Optical system polarization aberration acquisition method

Abstract

This invention relates to the field of optical design, and more particularly to a method for obtaining polarization aberrations in an optical system. The method includes: S1: Tracing N rays using a three-dimensional polarization ray tracing algorithm to extract the corresponding biaxial attenuation-related Jones matrices and phase delay-related Jones matrices; S2: Fitting the Jones matrices and the Jones matrices using N directional Zernike polynomials to obtain the components of biaxial attenuation and phase delay, and reconstructing the biaxial attenuation and phase delay to obtain the polarization aberration distribution across the entire pupil of the optical system. This invention requires only a small number of rays to accurately obtain the polarization aberrations across the entire pupil, significantly reducing computational complexity. It also overcomes the limitations of existing simplified methods on the optical system structure, making it applicable to various complex optical systems.

Description

Technical Field

[0001] This invention belongs to the field of optical design technology, and in particular relates to a method for obtaining polarization aberrations in an optical system. Background Technology

[0002] Polarization aberration describes the changes in amplitude, phase, and polarization state of light as it passes through an optical system, and is a key factor affecting image quality and detection accuracy. With the widespread application of optical systems in high-precision fields such as photolithography, astronomical observation, and polarization remote sensing, polarization aberration has become a significant source of error. Therefore, accurately calculating the polarization aberration of an optical system and using it as an evaluation metric is a crucial step in the design of high-performance optical systems.

[0003] Polarization aberration is determined by the structural and thin-film parameters of the optical system and is closely related to the pupil coordinates, object position, and wavelength, exhibiting complex, multi-dimensional variations. To comprehensively evaluate the polarization aberration of an optical system, extensive calculations are required at different fields of view, aperture positions, and wavelengths.

[0004] Existing methods for obtaining polarization aberration rely on polarization ray tracing algorithms to calculate the polarization aberration of the optical system. These algorithms require extensive ray tracing across the entire pupil plane for each wavelength and field of view to obtain an accurate evaluation function, which undoubtedly consumes significant computational time. Especially with the deep integration of artificial intelligence and optics, automated design methods that iteratively optimize the structural parameters and thin-film properties of optical systems using intelligent algorithms and neural networks are emerging. While these methods reduce reliance on manual design experience and effectively approximate the global optimum, the computational complexity and time cost increase significantly because polarization aberration needs to be recalculated in each iteration.

[0005] To reduce computational burden, some simplified methods for obtaining polarization aberrations have been proposed in existing technologies. For example, the Pauli matrix fitting method only requires tracing data from three rays to estimate polarization aberrations, but its derivation is based on the paraxial approximation, which is only applicable to optical systems with small-angle incidence and planar symmetry, and can only cover three low-order polarization aberration components, thus limiting its applicability. Another method is to process a small amount of ray tracing data through interpolation to estimate the polarization aberration of the entire pupil, but the calculation results have large errors and are difficult to meet the requirements of high-precision applications.

[0006] In summary, existing methods for acquiring polarization aberrations present a trade-off between computational efficiency, applicability, and accuracy. Therefore, there is an urgent need for a method that can significantly improve computational efficiency while maintaining high accuracy, and is applicable to complex optical systems. Summary of the Invention

[0007] In view of this, the present invention aims to provide a method for obtaining polarization aberrations in an optical system, so as to solve the technical problems of existing polarization aberration acquisition methods, such as large computational load, long time consumption, strong dependence on plane symmetry and small angle incident conditions, and limited applicability.

[0008] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A method for obtaining polarization aberration in an optical system includes the following steps: S1: Track N rays using a three-dimensional polarization ray tracing algorithm and extract the Jones matrix corresponding to the bidirectional attenuation of the N rays. Jones matrix related to phase delay ; S2: Using N-term directional Zernik polynomials to transform the Jones matrix respectively and Jones Matrix By fitting the data, the components of biaxial attenuation and phase delay are obtained, and the biaxial attenuation and phase delay are reconstructed to obtain the polarization aberration distribution within the full pupil range of the optical system.

[0009] Furthermore, N≤36.

[0010] Furthermore, step S1 specifically includes the following steps: S11: Based on the calculation requirements of polarization aberration of the optical system, determine the wavelength and field of view to be analyzed, and determine the refractive index of the optical thin film; S12: N sampling points are uniformly selected within the pupil plane of the optical system. For each sampling point, the extended Jones matrix of the light ray on each optical surface is calculated, and the Jones pupil function of the N light rays at the exit pupil of the optical system is obtained by a three-dimensional polarization ray tracing algorithm. S13: Perform singular value decomposition on the Jones pupil function of N rays at the exit pupil of the optical system to extract the Jones matrix. and Jones Matrix .

[0011] Further, in step S12, the extended Jones matrix includes the extended Jones matrix of the reflective optical surface. and the extended Jones matrix of the transmission optical surface The expressions are as follows: ; ; in, This represents the Fresnel reflection coefficient of s-polarized light. This represents the Fresnel reflection coefficient of p-polarized light. This represents the Fresnel transmission coefficient of s-polarized light. This represents the Fresnel transmission coefficient of p-polarized light.

[0012] Furthermore, in step S12, the Jones pupil function is calculated as follows: The extended Jones matrix in the local coordinate system is transformed into the polarization ray tracing matrix in the global coordinate system using an orthogonal transformation matrix, and then further transformed into the Jones matrix in the exit pupil coordinate system. The calculation formula is as follows: ; ; in, This represents the polarization ray tracing matrix of the reflecting surface. This represents the polarization ray tracing matrix of the transmission surface. Denotes the orthogonal transformation matrix on the entrance pupil side. Express the pupil-side orthogonal transformation matrix. Indicates the first q Orthogonal transformation matrix of entrance pupil side of each optical surface Indicates the first q Orthogonal transformation matrix of the exit pupil side of each optical surface Indicates that the light passes through the first q After the optical surface, the Jones matrix at the exit pupil, Indicates the first q The polarization ray tracing matrix of an optical surface.

[0013] Furthermore, in step S13, the singular value decomposition of the Jones pupil function is performed as follows: ; in, J The Jones pupil function represents the distance of each ray from the exit pupil of the optical system. t Indicates average transmittance. Φ represents the scalar phase factor, and Φ represents the scalar phase. i Represents the imaginary unit. d Indicates the relative amplitude difference. These represent the relative phase difference; θ d Indicates the direction angle of the maximum transmission axis. θ r Indicates the direction angle of the fast axis. δ Indicates the elliptic deviation parameter. Represents the rotation matrix. α Indicates the rotation angle.

[0014] Furthermore, the Jones matrix obtained after decomposition for: ; The Jones matrix obtained after decomposition for: .

[0015] Furthermore, step S2 specifically includes the following steps: S21: Using N-term directional Zernik polynomials to transform the Jones matrix respectively and Jones Matrix By fitting the data, the components of the biaxial attenuation and the components of the phase delay are obtained; S22: Determine the pupil sampling points to be reconstructed within the pupil plane of the optical system. Combine the components of the reconstructed biaxial attenuation and phase delay to reconstruct the Jones matrix at each pupil sampling point. and Jones Matrix ; S23: The Jones matrix reconstructed based on each pupil sampling point and Jones Matrix The biaxial attenuation and phase delay at each pupil sampling point are calculated to obtain the polarization aberration distribution across the entire pupil range of the optical system.

[0016] Furthermore, in step S21, the fitting formula for the directional Zernike polynomial is: ; in, Indicates the first j The polarization aberration components corresponding to the Zernik polynomials in the term direction, This represents the amplitude corresponding to each component in the biaxial attenuation. This represents the amplitude corresponding to each component in the phase delay. Represents a 2×2 identity matrix. This indicates the relative phase difference.

[0017] Further, in step S22, the Jones matrix is ​​reconstructed. and Jones Matrix The method is as follows: The coordinates of the pupil sampling point to be reconstructed are determined by polar coordinate sampling. ρ c , φ c ),in ρ c , φ c These represent the radial and angular coordinates of the pupil sampling point, respectively. c This indicates the number of pupil sampling points to be reconstructed; Based on the components of bidirectional attenuation and phase delay, and combined with the pupil coordinates, the Jones matrix is ​​solved inversely using the fitting formula of the directional Zernike polynomial. and Jones Matrix .

[0018] Furthermore, in step S23, the bidirectional attenuation of each pupil sampling point is calculated as follows: First, regarding the Jones matrix Perform singular value decomposition to obtain a diagonal matrix. S diagonal matrix S The diagonal elements include the singular values ​​corresponding to the maximum amplitude transmittance. Singular values ​​corresponding to minimum amplitude transmittance The decomposition relation satisfies:

[0019] in, U and They represent unitary matrices, Represents the symbol for a diagonal matrix; Secondly, based on singular values and singular values Calculate the bidirectional attenuation corresponding to each pupil sampling point. D : .

[0020] Furthermore, in step S23, the phase delay of each pupil sampling point is calculated as follows: First, regarding the Jones matrix Normalization is performed to obtain the normalized matrix. : ; in, Represents the Jones matrix The determinant of; Secondly, based on the normalized matrix Calculate the phase delay corresponding to each pupil sampling point. R : ; Where Re represents taking the real part of the complex number.

[0021] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) This invention employs a technique of selecting a small number of sampling points within the pupil plane for ray tracing, combined with directional Zernike polynomials to decompose the composition of polarization aberrations and fitting the entire pupil. This overcomes the technical bottleneck of traditional polarization ray tracing methods, which require dense ray sampling across the entire pupil to obtain an accurate polarization aberration distribution. Since only a small number of rays need to be traced to obtain the polarization aberration distribution of the entire pupil through mathematical fitting, the computational load is reduced by more than an order of magnitude compared to traditional polarization ray tracing methods, and the computation time is significantly shortened. Especially in the automated optical system design process based on intelligent algorithms, this method can quickly complete polarization aberration evaluation in each iteration, effectively solving the problem of significantly increased computational complexity and time cost in the intelligent optimization process, and providing efficient computational tools to support the deep integration of artificial intelligence and optical design.

[0022] (2) This invention does not rely on paraxial approximation conditions and is not constrained by planar symmetric optical systems. It can be adapted to complex optical systems with large angles of incidence and non-planar symmetry. It is also compatible with various optical systems such as refractive, reflective, and catadioptric systems, thus solving the limitation that existing simplified methods can only be applied to small-angle, symmetric systems. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic flowchart of the method for obtaining polarization aberrations of an optical system as described in an embodiment of the present invention; Figure 2 A schematic diagram of the structure of the optical system described in the embodiments of the present invention; Figure 3 A schematic diagram of the polarization aberration distribution results obtained by three-dimensional polarization ray tracing calculation according to the embodiment of the present invention; wherein, (a) is the biaxial attenuation distribution and (b) is the phase delay distribution; Figure 4 A schematic diagram of the polarization aberration components obtained by directional Zernike polynomial decomposition according to an embodiment of the present invention; wherein, (a) is the component of biaxial attenuation, and (b) is the component of phase delay; Figure 5 A schematic diagram of polarization aberration distribution within the full pupil range as described in the embodiment of the present invention; wherein, (a) is the biaxial attenuation distribution and (b) is the phase delay distribution; Figure 6 A schematic diagram comparing the error distribution of the method of the present invention described in the embodiments of the present invention with that of the traditional dense ray tracing method; wherein, (a) is the bidirectional attenuation error distribution and (b) is the phase delay error distribution. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0026] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0027] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "assembly," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0028] This invention provides a method for obtaining polarization aberrations in an optical system. The overall idea is to select a small number of sampling points within the pupil plane of the optical system for ray tracing. Using the ray tracing data, combined with the directional Zernike polynomial, the composition of polarization aberrations (including biaxial attenuation and phase delay) of the optical system is decomposed. Based on the components of polarization aberrations, the entire pupil is fitted, and finally the polarization aberration distribution of the entire pupil plane is obtained.

[0029] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0030] like Figure 1As shown, the method for obtaining polarization aberration in an optical system provided by the present invention specifically includes the following steps: S1: Track N rays using a three-dimensional polarization ray tracing algorithm and extract the Jones matrix corresponding to the bidirectional attenuation of the N rays. Jones matrix related to phase delay .

[0031] Step S1 specifically includes the following steps: S11: Based on the calculation requirements of polarization aberration of the optical system, determine the wavelength and field of view to be analyzed, and determine the refractive index of the optical thin film.

[0032] Polarization aberration is a function of object position, wavelength, and pupil coordinates. Calculating polarization aberration requires selecting the wavelength and field of view to be analyzed based on the specified requirements, and then calculating the polarization aberration distribution across the entire pupil at that wavelength and field of view. Furthermore, the refractive index of the optical thin film is crucial for calculating polarization aberration, as it is related to the incident light wavelength; therefore, the refractive index of the optical thin film must be determined after selecting the wavelength.

[0033] S12: N sampling points are uniformly selected within the pupil plane of the optical system. For each sampling point, the extended Jones matrix of the light ray on each optical surface is calculated, and the Jones pupil function of the N light rays at the exit pupil of the optical system is obtained by a three-dimensional polarization ray tracing algorithm.

[0034] Each sampling point selected within the pupil plane corresponds to an incident ray. At the same time, the number of sampling points corresponds to the number of terms in the directional Zernike polynomial, that is, the sampling point, the ray, and the number of terms in the Zernike polynomial are in one-to-one correspondence.

[0035] In a preferred embodiment of the present invention, a uniform sampling method with 6 rings and 6 arms is selected, resulting in a total of 36 sampling points, i.e., N=36. Ray tracing is performed using 36 rays, and simultaneously, 36 directional Zernike polynomials are used to fit the polarization aberrations of the optical system (including bidirectional attenuation and phase delay).

[0036] The reason for choosing 36 directional Zernike polynomials is that they are sufficient to accurately reproduce the polarization aberration distribution of most optical systems. For a few optical systems with extremely complex polarization aberration components, increasing the number of terms in the directional Zernike polynomials requires a corresponding increase in the number of rays to be traced. However, for most optical systems, the polarization aberration components are simple, mainly low-order, so reducing the number of terms in the directional Zernike polynomials requires a corresponding reduction in the number of rays to be traced, thus improving computational efficiency.

[0037] The extended Jones matrix includes the extended Jones matrix of the reflective optical surface. and the extended Jones matrix of the transmission optical surface The expressions are as follows: (1); (2); in, This represents the Fresnel reflection coefficient of s-polarized light. This represents the Fresnel reflection coefficient of p-polarized light. This represents the Fresnel transmission coefficient of s-polarized light. This represents the Fresnel transmission coefficient of p-polarized light.

[0038] During the calculation process, data communication between numerical calculation software (such as Matlab) and optical design software (such as CodeV) can be used to extract the global coordinate system and exit pupil coordinate system information of the optical system, and obtain information such as the ray propagation vector k and surface normal n, in order to calculate the aforementioned... , , and .

[0039] The Jones pupil function for a single ray passing through an optical surface is calculated as follows: The extended Jones matrix in the local coordinate system is transformed into the polarization ray tracing matrix in the global coordinate system using an orthogonal transformation matrix. Then, the polarization ray tracing matrix is ​​transformed into the exit pupil coordinate system. The Jones matrix below is calculated using the following formula: (3); (4); (5); (6); in, This represents the polarization ray tracing matrix of the reflecting surface; Represents the polarization ray tracing matrix of the transmission surface; This represents the entrance pupil-side orthogonal transformation matrix, used to transform vectors in the global coordinate system to the entrance pupil-side local coordinate system of the optical surface; This represents the orthogonal transformation matrix on the pupil side, used to transform vectors in the local coordinate system on the pupil side back to the global coordinate system. Indicates the first q The entrance pupil orthogonal transformation matrix of each optical surface is used to transform the local coordinate system of the entrance pupil into the global coordinate system. Indicates the first q The exit pupil orthogonal transformation matrix of each optical surface is used to transform the global coordinate system into the exit pupil local coordinate system; Indicates that the light passes through the first q After an optical surface, the Jones matrix at the exit pupil; Indicates the firstq The polarization ray tracing matrix of an optical surface; Indicates the direction of s-polarization of the outgoing ray; Indicates the direction of p-polarization of the outgoing ray; Indicates the direction of propagation of the emitted light ray; Indicated on optical surface q The three unit basis vectors of the local coordinate system at the location; Represents the unit basis vector Components in the x, y, z directions of the global coordinate system; Represents the unit basis vector Components in the x, y, z directions of the global coordinate system; Represents the unit basis vector Components in the x, y, z directions of the global coordinate system; Indicated on optical surface q The three unit basis vectors of the local coordinate system at +1; Represents the unit basis vector Components in the x, y, z directions of the global coordinate system; Represents the unit basis vector Components in the x, y, z directions of the global coordinate system; Represents the unit basis vector Components in the x, y, z directions of the global coordinate system.

[0040] S13: Perform singular value decomposition on the Jones pupil function of N rays at the exit pupil of the optical system to extract the Jones matrix. and Jones Matrix .

[0041] Jones pupil function for each ray at the exit pupil of the optical system J Perform singular value decomposition to obtain the Jones matrix. and Jones Matrix The specific decomposition method is as follows: (7); in, t Indicates average transmittance. Φ represents the scalar phase factor, and Φ represents the scalar phase. i Represents the imaginary unit. d Indicates the relative amplitude difference. These represent the relative phase difference; θ d Indicates the direction angle of the maximum transmission axis. θ r Indicates the direction angle of the fast axis. δ Indicates the elliptic deviation parameter. Represents the rotation matrix. αIndicates the rotation angle.

[0042] The Jones matrix obtained after decomposition and Jones Matrix The complete expression is: (8); (9).

[0043] S2: Using N-term directional Zernik polynomials to transform the Jones matrix respectively and Jones Matrix By fitting the data, the components of biaxial attenuation and phase delay are obtained, and the biaxial attenuation and phase delay are reconstructed to obtain the polarization aberration distribution within the full pupil range of the optical system.

[0044] Step S2 specifically includes the following steps: S21: Using N-term directional Zernik polynomials to transform the Jones matrix respectively and Jones Matrix By fitting the data, we can obtain the components of biaxial attenuation and phase delay.

[0045] The fitting formula for the directional Zernike polynomial is: (10); in, Indicates the first j The polarization aberration components corresponding to the Zernik polynomials in the term direction, This represents the amplitude corresponding to each component in the biaxial attenuation. This represents the amplitude corresponding to each component in the phase delay. This represents a 2×2 identity matrix.

[0046] When the number of terms in the directional Zernike polynomial is 36, N=36.

[0047] S22: Determine the pupil sampling points to be reconstructed within the pupil plane of the optical system. Combine the components of the reconstructed biaxial attenuation and phase delay to reconstruct the Jones matrix at each pupil sampling point. and Jones Matrix .

[0048] Reconstructing the Jones Matrix and Jones Matrix The method is as follows: The coordinates of the pupil sampling point to be reconstructed are determined by polar coordinate sampling. ρ c , φ c ),in ρ c , φc These represent the radial and angular coordinates of the pupil sampling point, respectively. c This indicates the number of pupil sampling points to be reconstructed; Based on the components of bidirectional attenuation and phase delay, and combined with the pupil coordinates, the Jones matrix is ​​solved inversely using the fitting formula (10). and Jones Matrix .

[0049] In this solution process, an appropriate threshold should be set to determine whether the obtained polarization aberration components belong to fitting errors rather than true polarization aberration components. By eliminating fitting error terms, the accuracy of the calculation results can be further improved.

[0050] S23: The Jones matrix reconstructed based on each pupil sampling point and Jones Matrix The biaxial attenuation and phase delay at each pupil sampling point are calculated to obtain the polarization aberration distribution across the entire pupil range of the optical system.

[0051] Each pupil sampling point corresponds to a ray. The biaxial attenuation and phase delay accumulated after each ray passes through the optical system are calculated to obtain the polarization aberration distribution of the entire pupil plane of the optical system.

[0052] The bidirectional attenuation corresponding to each ray D The calculation method is as follows: First, regarding the Jones matrix Perform singular value decomposition to obtain a diagonal matrix. S diagonal matrix S The diagonal elements include the singular values ​​corresponding to the maximum amplitude transmittance. Singular values ​​corresponding to minimum amplitude transmittance The decomposition relation satisfies: (11): in, U and They represent unitary matrices, Represents the symbol for a diagonal matrix; Secondly, based on singular values and singular values Calculate the bidirectional attenuation corresponding to each pupil sampling point. D : (12).

[0053] Phase delay corresponding to each ray R The calculation method is as follows: First, regarding the Jones matrix Normalization is performed to obtain the normalized matrix. : (13); in, Represents the Jones matrix The determinant of; Secondly, based on the normalized matrix Calculate the phase delay corresponding to each pupil sampling point. R : (14); Where Re represents taking the real part of the complex number.

[0054] By performing the above-mentioned bidirectional attenuation and phase delay calculations on each ray within the entire pupil plane of the optical system, the polarization aberration distribution of the entire pupil of the optical system can be obtained.

[0055] The following section uses a catadioptric optical system as an example to demonstrate the polarization aberration distribution of the system using this method. The results are then compared with those obtained by the traditional polarization ray tracing method based on a large number of light samples to illustrate the effectiveness of the invention.

[0056] The effective field of view of this catadioptric optical system is 2°×2°, with a focal length of 100mm and an F-number of 3.7. The average RMS wavefront aberration of the effective field of view is 0.018λ (λ=600nm). This catadioptric optical system is coaxial in configuration, and its specific structure is as follows: Figure 2 As shown. The lens surface of this catadioptric optical system is coated with λ / 4 MgF2, and the surface of the reflector is coated with an aluminum film. When the incident light wavelength is 600 nm, its refractive index is 1.2+7.26i.

[0057] According to the proposed method for obtaining polarization aberrations in an optical system, a reference wavelength of 600 nm is selected, and an analysis is performed using a field of view of (2°, 1°) as an example. In this field of view, the catadioptric optical system is not symmetrical about the meridional plane; therefore, analysis of this field of view demonstrates the applicability of the polarization aberration acquisition method of the present invention in non-planar symmetric optical systems. Furthermore, to evaluate the correctness of the method, a conventional three-dimensional polarization ray tracing method is used to densely sample the rays within the pupil (60,000 rays sampled, corresponding to a 1000-ring, 60-arm polar coordinate sampling method), and the biaxial attenuation distribution and phase delay distribution in this field of view are calculated, as shown below. Figure 3 As shown in (a) and (b). As... Figure 3 The bidirectional attenuation distribution and phase delay distribution shown in (a) and (b) are used as reference benchmarks and compared with the results of the method of the present invention to demonstrate the effectiveness and accuracy of the method of the present invention.

[0058] When analyzing this catadioptric optical system using the method of this invention, a 6-ring, 6-arm sampling method is used only within the pupil area of ​​the system to uniformly sample 36 rays. Subsequently, data communication between numerical computation software (such as Matlab) and optical design software (such as CodeV) is used to acquire the relevant data of these 36 rays, and the extended Jones matrix of each ray on the reflective optical surface is calculated. and the extended Jones matrix of the transmission optical surface Next, the Jones pupil function calculated from these 36 rays is decomposed using singular value decomposition to obtain the Jones matrix related to bidirectional attenuation. and the Jones matrix related to phase delay Furthermore, the Jones matrix is ​​subjected to directional Zernikal polynomials. and Jones Matrix The optical system's polarization aberrations are decomposed to obtain their components, including biaxial attenuation and phase retardation. It's important to note that because light rays interact differently at reflecting and transmitting surfaces (s-rays and p-rays), and because polarization aberrations at different optical surfaces can be compensated for through refraction or combinations of reflecting surfaces, the spatial distribution of biaxial attenuation and phase retardation in the optical system may differ, leading to variations in their components.

[0059] like Figure 4 As shown in (a) and (b), the components of biaxial attenuation and phase retardation in a (2°, 1°) field-of-view catadioptric optical system obtained by directional Zernike polynomial decomposition are respectively. Clearly, the components of biaxial attenuation and phase retardation are significantly different. Therefore, when calculating the components of polarization aberration using directional Zernike polynomials, the Jones matrix related to biaxial attenuation must be calculated separately. Jones matrix related to phase delay Perform independent decomposition.

[0060] Because s-polarized light and p-polarized light interact differently on reflecting and transmitting optical surfaces, and because polarization aberrations on each optical surface can be compensated for through refraction or combinations of reflecting surfaces, the biaxial attenuation and phase delay of an optical system may exhibit significant differences in spatial distribution. The independent decomposition strategy of this invention accurately captures the different compositional characteristics of both, avoiding accuracy loss caused by mixed calculations and ensuring an accurate description of the physical nature of polarization aberrations.

[0061] Furthermore, when obtaining the polarization aberration of this example optical system using the proposed method, data from 36 rays were sampled based on 36 directional Zernike polynomials. It should be noted that this number is not fixed and is only used here to describe the method in detail. Figure 4 As shown in (a) and (b), the polarization aberration components of this optical system are concentrated in the low order, while the coefficients of the higher-order directional Zernike polynomials are almost zero. Therefore, for optical systems with simple polarization aberration components, when using this method to obtain the polarization aberrations of the optical system, the number of terms N of the selected directional Zernike polynomial and the corresponding number of sampled rays N can be reduced accordingly, to less than the 36 used in this example, in order to further improve the computational efficiency.

[0062] After calculating the components of biaxial attenuation and phase delay, based on the calculated directional Zernike terms and their corresponding coefficients, and combined with the pupil sampling point coordinates required for detailed evaluation, the polarization aberration of the full pupil of the refracting optical system is restored according to Equation (10). Figure 5 Figures (a) and (b) respectively show the biaxial attenuation distribution and phase delay distribution obtained by the method of this invention, which are compared with... Figure 3 The results obtained from extensive ray tracing shown in (a) and (b) are highly consistent.

[0063] The error between the method of this invention and a large number of ray tracing results is as follows: Figure 6 Figures (a) and (b) show the error distributions for bidirectional attenuation and phase delay, respectively. The RMS value of the bidirectional attenuation error is 4.91e-5, and the PV value is 1.11e-4. The RMS value of the phase delay error is 4.39e-5, and the PV value is 1.15e-4, all at extremely low levels. This indicates that the method of this invention, using only 36 rays for ray tracing, can achieve almost the same computational accuracy as traditional three-dimensional polarized ray tracing methods (dense sampling, with 60,000 rays in this embodiment). This fully demonstrates that the present invention, while significantly reducing the number of rays to be traced, still maintains computational accuracy comparable to traditional dense sampling methods, achieving a good balance between computational efficiency and computational accuracy.

[0064] Compared to traditional methods that require tracking thousands of rays, the method of this invention reduces the computational scale from tens of thousands of rays to tens of rays, significantly shortening the computation time. It is especially suitable for automated design scenarios where repeated iterations of polarization aberration are required.

[0065] This invention calculates polarization aberrations based on their components, independent of paraxial approximation conditions and the assumption of planar symmetry. This effectively overcomes the limitations of Pauli matrix fitting methods, which are only applicable to planar symmetric optical systems with small incident angles. Analysis results for a catadioptric optical system with a non-planar symmetric field of view (2°, 1°) in the embodiments demonstrate that the method of this invention can accurately obtain the polarization aberration distribution of this complex system. Therefore, this invention is applicable to various types of optical systems, including reflective, refractive, and catadioptric systems, as well as optical systems with large incident angles or non-planar symmetric optical systems with complex polarization aberration components, exhibiting broad applicability and practical engineering value.

[0066] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0067] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for acquiring polarization aberration in an optical system, characterized in that, Includes the following steps: S1: Track N rays using a three-dimensional polarization ray tracing algorithm and extract the Jones matrix corresponding to the bidirectional attenuation of the N rays. Jones matrix related to phase delay ; S2: Using N-term directional Zernik polynomials to transform the Jones matrix respectively and Jones Matrix By fitting the data, the components of biaxial attenuation and phase delay are obtained, and the biaxial attenuation and phase delay are reconstructed to obtain the polarization aberration distribution within the full pupil range of the optical system.

2. The method for acquiring polarization aberration in an optical system according to claim 1, characterized in that, N≤36。 3. The method for obtaining polarization aberrations in an optical system according to claim 1 or 2, characterized in that, Step S1 specifically includes the following steps: S11: Based on the calculation requirements of polarization aberration of the optical system, determine the wavelength and field of view to be analyzed, and determine the refractive index of the optical thin film; S12: N sampling points are uniformly selected within the pupil plane of the optical system. For each sampling point, the extended Jones matrix of the light ray on each optical surface is calculated, and the Jones pupil function of the N light rays at the exit pupil of the optical system is obtained by a three-dimensional polarization ray tracing algorithm. S13: Perform singular value decomposition on the Jones pupil function of N rays at the exit pupil of the optical system to extract the Jones matrix. and Jones Matrix .

4. The method for obtaining polarization aberration in an optical system according to claim 3, characterized in that, In step S12, the extended Jones matrix includes the extended Jones matrix of the reflective optical surface. and the extended Jones matrix of the transmission optical surface The expressions are as follows: ； ； in, This represents the Fresnel reflection coefficient of s-polarized light. This represents the Fresnel reflection coefficient of p-polarized light. This represents the Fresnel transmission coefficient of s-polarized light. This represents the Fresnel transmission coefficient of p-polarized light.

5. The method for acquiring polarization aberration in an optical system according to claim 4, characterized in that, In step S12, the Jones pupil function is calculated as follows: The extended Jones matrix in the local coordinate system is transformed into the polarization ray tracing matrix in the global coordinate system using an orthogonal transformation matrix, and then further transformed into the Jones matrix in the exit pupil coordinate system. The calculation formula is as follows: ； ； in, This represents the polarization ray tracing matrix of the reflecting surface. This represents the polarization ray tracing matrix of the transmission surface. Denotes the orthogonal transformation matrix on the entrance pupil side. Express the pupil-side orthogonal transformation matrix. Indicates the first q Orthogonal transformation matrix of entrance pupil side of each optical surface Indicates the first q Orthogonal transformation matrix of the exit pupil side of each optical surface Indicates that the light passes through the first q After the optical surface, the Jones matrix at the exit pupil, Indicates the first q The polarization ray tracing matrix of an optical surface.

6. The method for obtaining polarization aberration in an optical system according to claim 3, characterized in that, In step S13, the singular value decomposition of the Jones pupil function is performed as follows: ； in, J The Jones pupil function represents the distance of each ray from the exit pupil of the optical system. t Indicates average transmittance. Φ represents the scalar phase factor, and Φ represents the scalar phase. i Represents the imaginary unit. d Indicates the relative amplitude difference. These represent the relative phase difference; θ d Indicates the direction angle of the maximum transmission axis. θ r Indicates the direction angle of the fast axis. δ Indicates the elliptic deviation parameter. Represents the rotation matrix. α Indicates the rotation angle.

7. The method for obtaining polarization aberration in an optical system according to claim 6, characterized in that, The Jones matrix obtained after decomposition for: ； The Jones matrix obtained after decomposition for: 。 8. The method for obtaining polarization aberration in an optical system according to claim 2, characterized in that, Step S2 specifically includes the following steps: S21: Using N-term directional Zernik polynomials to transform the Jones matrix respectively and Jones Matrix By fitting the data, the components of the biaxial attenuation and the components of the phase delay are obtained; S22: Determine the pupil sampling points to be reconstructed within the pupil plane of the optical system. Combine the components of the reconstructed biaxial attenuation and phase delay to reconstruct the Jones matrix at each pupil sampling point. and Jones Matrix ; S23: The Jones matrix reconstructed based on each pupil sampling point and Jones Matrix The biaxial attenuation and phase delay at each pupil sampling point are calculated to obtain the polarization aberration distribution across the entire pupil range of the optical system.

9. The method for acquiring polarization aberration in an optical system according to claim 8, characterized in that, In step S21, the fitting formula for the directional Zernike polynomial is: ； in, Indicates the first j The polarization aberration components corresponding to the Zernik polynomials in the term direction, This represents the amplitude corresponding to each component in the biaxial attenuation. This represents the amplitude corresponding to each component in the phase delay. Represents a 2×2 identity matrix. This indicates the relative phase difference.

10. The method for obtaining polarization aberrations in an optical system according to claim 9, characterized in that, In step S22, the Jones matrix is ​​reconstructed. and Jones Matrix The method is as follows: The coordinates of the pupil sampling point to be reconstructed are determined by polar coordinate sampling. ρ c , φ c ),in ρ c , φ c These represent the radial and angular coordinates of the pupil sampling point, respectively. c This indicates the number of pupil sampling points to be reconstructed; Based on the components of bidirectional attenuation and phase delay, and combined with the pupil coordinates, the Jones matrix is ​​solved inversely using the formula in claim 9. and Jones Matrix .

11. The method for obtaining polarization aberrations in an optical system according to claim 8, characterized in that, In step S23, the bidirectional attenuation of each pupil sampling point is calculated as follows: First, regarding the Jones matrix Perform singular value decomposition to obtain a diagonal matrix. S diagonal matrix S The diagonal elements include the singular values ​​corresponding to the maximum amplitude transmittance. Singular values ​​corresponding to minimum amplitude transmittance The decomposition relation satisfies: in, U and They represent unitary matrices, Represents the symbol for a diagonal matrix; Secondly, based on singular values and singular values Calculate the bidirectional attenuation corresponding to each pupil sampling point. D : 。 12. The method for acquiring polarization aberration in an optical system according to claim 8, characterized in that, In step S23, the phase delay of each pupil sampling point is calculated as follows: First, regarding the Jones matrix Normalization is performed to obtain the normalized matrix. : ； in, Represents the Jones matrix The determinant; Secondly, based on the normalized matrix Calculate the phase delay corresponding to each pupil sampling point. R : ； Where Re represents taking the real part of the complex number.

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