EP0058592B1 - Optical fourier transform device and optical correlator using the same - Google Patents

Description

The invention relates to the field of optical correlation which makes it possible to obtain the function of correlation of one image by another. Such systems make it possible, for example, to recognize a graphic in a given pattern.

A device described in the article published in "APPLIED OPTICS", volume 15, No. 6 of June 1976, pages 1418 to 1424 includes a source, a modulating object, a lens and optical means ensuring the illumination of a plane by a distribution of light amplitudes Fourier transform of the optical modulation created by this object. These optical means comprise an interaction medium receiving the pumping beam emerging from a lens. A reflector is formed on one side of the interaction medium, which is a Pockels Readout Optical Modulator (PROM), to reflect the pumping beam, which therefore crosses the PROM twice. This reflector is also used to deflect the beam emerging from the PROM towards the plane where the Fourier transform of the optical modulation created by this object is projected.

Unlike this cited document, the system according to the invention implements the reproduction of a wave front of complex morphology emerging from a modulating object, generated by interference in an interaction medium of an optical wave. incident having this wavefront with a pumping wave. This interference occurs in a photoexcitable interaction medium with three-dimensional index variation whose physical characteristics and in particular the refractive index are spatially modulated by a network of fringes resulting from the incident wavefront wave. ¿Oz and pumping wave.

In addition, the cited document considers a PROM (Pockels Readout Optical Modulator) interaction medium using a longitudinal electro-optical effect whose spatial resolution is limited by the thickness of the material. This PROM interaction medium is, in fact, produced by a thin layer of electro-optical material covered with an insulating layer and comprising transparent electrodes deposited on its front and rear faces. Unlike the device of the invention which considers an interactive medium using a transverse electro-optical effect which has a high spatial resolution, electrodes being deposited on the lateral faces of the electro-optical crystal.

A known optical correlator system is described in the French patent application published on May 8, 1981 under No. 2,468,947. A system of interference fringes representing the diffraction pattern obtained is recorded on a photosensitive support. from two parallel coherent beams, on the path of which have been interposed two objects with non-uniform transparency, after focusing by a lens. This photosensitive support is read by one of the beams and one obtains in the focal plane of a second lens a distribution of intensity characteristic of the correlation product between the two objects; when one wants to find a graphic in a given pattern, the image obtained is formed of peaks indicating the presence and the position of this graphic in the considered motif. In this patent application, the photosensitive support is a continuously recyclable medium, that is to say writable without development and erasable at will. However, in such a system there are parasitic phase distortions induced by the optical components and, for the input of the data, by photographic transparencies or by electro-optical transducers. It is known, moreover, to interpose on the wave propagation a transparency whose phase characteristic allows a rigorous compensation for the distortions of the incident wave surface: So that this filter remains valid whatever the translation of the transparency in the object plane, this filter is positioned in the Fourier plane.

The Fourier transformer system of the invention compensates for these distortions in a simpler way. It uses, in fact, a wavefront conjugate of the incident wavefront which, at each point, is isomorphic of it. This conjugate wavefront, by reverse return, is modulated a second time by the object. But because of the reverse path, there is compensation for the modulation deformations of the outward path. It is the same for the deformations due to the aberrations of the lens: they are compensated.

The optical correlator system which includes the Fourier transformer system, allows a significant gain on the signal / noise ratio of the correlation peak. This is made equivalent to that resulting from an inconsistent illumination.

Indeed, by moving the source point along a line segment, an incoherent integration of the coherent images is carried out in the image plane, the noises of which are uncorrelated. One can also interpose on the passage of the beam an electro-optical tank which allows a translation of the latter. By simply dosing the ratio of the different beams, the low frequencies of the spectrum of object transparency are attenuated. This system therefore makes it possible to process a large quantity of information in parallel and in real time with optical components of reduced quality.

The subject of the invention is an optical Fourier transformer device, comprising a point source of coherent radiation disposed at the focal point of a converging lens, means for positioning a modulating object in the collimated beam emerging from this lens and optical means. ensuring the illumination of a plane by a distribution of light amplitudes transformed by Fourier of the optical modulation created by this object, these optical means comprising a photo-excitable medium of interaction with index variation receiving collimated beam via this object and a pumping beam, characterized in that this interaction medium with three-dimensional index variation is an electro-optical crystal comprising electrodes arranged on its lateral faces at the terminals of which a voltage is applied so as to use an electro- transverse optics, this pumping beam coming from this source; a plane reflector being arranged to reflect in normal incidence and towards this medium the radiation which emerges therefrom in the direction of propagation of this pumping beam, this radiation having a conjugate wavefront and isomorphic to the wavefront of the collimated beam of so as to compensate for the defects due to a parasitic modulation of the wavefront of this collimated beam and a semi-transparent plate being located between this source and this lens to deflect towards this plane the radiation contained in the conjugate wave re-radiated by this medium towards this lens.

The invention further relates to a double diffraction optical correlator comprising a first Fourier transformer device, a photo-excitable interaction medium with index variation which comprises electrodes arranged on its lateral faces at the terminals of which is applied a voltage arranged to receive simultaneously the radiation emerging from this first transformer device and another radiation contained in a reference beam and a second Fourier transformer intended to project into an image plane an illumination representative of the correlation function of the two patterns of a modulating object introduced into this first Fourier transformer device, characterized in that this first optical Fourier transformer device is an optical Fourier transformer device as described above.

• - la figure 1 est un schéma de principe du fonctionnement du transformateur de Fourier mis en oeuvre dans le dispositif selon l'invention;
• - la figure 2 est le schema d'un exemple de réalisation du système selon l'invention;
• - la figure 3 est un schéma explicatif du cor- rélateùr optique mis en oeuvre dans le dispositif selon l'invention;
• - la figure 4 illustre un aspect particulier du dispositif selon l'invention;
• - la figure 5 est un autre exemple de réalisation dv système selon l'invention.

The invention will be better understood with the aid of the description which follows, illustrated by the appended figures, the content of which is as follows:

• - Figure 1 is a block diagram of the operation of the Fourier transformer used in the device according to the invention;
• - Figure 2 is a diagram of an exemplary embodiment of the system according to the invention;
• FIG. 3 is an explanatory diagram of the optical corrector used in the device according to the invention;
• - Figure 4 illustrates a particular aspect of the device according to the invention;
• - Figure 5 is another embodiment of the system according to the invention.

The system according to the invention implements the reproduction of a wave front of complex morphology emerging from a modulating object, generated by interference in an interaction medium of an incident optical wave before this front of wave with a pumping wave.

In FIG. 1, this interference occurs in a photoexcitable interaction medium 2 with variation of three-dimensional incide whose physical characteristics and in particular the refraction incide, are spatially modulated by a network of fringes resulting from the incident wavefront wave Σ ₂ and pumping wave Fp.

Due to the existence of this spatial modulation, a fraction of the energy of the pumping wave is diffracted in the form of an emerging wave. Another fraction of the energy passes through the medium 2, and is returned to the medium by a plane reflector 4 normally arranged in its path. Part of its energy is then diffracted by the network of strata inscribed in the medium in the form of an emerging wave with a complex wavefront Σ ₂ ^* , conjugated to the wave Σ ₂ . Σ2 * has characteristics isomorphic to those of Σ ₂ and follows the same optical path but in the opposite direction; Σ ₂ * returns to the object from which Σ ₂ emanates. The return of the wave Σ ₂ is performed in real time at time rd'établissement strata network near which can range from 10- ³ to 10- ¹² seconds. Variations in this network may be slow with respect to the time constant r. The interactive medium 2 consists, for example, of a photoconductive electro-optical material such as bismuth-silicon oxide (BSO). It could also be an oxide such as bismuth-germanium oxide (BGO). These two oxides are particularly suitable for the invention because they are very sensitive in the range of wavelengths commonly used which constitutes the field of visible light waves. In addition one can obtain single crystals of sufficient dimensions having good optical qualities. This medium is polarized at the voltage Vo.

The incident wave Σ ₂ comes from a beam focused at a source point S. This source point is located at the focus of a spherical lens L1. Thus the wave front which is spherical Σ ₀ becomes linear Σ ₁ . The light beam collimated by the lens L ₁ is then modulated by the non-linearly transparent object 1. This is located in the focal plane Po of the lens, or object plane. Thus during the return path of the wave front Σ2 * there will be focusing of the beam at an image point of S after reflection on a semitransparent plate 9.

The forward path through the lens L ₁ and the transparent object 1 creates parasitic phase distortions of the waves Σ ₁ and Σ ₂ . These distortions are due to the aberrations of the lens Li and to the deformations relating to the support of the transparent object. The return path through the same transparent object and lens L _i makes it possible to compensate for these defects due to a parasitic phase modulation of the wave fronts. It also makes it possible to double the contrast of the amplitude modulation due to the object.

In the focal plane of the lens L _i , in which the image of S is located after reflection on the semi-transparent plate 9, an amplitude distribution is obtained proportional to the Fourier transform of the amplitude distribution in the object plane Po; we therefore produced a Fourier transformer of the optical modulation created by object 1.

In Figure 2, the system described in Figure 1 is retained. We find the different constitutive elements of the system of FIG. 1. A photosensitive medium 10 is added to it in the plane of the image point S ', perpendicular to the direction of the rays passing through the optical centers. This plane is the focal plane of a lens L _z the other focal plane is composed of the detec medium _- teur7.

To understand the principle of optical correlation, we consider Figure 3. In it a parallel ray after being modulated by a transparent object consisting of two patterns A and B is focused by a spherical lens L inside a interaction medium 10 located in the focal plane thereof. In this medium, there is recording of the algebraic sum of the Fourier transforms, that is to say spectra of two two-dimensional functions which represent the transmittances of the two transparent object patterns A and B. Indeed this medium is located in the focal plane of L or Fourier plane. We therefore obtain an amplitude distribution proportional to the Fourier transform of the amplitude distribution of the object plane. As in the time signal spectrum, the spectra of the space signals are symmetrical with respect to the zero frequency. But this is a symmetry in the plane and no longer only on an axis. If we translate the transparent object of Ax in an object plane, the spectrum remains unchanged in the Fourier plane, indeed the Fourier transform is invariant in translation.

There is no difference in amplitude but there is an appearance of a phase shift of the form e ⁱ ax which causes a displacement in the image plane or exit plane Ps. Thus in our case, it does not matter the position of the transparent object patterns A and B in the object plane, their resulting spectrum which corresponds to the superposition of each of their spectra will be in the same place. The medium 10 therefore records the superposition of fringes of different steps, the average step being equal to λ1 _2sinα where λ ₁ war the optical wavelength of the incident beams which interfere, and the half-angle between these beams. The interference fringes resulting from the superposition of these beams which illuminate A and B, after the focusing operated by the lens L, are therefore recorded in an interaction medium 10 consisting for example of an electro-optical material polarized by a electric field obtained by means of a voltage source Vo. Its orientation is such that the electric field produces a transverse electro-optical effect. The spatial variations in light intensity existing in this plane P _F are instantly reflected in the plate by spatial variations in the refractive index. These plans are virtually interference _- perpendicular to the direction of the applied electric field. The index modulation disappears with its cause, that is to say with the presence of object patterns A and B in the path of the beams.

où p est le pas de réseau de plans de franges et Â₃ la longueur d'onde du faisceau F_R. Cette condition ne peut être réalisée pour tous les systèmes qui se superposent, aussi l'invention prévoit un balayage du faisceau de lecture F_R. Celui-ci est par exemple un laser de faible puissance et de longuer d'onde choisie en dehors des longueurs d'onde auxquelles est sensible le matériau constituant le milieu 10. Le faisceau F_R est, par exemple, défléchi par un déflecteur classique acousto-optique ou mécanique. Il est ici, renvoyé par une lame semi-transparente en direction du milieu 10. Ainsi à chaque instant, pour une orientation donnée du faisceau F_R, seuls sont obtenus avec un rendement maximum les points situés sur une droite perpendiculaire au plan de la figure et auxquels on peut associer une inclinaison P et un pas p des réseaux de plans dans le cristal 10 pour lesquels l'incidence 0 du faisceau par rapport au plan est l'incidence de Bragg. Sont également obtenus avec un rendement réduit les points voisins pour lesquels l'incidence est comprise dans une gamme

où n est l'indice de réfraction du milieu et l'épaisseur de la zone utile de diffraction dans le milieu. Tous les pics de corrélation apparaissent donc séquentiellement.We therefore obtain a real-time registration, erasable at will. To obtain all the information with maximum resolution, the thickness of the crystal must be equal to or greater than the width of the diffraction zone. A thickness can be defined which is clearly greater than the wavelength of the beams so that the recording in the slide can be considered as three-dimensional. It is a superposition of arrays of surfaces. When the width of the blade is not too large, these surfaces can be assimilated to planes perpendicular to the plane of the figure. Their pitch p and the inclination Φ with respect to an axis normal to the plane P _F and in the plane of the figure depend on the angle of the interfering rays, their wavelength λ ₁ and the refractive angle n crystal 10. The usable materials must be photosensitive and electro-optical such as bismuth-silicon oxide or bismuth-germanium oxide. Once the recording on this photosensitive support has been carried out, the reading is carried out using a coherent parallel beam F _R illuminating the support under normal incidence. To obtain an optimum efficiency in one of the diffraction orders, there is an angle between the reading beam F _R and these diffraction planes defined by the Bragg condition. In this case the different recorded networks diffract the beam F _R according to angles such as

where p is the network pitch of fringe planes and et ₃ the wavelength of the beam F _R. This condition cannot be fulfilled for all the superimposed systems, so the invention provides for scanning of the reading beam F _R. This is for example a low power laser with a wavelength chosen outside the wavelengths to which the material constituting the medium is sensitive 10. The beam F _R is, for example, deflected by a conventional acousto deflector -optical or mechanical. It is here, returned by a semi-transparent plate in the direction of the medium 10. Thus at each instant, for a given orientation of the beam F _R , only the points located on a line perpendicular to the plane of the figure are obtained with maximum efficiency. and to which one can associate an inclination P and a pitch p of the plane arrays in the crystal 10 for which the incidence 0 of the beam with respect to the plane is the Bragg incidence. Neighboring points for which the incidence is within a range are also obtained with reduced efficiency.

where n is the refractive index of the medium and the thickness of the useful diffraction zone in the medium. All the correlation peaks therefore appear sequentially.

There is an emergence of a parallel beam which is focused by a second spherical lens L ₂ at a point of the image plane or output plane Ps. This plane is the focal plane of the lens Lz. This generates a new Fourier transformation. This second Fourier transform makes it possible to obtain an image filtered by optical correlation. Indeed it is the Fourier transform of the algebraic sum of the two Fourier transforms of the functions representing the transmittance of A and B. It allows to go back to the initial space. The correlation of one signal by another can be broken down into two correlations. An autocorrelation function of the signal to be observed and a signal correlation function by noise. The autocorrelation function is a symmetrical function which has the appearance of a peak. We have here a non-diffracted radiation in the center and two peaks of symmetrical correlations with respect to this center. In our case a correlation peak is a focal point of the light in the exit plane. The noise correlation function of the signal represents on the contrary a spread background from which some secondary peaks emerge but whose amplitude is lower than that of the autocorrelation peaks.

The parallel reading beam F _R may have a wavelength A ₂ different from that of the source beam which is modulated by A and B. A color filter 5 is then inserted between the medium 10 and the lens L ₂ so that 'it only lets through the part of the emerging beam of wavelength λ ₂ . Indeed it is necessary to eliminate the part of the emerging beam of wavelength λ ₁ .

The beam emerging from the interaction medium 10 has undergone a reflection on the interference strata of this medium. This wave beam is therefore assigned a horizontal polarization. Indeed, the interference strata are perpendicular to the direction of the applied field. If a polarizer 6 is inserted in this emerging beam, a better signal / noise ratio is obtained by promoting the transmission of the polarized waves.

In Figure 2 are all the elements considered in Figure 3. The beam modulated by the object patterns A and B is the conjugate return beam emerging from the medium 2. This beam then passes through the lens L _i . The lens L in FIG. 3 therefore becomes the lens Li in FIG. 2. This device in FIG. 2 makes it possible to perform an optical correlation. It incorporates the Fourier transformer of Figure 1. The wavefront return beam Σ ₀ * which is reflected on the semi-transparent plate is a beam modulated in amplitude by the object 1 which includes two patterns; A and B in FIG. 3. There is compensation for the phase distortions obtained by real-time generation of the conjugate wavefront in the medium 2. There is both compensation for the aberrations of the lens Li effecting the transform of Fourier, and distortions induced by the data entry device which operates here by transmission.

The discriminating power in the source plane of the correlator is weak. There are speckles due to the use of coherent light. To improve the signal / noise ratio, averaging is carried out by supposing the intensities of a certain number of images; each image is obtained with an identical transparent object, but with a different speckle shape.

This averaging can be achieved by moving the source beam F _s along a straight line Si S _z , the reference beam F _R being moved synchronously to strike the medium 10 at the same point as the input source beam S ' _i and S ' _z . These displacements can be obtained by any acousto-optical, electro-optical deflection device or even by the mechanical displacement of a lens or end of optical fiber.

FIG. 4 illustrates this possibility of displacement of the ends of two single-mode optical fibers 20 and 21. The light beam coming from a laser 22 is split by the interposition of a semi-transparent plate 23 into two components which after focusing by two lenses L ₃ and L ₄ propagate in these fibers 20 and 21.

The ends of these two fibers are moved synchronously by two motor 24 and 25 controlled by a generator 26, the component of the beam flowing in the fiber 20 is collimated by a lens L ₅ to give the reference beam F _R.

A simpler electro-optical configuration is indicated in FIG. 5. In this diagram the source So remains fixed and the fictitious translation of So, from Si to S ₂ obtained using an acousto-optical tank arranged to deflect the return beam which is modulated by the object, for example in the object plane. But then the aberrations induced by the lens Li are compensated rigorously only for the point S ' _o . Also the fictitious points Si and S ₂ are in the vicinity of S _o and it can be considered that the residual distortions induced by the lens L _i remain low. The beam F _R must move as in the previous case.

By carrying out this averaging, an integration is made in the output plane of N images whose noises are decorrelated. An incoherent integration of N coherent images is therefore carried out. The gain on the signal / noise support of the correlation peaks is proportional to √N.

Another way to improve the signal-to-noise ratio is to attenuate the low spatial frequencies of the object transparency spectrum. This can be achieved by considering a pumping beam Fp of intensity lower than that of the object beam. Only the high spatial frequencies are retained in the conjugate wave front, which corresponds to a reinforcement of the contours of the transparent object.

By way of nonlimiting example, the optical correlator system of FIG. 2 was produced with a first monocrystalline plate 2 of bismuth-silicon oxide. This blade has a surface of 30 x 30 square millimeters and a thickness of 3 millimeters. The second blade is also a monocrystalline bismuth-silicon oxide blade. It has a surface of 2 x 10 square millimeters and a thickness of 1 millimeter. These blades are polarized with a voltage Vo of gold dre of 2000 volts. The transparent object has a surface of 25 × 25 square millimeters. If T is the time taken by the source point S to move from Si to Sz, here distant by 5 millimeters, if the time of registration of the space charge field in the crystal BSO 10 (bismuth-silicon oxide) remains ), T is, for example, equal to 1 second and τ to 1 millisecond.

In this case, we can consider that over a period of time T, an inconsistent integration of N = T / τ "coherent" images is performed on the detector medium 7. Here N is equal to 1000. The gain on the signal-to-noise ratio of the correlation peak is proportional to √N, which is approximately 30.

Thus this optical correlator system provides a new solution to the problems posed by any coherent optical correlation device. It allows operation at the limits of diffraction with optical components of reduced quality, in particular the spherical lens Li. The signal / noise ratio can be made equivalent to that resulting from incoherent lighting.

The use of dynamic materials such as BSO allows an improvement in the performance of this optical processing system based on the properties of Fourier transforms of lenses.

The main applications concern, for example, target tracking or robotics.

Claims (8)

1. An optical Fourier transformer device comprising a coherent radiation point source (S) located in the focus of a convergent lens (L_i), means for positioning a modulating object (1) in the collimated beam emerging from said lens (L_i), and optical means illuminating a plane by a distribution of Fourier transformed light amplitudes of the optical modulation produced by said object, these optical means comprising a photo- excitable interaction medium (2) with index variation receiving the collimated beam via said object (1) and a pumping beam (Fp), characterized in that this interaction medium (2) with three-dimensional index variation is constituted by an electro-optical crystal comprising electrodes located on its lateral faces to which a voltage (Uo) is applied in such a way that a transverse optical effect is used, the pumping beam emerging from said source, a plane reflector (4) being arranged so as to reflect in normal incidence and towards the said medium (2) the radiation emerging therefrom in the propagation direction of the pumping beam (Fp), this radiation having a wavefront which is conjugate and isomorph with the wavefront of the collimated beam such that the errors due to a parasite modulation of the wavefront of this collimated beam are compensated, and a semitransparent plate being positioned between the said source (S) and said lens (L_i) for deflecting towards the said plane the radiation contained in the conjugate wave re-radiated by said medium (2) in the direction of said lens (L_i).

2. A device according to claim 1, characterized in that the interaction medium (2) is a monocrystalline bismuth-silicium plate.

3. An optical correlator with double diffraction comprising a first Fourier transformer device, a photoexcitable interaction medium (10) with index variation comprising on its lateral faces electrodes to which a voltage (Vo) is applied, this medium being arranged for simultaneously receiving the radiation emerging from the first transformator device and another radiation contained in a reference beam (F_R), and a second Fourier transformer for projecting into an image plane an illumination representing the correlation function of the two motifs of a modulating object introduced into said first Fourier transformer device, characterized in that said first Fourier transformer device is defined in accordance with either of the preceding claims.

4. An optical correlator according to claim 3, characterized in that angular scanning means for the reference beam (F_R) ensure an optimum diffraction efficiency for the different points of the observed medium (10).

5. An optical correlator according to claims 3 and 4, characterized in that the optical means synchronously ensure the displacement of the source contained in the first Fourier transformer device and of the reference beam (F_R) in order to average the optical noise superimposed on this illumination in the image plane.

6. An optical correlator according to any one of claims 3 to 5, characterized in that the source (S) and the reference beam (F_R) emerge from the ends of two monomode optical fibres (20,21).

7. An optical correlator according to any one of claims 3 to 6, characterized in that an acousto- optical deflector (11) is interposed in the objet plane to deflect the return beam, which is modulated by the object.

8. An optical correlator according to any one of claims 3 to 7, characterized in that the interaction medium (10) is a bismuth-silicium plate.

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