion liquid or slide are provided (nominal index equal to 1) and if the sample is thin or of average index close to 1, it can also be done in the same way. object abscence. During this step, the FEG and FRD beams are used.

It is necessary that the mirror (5113) is removable and can be replaced by an absorbent plate at any point except at a central point or is placed a small reflector. The size of this reflector should be about D or D is the diameter of the incident beam on the mirror
2Npix (5113). This plate must be temporarily placed on the mirror so that the reflector occupies roughly the center of the incident beam on the mirror. The positioner of the mirror must itself be fixed on a positioner three axes in translation.

 This adjustment must be made immediately after the set of adjustments described in 9. 5. and the lenses must not be moved afterwards. It comprises the following steps: step 1: the mirror is replaced by the absorbing plate step 2: using only the FRD beam, the mirror is moved in translation so that the image produced on the CCD (4339) is punctual and centered. step 3: using only the FEG beam, the lenses are moved in such a way that the image produced on the CCD (4339) is punctual and centered. step 4: we can then replace the mirror.

9. 20.2. algorithm for calculating the three-dimensional representation
Steps 1 and 2 of the algorithm described in 7. 17.2. can be deleted. In fact, the additional adjustment made and the absence of vibrations make it possible to avoid any phase shift of the illumination beam.

<Desc / Clms Page number 238>

 10. Device for positioning optical elements.

 The embodiments described, and in particular embodiment 4, require the use of numerous positioners of good accuracy. These positioners are expensive elements that are not well suited to mass production and that may become unstable over time. These positioners, with the exception of the objective and sample positioners, should normally only be adjusted once during the initial adjustment phase.

 A solution to this problem is to use in the manufacture of the microscope removable positioners. After positioning, each element can be fixed with a suitable glue. For example, in Embodiment 4, the SLMs can be attached using the device of Figs. 83 to 85. The part of the fixing device which is integrated into the microscope has three moving assemblies: assembly 1: it consists of the following elements, joined together: - a fixing plate (5801) detailed Fig.83 and having a porous surface to be glued (5802).

 - the SLM (5804) fixed on the unsized part (5803) of this plate.

- A plate (5808) of magnetizable material, for example iron, fixed to the rear of the plate (5801) together 2: consists of the following elements, secured together: - a plate (5805) detailed FIG. 84 having a porous surface to be glued (5806) and a recess (5807) at its center - a plate (5809) having a surface to be glued (5817) - a plate (5810) of magnetizable material, for example iron, attached to the plate (5809). assembly 3: consists of a plate (5811) having a porous surface to be glued (5816)
The removable part of the fixing device comprises the following sets: assembly 4: is composed of an arm (5815) having a magnetizable portion (5814) and connected to a POS1 positioner not shown. The portion (5814) comprises a winding of electric wire around an iron core, not shown. Feeding this winding is secured (5814) and (5810) and interrupting the supply disassociates these elements. set 5: it is composed of an arm (5813) having a magnetizable portion (5812) and connected to a POS2 positioner not shown. Part (5812) comprises a winding of electrical wire around an iron core, not shown. Feeding this winding is secured (5808) and (5812) and interrupting the supply disassociates these elements.

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 The fixed part of POS1 positioner and element 3 are integral with the optical table. The fixed part of the POS2 positioner is integral with the moving part of the POS positioner 1. The POS positioner allows an axis to be displaced in the direction of the axis # and a rotation about the axis j. The positioner POS2 allows a translation according to each of the vectors 7 and k and a rotation about the axis! . It also allows, but with a very small adjustment margin, a rotation around the axis.

 To perform the positioning of the system, previously glued the surfaces to be bonded designated above. The magnets of the parts (5812) and (5814) are energized so as to secure the removable parts and the non-removable parts. The adjustment is normally carried out with POS1 and POS2 positioners. The system is left in place long enough for the glue to dry. We then stop feeding the magnets so as to separate the removable parts non-removable parts. The setting is then definitive and the removable part can be removed.

 The adhesive used must have a setting time long enough not to interfere with the setting and must have a minimum shrinkage during drying. It is also possible to provide dedicated orifices in the plates (5811) and (5805) to inject the adhesive after positioning. This example is given for the positioning of the SLM but is simply adaptable to all the elements to be positioned in the system. Depending on the number of degrees of freedom required and the type of element to be positioned, the shape of the mobile platforms must be adapted. The principle of using removable positioners and final fixing by gluing, however, remains valid.

11. Support suitable for transporting and maintaining the settings made
The microscopes described in Embodiments 3 to 5 consist of a set of elements attached to an optical table. During a possible transport, even slight shocks can cause a disturbance of the system. During prolonged use, dust can be deposited on the various optical elements.

 In order to overcome these drawbacks, the described microscope can be protected by a system whose principle is shown in FIG. 86. The optical table, which can be for example made of granite, constitutes the lower part of a hermetically sealed box (5901 ). The fact that the box (5901) is hermetically sealed protects the assembly against dust. The box (5901) is included in a larger box (5902), with no direct contact between the two boxes. The two boxes are separated by dampers which may be appropriately inflated rubber balls (5903), which are arranged on the 6 sides of the box (5901). This system makes it possible to dampen shocks and to avoid a loss of settings during transport, while ensuring good suspension of the optical table during use.

 However, it is necessary that the part of the system constituted by the two objectives and their positioners remains accessible. This entails certain adaptations of the shape of the boxes, visible in FIG.

87, adapted to the example constituted by the embodiments 4 and 5. The front wall of the box (5901) constitutes a vertical plane passing in FIG. 63 between the mirrors (4451) and (4452). The box (5901) presents

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 an excrescence (5903) allowing the fixing of the mirrors (4454) (4455) (4456) and the objective (4317) below the plane of the optical table itself. The box (5902) shown in dashed lines has a notch (5904) providing access to the lenses and the sample.

 So that the mirrors (4453) and (4454) as well as the entries of the objectives remain inaccessible, and in order to avoid any entry of dust, the shape of the box (5902) must also be adapted locally. This adaptation is detailed in FIG. 88. The box has two protuberances (5905) and (5906) respectively containing the mirrors (4453) and (4454), and has two openings related to the entry of the lenses (in fact, to the frames of these lenses) by sleeves rubber (6001) (6002). The positioners of the objectives and the sample, not shown, are outside the box (5902).

 In FIG. 87, the dampers (5903) have not been shown, but they are present in the entire area between the two boxes.

 A closure cover allowing protection of the accessible part (objectives and sample, as well as their positioners) must also be provided.

 In the case of Embodiment 5, the outer box (5901) must have an additional compartment to hold the items that are not on the optical table.

12. Variants:
Other embodiments are of course possible and the above description is not limiting. In particular, it is possible to use more objectives, or to perform other combinations of the receiver and beam deflector types, or to modify the phase registration algorithms.

13. Potential for industrial application:
13. 1. References [Thomas]: 4-D imaging software observes living cells, Charles Thomas & John White, Scientific Computing World p.31, December 1996.

[Holton]: Under a Microscope: Confocal Microscopy Casts New Light on the Dynamics of Life, W.Conard Holton, Photonics Spectra p. 78, February 1995.

[Juskaitis]: Differentialphase-contrast microscope with a split detectorfor the readout system of a multilayered optical memory, Y. Kawata, R.Juskaitis, T. Tanaka, T. Wilson & S. Kawata, Applied Optics vol.35 no 14 p. 2466, 10 mai 1996 [Walker]: Measurng scanning optical microscope phase, JGWalker & ERPike, Patent WO 91/07682 [Bertero]: Analytical inversionformulafor confocal scanning microscopy, B. Bertero, C. De Mol, ERPike, Journal of the Optical Society of America vol.4 no. 9, September 1987 [Ueki]: Three-dimensional optical memory with a photorefractive crystal, Y. Kawata, H. Ueki, Y. Hashimoto, S. Kawata, Applied Optics vol.34 No. 20 p. 4105, July 10, 1995

[Juskaitis]: Differentialphase-contrast microscope with a split detector for the readout system of a multilayered optical memory, Y. Kawata, R.Juskaitis, T. Tanaka, T. Wilson & S. Kawata, Applied Optics vol.35 No. 14 p. 2466, May 10, 1996

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 [Parthenopoulos]: Three-dimensional optical storage memory, D.A.Parthenopoulos & P.M.Rentzepis, Science 245, p. 843, 1989 [Strickler]: Three dimensional optical data storage in refractive media by two-photon excitation, JHStrickler & WW Webb, Optics Letters 16, p.1780, 1991 [McMichael]: Compact holographic storage demonstrator with rapid access, I. McMichael, W. Christian, D. Pletcher, TYChang & JHHong, Applied Optics vol.35 No. 14 p.2375, May 10, 1996.

[Bashaw]: Cross-talk considerations for angular and phase-encoded multiplexing in holography volume, MCBashaw, JFHeanue, A. Aharoni, JFWalkup & L. Hesselink, Journal of the Optical Society of America B vol. 11 No. 9 p.1820 September 1994 [Barbarstatis]: Shift multiplexing with spherical reference waves, G. Barbarstatis, M. Levene, D. Psaltis, Applied Optics vol.35 No. 14 p. 2403, May 10, 1996
13.2. Discussion
The current microscopes form by an optical process a two-dimensional image corresponding to an enlarged section of the observed object. This image can, if necessary, be recorded by a video camera so that it can be retrieved later.

 It is possible to generate a three-dimensional image using one of these microscopes and varying the focus setting. Each setting corresponds to a different cutting plane, and a three-dimensional image can be reconstructed from these cutting planes. Some microscopes equipped with a motorized focusing device and appropriate software perform this operation automatically. Such microscopes are described for example in [Thomas]. The major flaw of these microscopes is that the image of a cutting plane is strongly disturbed by the contents of the other planes.

 There are also confocal microscopes in which the illumination is focused on a point and the three-dimensional image is generated by scanning all the points of the object. Such microscopes are described for example in [Holton]. These microscopes make it possible to solve the problem of the systems described in [Thomas], namely that the value detected at a given point is not disturbed by the value of the near points.

 Confocal microscopes have the defect of being able to detect only the intensity of the received wave and not its phase. As many commonly observed objects are characterized essentially by index variations causing phase variations of the transmitted wave, this defect causes significant discomfort for users who must color the samples observed. This is why efforts have been made to make confocal microscopes sensitive to the phase of the transmitted wave [Walker]. For various reasons, these microscopes remain ineffective.

 The image generated by the confocal microscopes does not have the best theoretical definition that can in principle be obtained from the wave received by the lens used. This is linked, as indicated in 7. 18.3., To the fact that the confocal microscopy method strongly filters the high frequencies. This is why efforts have been made to improve the resolution of these confocal microscopes [Bertero].

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 The present microscope overcomes the defects of the foregoing microscopes in terms of resolution and in terms of phase detection. It can be advantageously used as a replacement for these microscopes, in all their applications.

 A new field of application of microscopes is the reading of three-dimensional optical memories.

 A first type of optical memory is where the data are recorded point by point in a three-dimensional material in the form of variations of the local properties of this material ([Ueki], [Parthenopoulos], [Strickler]). These data must therefore be read by a microscope capable of reading three-dimensional data without the data recorded in several successive layers of material disturbing each other. The disturbance of the image of a point by the rays diffracted by the neighboring points is thus reflected here by intersymbol interference. In general, the authors used few layers at a great distance from each other, which limits these interferences.

However, if a larger amount of data were to be recorded in a given volume, conventional microscopy methods would be insufficient. Especially in the case of [Strickler] and [Ueki] the data are recorded as index variations and the confocal microscope is particularly poorly adapted to their reading. This is why efforts have been made to improve the data reading system [Juskaitis].

 The present microscope is the reading solution for maximum integration of this type of memory. Indeed, the image that can be obtained takes into account the index and strongly decreases intersymbol interference. In the ideal case where the whole beam from the sample would be detected, which can be achieved by increasing the number or the opening of the objects, the intersymbol interference is entirely removed.

Another type of optical memory consists of holographic memories. For example, in the [McMichael] document, the data is read by illuminating the object constituted by the optical memory with a variable direction parallel beam and detecting the sample wave for each direction of the illumination beam. . A direction of the illumination beam corresponds to a data page and each point of the two-dimensional frequency representation of the wave coming from the object for a given illumination wave corresponds to a bit stored in the optical memory. Since each point of the two-dimensional representation of the wave coming from the object corresponds moreover to a point of the three-dimensional representation of the object itself, a bit stored in the optical memory corresponds to a point of the three-dimensional frequency representation. of this optical memory. An analysis of this type of memory in terms of frequency representations can be found in [Bashaw]
The present microscope can therefore advantageously be used to read such optical memories, the bits stored in memory corresponding directly to points of the three-dimensional frequency representation obtained by the present microscope from the object constituted by the optical memory. The optical memory write system must, however, be designed not to use the points of the three-dimensional frequency representation which are not obtained by the present

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 microscope, except to increase the number of lenses used to avoid the non-detection of certain frequencies.

 Other types of holographic optical memories exist [Barbarstatis]. In general, the present microscope makes it possible to obtain a representation of the observed object that would be perfect in the ideal case where the objectives used would cover the entire space around the object.

In the case where the representation obtained is perfect, the data stored in memory and detected in the form of a three-dimensional frequency representation of the object can then be restored in any form: it is possible to simulate, using the representation known from the object constituted by the optical memory, the wave that would be obtained from any lighting or by any other reading method (at the wavelength used by the microscope). All types of optical memory can therefore be read by the present microscope, by means of the general case of additional operations allowing the reconstitution of the data from the frequency representation of the object constituted by the optical memory. In the case where the representation is not perfect, adequate precautions must be taken to take into account the shadow areas of the frequency representation of the object.

Claims (9)

1-Microscope comprising: - one or more receivers each allowing the digital recording of interference patterns formed on a receiving surface by a wave coming from the observed object and a reference wave that has not passed through the object observed a device for generating a plane wave illuminating the observed object, enabling the formation of plane waves whose direction, evaluated in a reference frame linked to one of the receivers, is variable, means for generating, from one or more of said digital recordings of interference figures, a three-dimensional representation of the object observed, characterized in that it comprises at least one of two groups of means (i) or (ii): (i ) - active or passive means for controlling the phase differences between the light waves and the reference waves so that on each sensor and for each light wave. the phase difference between the illumination wave and the reference wave used on said sensor has a predetermined value.  (ii) means for generating, from one or more of said interference figure recordings, sub-representations of the observed object, and means for determining the phase differences between sub-representations of the object; observed object. 2 - Microscope according to claim 1, characterized in that said means for determining said phase difference between two sub-representations of the object comprise means for determining the most probable phase difference between the restrictions of said sub-representations to a set included in the intersection of said sub-representations in frequency representation, or an approximation of this difference. 3-microscope according to one of claims 1 or 2, characterized in that said means for determining said three-dimensional representation of the object comprise means for determining, at each point of said three-dimensional representation in frequency representation: the values at this point of each under-representation reaching this point. the standard deviation of the noise affecting each of said values, or an approximation of this standard deviation, or a quantity related to this standard deviation or to its approximation. - the most probable value of the three-dimensional representation at this point taking into account the value of each under-representation at this point and the noise affecting each under-representation at this point, or an approximation of this value. 4- Microscope according to one of Claims 1 to 3, characterized by the following facts: <Desc / Clms Page number 245>  it comprises means for recording on each receiver a reference wave coming from the object, the wave illuminating the object having a reference direction during this recording.  it comprises means for periodically recording on each receiver the wave coming from the object, the wave illuminating the object having the reference direction during these recordings, it comprises means for determining, for each receiver and for each of said periodic recordings, the current phase difference between the wave thus recorded and the reference wave, - it comprises means for shifting each flat frequency image of a phase corresponding to said current phase difference obtained from a periodic recording made at a time close to the moment of acquisition of the wave or waves that allowed the calculation of said under-representation. 5. Microscope according to one of claims 1 to 4, characterized in that the lighting beam generating system comprises a beam deflector, and in that said beam deflector comprises. an appropriately controlled spatial modulator generating, from a given incident beam of direction, an outgoing beam whose direction can be controlled by modifying the state of the modulator. a diaphragm and / or a binary modulator of intensity allowing the suppression of the parasitic beams generated by the first modulator. 6. Microscope according to one of claims 1 to 5, characterized in that the system for generating the illumination and reference beams comprises: a beam deflector. a beam splitter, which divides the beam from said beam deflector into a reference beam and a lighting beam. 7- microscope according to one of claims 1 to 6, characterized in that it comprises: - a means for generating two distinct polarizations of each lighting beam - a means for analyzing the wave from the object in two directions polarization. 8- Microscope according to one of claims 1 to 7, characterized in that it comprises a means for removing the non-diffracted portion of the illumination wave, consisting of a device placed in a plane or the non-diffracted portion of the lighting wave has a point image and allowing to absorb <Desc / Clms Page number 246> CLAIMS (3/3) this wave over a reduced area around the point of impact of the non-diffracted portion of the illumination wave. 9- Microscope according to one of claims 1 to 8, characterized by the following facts: - It has several microscope objectives focused on the same area of the sample. - The optical chain associated with each lens allows on the one hand the recording on a wave sensor from said sample and received by said lens, and on the other hand the generation of a plane wave of variable direction directed from said lens to said sample. - The set of waves measured on each sensor and for each light wave are combined by a calculation system to obtain a three-dimensional representation of the observed object.