RU2536764C1 - Method of interference microscopy - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: investigated microobject is illuminated by incoherent radiation, which is used for generation of an increased image of a microobject in the front focal plane of the 4f optical system, the radiation is divided with the help of a beam splitter, from two identical Dove prisms, glued along the bases of prisms, and both beams are sent to one flat mirror. The beam, which passed via both Dove prisms, is sent via a pin hole. After reverse passage via the beam splitter both beams of radiation are sent to an angle reflector, and the initial interference image is recorded, and then the beam splitter and angle reflector are displaced many times along the direction, which is perpendicular to the bases of the prisms. At the same time the phase of interference images changes in respect to the initial one, and a set of interference images is recorded, by which, using the method of phase steps, they calculate 2D distribution of optical difference of radiation travel that passed via the microobject.

EFFECT: reduced level of coherent noise, lower requirements to alignment of an interferometer, increased stability of measurement results, increased accuracy of measurements.

3 cl, 6 dwg

Description

The present invention relates to microscopy and can be used in biology, medicine, mechanical engineering, optical instrumentation.

Known methods of interference microscopy, see, for example, M. Franson "Phase-contrast and interference microscope", M .: State publishing house of physical and mathematical literature, 1960. They are designed to study phase objects.

Phase objects transparent to visible optical radiation are widespread both in industry and in biology and medicine. These include various polymer films, crystals, optical micro-parts, fiber-optic products, and, finally, biological objects - cells, etc. These objects are described by three-dimensional (3D) spatial distribution of the refractive index, which is associated with density, temperature, concentration and other physical parameters object (Ch. West. Holographic interferometry. M .: Mir, 1982).

When studying phase objects, the task arises of visualizing them, since they are usually transparent to probe radiation. To date, the following methods for visualizing phase microobjects are widely known:

- a phase contrast method, also called the Zernike method, consisting in the fact that the phase shift in the light beam passing through the phase object is converted into a change in the brightness of the image (Bennett, A., Osterberg, H, Jupnik, H. and Richards, O. Phase Microscopy: Principles and Applications, John Wiley and Sons, Inc., New York, 1951);

- a method of interference contrast, consisting in the fact that the light beam is divided into two beams, one of which passes through the phase object, and the second passes it; the interference of both beams makes it possible to detect and measure the optical path difference introduced by the phase object (Hariharan P., Optical Interferometery, 2 ^nd ed., Academic Press, 2003);

- a method of differential interference contrast (Nomarsky method, DIC), which consists in the fact that a polarized light beam is divided into two orthogonally polarized coherent beams, which pass through a phase object by optical paths of different lengths, are reduced and interfere (Murphy, D., Differential interference contrast (DIC) microscopy and modulation contrast microscopy, in Fundamentals of Light Microscopy and Digital Imaging, Wiley-Liss, New York, 2001);

- a dark field method, consisting in the fact that only light beams scattered by this object are recorded to form an image of a phase object (G. Roskin, Microscopic technique, M .: Publishing house "Soviet Science", 1946);

- a method of polarization contrast, consisting in the fact that an anisotropic phase object is placed between two polarization filters, the plane of polarization of one of which is rotated 90 ° relative to the other; only those light beams pass through the second filter, the plane of polarization of which turned out to be a rotated phase object (G. Roskin, Microscopic Technique, M.: Sovetskaya Nauka Publishing House, 1946).

A common drawback of the listed and other similar methods for measuring the characteristics of phase objects is the difficulty of implementation in practice due to the high requirements for alignment of the interferometer and, as a result, the low reliability and stability of the method, insufficiently high measurement accuracy.

Currently, research requires not only to observe and evaluate various geometric parameters (area, perimeter), but also to measure their local and integral characteristics.

Quantitative studies of the characteristics of phase objects can be carried out using the method of interference microscopy, since only it allows you to measure the optical path difference (ORX). Other methods allow you to either visualize or measure the derivative in the direction from ORX (differential interference contrast method).

To form the object and reference beams in the method of interference microscopy, two-beam Michelson and Mach-Zehnder interferometers were usually used (AN Zakharyevsky, AF Kuznetsova. Biological interference microscopes. Cytology, 1961).

The main disadvantage of double-beam interference microscopy schemes is the need to use coherent radiation. This leads to large noise in the interferograms and, as a result, to an increase in the error in the reconstruction of the phase from interferograms. The separation in space of the object and support branches also leads to the fact that the rays going into them react differently to vibration and temperature fluctuations, which greatly impairs the vibration resistance of interference microscopy.

The current trend in interference microscopy is the transition to incoherent light from a conventional halogen lamp or from an LED with a short coherence length. This allows one to significantly reduce the noise characteristic of coherent radiation (speckle noise, etc.). The use of radiation sources with a short coherence length leads to the necessity of using interferometer circuits with combined object and reference branches. Such interferometers are usually compensated for by white light, i.e. the optical path difference in the center of the field of view is zero.

A known method of interference microscopy, described in the work of B. Bhaduri et al. "Diffraction phase microscopy with white light." Optics Letters, Vol. 37, No. 6, PP.1094-1096, 2012. It consists in the fact that the investigated microobject is illuminated with incoherent radiation from a halogen lamp, which is used to form an enlarged image of the microobject in the front focal plane 4f of the optical system. The radiation received in the 4f optical system is passed through a diffraction grating, which produces many beams containing all the information about the object, and then these beams are directed to the first Fourier lens and form radiation in the common focal plane as a set of diffraction orders. Radiation of the zeroth diffraction order is passed through an amplitude spatial frequency filter consisting of a point diaphragm aligned with the optical axis and a reference beam is formed from it, and radiation of higher diffraction orders is passed through an amplitude spatial frequency filter in the form of a large rectangular diaphragm that completely transmits radiation , and form an object bundle from it. Next, the radiation is directed to a second Fourier lens, after which two plane beams are formed at a small angle and form in the rear focal plane 4f of the optical system an interference image of a micro-object in bands of finite width, which is recorded and used to calculate the two-dimensional distribution of the optical difference in the radiation path.

This method, in fact, is a double-beam Mach-Zehnder interferometry method in which the reference beam is formed from radiation transmitted through a point aperture, and the second object beam from radiation in the 1st and higher diffraction orders. The disadvantage of this method of interference microscopy is that the object and reference beams are formed at the entrance to the 4f system and therefore they pass different paths in free air space. Therefore, they will be subject to air fluctuations in different ways, which leads to instability of the interference pattern. Another disadvantage is that when deciphering the interference pattern and calculating the two-dimensional distribution of the optical difference of the radiation path, only the Fourier algorithm can be used. A more accurate method — the phase shift method — requires changing the optical path length of one of the reference or object beams, which is difficult to do in this method.

There is another method of interference microscopy described in the work of Z. Wang et.al. "Spatial light interference microscopy (SLIM)", Optics Express, Vol.19, No.2, PP.1016-1028, 2011. It, like the previous method of interference microscopy, consists in the fact that the investigated microobject is illuminated with incoherent radiation, which used to form an enlarged image of a micro-object in the front focal plane 4f of the optical system. The radiation received in the 4f optical system passes through the first Fourier lens and is directed to a phase spatial filter, which operates on reflection, installed in the common focal plane 4f of the optical system. The filter is made in the form of a purely phase spatio-temporal light modulator controlled by a computer, which shifts the phase of the unscattered radiation focused near the optical axis, i.e. It works as a Zernike variable phase filter. When using an annular diaphragm in a condenser, the phase filter also has the form of a ring. The light reflected from this part of the modulator forms a reference beam. The light that has undergone diffraction on the object is reflected from the rest of the modulator and forms an object beam. As a result, in the rear focal plane 4f of the optical system, in the plane of the recorder, two plane beams converge at zero angle and form an interferogram similar to that obtained when the interferometer is tuned to an infinitely wide (zero) band. Since one of the light beams is formed from radiation scattered on the object, such an interferogram can be considered as a Gabor hologram. To decrypt the interferogram, four frames with a phase shift of π / 2 are used. The main disadvantage of this method of interference microscopy is the use of an expensive phase space-time digital light modulator. Another drawback is that a more complex mathematical procedure is used to obtain quantitative information about a phase object than in the conventional phase shift method. In particular, additional recording of the amplitude image formed from the scattered radiation, normalized to the amplitude of the unscattered radiation, is required.

A known method of interference microscopy is described by P. Gishovitz, N. T. Shaked "Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy". Optics Express, Vol. 21, No. 5, PP. 5701-5714, 2013, the closest to the proposed method of interference microscopy.

This method of interference microscopy consists in the fact that the investigated microobject is illuminated with incoherent radiation, which is used to form an enlarged image of the microobject in the front focal plane 4f of the optical system, the radiation received in the 4f optical system is directed to the first Fourier lens and, not reaching the total the focal plane 4f of the optical system, is divided using a beam splitter into two radiation beams, each of which is focused on reflective elements, and reflected from these elements In this case, the beams are directed back to the beam splitter, and one of the beams is passed through a pinhole diaphragm before focusing, after passing back through the beam splitter, the radiation beams are directed to a second Fourier lens and an interference image of a micro object is recorded in the rear focal plane 4f of the optical system, which is recorded and used for calculation two-dimensional distribution of the optical difference in the path of radiation transmitted through a micro-object.

The disadvantage of this method of interference microscopy is the difficulty of adjustment, due to the fact that the beam splitter forms two spatially separated light beams, the axes of which are located at 90 degrees. Therefore, two retro-reflective elements are located at an angle of 90 degrees to each other. It is very difficult to install these elements exactly at the same distance from the side faces of the beam splitting cube, this distance will always be different, therefore, the optical path difference between the beams will always exist.

Another disadvantage of this method of interference microscopy is that it is based on off-axis interferometry, i.e. at the output, an interference image of a microobject is formed in bands of finite width. In this case, an algorithm based on the application of the two-dimensional Fourier transform to the obtained image is used to automatically decode the interferograms and calculate the two-dimensional distribution of the optical difference in the radiation path. For the correct operation of this algorithm, a sufficiently large number of interference fringes is required, at least 50 for the entire field of view. In the above work, the figure is 48 lines per mm. To obtain such an interferogram, radiation with a sufficiently large coherence length of the order of 27 μm, which is used in this method of interference microscopy, is required. In this case, the half-width of the emission band of the light source is only 6.7 nm and, as a result, coherent noise increases.

Another drawback of this method is that it uses an algorithm for recovering the phase from interferograms, based on the application of the two-dimensional Fourier transform to the resulting image (M. Takeda, "Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [ Invited] ", Appl. Opt., V.52, No. 1, P.20-29, 2013). However, the Fourier method is limited in the class of objects under study, the spatial spectrum of objects cannot exceed a certain value, i.e. objects with large gradients of the refractive index or height differences are not restored by this method. Another drawback of the Fourier method is the overlap of spectra of zero and higher orders (JFCasco-Vasquez et al. "Fourier normalized-fringe analysis by zero-order spectrum suppression using a parameter estimation approach". Opt. Engineering, V.52, no. 7, 074109, 2013), as well as with edge diffraction effects. The fact is that any interferogram is given in a limited area - a binary mask, so the spectrum of the phase object under study is always distorted by convolution with the spectrum of this mask. Since the mask is binary, its spectrum is wide and oscillating, therefore, strong distortions appear in the reconstructed phase image at the edges of the object’s target area.

The technical problem solved by the present invention is to reduce the level of coherent noise, reduce the requirements for alignment of the interferometer, to increase the stability of the interferometer, to increase the accuracy of measurements of the two-dimensional distribution of the optical path difference.

, где $$\text{k(}\alpha \text{)}=\frac{\text{2tg}\alpha }{{\text{1-tg}}^{\text{2}}\alpha }$$

, λ - длина волны излучения, и по полученному набору из N интерференционных изображений вычисляют двумерное распределение оптической разности хода излучения, прошедшего через микрообъект.The solution of the problem in the proposed method of interference microscopy is achieved as follows: the investigated microobject is illuminated with incoherent radiation, which is used to form an enlarged image of the microobject in the front focal plane 4f of the optical system, the radiation received in the 4f optical system is directed to the first Fourier lens and, not reaching the general focal plane 4f of the optical system, they are divided using a beam splitter into two radiation beams, each of which is focused on the light reflective elements, and the beams reflected from these retroreflective elements are sent back to the beam splitter, one of the beams in the focusing plane being passed through a point aperture, after passing back through the beam splitter, the radiation beams are directed to the second Fourier lens and interference form in the rear focal plane 4f of the optical system image of a microobject that is recorded and used to calculate the two-dimensional distribution of the optical difference in the path of radiation transmitted through the mic The object, the radiation is divided using a beam splitter of two identical Dove prisms glued along the bases of the prisms, so that the resulting beams have zero travel difference, and their optical axes are parallel to the bases of the prisms, then both beams are directed to one flat mirror, the normal to which parallel to the plane passing through the optical axes of the beams, and makes an angle α to the optical axes of the beams, and the beam that passed through both Dove prisms is passed through a point diaphragm mounted in a direct block isostomy to a flat mirror, and after the return pass through the beam splitter, the radiation beams are directed to a corner reflector, the axis of symmetry of which is parallel to the prism bases, and the initial interference image is recorded, the beam splitter and the corner reflector are repeatedly shifted along the direction perpendicular to the prism bases, N times by the values of d _i , i = 1, 2, 3, ..., N, and N interference images are recorded, the phase of which with respect to the initial interference image changes by $$\frac{\text{four}\pi {\text{d}}_{\text{i}}}{\lambda }\text{k (}\alpha \text{)}$$

where $$\text{k (}\alpha \text{)}=\frac{\text{2tg}\alpha }{{\text{1-tg}}^{\text{2}}\alpha }$$

, λ is the radiation wavelength, and from the obtained set of N interference images, the two-dimensional distribution of the optical difference in the path of radiation transmitted through the micro-object is calculated.

Reducing the level of coherent noise is achieved through the use of an incoherent light source with a larger half-width of the emission band and a short coherence length than the prototype. This becomes possible because in the proposed method, the radiation is divided using a beam splitter of two identical Dove prisms glued along the bases of the prisms, so that the resulting beams have a zero path difference, i.e. an on-axis interferometry scheme is implemented with combined reference and object beams, and the coherence length can be reduced to a few microns.

Reducing the alignment requirements of the interferometer is achieved by the fact that after division, the optical axes of the beams will be parallel to the bases of the prisms and, accordingly, to each other, this allows you to direct both beams to one flat mirror, and they will automatically pass the same distance to this mirror and will have a zero travel difference . Because radiation is divided using a beam splitter of two identical Dove prisms glued along the base of the prisms, and the Dove prisms themselves are made with high accuracy and glued together without skewing or tilting (Yu.G. Kozhevnikov. “Optical Prisms”, M .: Mechanical Engineering, 1984), the resulting beams have a zero path difference at the output of the beam splitter.

Improving the stability of the interferometer is achieved by the fact that the beam splitter and the flat mirror are rigidly fixed on a common base, as a result of which the vibration has the same effect on the nodes of the interferometer, which does not affect the measurement results.

, где $$\text{k(}\alpha \text{)}=\frac{\text{2tg}\alpha }{{\text{1-tg}}^{\text{2}}\alpha }$$

, λ - длина волны излучения, и по полученному набору из N интерференционных изображений вычисляют двумерное распределение оптической разности хода излучения, прошедшего через микрообъект.Improving the measurement accuracy of the two-dimensional distribution of the optical path difference is achieved by the fact that in the proposed method for automatic decoding of interferograms, the method of phase steps is implemented, and not the Fourier method, as in the prototype. The phase-step method is known to be more accurate than the Fourier method (see, for example, the book “Interfere gram analysis for optical testing” / Ed. By D. Malacara. Taylor & Francis Group, 2005, chapters 7 and 8). To implement the method of phase steps, the beam splitter and the corner reflector are repeatedly shifted along the direction perpendicular to the prism bases N times by the values of d _i , i = 1, 2, 3, ..., N and N interference images are recorded, the phase of which is relative to the original interference image changes by $$\frac{\text{four}\pi {\text{d}}_{\text{i}}}{\lambda }\text{k (}\alpha \text{)}$$

where $$\text{k (}\alpha \text{)}=\frac{\text{2tg}\alpha }{{\text{1-tg}}^{\text{2}}\alpha }$$

, λ is the radiation wavelength, and from the obtained set of N interference images, the two-dimensional distribution of the optical difference in the path of radiation transmitted through the micro-object is calculated.

A second variant of interference microscopy is possible, characterized in that the radiation is divided using a beam splitter of two identical mirror analogues of the Dove prism, in which the upper mirror is made in the form of a translucent beam splitter plate and is common to both prisms, and the beam splitter face of the plate is parallel to the optical axis a beam incident on it.

A third variant of interference microscopy is possible, characterized in that the radiation is divided using a beam splitter, rotated relative to the optical axis of the incident beam by 45 degrees so that its beam splitter is parallel to the specified optical axis.

Further, the invention is illustrated by specific examples of its implementation and the accompanying drawings.

Figure 1 illustrates a schematic optical diagram of a microscope that implements the proposed method of interference microscopy. The scheme consists of two parts: a conventional bright field microscope I and interference prefix II. Microscope I consists of an incoherent light source 1, for example an LED; a collecting optical element 2, for example a collector lens; an element restricting the cross section of the light beam 3, for example a field diaphragm; an element forming a point light source 4, for example a point diaphragm; an optical element 5 forming a parallel beam of radiation, for example a collimation lens; phase object 6; an optical element 7, for example a micro lens; reflective element 8, for example a flat mirror; an optical element 9, for example an ocular lens, forming an enlarged image in the rear focal plane 10 of the optical element 9. The interference device II includes a 4f optical system of optical elements 11 and 13, for example, Fourier lenses, the front focal plane of which is aligned with the rear focal plane 10 of the microscope and in the rear focal plane 14 of which an image recorder 15 is mounted, for example, a CCD; a beam splitter 16, for example, of two identical Dove prisms glued along the bases of the prisms (hereinafter referred to as Dove biprism), located up to the common focal plane 4f of the system; flat mirror 18; spatial frequency filter 19, for example, a pinhole, which is fixed in close proximity to a flat mirror 18; corner reflector 12; a movable platform 17 with a drive 20, for example a stepper motor, on which Dove 16 biprism and a corner reflector 12 are fixed.

Figure 2 shows in more detail the progress of the optical axes of the beams in the beam splitter 16 when reflected from the mirror 18 when it is inclined.

Figure 3 shows in more detail the progress of the optical axes of the beams in the beam splitter 16 when it is offset from its original position and reflected from the mirror 18.

Figure 4 shows in more detail the progress of the optical axes of the beams after direct and return passage through the beam splitter 16 and the corner reflector 12 before and after their simultaneous displacement.

In figure 1, the radiation from an incoherent source 1 with the help of optical elements 2-5 is converted into a parallel beam that passes through a phase object 6 located in the front focal plane of the optical element 7. The rear focal plane of the element 7 is aligned with the front focal plane of the optical element 9 An enlarged image of the phase object 6 is constructed in the rear focal plane 10 of the optical element 9. A retroreflective element 8 is auxiliary to reduce the construction of the microscope.

The back focal plane of the microscope is aligned with the front focal plane 4f of the optical system. In it, radiation passes through the first Fourier lens 11, then through a beam splitter 16 of two identical Dove prisms glued along the bases of the prisms, behind which two identical radiation wave fronts are formed in the common focal plane, the complex amplitude of which is described by the Fourier spectrum of the spatial frequencies of the phase object 6. Since the beam splitter 16 is made of two identical Dove prisms, the radiation of the resulting two beams will have a zero path difference, i.e. these bundles will be coherent.

A plane mirror 18 is installed in the common focal plane 4f of the system 18. First, let this mirror be installed strictly perpendicular to the incident beams. The beam that passed to the mirror 18 through both Dove prisms (Fig. 1 is the upper beam) is passed through the spatial frequency filter 19, made in the form of a point diaphragm 19, installed in close proximity to the planar mirror 18. As will be shown below, namely this beam remains stationary when the beam splitter 16 is shifted; therefore, it is precisely at it that the spatial frequency filter 19 is installed, transmitting only non-scattered radiation, which, reflected from the plane mirror 18, propagates in the opposite direction. A reference beam is formed from this radiation. The radiation that passed to the mirror 18, reflected from the beam splitting edge of the Dove 16 biprism (in Fig. 1, this is the lower beam), is freely reflected from the planar mirror 18 and propagates in the opposite direction. An object beam is formed from this radiation.

Since the flat mirror 18 is initially set strictly perpendicular to the incident beams, both beams automatically pass the same optical path from the beam splitter 16 to the flat mirror 18 and back to the beam splitter 16. In contrast to the prototype, there is no need to align the optical paths of both beams. In the proposed method, this happens automatically, because To return the beams, one flat mirror is used, and not two spaced apart in space, as in the prototype. Thus, the beams that are reflected from the planar mirror 18 will also have a zero path difference, i.e. will remain coherent.

In the reverse stroke, the beams reflected from the planar mirror 18 are combined in space by the beam splitter 16, pass through the corner reflector 12 and the second Fourier lens 13, which builds in the rear focal plane 14 the image of the phase object 6 fixed by the recorder 15. The reference and object beams have a zero difference the path and are formed from one light beam, therefore, upon registration, they form an interferogram of the phase object 6, similar to that which is formed in the interferometer tuned to an infinitely wide band.

Now we consider the case when the flat mirror 18 is installed at a small angle α to the incident beams, more precisely, the normal to the flat mirror 18 is parallel to the plane passing through the optical axes of the beams (the plane of the figure in Fig. 1) and makes the angle α to the optical axes of these beams. Turning to FIG. 2, on an enlarged scale, the optical axes of the beams are reflected in reflection from a planar mirror 18 in its inclined position. Without loss of generality, let the planar mirror 18 be rotated through an angle α, for example, relative to point A, then the optical axes AD and B ″ C of the reflected beams will propagate at an angle 2α with respect to the axes A'A and B'B of the incident beams. When the plane is tilted mirror 18 between the beams of radiation there is an optical path difference Δ, which is equal to

Δ = (B'B "+ B" C) - (A'A + AD) = (B'B "-A'A) + (B" C-AD) = BB "+ (B" C-AD) .

From ΔABB "it follows that BB" = AB tgα = htgα. From ΔA'AD and ΔB'B "C you can write:

AD = A'A / cos2α, B "C = B'B" / cos2α = (A'A + htgα) / cos2α,

then (B "C-AD) = htgα / cos2α and finally we get

$$\Delta =htg\alpha +htg\alpha /\cos 2\alpha =htg\alpha (\mathrm{one}+\cos 2\alpha )/\cos 2\alpha =2htg\alpha /(\mathrm{one}-t{g}^2\alpha )=k(\alpha )h,(\mathrm{one})$$

where is the angular coefficient

$$\text{k (}\alpha \text{)}=\text{2tg}\alpha {\text{/ (1-tg}}^{\text{2}}\alpha ).(2)$$

Thus, the optical path difference between the radiation beams after the beam splitter 16 will be directly proportional to the distance h between the beam axes after the passage of the beam splitter. Figure 2 also shows that the optical axes of the resulting beams after going back through the beam splitter will go at an angle of 4α, however, after the second Fourier lens 13 (see figure 1), the optical axes of these beams will be parallel to each other and to the optical axis 4f of the system . This is due to the fact that the inclined mirror 18 is located in the common focal plane 4f of the system and all the rays reflected from this mirror after the Fourier lens 13 will be parallel to the optical axis 4f of the system.

In the proposed method for phase recovery from interferograms, the method of phase steps is used. The essence of this method is to register a series of interference images of the phase object under study at different phase shifts between the reference and object beams. To introduce this phase shift, it is necessary to change the optical path difference between the reference and object beams. In the proposed method, this operation is performed by the original method, namely by displacing the beam splitter 16 along the direction perpendicular to the bases of the prisms. We show that with such a shift, the optical travel difference Δ changes, since the distance h between the optical axes of the beams changes.

Figure 3 shows the path of the optical axes of the beams when the beam splitter 16 is offset and reflected from the mirror 18. The optical axis of the beam that passes through both Dove prisms arrives at point A on the flat mirror 18, and the optical axis of the second beam, which is reflected from the beam splitter OO ', comes to point B. Let the initial distance between these axes be equal to h ₀ . When the beam splitter 16 is shifted along the direction perpendicular to the bases of the prisms OO ', for example, downward by the value of d _i , the prism will occupy the position indicated by dashed lines in FIG. 3, and the beam splitter face OO' will move to the position CC '. Figure 3 also shows that the optical axis of the beam passing through both Dove prisms does not change its position and remains at point A. This is due to the fact that for this beam the beam splitter acts as a plane-parallel plate. The optical axis of the second beam from position B will shift to position B ', because the beam-splitting face also moved and upon reflection from it the second beam will shift. The distance h (d _i ) between the axes of the beams when the beam splitter is shifted by d _i will be equal to:

. $${\text{h (d}}_{\text{i}}\text{) -AB '}=\text{2AC}=\text{2 (AO}+\text{OC)}$$

.

Since AO = h _0/2 , a OC = d _i , then

h (d _i ) = h ₀ + 2d _i .

When the prism is shifted up, the sign in this expression will be reversed. In general, you can write:

$${\text{h (d}}_{\text{i}}\text{)}={\text{h}}_0\pm {\text{2d}}_{\text{i}}\text{. (3)}$$

Substituting (3) into (1) we get that when the beam splitter 16 is shifted by d _{i, the} optical path difference Δ will change as follows:

$$\Delta =\text{k (}\alpha \text{)}\times {\text{(h}}_{\text{0}}\pm {\text{2d}}_{\text{i}}\text{)}=\text{k (}\alpha \text{)}\times {\text{h}}_{\text{0}}\pm \text{k (}\alpha \text{)}\times {\text{2d}}_{\text{i}}=\text{k (}\alpha \text{)}\times {\text{h}}_{\text{0}}\pm \Delta {\text{(d}}_{\text{i}}\text{), (four)}$$

where the first term is the constant difference of the stroke, and the second is the variable part of the difference of the stroke, equal to

$$\Delta {\text{(d}}_{\text{i}}\text{)}=\text{k (}\alpha \text{)}\times {\text{2d}}_{\text{i}}\text{. (5)}$$

From expression (4), we can estimate the numerical value of the coefficient k (α) from the following considerations. The value of h ₀ cannot exceed the size of the aperture of one Dove prism and it can be made no more than 3 mm. The amount of displacement of the beam splitter d _{i is} much less than h ₀ . Therefore, for the estimates in (4), only the first term can be taken into account, and then

$$\text{k (}\alpha \text{)}=\Delta {\text{/ h}}_{\text{0}}\text{. (6)}$$

Since we want to use a non-monochromatic radiation source to reduce coherent noise, we can require that the maximum optical path difference Δ not exceed the coherence length of this source, for example, equal to 3 μm. Recall that in the method adopted for the prototype, the coherence length is almost 10 times greater and is 27 microns. Then it follows from (6) that

, а из (2) угол α≤0,03°. $$k(\alpha )=\frac{3m\mathrm{to}m}{3mm}=0,001$$

, and from (2) the angle α≤0.03 °.

, где λ - центральная длина волны излучения. Подставляя сюда (5) получим, что фаза меняется на величинуThe phase of the interference image obtained after the beam splitter is shifted by d _i in relation to the original interference image obtained before the beam splitter is shifted by $$\frac{\text{2}\pi }{\lambda }\Delta {\text{(d}}_{\text{i}}\text{)}$$

where λ is the central radiation wavelength. Substituting here (5), we obtain that the phase changes by

$$\frac{\text{four}\pi {\text{d}}_{\text{i}}}{\lambda }\text{k (}\alpha \text{)}\text{. (7)}$$

For better reconstruction of the phase image from the interferogram by the method of phase steps, a phase change range from 0 to 4π with a step of π / 2 is required. Then it follows from (7) that the range of motion of the beam splitter 16 will be λ / k (α) = λ / 0.001 = 1000λ with a step of λ / 8k (α) = 125λ. Therefore, for the central wavelength λ = 0.6 μm, the range of displacements will be 600 μm, and the pitch 75 μm. Such movements can be performed using conventional motorized linear translators based on stepper motors, for example, Vicon Standa, model 8МТ175, with a minimum pitch or accuracy of movements of 2.5 μm in the range of 5 mm.

Usually, the implementation of the phase-step method requires a very small range of displacements of about 2λ, i.e. within 2 interference fringes with a step of λ / 8 and the corresponding accuracy of displacements an order of magnitude higher than the displacement step. For this, precision actuators with piezoelectric elements are used. In our case, you can do with simpler and more affordable tables with linear movement. This is also an important advantage of the proposed method.

The offset is repeated N times and from the obtained set of N interference images, the two-dimensional distribution of the optical difference in the path of radiation transmitted through the micro-object is calculated using any of the phase-step algorithm algorithms (see, for example, the electronic book Wyant JC Phase Shifting Interferometry.nb, 1998, http://www.optics.arizona.edu/fab&test/Fall09/415L_515L/Lab3/Wyants%20PSI.pdf).

Thus, we have proved the technical feasibility of the method of phase steps in the proposed method.

Figure 3 also shows that when the beam splitter 16 is shifted, the optical axes of the beams after their return passage through the beam splitter are also shifted. Unless special measures are taken, the image of the object in plane 14 will also shift, which cannot be allowed to implement the phase-step method. In this method, the image of the object should be motionless, and only interference fringes along the object will shift.

To avoid this, the proposed method uses additional reflection from the corner reflector 12, which also moves along the direction perpendicular to the prism bases simultaneously with the beam splitter 16 and by the same amount. To implement such a joint bias beam splitter - biprism Dove 16 and corner reflector 12 are mounted on one movable platform 17 with a drive 20, for example a stepper motor (see figure 1).

To prove this fact, we turn to Figure 4, which shows the course of the optical axes of the beams after direct and return passage through the beam splitter 16 and the corner reflector 12 before and after simultaneous displacement. From the property of the corner reflector it is seen that the optical axis 4f of the system is not shifted and, accordingly, the images of the object formed in the plane 14 will be stationary.

The operation of the device that implements the proposed method should be performed in two stages. The first step is to calibrate the interference microscope. The optical system is imperfect, as a result of which various kinds of aberrations arise, distorting the image of the object under study. To eliminate such negative effects, at the first stage, the phase image is formed, formed by the optical system, without the investigated phase object.

The second stage is the direct measurement process of the investigated phase object 6. The reconstructed phase image of the object is adjusted using the phase image obtained at the calibration stage by subtracting from the first second phase image. Thus, the obtained phase image of the object will be free from phase distortions (aberrations) of the optical system of the interference microscope.

A second embodiment of the invention is possible when radiation is divided by a beam splitter of two identical mirror analogues of the Dove prism (BC Nuzhin et al. “Design and manufacture of mirror analogue of the Dove prism”, Optical Journal, vol. 52, No. 6, p. 70-72), in which the upper mirror is made in the form of a translucent beam splitting plate and is common to both prisms, and the beam splitting face of the plate is parallel to the optical axis of the incident beam. Such a beam splitter is depicted in figure 5. The beam splitting plate OO 'should be made in the form of gluing two identical plane-parallel transparent plates, one of which is coated with a 50% mirror coating. This is necessary in order to align the optical path length of the beams at the output of the beam splitter 16 — mirror 18. Using mirrors in an analogue of the Dove prism allows to reduce the chromatic aberration of the microscope caused by dispersion of the refractive index of ordinary (glass) Dove prisms, as well as to expand the spectral range of the used radiation from UV to IR.

A third variant of interference microscopy is possible, characterized in that the radiation is divided using a beam splitter, rotated relative to the optical axis of the incident beam by 45 degrees so that its beam splitter is parallel to the specified optical axis. Such a beam splitter is shown in Fig.6.

Although the inventive method is described as an example of a number of its specific embodiments, specialists will be able to understand the numerous modifications of this method that do not go beyond the idea and scope of legal protection of the invention defined by the attached claims.

Claims (3)

1. The method of interference microscopy, which consists in the fact that the investigated microobject is illuminated with incoherent radiation, which is used to form an enlarged image of the microobject in the front focal plane 4f of the optical system, the radiation received in the 4f optical system is directed to the first Fourier lens and, without reaching to the common focal plane 4f of the optical system, is divided by a beam splitter into two radiation beams, each of which is focused on retro-reflective elements, and reflected from these of the reflective elements, the beams are directed back to the beam splitter, and one of the beams in the focusing plane is passed through the pinhole, after passing back through the beam splitter, the radiation beams are sent to the second Fourier lens and an interference image of the micro object is recorded in the rear focal plane 4f of the optical system, which is recorded and used for calculating the two-dimensional distribution of the optical difference of the path of radiation transmitted through a microobject, characterized in that the division of radiation Using a beam splitter, they are made of two identical Dove prisms glued along the bases of the prisms, so that the resulting beams have zero travel difference and their optical axes are parallel to the bases of the prisms, then both beams are directed to one flat mirror, the normal to which is parallel to the plane passing through the optical axes of the beams, and makes the angle α to the optical axes of the beams, moreover, the beam that passed through both Dove prisms is passed through a point diaphragm installed in close proximity to a flat mirror, and after the return pass through the beam splitter, both radiation beams are directed to an angle reflector, the axis of symmetry of which is parallel to the prism bases, and the initial interference image is recorded, the beam splitter and the corner reflector are repeatedly shifted along the direction perpendicular to the prism bases, N times by the values of d _i , i = 1, 2, 3, ..., N and N interference images are recorded, the phase of which with respect to the original interference image changes by

where

λ is the radiation wavelength, and from the obtained set of N interference images, the two-dimensional distribution of the optical difference of the radiation path passing through the micro-object is calculated. 2. The interference microscopy method according to claim 1, characterized in that the radiation is divided by a beam splitter of two identical mirror analogues of the Dove prism, in which the upper mirror is made in the form of a translucent beam splitter plate and is common to both prisms, and the beam splitter edge of the plate is parallel to the optical axis of the incident beam. 3. The interference microscopy method according to claim 1, characterized in that the radiation is divided using a beam splitter, rotated relative to the optical axis of the incident beam by 45 degrees so that its beam splitter is parallel to the specified optical axis.

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