RU2554594C1 - Method of correcting lens aberrations - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method includes using a correcting holographic optical element in the form of a digital hologram; positioning a CCD array behind the paraxial image plane of the object; recording the defocused image constructed by the lens, said image being taken as the digital axial hologram of the image with which, using digital holography techniques, holographic fragments of the entire image are reconstructed numerically and layer-by-layer, after which the reconstructed image fragments are transferred to a single plane.

EFFECT: wider field of use, faster operation and quality of holographic correction of lens aberrations.

10 dwg

Description

The invention relates to optical instrumentation and can be used in optical surveillance systems, photographic recording, as well as in holographic systems.

A known method of stationary correction of field curvature. The method consists in using fiber optic elements with a curved surface, the surface shape of which repeats the shape of the field of view. Such an element may be, for example, a focal lens. The image from the curved surface is transferred along the fiber of the element to the flat opposite side, which is the image formation plane [1].

The disadvantage of this method is the high cost and complexity of manufacturing corrective elements. In addition, the solution is stationary, since such elements should be used only for given distances to the object and with the amount of residual aberration for which they are designed. For other distances to the object and other residual aberration, it is necessary to calculate and use other elements.

The closest in technical essence to the claimed technical solution is the lens according to patent RU 2244330 [2], in which the correction of the field curvature is achieved by applying a hologram optical element with an optical power of 0.01-0.1 on one of the optical surfaces of the lenses of the positive component. The characteristic equation of the hologram optical element has the form V _H = A ₁ y ² + A ₂ y ⁴ + A ₃ y ⁶ , where A ₁ , A ₂ , A ₃ are the coefficients; y is the height on the surface of the hologram optical element. The coefficient A _{1 is} proportional to the optical power of the hologram optical element, and the coefficients A ₂ and A _{3 are} proportional to the spherical aberration of the positive and negative components of the lens, respectively.

Since the corrective hologram optical element is stationary, its correction capabilities are limited: when changing the distance to the object and other residual aberration, it is necessary to use an optical element with other parameters.

The objective of the invention is to expand the scope, increasing the efficiency and quality of the hologram correction of lens aberrations.

The problem is solved due to the fact that the corrective hologram optical element is performed in the form of a digital hologram, for which, by positioning the CCD matrix behind the plane of the paraxial image of the object, the defocused image constructed by the lens is taken, taken as a digital axial hologram of the image, which is numerically with methods of digital holography, layer-by-layer restore hologram fragments of the entire image, after which lead the restored fragments of the image to one square sharpness.

The invention and the possibility of its industrial application is illustrated by an example of a specific implementation for a test object and is illustrated by figures 1 - 10.

In FIG. 1 shows an optical diagram of an experiment for correcting lens aberrations, where figure 3 shows the plane of the paraxial image, hereinafter referred to as PR-3, and figure 4 shows the plane of focused off-axis image fragments, hereinafter referred to as PR-4.

In FIG. Figure 2 shows a photograph of a fragment of a test object - a glass substrate with model particles.

In FIG. Figure 3 presents a digital hologram of model particles located near the optical axis in the plane of their defocused images (at a distance of 1882 μm behind the plane of registration PR-3).

In FIG. Figure 4 shows the focused images directly constructed by the lens in PR-3 of the model particles of the test object located on the optical axis.

In FIG. Figure 5 shows defocused images of model particles of a test object (registration plane — PR-3) located in the vicinity of point B, which is a = 16 mm from the optical axis.

In FIG. Figure 6 shows the focused images of particles located in the vicinity of point B, a = 16 mm away from the optical axis, directly constructed by the lens and fixed by the CCD matrix in PR-4;

In FIG. 7 presents images of model particles (located on the optical axis and corresponding to the images of FIG. 4) after correction, i.e. after restoration of the hologram shown in FIG. 3.

FIG. 8 illustrates an increase in resolution at the edge of an image field.

FIG. 9 illustrates a methodology for evaluating image quality.

Figure 10 presents an example of aberration correction for the image of a triangular model particle.

The optical scheme explaining the principle of aberration correction (Fig. 1) includes: 1 - the subject plane with the test object, 2 - the lens, 3 - the registration plane PR-3 is the plane of the best image for particles located on the optical axis, 4 - the plane registration PR-4 is the plane of the best image for particles offset from the optical axis by a distance a and located at point B, 5 is the photodetector matrix of a digital camera with the ability to accurately position it in the axial and transverse directions, a is the half-size of the field of view, a ' is the half-size of the image field, S is the segment specifying the position of the object relative to the front main plane H of the lens 2, S 'is the segment specifying the position of the image relative to the rear main plane H of the lens 2.

In the subject plane (see Fig. 1) at a distance (-S) from the main plane of the lens there is a test object (see the example in Fig. 2), which is a set of flat opaque figures in the form of regular polygons (hexagon, square, triangle ), as well as in the form of a rectangle (aspect ratio 1: 2), rhombus, circle, etc., deposited by photolithography on a glass substrate [3]. Such fragments filled the entire field of view of the lens. The dimensions of the model figures used: the sides of the square, the regular triangle and the hexagon - 200 microns, the diameter of the circle - 200 microns, the small side of the rectangle 200 microns. In a number of experiments, test objects with model particles of other sizes were used. In the experiments, test objects were illuminated with a coherent radiation source - SLC-DLT 317 solid-state laser, wavelength 532 nm.

The defocused image formed by the lens behind the PR-3 best-focus plane is recorded using the C-cam BCi4-6600 CCD camera. The distance from the registration plane is chosen so as to ensure the formation of a Fresnel diffraction pattern from images of all fragments of the test object. For used model particles, the distance should be at least 2 mm. In this case, in the plane of the defocused image of each particle, the pattern of interference of the diffracted wave and the wave transmitted without diffraction is observed. The waves are coherent; therefore, the interference pattern is stationary. The image is recorded on a digital camera in the form of a two-dimensional digital array, which is taken as a digital axial hologram of the image. The characteristics of the camera are chosen so as to ensure registration of digital holograms of model particles, namely: matrix size 7.74 × 10.51 mm, pixel size 3.5 × 3.5 μm. Despite the fact that in some of the figures the interference pattern (the fine structure of the hologram) is not displayed due to the limited capabilities of the printer (monitor), a comparison of its parameters and the characteristics of the selected camera shows that the fine structure of the hologram is recorded without distortion.

Depending on the size of the CCD matrix used, it registers either the entire field of the defocused image, or it is necessary to scan the field of the defocused image by the CCD matrix, registering all its segments.

In the example, the positioning system provided movement of the CCD camera with an accuracy of 2.5 μm in the longitudinal and 1 μm in the transverse directions, which makes it possible to segment the image field into fragments in any plane, including the plane of the paraxial image PR-3, as well as any planes in front of it , for example PR-4, or behind it.

An example of a digital axial hologram of model particles is shown in FIG. 3. This hologram was recorded in the Fresnel diffraction zone - at a distance of 1882 μm behind the plane of the paraxial image PR-3. Here, the fine structure of the intensity distribution in the axial hologram is clearly visible.

We study image fragments in the plane of PR-3. Focused images of the axial part of the test object, that is, particles located near point O (Fig. 1), are located in the central part of the plane of the paraxial image PR-3 near point O '(shown in Fig. 4).

In FIG. 5 shows directly constructed by the lens images of particles located at the edge of the field of view, near point B, located at a distance of 16 mm from the axis of the lens. Their images in the plane of PR-3 near point B 'are defocused due to lens aberrations, which is observed visually. In order to register a focused image of these particles located at the edge of the field of view, it was necessary to move the CCD using the aforementioned positioning system to the PR-4 plane near point B ₁ , which is located at a distance of 192 μm from PR-3.

Note that due to the curvature of the field of view, the distance of the PR-4 registration plane from the PR-3 registration plane will be different for different points of the image field, characterized by different transverse coordinates.

To solve the problem of correcting defocusing (for example, the image shown in Fig. 5), the method according to the invention uses the known method of digital holography, which allows you to numerically restore the distribution of the light field in any plane located at a given distance from the recording plane of the digital hologram [4]. As already noted, a defocused image with a registered interference pattern, an example of which is shown in FIG. 3, is an axial digital hologram. Figure 7 presents images of model particles located on the axis, after correction, i.e. after numerical restoration from the axial hologram of FIG. 3.

The increase in resolution at the edge of the image field when using the method according to the invention is illustrated by photographs of Fig. 8. Here 8a) is an image of a rectangular model particle with a smaller side size of 10 μm, located in PR-3 on the optical axis; 8b) - image of a rectangular model particle with a smaller side size of 10 μm, 16 mm from the optical axis (PR-3 registration plane), it is also an axial digital hologram; 8c) - the image of this rectangular model particle directly constructed by the lens (fixed by a CCD matrix in the PR-4 plane, which is 192 μm apart from the PR-3 plane); 8 g) - image of a rectangular model particle with a smaller side size of 10 μm, 16 mm from the axis, after correction, i.e. after numerical reconstruction of the image from the hologram shown in FIG. 8b. In the center of the image field of FIG. 8a, the resolution is more than 100 lines / mm. This conclusion is made on the basis that it is possible to unambiguously determine the shape of a rectangular model particle with a size of the smaller side of a rectangle of 10 μm (even visually). At the edge of the image field (at a height of 16 mm in the plane of PR-3), the resolution is less than 100 lines / mm (Fig. 8b). After reconstructing the image from the hologram of this fragment, the resolution was more than 100 lines / mm, as for the axial fragment (see Fig. 8 g).

и собственно предмета

. Границы фигур определялись методом наибольшего градиента. После совмещения и вычитания таких бинаризованных фигур определялась суммарная площадь областей, ошибочно включенных и ошибочно исключенных из фигуры

. Степень несовпадения формы изображения модельной частицы с ее оригиналом

назовем критерием различения формы изображения. Форму изображения будем считать однозначно различимой при δ<0,5 и неразличимой при δ>0,5. Отметим, что в зависимости от решаемой задачи могут быть установлены другие значения критерия различения.To assess the quality of image correction, a well-known numerical algorithm was used, based on a comparison of the areas of the image and the original and allowing numerically expressing the degree of image correspondence to the original [5]. The idea of the algorithm is to compare binarized figures: images

and the subject itself

. The boundaries of the figures were determined by the largest gradient method. After combining and subtracting such binarized figures, the total area of areas erroneously included and erroneously excluded from the figure was determined

. The degree of mismatch in the image shape of the model particle with its original

call the criterion for distinguishing the shape of the image. The image shape will be considered unambiguously distinguishable at δ < 0.5 and indistinguishable at δ> 0.5. Note that, depending on the problem being solved, other values of the distinction criterion can be established.

; фиг.9 г - изображение фиг.9б с наложенным оригиналом,

.An example of the operation of the described algorithm for a triangular model particle with a side of 200 μm is shown in FIG. 9. The degree of mismatch is characterized by white areas mistakenly included or mistakenly excluded from / from the image, quantitatively the mismatch is characterized by the fraction of δ white area in the particle area. Here figa is an image directly constructed by the lens at a distance of 1.25 mm from the plane of the paraxial image PR-3 (it is also an axial hologram of the particle); figb - image after correction (numerical restoration of the hologram figa); figv - image figa with the original,

; Fig.9 g - image figb with the original,

.

During the experiments it was found that the criterion for distinguishing δ takes a minimum value in the plane of the best focusing of the image. This fact coincides with the general physical concepts, confirms the representativeness of the introduced criterion, and can be used to find the plane of the best image focusing.

Figure 10 presents images of a triangular model particle with a side size of 50 μm, spaced 8 mm from the axis: a) a defocused image of the particle constructed by the lens directly in the plane of PR-3 and hereinafter used as an axial hologram; b) - the image of FIG. 10a with the original overlaid, where areas marked by mistake or excluded by mistake in / from the image, their share in the particle area δ = 1.26, are marked in white; c) - image of a particle after correction (restoration from the axial hologram of Fig. 10a); d) - the image of FIG. 10c with the original overlaid, white areas marked by mistake or excluded by mistake from / to the image, their share in the particle area δ = 0.31.

On figa it is seen that the image of a triangular particle built by the lens directly in the plane of PR-3 is highly defocused due to the curvature of the field of view (hereinafter it is used as an axial hologram). In FIG. 10b, the original of the triangular particle is superimposed on the image 10a, white areas marked by mistake or excluded from / from the image, their share in the particle area δ = 1.26> 0.5, which corresponds to the indistinguishability of the particle shape. Figure 10c shows an image of a triangular particle after correction (numerical image restoration). Visually visible significantly clearer display of the shape of the model particles. This clearer correspondence of the reconstructed image to the original is illustrated in FIG. 10d, where the white color indicates the areas that are mistakenly included or mistakenly excluded in / from the image, their share in the particle area is δ = 0.31 <0.5, which corresponds to a unique distinction of the particle shape. Note that an image with the same form distinguishability (Fig.10c) is obtained with a longitudinal displacement of the CCD using a positioning system at a distance of 95 μm, i.e. the distance between the planes PR-3 and PR-4 for a given transverse coordinate of the object is 95 μm.

The obtained experimental data of figure 2 - figure 10 demonstrate the achievement of a technical result, however, the greatest efficiency is achieved under optimal conditions for the implementation of the proposed method:

- monochromatic lighting of the subject;

- small pixel size and a large number of matrix pixels;

- ensuring the registration of the hologram not in the plane of the paraxial image, but in the field of Fresnel diffraction, depending on the size of the image details.

Note that the method allows you to fully correct the aberrations associated with defocusing, other aberrations are corrected to the extent that they are compensated by defocusing.

The industrial applicability of the invention is confirmed by using the method for quantifying and improving the image quality of planktonic particles in an experimental complex for underwater registration of digital holograms of particles, described in more detail in the authors [6].

The technical result of the invention is to expand the scope, increasing the efficiency and quality of the hologram correction of lens aberrations.

List of sources used

1. Weinberg VB, Sattarov D.K. Optics of optical fibers. Ed. 2nd, rev. and add., L .: Engineering (Leningrad. Dep.), 1977, p. 25, Fig. eighteen.

2. Patent RU 2244330, IPC ⁷ G02B 9/34, G02B 13/18, Objective, 2005. Prototype.

3. Demin V.V., Donchenko V.A. A method for modeling the optical characteristics of atmospheric aerosol // A.S. 1245873 USSR, MKI ³ G01B 9/021, Bull. No. 27, 1986.

4. Schnars U. Digital Hologram Recording, Numerical Reconstruction, and Related Techniques / Schnars U., Jueptner W. - Berlin: Sprinder, 2005 .-- 164 p.

5. Dyomin V.V., Olshukov A.S. Technique for Estimation of Quality of the Particles Images Reconstructed from Digital Holograms // Adaptive Optics: Analysis and Methods; Computational Optical Sensing and Imaging; Digital Holography and Three-Dimensional Imaging; and Signal Recovery and Synthesis (The Optical Society of America, Washington, DC, 2007), DTuB2. ISBN 1-55752-838-1.

6. Demin V.V., Polovtsev I.G., Olshukov A.S., Kamenev D.V. The experimental complex and software for developing the process of underwater registration of digital holograms of particles // Holography: theoretical and applied issues. Materials of the XXVIII School-Symposium on Holography and Coherent Optics. Nizhny Novgorod, August 22-26, 2013 / Ed. ed. Yu.N. Zakharov. - Nizhny Novgorod: Publishing House of the Nizhny Novgorod University, 2013 .-- S. 100-105.

Claims (1)

A method for correcting lens aberrations, including the use of a corrective hologram optical element, characterized in that the corrective hologram optical element is performed in the form of a digital hologram, for which, by positioning the CCD matrix behind the plane of the paraxial image of the object, the defocused image constructed by the lens, taken as a digital axial hologram, is recorded images with which, using digital holography methods, hologram fragments are restored in layers ents of the entire image, after which the restored fragments of the image are brought to one plane.

Images