Birefringent lens, and system and method for realizing FINCH imaging based on birefringent lens

Abstract

The invention discloses a birefringence lens and a system and method for realizing FINCH imaging based on the birefringence lens, the birefringence lens comprises a birefringence generation module and an optical path difference compensation module, the birefringence generation module comprises a first birefringence lens and a first lens, and generates a combined focal plane and a holographic plane; the optical path difference compensation module comprises a third birefringent lens, the optical axis of the third birefringent lens and the optical axis of the first birefringent lens are in an orthogonal relation, the focal power symbols of the third birefringent lens and the first birefringent lens are the same, and the optical path difference generated by the first birefringent lens is compensated and controlled within the coherence length of light. And the total optical path of the formed first polarized light is close to that of the second polarized light. According to the invention, one or two groups of birefringent lenses with the same focal power symbol are used for compensating the optical path difference, the curvature radiuses of the two surfaces of the lenses are controlled, so that the thicknesses of all radial positions are very close, and the error is within a smaller range for all light rays penetrating through the lens.

Description

Technical Field

[0001] The present invention relates to the field of image technology, and in particular, to a birefringent lens, a FINCH imaging system and method implemented based on the birefringent lens. Background Art

[0002] Fresnel incoherent correlation holography (FINCH) technology is a method for recording and reconstructing three-dimensional object holographic images. This technology divides the incident light beam into two parts through a beam splitting device and focuses them on different planes, and forms a holographic image by generating an interference effect in the overlapping area. Subsequently, by analyzing these images, the three-dimensional image of the sample can be reconstructed. This technology uses an incoherent light source for illumination, and only needs to collect a single image to double the spatial resolution to the coherent diffraction limit. In addition, it can achieve an extremely large depth of field range through digital focusing technology and is easy to integrate into existing optical microscope systems, showing broad application potential.

[0003] The commonly used beam splitting elements in a FINCH system mainly include three types: a spatial light modulator, which separates the light beam through its polarization selectivity function; a birefringent lens, which uses the characteristic that birefringent materials have different refractive indices for light with different linear polarization states to achieve beam splitting; a metasurface device, such as a geometric phase lens, which achieves beam splitting through the principle that light with different optical rotation states has different refractive indices. However, there are still such defects at present: the spatial light modulator has large chromatic aberration, aberration, discrete error and other deviations, which will reduce the imaging quality; the manufacturing and mass production of metasurface devices are extremely difficult.

[0004] Therefore, the birefringent lens is the most promising FINCH beam splitting device to be popularized. Birefringent materials, such as barium metaborate crystals and quartz crystals, have been widely used in optical systems because they can distinguish light with different polarization states. This characteristic endows the birefringent lens with unique advantages in polarization light modulation, wavefront control and optical path difference generation. One of the major difficulties in applying the birefringent lens to FINCH is to control the optical path difference between the two separated light beams to be as small as possible, making it less than the coherence length of light, so that a hologram can be formed by interference. Summary of the Invention

[0005] The present invention aims at the deficiencies in the prior art and provides a birefringent lens, a FINCH imaging system and method implemented based on the birefringent lens.

[0006] A birefringent lens includes a birefringence generation module and an optical path difference compensation module; The birefringence generation module includes a first birefringent lens and a first lens, and generates a combined focal plane and a holographic plane; The optical path difference compensation module includes a third birefringent lens, and the optical axis of the third birefringent lens is orthogonal to the optical axis of the first birefringent lens, that is, the direction of the optical axis of the third birefringent lens is perpendicular to the direction of the optical axis of the first birefringent lens, and they have the same sign of optical power; The incident light is diverged by the first birefringent lens into two beams of light with different polarization directions, namely the first polarized light and the second polarized light; The first polarized light and the second polarized light are focused by the first lens and then incident on the third birefringent lens, and are diverged again into two beams of light with different polarization directions. The third birefringent lens compensates for the optical path difference generated by the first birefringent lens and controls the optical path difference within the coherence length of light, so that the total optical paths of the formed first polarized light and second polarized light are close.

[0007] As an implementable embodiment, the optical path difference compensation module further includes a second lens, and the second lens and the third birefringent lens form a first doublet lens; The first doublet lens diverges the focused first polarized light and second polarized light again into two beams of light with different polarization directions.

[0008] As an implementable embodiment, the optical path difference generated by the first birefringent lens is expressed as: ; If , then an optical path difference of is generated at the third birefringent lens, , when , optical path difference compensation is achieved ; Among them, respectively represent the optical path difference generated by the first birefringent lens and the optical path difference generated by the third birefringent lens, respectively represent the central thicknesses of the first birefringent lens and the third birefringent lens, represents the refractive index difference between the two beams of light in the first birefringent lens, respectively represent the refractive indices when light propagates along the ordinary axis and extraordinary axis of the birefringent material, represents the refractive index difference between the two beams of light in the third birefringent lens.

[0009] As an implementable embodiment, the birefringence generation module further includes a second birefringent lens, and the optical path difference compensation module further includes a fourth birefringent lens; The first birefringent lens and the second birefringent lens form a second doublet lens, and the third birefringent lens and the fourth birefringent lens form a third doublet lens; The second doublet lens disperses the incident light into two beams of light with different polarization directions, namely the first polarized light and the second polarized light, and forms focused polarized light after being focused and adjusted by the first lens; The focused polarized light enters the third doublet lens, and the focused polarized light is again dispersed into two beams of light with different polarization directions. The two beams of light with different polarization directions propagate along different paths, thereby forming different focal points.

[0010] As an implementable mode, the optical axis of the first birefringent lens is perpendicular to the optical axis of the second birefringent lens, the optical axis of the third birefringent lens is perpendicular to the optical axis of the fourth birefringent lens, the optical axis direction of the first birefringent lens is the same as the optical axis direction of the fourth birefringent lens, but the optical power signs are opposite; the optical axis direction of the second birefringent lens is the same as the optical axis direction of the third birefringent lens, and the optical power signs are opposite; the fourth birefringent lens is used to compensate for the optical path difference generated by the second birefringent lens, and the third birefringent lens is used to compensate for the optical path difference generated by the first birefringent lens.

[0011] As an implementable mode, the optical path difference generated by the first birefringent lens , the optical path difference generated by the second birefringent lens ; the optical path difference generated by the fourth birefringent lens , the optical path difference generated by the third birefringent lens , then the total optical path difference is ; The relationship between the thicknesses at the centers of each lens: 、 , then the combination of the first birefringent lens and the third birefringent lens compensates for the optical path difference ; the combination of the second birefringent lens and the fourth birefringent lens compensates for the optical path difference , 、 When, then the compensation of the optical path difference is achieved; Among them, respectively represent the optical path difference generated by the first birefringent lens, the optical path difference generated by the second birefringent lens, the optical path difference generated by the third birefringent lens, and the optical path difference generated by the fourth birefringent lens, respectively represent the central thicknesses of the first birefringent lens, the second birefringent lens, the third birefringent lens, and the fourth birefringent lens, represents the refractive index difference between the two beams of light in the first birefringent lens and the fourth birefringent lens, represents the refractive index difference between the two beams of light in the second birefringent lens and the third birefringent lens.

[0012] A FINCH imaging system implemented based on a birefringent lens includes an optical system, a polarization module, a birefringent lens, a quarter-wave plate, and a polarization camera; After the sample light is collimated by a standard optical system, it forms polarized light through the polarization module; The polarized light enters the birefringent lens and is divided into the first polarized light and the second polarized light with orthogonal polarizations, and the optical path difference is compensated to form different focal points and focus on different focal planes; The quarter-wave plate converts the first polarized light and the second polarized light into the first polarized light and the second polarized light with orthogonal circular polarizations and interferes with each other to construct a holographic image, and the polarization camera acquires the holographic image, wherein the polarization camera is located at the maximum overlap surface, that is, the intersection of the first polarized light and the second polarized light with orthogonal circular polarizations.

[0013] As an implementable manner, the polarization camera includes a plurality of pixel units, and a micro linear polarizer grid is respectively arranged in front of each pixel unit, and the micro linear polarizer grid can collect light with different polarization states; The micro linear polarizer grid is provided with four equally spaced polarization directions, which are 0, π / 4, π / 2, and 3π / 4 respectively, and are arranged in a repeated manner; When the phase delay difference between the first polarized light and the second polarized light with orthogonal circular polarizations is 0, π / 2, π, and 3π / 2, the synthesized linearly polarized light is respectively in the directions of 0, π / 4, π / 2, and 3π / 4, and the images generated when the polarization phase difference is 0, π / 2, π, and 3π / 2 are used as a polarization image set, and the polarization image set includes a first polarization image, a second polarization image, a third polarization image, and a fourth polarization image.

[0014] As an implementable manner, the following steps are further included: Based on the first polarization image, the second polarization image, the third polarization image, and the fourth polarization image, a complex amplitude holographic image is obtained; According to the hologram propagation distance and the complex amplitude holographic image, image reproduction calculation is performed in the Fresnel diffraction region to obtain a reproduced image; The first polarization image, the second polarization image, the third polarization image, and the fourth polarization image are respectively represented as follows:

[0015]

[0016]

[0017]

[0018] Then the complex amplitude light field image is represented as follows:

[0019] The reproduced image is represented as follows:

[0020] Wherein, , represents the light ray at The projection of the plane and the included angle with the axis, which represents the projection of the light ray on the plane and the included angle with the axis, representing the reconstruction distance of the hologram, expressed as: , when the incident light beam is a plane wave, , then it is converted to: , represents the distance between the center of the birefringent lens and the polarization camera, respectively represent the focal lengths of the birefringent lens; represents the radius of curvature of the light beam before it is incident on the birefringent lens, , , , respectively represent the subscripts corresponding to the polarization images indicating the polarization directions of 0°, 45°, 90°, and 135°, represents the complex amplitude holographic image, represents the reconstructed image, represents the Fourier transform, represents the inverse Fourier transform, represents the complex amplitude transfer function of Fresnel diffraction, respectively represent the light fields of the first polarized light, i.e., the S light, and the second polarized light, i.e., the P light, represents the imaginary unit, represents the wave number.

[0021] A method for implementing a FINCH imaging system based on a birefringent lens includes the following steps: After the sample light is collimated by a standard optical system, it forms polarized light through a polarization module; The polarized light enters the birefringent lens and is divided into the first polarized light and the second polarized light with orthogonal polarizations, and the optical path difference is compensated, and they are focused on different focal planes. Specifically: the first birefringent lens diverges the polarized light into two light beams with different polarization directions, i.e., the first polarized light and the second polarized light. The first polarized light and the second polarized light are focused by the first lens and then incident on the third birefringent lens, and are diverged again into two light beams with different polarization directions. The third birefringent lens compensates for the optical path difference generated by the first birefringent lens, so that the total optical paths of the formed first polarized light and second polarized light are close, and the optical path difference is controlled within the coherence length of the light; The quarter-wave plate converts the first polarized light and the second polarized light into the first polarized light and the second polarized light with orthogonal circular polarizations and interferes with each other to construct a holographic image, and the polarization camera acquires the holographic image.

[0022] Due to the adoption of the above technical solutions, the present invention has remarkable technical effects: The present invention uses one or two groups of birefringent lenses with the same optical power sign to compensate for the optical path difference, and controls the curvature radii of both sides of the lenses so that the thickness at each radial position is very close, that is, the optical path difference compensation is not only satisfied at the center of the lens, but its error is also within a small range for all the light rays passing through the lens.

[0023] Compared with the prior art solution that uses a birefringent flat plate to compensate for the optical path difference, the optical path difference compensation of the present invention is more thorough, and higher interference contrast and a larger imaging range can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0025] Figure 1 is a schematic diagram of the birefringent lens of the present invention; Figure 2 is a structural schematic diagram of the birefringent lens of the present invention; Figure 3 is a detailed schematic diagram of a specific embodiment of the birefringent lens; Figure 4 is a detailed schematic diagram of another specific embodiment of the birefringent lens; Figure 5 is a schematic diagram of the FINCH imaging system implemented based on the birefringent lens of the present invention; Figure 6 is a schematic diagram of the micro linear polarizer grid of the polarization camera of the present invention; Figure 7 is a schematic flow diagram of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] The following will further describe the present invention in detail with reference to the embodiments. The following embodiments are explanations of the present invention, and the present invention is not limited to the following embodiments.

[0027] Embodiment 1: A birefringent lens, as Figure 1 and 2 shown, includes a birefringence generation module 100 and an optical path difference compensation module 200; The birefringence generation module 100 includes a first birefringent lens 110 and a first lens 120, which generate a combined focal plane and a holographic plane; The optical path difference compensation module 200 includes a third birefringent lens 220. The optical axis of the third birefringent lens 220 is orthogonal to the optical axis of the first birefringent lens 110, that is, the direction of the optical axis of the third birefringent lens 220 is perpendicular to the direction of the optical axis of the first birefringent lens 110, and they have the same sign of optical power. The incident light is diverged by the first birefringent lens 110 into two beams of light with different polarization directions, namely the first polarized light and the second polarized light. The first polarized light and the second polarized light are focused by the first lens 120 and then incident on the third birefringent lens 220, and are diverged again into two beams of light with different polarization directions. The third birefringent lens 220 compensates for the optical path difference generated by the first birefringent lens 110 and controls the optical path difference within the coherence length of light, so that the total optical paths of the formed first polarized light and second polarized light are close.

[0028] In the actual experimental process, the optical path difference compensation module can be a birefringent flat plate or a combination of a concave lens and a convex lens. In the present invention, a lens combination is used. The advantage of using a combination of a concave lens and a convex lens to compensate for the optical path difference is that the optical path difference compensation effect is better, and it can make the marginal rays and the central rays correctly compensate for the optical path difference in the same way. In the present invention, a fixed lens combination is used, that is, all lenses are fixed according to their relative positions to form a lens assembly as a whole. The fixed lens combination has the following advantages: the first is that it is convenient to carry, load and debug; the second is that the optical path difference compensation and aberration correction are more accurate.

[0029] The principle of optical path difference compensation is: the total optical path is the thickness of each layer of medium through which light propagates d i and the refractive index n i function. The optical path difference OPD of the two polarized light beams has a geometric component caused by different physical paths, but this component is less than the coherence length and will not prevent light from interfering. However, in actual optical path difference compensation, the refractive index difference of the birefringent lens is sufficient to cause an optical path difference greater than the coherence length. To observe interference, this component must be compensated. Assume d BRL is the thickness of the birefringent lens through which the light passes. A compensating birefringent lens with a thickness equal to d BRL and cut along the same crystal axis direction is placed in the optical system. Its extraordinary axis rotates 90° relative to the extraordinary axis of the birefringent lens in the transverse plane. The light polarized along the ordinary axis in the birefringent lens is polarized along the extraordinary axis of the compensating birefringent lens, and vice versa. In this way, the surface ΔOPD of the birefringent lens is offset by the compensating birefringent lens.

[0030] See the appendix Figure 3 as shown. The appendix Figure 3This is a specific embodiment. The optical path difference compensation module 200 further includes a second lens 2101. The third birefringent lens 220 and the second lens 2101 form a first doublet lens 201. The first doublet lens 201 diverges the first polarized light and the second polarized light after focusing into two beams of light with different polarization directions again.

[0031] With this structure, the optical path difference generated by the first birefringent lens 110 is expressed as: ; If , then an optical path difference of is generated at the third birefringent lens, . When , optical path difference compensation is achieved . respectively represent the optical path difference generated by the first birefringent lens and the optical path difference generated by the third birefringent lens, respectively represent the central thicknesses of the first birefringent lens and the third birefringent lens, represents the refractive index difference between the two beams of light in the first birefringent lens, respectively represent the refractive indices of the two beams of light when light propagates along the ordinary axis and the extraordinary axis of the birefringent material, represents the refractive index difference between the two beams of light in the third birefringent lens.

[0032] Figure 3 The working principle of the birefringent lens is as follows: The light rays emitted from the object plane are diverged by the first birefringent lens 110 into two light rays with different polarization directions, namely S-polarized light and P-polarized light. After being focused by the first lens 120, they reach the first doublet lens 201, and a birefringence effect similar to that of the first birefringent lens 110 occurs again. The S light, i.e., the first polarized light, and the P light, i.e., the second polarized light, propagate along different paths and form different focal points.

[0033] Since the optical axis direction of the third birefringent lens 220 is perpendicular to the optical axis direction of the first birefringent lens 110 and they have the same sign of optical power, it can be used to compensate the optical path difference between the two beams of light. Finally, the two polarized lights with different focal lengths can produce a coherent superposition effect on the subsequent holographic imaging plane. The optical path difference is: The optical path difference generated by the first birefringent lens 110 is . Let's assume that here , then an optical path difference will be generated at the third birefringent lens 220. . Then, by setting , optical path difference compensation can be achieved .

[0034] In this embodiment, a third birefringent lens with the same optical power sign as that of the first birefringent lens is used for optical path difference compensation, and the curvature radii of both surfaces of the lens are designed such that the thickness at each radial position is very close, that is, It is not only satisfied at the center of the lens, but the error is also within a small range for all the light rays passing through the lens. Compared with the solution using a birefringent plate for optical path difference compensation, the optical path difference compensation of the present invention is more thorough, and higher interference contrast and a larger imaging range can be achieved.

[0035] Figure 4 Another design of a birefringent lens is given. Since multiple birefringent lenses can achieve a larger range of focal length separation and optical path compensation, in an actual embodiment, Figure 4 The structure is used to fabricate the relevant birefringent lens. The birefringent lens in this example is suitable for being fabricated using materials with a small birefringence such as quartz crystal or magnesium fluoride. In this embodiment, the birefringence generation module 100 further includes a second birefringent lens 130; the optical path difference compensation module 200 further includes a fourth birefringent lens 2102; the first birefringent lens 110 and the second birefringent lens 130 form a second doublet lens 101, and the third birefringent lens 220 and the fourth birefringent lens 2102 form a third doublet lens 202; the second doublet lens 101 disperses the incident light into two beams of light with different polarization directions, namely the first polarized light and the second polarized light, which are focused and adjusted by the first lens 120 to form focused polarized light; the focused polarized light enters the third doublet lens 202, and the focused polarized light is dispersed into two beams of light with different polarization directions again. The two beams of light with different polarization directions propagate along different paths, and thus different focal points are formed.

[0036] Then the entire birefringent lens includes a first birefringent lens 110, a second birefringent lens 130, a first lens 120, a third birefringent lens 220, and a fourth birefringent lens 2102. The first birefringent lens 110 and the second birefringent lens 130 form a second doublet lens 101, and the third birefringent lens 220 and the fourth birefringent lens 2102 form a third doublet lens 202.

[0037] The optical axes of the first birefringent lens 110 and the second birefringent lens 130 are perpendicular to each other, so that the light is divided into two beams of light with different polarization directions, namely S-polarized light and P-polarized light, and then is focused and adjusted by the first lens 120. After the light enters the third doublet lens 202, a birefringence effect similar to that of the second doublet lens 101 occurs again. The S light, that is, the first polarized light, and the P light, that is, the second polarized light, still propagate along different paths, forming different focal points.

[0038] Since the optical axes of the third doublet lens 202 are perpendicular to each other, the paths of the two polarized light beams will change again. The optical axis direction of the fourth birefringent lens 2102 is the same as that of the first birefringent lens 110, but the sign of the optical power is opposite. The optical axis direction of the third birefringent lens 220 is the same as that of the second birefringent lens 130, and the sign of the optical power is also opposite. The fourth birefringent lens 2102 is used to compensate for the optical path difference of the second birefringent lens 130, and the third birefringent lens 220 is used to compensate for the optical path difference of the first birefringent lens 110. Finally, the two polarized light beams can produce a coherent superposition effect on the subsequent holographic imaging plane. The optical path difference is calculated as follows: Optical path difference generated by the first birefringent lens 110 , and the optical path difference generated by the second birefringent lens 130 ; the optical path difference generated by the fourth birefringent lens 2102 , and the optical path difference generated by the third birefringent lens 220 , then the total optical path difference is ; the relationship between the thicknesses at the centers of each lens: 、 , then the combination of the first birefringent lens 110 and the third birefringent lens 220 compensates for the optical path difference ; the combination of the second birefringent lens 130 and the fourth birefringent lens 2102 compensates for the optical path difference , 、 , when, then the optical path difference compensation is achieved; further design the curvature radii of both sides of each lens so that the above 、 are approximately satisfied at each radial position, that is The deviation of relative to 0 is within a small range for all the light rays passing through the lens, that is, the optical path difference of the entire lens is compensated.

[0039] Embodiment 2: A FINCH imaging system implemented based on a birefringent lens, as Figure 5 shown, includes a standard optical system 1, a polarization module 2, i.e., a polarizer, a birefringent lens 0, a quarter-wave plate 3, and a polarization camera 4; After the sample light is collimated by the standard optical system 1, it forms polarized light through the polarization module 2; the polarized light enters the birefringent lens 0 and is divided into the first polarized light and the second polarized light with orthogonal polarizations, and the optical path difference is compensated, forming different focal points and focusing on different focal planes; the quarter-wave plate 3 converts the first polarized light and the second polarized light into the first polarized light and the second polarized light with orthogonal circular polarizations and interferes with each other to construct a holographic image, and the polarization camera acquires the holographic image, where the polarization camera 4 is located at the maximum overlap surface. It can be seen in the appendix Figure 2 The red line shown in represents the maximum overlap surface.

[0040] In one embodiment, the polarization camera 4 includes a plurality of pixel units, and a micro linear polarizer grid is respectively arranged in front of each pixel unit. As Figure 6 shown, the micro linear polarizer grid can collect light with different polarization states; the micro linear polarizer grid has four equally spaced polarization directions, which are 0, π / 4, π / 2, and 3π / 4 respectively, and are arranged in a repeated manner; when the phase delays of the first polarized light and the second polarized light of orthogonal circular polarization differ by 0, π / 2, π, and 3π / 2, the synthesized linearly polarized light is respectively in the 0, π / 4, π / 2, and 3π / 4 directions. The images generated when the polarization phase difference is 0, π / 2, π, and 3π / 2 are used as a polarization image set, and the polarization image set includes a first polarization image, a second polarization image, a third polarization image, and a fourth polarization image.

[0041] In one embodiment, the following steps are further included: Based on the first polarization image, the second polarization image, the third polarization image, and the fourth polarization image, a complex amplitude holographic image is obtained; according to the hologram propagation distance and the complex amplitude holographic image, image reconstruction calculation is performed in the Fresnel diffraction region to obtain a reconstructed image; wherein, the first polarization image, the second polarization image, the third polarization image, and the fourth polarization image are respectively expressed as follows:

[0042]

[0043]

[0044]

[0045] Then the complex amplitude light field image is expressed as follows:

[0046] The reconstructed image is expressed as follows:

[0047] Wherein, , represents the angle between the projection of the light ray on the plane and the axis, represents the angle between the projection of the light ray on the plane and the axis, represents the reconstruction distance of the hologram, which is expressed as: , when the incident light beam is a plane wave, , then it is converted to: , Represents the distance between the center of the birefringent lens and the polarization camera, respectively represent the focal lengths of the birefringent lens; Represents the radius of curvature of the light beam before it enters the birefringent lens, 、 、 、 respectively represent the subscripts corresponding to the polarization images indicating the polarization directions of 0°, 45°, 90°, and 135°, Represents the complex amplitude holographic image, Represents the reconstructed image, Represents the Fourier transform, Represents the inverse Fourier transform, Represents the complex amplitude transfer function of Fresnel diffraction, respectively represent the optical fields of the first polarized light, i.e., the S light, and the second polarized light, i.e., the P light, Represents the imaginary unit, Represents the wave number.

[0048] Figure 5 The implementation process is as follows: The light emitted from the object plane is collimated by a standard optical system, then becomes polarized light through a polarizer and enters the birefringent lens of the present invention, is divided into two orthogonally polarized light beams, and the optical path difference is compensated, and then focused on different focal planes. The quarter-wave plate then converts the light beam into orthogonal circular polarization, and then interferes with each other to create a hologram, which is captured by the polarization camera placed at the maximum overlap plane.

[0049] In front of each pixel unit of the polarization camera, there is an inlaid micro wire polarizer grid, which can independently collect light of different polarization states. The micro wire polarizer grid has four equally spaced polarization directions (0, π / 4, π / 2, 3π / 4), which are repeatedly arranged on the image sensor. For the schematic diagram, refer to Figure 6 as shown. When the phase delay between the P light, i.e., the second polarized light, and the S light, i.e., the first polarized light, of the orthogonal circular polarization is 0, π / 2, π, and 3π / 2, the synthesized linearly polarized light is respectively in the directions of 0, π / 4, π / 2, and 3π / 4. Therefore, four holograms with phase differences of 0, π / 2, π, and 3π / 2 can be collected by the polarization camera in one imaging, that is, a four-step phase-shifted hologram is obtained by single exposure. Let the electric field components of the P light, i.e., the second polarized light, and the S light, i.e., the first polarized light, be E P and E S , then the first polarized image, the second polarized image, the third polarized image, and the fourth polarized image collected by the polarization camera are expressed as:

[0050] Thus, the complex amplitude optical field image is: , and then according to the wavelengthλ 、Wavenumber k = 2π / λ and U ,the reconstructed image is calculated in the Fresnel diffraction region and is expressed as follows:

[0051] where , cosα and cosβ are the angles between the projections of the light rays on the x - z plane and the y - z plane and the z axis respectively, and z r is the reconstruction distance of the hologram:

[0052] where z h is the distance between the center of the birefringent lens and the polarization camera, represent the focal lengths of the birefringent lens respectively, z d is the radius of curvature of the light beam before it enters the birefringent lens. When the incident light beam is a plane wave, z d = ∞ the above formula is simplified to:

[0053] Compared with the main features of the traditional system, the innovation of this system lies in the use of a combination of a fixed concave lens and a convex lens, which has better optical path difference compensation and aberration correction effects, can make the marginal rays and the central rays correctly compensate the optical path difference in the same way, and is convenient for carrying, installation and debugging.

[0054] Example 3: A method for implementing a FINCH imaging system based on a birefringent lens, as Figure 7 ,includes the following steps: S100. After the sample light is collimated by a standard optical system, it forms polarized light through a polarization module; S200. The polarized light enters the birefringent lens and is divided into the first polarized light and the second polarized light with orthogonal polarizations, and the optical path difference is compensated and focused on different focal planes. Specifically: the first birefringent lens diverges the polarized light into two light beams with different polarization directions, namely the first polarized light and the second polarized light. The first polarized light and the second polarized light are focused by the first lens and then incident on the third birefringent lens, and are diverged again into two light beams with different polarization directions. The third birefringent lens compensates the optical path difference generated by the first birefringent lens, so that the total optical path of the formed first polarized light and the second polarized light is close, and the optical path difference is controlled within the coherence length of the light; The S300 and the quarter-wave plate convert the first polarized light and the second polarized light into the first polarized light and the second polarized light with orthogonal circular polarization and interfere with each other to construct a holographic image, and the polarization camera acquires the holographic image.

[0055] All changes and modifications made without departing from the spirit and scope of the present invention, and all equivalent technical solutions also fall within the scope of the present invention.

[0056] Each embodiment in this specification is described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other.

[0057] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a device, or a computer program product. Therefore, the present invention can be implemented in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can be implemented in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0058] The present invention is described with reference to the flowcharts and / or block diagrams of methods, terminal devices (systems), and computer program products according to the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, and the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal devices generate a device for realizing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0059] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing terminal device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured product including an instruction device, and the instruction device realizes the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0060] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device, so that a series of operation steps are executed on the computer or other programmable terminal device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable terminal device provide for implementing the process Figure 1 one process or multiple processes and / or blocks Figure 1 steps for the functions specified in one block or multiple blocks.

[0061] It should be noted that: "An embodiment" or "embodiments" mentioned in the specification means that the specific features, structures or characteristics described in connection with the embodiments are included in at least one embodiment of the present invention. Therefore, the phrases "an embodiment" or "embodiments" that appear throughout the specification do not necessarily all refer to the same embodiment.

[0062] In addition, it should be noted that for the specific embodiments described in this specification, the shapes, names of the components, etc. can be different. Any equivalent or simple changes made according to the structure, features and principles described in the inventive concept of the present invention are included in the protection scope of the present invention. Those skilled in the art to which the present invention pertains can make various modifications or supplements to the described specific embodiments or use similar ways to replace them, as long as they do not deviate from the structure of the present invention or exceed the scope defined by this claims, they should fall within the protection scope of the present invention.

Claims

1. A birefringent lens, characterized in that, It includes a birefringence generation module and an optical path difference compensation module; The birefringence generation module includes a first birefringent lens and a first lens, which generate a combined focal plane and a holographic plane; The optical path difference compensation module includes a third birefringent lens. The optical axis of the third birefringent lens is orthogonal to the optical axis of the first birefringent lens, that is, the direction of the optical axis of the third birefringent lens is perpendicular to the direction of the optical axis of the first birefringent lens, and they have the same sign of optical power; The incident light is diverged by the first birefringent lens into two beams of light with different polarization directions, namely the first polarized light and the second polarized light; The first polarized light and the second polarized light are focused by the first lens and then incident on the third birefringent lens, and are diverged again into two beams of light with different polarization directions. The third birefringent lens compensates for the optical path difference generated by the first birefringent lens and controls the optical path difference within the coherence length of light, so that the total optical paths of the formed first polarized light and second polarized light are close.

2. The birefringent lens according to claim 1, characterized in that, The optical path difference compensation module further includes a second lens, and the second lens and the third birefringent lens form a first doublet lens; The first doublet lens diverges the focused first polarized light and second polarized light again into two beams of light with different polarization directions.

3. The birefringent lens according to claim 1 or 2, characterized in that, The optical path difference generated by the first birefringent lens is expressed as: ; If , an optical path difference of is generated at the third birefringent lens. When , optical path difference compensation is achieved. ; wherein, respectively represent the optical path differences generated by the first birefringent lens and the third birefringent lens, respectively represent the central thicknesses of the first birefringent lens and the third birefringent lens, represents the refractive index difference between the two beams of light in the first birefringent lens, respectively represent the refractive indices when light propagates along the ordinary axis and the extraordinary axis of the birefringent material, represents the refractive index difference between the two beams of light in the third birefringent lens.

4. The birefringent lens according to claim 1, wherein, The birefringence generation module further includes a second birefringent lens, and the optical path difference compensation module further includes a fourth birefringent lens; The first birefringent lens and the second birefringent lens form a second doublet lens, and the third birefringent lens and the fourth birefringent lens form a third doublet lens; The second doublet lens disperses the incident light into two beams of light with different polarization directions, namely the first polarized light and the second polarized light, and after being focused and adjusted by the first lens, forms focused polarized light; The focused polarized light enters the third doublet lens, and the focused polarized light is dispersed again into two beams of light with different polarization directions. The two beams of light with different polarization directions propagate along different paths, and thus form different focal points.

5. The birefringent lens according to claim 4, wherein The optical axis of the first birefringent lens is perpendicular to the optical axis of the second birefringent lens. The optical axis of the third birefringent lens is perpendicular to the optical axis of the fourth birefringent lens. The direction of the optical axis of the first birefringent lens is the same as the direction of the optical axis of the fourth birefringent lens, but they have opposite signs of optical power; the direction of the optical axis of the second birefringent lens is the same as the direction of the optical axis of the third birefringent lens, and they have opposite signs of optical power; the fourth birefringent lens is used to compensate for the optical path difference generated by the second birefringent lens, and the third birefringent lens is used to compensate for the optical path difference generated by the first birefringent lens.

6. The birefringent lens according to claim 5, wherein Optical path difference generated by the first birefringent lens , optical path difference generated by the second birefringent lens ; Optical path difference generated by the fourth birefringent lens , optical path difference generated by the third birefringent lens , then the total optical path difference is ; Relationship of thicknesses at centers of respective lenses: and then the first birefringent lens and the third birefringent lens are combined to compensate for the optical path difference ; The combination of the second birefringent lens and the fourth birefringent lens compensates the optical path difference , 、 When this occurs, optical path difference compensation is achieved; Among them, respectively represent the optical path differences generated by the first birefringent lens, the optical path differences generated by the second birefringent lens, the optical path differences generated by the third birefringent lens, and the optical path differences generated by the fourth birefringent lens, respectively represent the central thicknesses of the first birefringent lens, the second birefringent lens, the third birefringent lens, and the fourth birefringent lens, represents the refractive index difference between the two beams of light in the first birefringent lens and the fourth birefringent lens, represents the refractive index difference between the two beams of light in the second birefringent lens and the third birefringent lens.

7. A FINCH imaging system implemented based on a birefringent lens, characterized in that, It includes an optical system, a polarization module, a birefringent lens, a quarter-wave plate and a polarization camera; The sample light is collimated by a standard optical system and then forms polarized light through the polarization module; The polarized light enters the birefringent lens and is split into the first polarized light and the second polarized light with orthogonal polarizations, and the optical path difference is compensated, forming different focal points and focusing on different focal planes; The quarter-wave plate converts the first polarized light and the second polarized light into the first polarized light and the second polarized light with orthogonal circular polarizations and they interfere with each other to construct a holographic image. The polarization camera acquires the holographic image, where the polarization camera is located at the maximum overlap surface, that is, the intersection of the first polarized light and the second polarized light with orthogonal circular polarizations.

8. The FINCH imaging system implemented based on a birefringent lens according to claim 7, characterized in that, The polarization camera includes a plurality of pixel units, and a micro linear polarizer grid is respectively arranged in front of each pixel unit. The micro linear polarizer grid can collect light with different polarization states; The micro linear polarizer grid is provided with four equally spaced polarization directions, which are 0, π / 4, π / 2, and 3π / 4 respectively, and are arranged in a repeated manner; When the phase delays of the first polarized light and the second polarized light of orthogonal circular polarization differ by 0, π / 2, π, and 3π / 2, the synthesized linearly polarized light is respectively in the directions of 0, π / 4, π / 2, and 3π / 4. The images generated when the polarization phase difference is 0, π / 2, π, and 3π / 2 are used as a polarization image set. The polarization image set includes a first polarization image, a second polarization image, a third polarization image, and a fourth polarization image.

9. The FINCH imaging system implemented based on a birefringent lens according to claim 8, wherein It further includes the following steps: Based on the first polarization image, the second polarization image, the third polarization image, and the fourth polarization image, a complex amplitude holographic image is obtained; According to the hologram propagation distance and the complex amplitude holographic image, image reproduction calculation is performed in the Fresnel diffraction region to obtain a reproduced image; The first polarization image, the second polarization image, the third polarization image, and the fourth polarization image are respectively represented as follows: Then the complex amplitude optical field image is represented as follows: The reproduced image is represented as follows: Among them, , represents the angle between the projection of the light ray on the plane and the axis, represents the angle between the projection of the light ray on the plane and the axis, represents the reconstruction distance of the hologram, expressed as: , when the incident light beam is a plane wave, , then it is converted to: , represents the distance between the center of the birefringent lens and the polarization camera, respectively represent the focal lengths of the birefringent lenses; represents the radius of curvature of the light beam before it enters the birefringent lens, , , , respectively represent the subscripts corresponding to the polarization images indicating the polarization directions of 0°, 45°, 90°, and 135°, represents the complex amplitude holographic image, represents the reconstructed image, represents the Fourier transform, represents the inverse Fourier transform, represents the complex amplitude transfer function of Fresnel diffraction, respectively represent the optical fields of the first polarized light, i.e., the S light, and the second polarized light, i.e., the P light, represents the imaginary unit, represents the wave number.

10. A method for implementing a FINCH imaging system based on a birefringent lens, characterized in that, It includes the following steps: After the sample light is collimated by a standard optical system, it forms polarized light through a polarization module; The polarized light enters a birefringent lens and is divided into the first polarized light and the second polarized light of orthogonal polarization, and the optical path difference is compensated and focused on different focal planes. Specifically: the first birefringent lens diverges the polarized light into two beams of light with different polarization directions, that is, the first polarized light and the second polarized light. The first polarized light and the second polarized light are focused by the first lens and then incident on the third birefringent lens, and are diverged into two beams of light with different polarization directions again. The third birefringent lens compensates for the optical path difference generated by the first birefringent lens, so that the total optical paths of the formed first polarized light and second polarized light are close, and the optical path difference is controlled within the coherence length of light; A quarter-wave plate converts the first polarized light and the second polarized light into the first polarized light and the second polarized light of orthogonal circular polarization and interferes with each other to construct a holographic image, and the polarization camera acquires the holographic image.

Images