Aberration coefficient inversion method and system for sparse-aperture polarized optical system

Abstract

The application discloses a kind of aberration coefficient inversion methods and systems for sparse aperture polarized optical system, belong to sparse aperture optical imaging and polarized optical cross technical field.This method first constructs the sub-aperture Jones matrix model containing wavefront aberration, two-way attenuation and phase delay parameter, and the system Jones pupil matrix is obtained by coherent synthesis;Real point spread function (PSF) under different polarization and defocus state is generated, and the loss function is established with PSF difference as the core;Avoid local optimum by multi-start optimization, realize fine optimization by combining dynamic learning rate and gradient clipping;Finally, the inversion parameter is output and the precision is evaluated.Experimental verification shows that the absolute error of the inversion parameter is 10 ‑8 ~10 ‑7 λ order of magnitude, PSF matching degree is high, and polarization aberration and common phase error can be accurately obtained, to provide support for high-resolution imaging.

Description

Technical Field

[0001] This invention relates to the field of sparse aperture optical imaging and polarization optics cross-technology, and in particular to a method and system for inverting aberration coefficients in sparse aperture polarization optical systems. Background Technology

[0002] Improving the spatial resolution of optical imaging technology has always been a core requirement in fields such as astronomical observation and Earth remote sensing. Limited by the diffraction limit formula, although traditional large-aperture optical systems can improve resolution, this technical approach faces many engineering bottlenecks. The core issues are that the mechanical strength of large-aperture mirror materials is difficult to match the needs of aperture scale expansion, the ultra-high manufacturing cost makes it difficult to apply on a large scale, and the large size and weight characteristics severely limit the payload capacity of scenarios such as aerospace launch vehicles.

[0003] Sparse aperture optical systems, through the non-redundant array arrangement of multiple sub-mirrors, achieve equivalent large-aperture imaging via interferometric synthesis, providing an innovative technical solution to overcome the engineering challenges of traditional large-aperture systems. Based on the principle of coherent superposition of sub-aperture light fields, this system significantly reduces the overall size and weight of the optical system, lowers manufacturing costs and transportation constraints, while achieving imaging resolution close to that of a full aperture, thus combining technical feasibility with engineering practicality.

[0004] However, while the sparse array structure of sparse aperture optical systems solves the problems of volume, weight and cost of traditional large aperture systems, it has inherent technical defects: its discontinuous aperture arrangement is prone to the loss of intermediate frequency information of the system modulation transfer function (MTF), which directly causes the attenuation of imaging contrast and significantly increases the system noise sensitivity, ultimately resulting in imaging quality degradation problems such as blurred details, insufficient sharpness of target edges and loss of high-frequency texture information.

[0005] To address the aforementioned imaging defects caused by sparse aperture structures, existing technological improvements often focus on optimizing back-end image restoration algorithms. These algorithms compensate for performance limitations at the hardware level. However, such studies have not incorporated the key influencing factor of the target object's own polarization characteristics. They have neglected the role of polarization effects in regulating the imaging process and subsequent image restoration accuracy of sparse aperture systems, making it difficult to fundamentally improve imaging quality from a physical mechanism perspective.

[0006] The point spread function (PSF), as a core parameter characterizing the imaging properties of an optical system, is a crucial basis for resolving system aberrations. For sparse aperture optical systems, the PSF further contains core error information such as system phase error, directly determining imaging resolution and fidelity. However, existing aberration resolution methods based on the PSF do not consider the regulatory effect of polarization factors on the imaging process of optical systems, and cannot effectively resolve the polarization aberration information present in sparse aperture optical systems. Consequently, it is difficult to achieve comprehensive and accurate correction of system-wide aberrations, thus hindering further breakthroughs in the imaging performance of sparse aperture optical systems. Summary of the Invention

[0007] Therefore, the technical problem to be solved by this invention is to overcome the problem that existing technologies do not consider the influence of polarization factors on the imaging of sparse aperture optical systems, and cannot simultaneously analyze the system's co-phase error and polarization aberration. Thus, this invention provides a method and system for inverting aberration coefficients in sparse aperture polarized optical systems. Specifically, the method for inverting aberration coefficients in sparse aperture polarized optical systems includes the following steps:

[0008] Step S1: Establish an independent Jones matrix model for each sub-aperture in the sparse aperture polarization optical system. The model parameters for each sub-aperture include wavefront aberration parameters characterizing wavefront distortion, biaxial attenuation parameters characterizing the amplitude difference of polarization components, and phase delay parameters reflecting the phase difference of polarization components. The Jones matrices of each sub-aperture are coherently synthesized on the pupil plane to obtain the Jones pupil matrix model of the system.

[0009] Step S2: Based on preset real optical parameters, calculate multiple sets of real point spread functions generated after passing through different polarization directions and different defocus states when the incident light is in a specified polarization state using the Jones pupil matrix model;

[0010] Step S3: Construct a Jones pupil prediction model with the same structure as the Jones pupil matrix model, set the optical parameters of the sub-aperture as the optimizable variables of the model, and construct a loss function based on the difference between the point spread function predicted by the model and the actual point spread function;

[0011] Step S4: Adopt a multi-starting point optimization strategy, set multiple different initial parameter points within the preset value range of the optimizable variable, and iteratively optimize the optimizable variable corresponding to each initial parameter point in parallel or serial manner, and select the parameter with the smallest loss function value among all the optimization results corresponding to the initial parameter points as the preliminary optimization result.

[0012] Step S5: Using the preliminary optimization result as the initial value, perform fine-grained optimization. During the optimization process, the learning rate is dynamically adjusted and the gradient magnitude is controlled. When the loss function is lower than the preset target threshold or the maximum number of iterations is reached, the wavefront aberration parameters, biaxial attenuation parameters and phase delay parameters corresponding to each sub-aperture obtained by optimization are output.

[0013] In one embodiment of the present invention, the method for establishing an independent Jones matrix model for each sub-aperture in the sparse aperture polarization optical system in step S1 is as follows:

[0014] The Jones matrix model for each sub-aperture is represented as follows:

[0015] ,

[0016] in, Jones' pupil matrix represents the sub-aperture. Represents the polar coordinates of the pupil plane. For normalized radial distance, It is the azimuth angle; The aperture function representing the sub-aperture. The wavefront phase of the sub-aperture, Indicates the operating wavelength; Represents the polarization modulation matrix;

[0017] The calculation formulas for each element of the polarization modulation matrix are as follows:

[0018] ,

[0019] ,

[0020] ,

[0021] ,

[0022] in For bidirectional attenuation parameters, For phase delay parameters, It is the imaginary unit.

[0023] In one embodiment of the present invention, the wavefront phase The bidirectional attenuation parameter The phase delay parameter Parametric representations are performed using low-order Zernike polynomials:

[0024] ,

[0025] ,

[0026] ,

[0027] in, , , , These are the Zernike polynomials for the piston term, the x-direction tilt term, and the y-direction tilt term, respectively. , , The Zernike polynomial coefficients represent the wavefront phase. , , The Zernike polynomial coefficients are the biaxial attenuation parameters; , , where are the Zernike polynomial coefficients for the phase delay parameter.

[0028] In one embodiment of the present invention, in step S2, the method for calculating multiple sets of real point spread functions generated after passing through different polarization directions and different defocus states when the incident light is in a specified polarization state, based on preset real optical parameters and using the Jones pupil matrix model, is as follows:

[0029] S21: Substitute the preset real optical parameters into the Jones pupil matrix model to complete the parameter configuration of the model; at the same time, define the incident light field as a column vector. The x-polarization component of this light field With y-polarization component The amplitudes are all 1, and the phases are consistent;

[0030] S22: The incident light field The Jones pupil matrix model with configured input parameters is used to calculate the outgoing light field through matrix multiplication. The x-direction emission component is The emission component in the y-direction is ; , , , For elements of the Jones pupil matrix model;

[0031] S23: Configure polarizers with multiple target polarization states to polarize the emitted light field. Multiple polarizers are respectively fed into the polarizers, according to the formula Calculate the filtered optical field corresponding to different polarization directions under the undefocused state. , where P is the Jones matrix of the polarizer;

[0032] S24: Based on the Jones pupil matrix model with parameter configuration, superimpose the global defocus phase to generate a Jones pupil matrix model with defocus characteristics. Repeat the light field propagation and polarization filtering process of steps S22-S23 to obtain the filtered light field corresponding to different polarization directions under the defocus state.

[0033] S25: Based on the filtered light fields in the non-defocused or defocused state, extract their x and y components and combine them with the system pupil mask to obtain the effective pupil function;

[0034] S26: Perform a two-dimensional Fourier transform on the effective pupil function, and then take the square of the modulus of the transformation result to convert the complex amplitude distribution of the pupil plane into the light intensity distribution of the image plane, thereby obtaining the preliminary point spread function under different polarization and defocus states.

[0035] S27: Perform peak normalization processing on the preliminary point spread function. By dividing it by its own maximum intensity value, the peak value of the preliminary point spread function is unified to 1, eliminating the absolute intensity difference, and finally forming multiple sets of standardized real point spread functions.

[0036] In one embodiment of the present invention, in S24, the method for generating a Jones pupil matrix model with defocus characteristics by superimposing a global defocus phase on the Jones pupil matrix model with configured parameters is as follows:

[0037] Global defocus phase is superimposed on the Jones pupil matrix model with the parameters configured. The expression for generating the Jones pupil matrix model with defocus characteristics is as follows:

[0038] ,

[0039] in, Indicates the system's operating wavelength. This is the defocus amount. It is a 2nd-order Zernike polynomial of degree 0, i.e., a defocus term. ; This represents the normalized radial distance of the pupil plane; express Exponentiation. Represents the imaginary unit. Represents the rectangular coordinates of the pupil plane. This indicates the total Jones pupil matrix of the basic system after parameter configuration is complete.

[0040] In one embodiment of the present invention, in S25, the effective pupil function is obtained. The calculation formula is as follows:

[0041] ,

[0042] in, Indicates the system's pupil mask. This represents the x-component of the filtered light field in either a non-defocused or defocused state. This represents the y-component of the filtered light field in either out-of-focus or defocused state.

[0043] In one embodiment of the present invention, the loss function is defined as:

[0044] ,

[0045] Where L represents the loss function value, This represents the mean squared error, used to calculate the average squared difference between the pixel intensity values ​​corresponding to the predicted point spread function and the true point spread function. The point spread function with no defocus at 0° polarization refers to the point spread function generated after incident light propagates through the system, is filtered by a 0° polarizer, and the system is in a state of no defocus. The 0° polarization defocus spread function refers to the point spread function generated after the incident light propagates through the system, is filtered by a 0° polarizer, and the system is in a preset defocus state. The point spread function for 90° polarization without defocus refers to the point spread function generated after incident light propagates through the system, is filtered by a 90° polarizer, and the system is in a state of no defocus. The 90° defocusing diffusion function refers to the point spread function generated after incident light propagates through the system, is filtered by a 90° polarizer, and the system is in a preset defocused state.

[0046] This invention also provides an aberration coefficient inversion system for sparse aperture polarization optical systems, comprising: a model building module, a multi-state true point spread function generation module, a prediction model building and loss function definition module, a multi-starting point global optimization solution module, and an optimization result output module; wherein,

[0047] The model building module is used to establish an independent Jones matrix model for each sub-aperture in a sparse aperture polarization optical system. The model parameters of each sub-aperture include wavefront aberration parameters characterizing wavefront distortion, biaxial attenuation parameters characterizing the difference in polarization component amplitude, and phase delay parameters reflecting the phase difference of polarization components. The Jones matrices of each sub-aperture are coherently synthesized on the pupil plane to obtain the Jones pupil matrix model of the system.

[0048] The multi-state real point spread function generation module is used to calculate multiple sets of real point spread functions generated after passing through different polarization directions and different defocus states when the incident light is in a specified polarization state, based on preset real optical parameters and the Jones pupil matrix model.

[0049] The prediction model construction and loss function definition module is used to construct a Jones pupil prediction model with the same structure as the Jones pupil matrix model, set the optical parameters of the sub-aperture as the optimizable variables of the model, and construct a loss function based on the difference between the point spread function predicted by the model and the actual point spread function.

[0050] The multi-starting point global optimization solution module is used to adopt a multi-starting point optimization strategy, set multiple different initial parameter points within the preset value range of the optimizable variable, and iteratively optimize the optimizable variable corresponding to each initial parameter point in parallel or serial manner, and select the parameter with the smallest loss function value among all the optimization results corresponding to the initial parameter points as the preliminary optimization result.

[0051] The optimization result output module is used to perform fine-grained optimization with the preliminary optimization result as the initial value. During the optimization process, the learning rate is dynamically adjusted and the gradient magnitude is controlled. When the loss function is lower than the preset target threshold or the maximum number of iterations is reached, the wavefront aberration parameters, biaxial attenuation parameters and phase delay parameters corresponding to each sub-aperture obtained by optimization are output.

[0052] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aberration coefficient inversion method for sparse aperture polarization optical systems.

[0053] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the aberration coefficient inversion method for sparse aperture polarization optical systems.

[0054] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0055] This invention innovatively achieves simultaneous inversion of co-phase error and polarization aberration in sparse aperture optical systems by fusing polarization dimension information with Jones matrix modeling, filling the technical gap of traditional methods that do not consider polarization factors. It uses low-order Zernike polynomials to parameterize core optical parameters and constructs a loss function based on PSF data under multiple polarization (0° / 90°) and multiple defocus (no defocus / defocus) states, comprehensively constraining the model optimization direction. A multi-starting-point optimization strategy avoids local optima, and a refined optimization process with dynamic learning rate adjustment and gradient clipping significantly improves parameter inversion accuracy. Simultaneously, GPU-accelerated computation and standardized normalization rules balance computational efficiency and data consistency. Verification shows that, except for specific periodic errors, the absolute and relative errors of most parameter inversions are close to zero, and the inverted PSF highly matches the real PSF, demonstrating strong practicality and reliability. Attached Figure Description

[0056] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0057] Figure 1 This is a flowchart illustrating the aberration coefficient inversion method for sparse aperture polarization optical systems provided in an embodiment of the present invention.

[0058] Figure 2 This is a graph showing the dynamic changes in the learning rate;

[0059] Figure 3 This is a comparison chart of the actual optical parameters and the inverted optical parameters of sub-aperture 1;

[0060] Figure 4 This is a comparison chart of the actual optical parameters and the inverted optical parameters of sub-aperture 2;

[0061] Figure 5 This is a comparison chart of the actual optical parameters and the inverted optical parameters of sub-aperture 3;

[0062] Figure 6 These are schematic diagrams of the actual point diffusion functions corresponding to the 0° and 90° polarization directions, respectively, in the non-defocused state and the defocused state.

[0063] Figure 7 These are schematic diagrams of the predicted point diffusion functions for the 0° and 90° polarization directions, respectively, in the non-defocused and defocused states.

[0064] Figure 8 These are residual diagrams corresponding to the 0° and 90° polarization directions, respectively, in the non-defocused state and the defocused state.

[0065] Figure 9This is a schematic diagram of the aberration coefficient inversion system for sparse aperture polarization optical systems provided in an embodiment of the present invention.

[0066] Explanation of the reference numerals in the instruction manual: 100, Model building module; 200, Multi-state true point spread function generation module; 300, Prediction model building and loss function definition module; 400, Multi-starting point global optimization solution module; 500, Optimization result output module. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0068] Example 1:

[0069] Reference Figure 1 As shown, this invention provides a method for inverting aberration coefficients in sparse aperture polarization optical systems, specifically including the following steps:

[0070] Step S1: Establish an independent Jones matrix model for each sub-aperture in the sparse aperture polarization optical system. The model parameters for each sub-aperture include wavefront aberration parameters characterizing wavefront distortion, biaxial attenuation parameters characterizing the amplitude difference of polarization components, and phase delay parameters reflecting the phase difference of polarization components. The Jones matrices of each sub-aperture are coherently synthesized on the pupil plane to obtain the Jones pupil matrix model of the system.

[0071] Step S2: Based on preset real optical parameters, calculate multiple sets of real point spread functions generated after passing through different polarization directions and different defocus states when the incident light is in a specified polarization state using the Jones pupil matrix model;

[0072] Step S3: Construct a Jones pupil prediction model with the same structure as the Jones pupil matrix model, set the optical parameters of the sub-aperture as the optimizable variables of the model, and construct a loss function based on the difference between the point spread function predicted by the model and the actual point spread function;

[0073] Step S4: Adopt a multi-starting point optimization strategy, set multiple different initial parameter points within the preset value range of the optimizable variable, and iteratively optimize the optimizable variable corresponding to each initial parameter point in parallel or serial manner, and select the parameter with the smallest loss function value among all the optimization results corresponding to the initial parameter points as the preliminary optimization result.

[0074] Step S5: Using the preliminary optimization result as the initial value, perform fine-grained optimization. During the optimization process, the learning rate is dynamically adjusted and the gradient magnitude is controlled. When the loss function is lower than the preset target threshold or the maximum number of iterations is reached, the wavefront aberration parameters, biaxial attenuation parameters and phase delay parameters corresponding to each sub-aperture obtained by optimization are output.

[0075] Further, in step S1, with the center wavelength ,focal length Taking a sparse aperture polarization optical system with an F-number of 5.22157 as an example, the system consists of... It consists of several circular sub-apertures, each with a diameter of 73.2 mm and center coordinates of (54.9 mm, -31.7 mm), (-54.9 mm, -31.7 mm), and (0, 63.4 mm).

[0076] Using the circumcircles of the three sub-apertures as the circumcircles of the system, with radius R, construct the system within the interval [-R, R]. From the two-dimensional mesh, the aperture plane rectangular coordinates are obtained. .

[0077] The area inside the circumcircle is set as the effective light-transmitting area (value 1), and the area outside the circumcircle is set as the light-blocking area (value 0). Subsequent optical calculations are performed only on the effective light-transmitting area.

[0078] Nine core parameters (all in wavelength) are set for any k-th sub-aperture, including:

[0079] 1. Wavefront aberration parameters characterizing wavefront distortion include:

[0080] Piston item Describes the overall offset of the wavefront; x-direction tilt term The term describes the linear tilt of the wavefront along the x-axis; the tilt term along the y-axis... Describes the linear tilt of the wavefront along the y-axis; the first sub-aperture It remains fixed as a global reference benchmark.

[0081] 2. Biaxial attenuation parameters characterizing the amplitude difference of polarization components include:

[0082] Average attenuation term The global average amplitude attenuation of the polarization component is described; the x-direction variation term. The term describes the linear change in biaxial attenuation along the x-axis; the term describing the change in the y-direction is also included. , describes the linear variation of biaxial attenuation along the y-axis.

[0083] 3. Phase delay parameters reflecting the phase difference of polarization components include:

[0084] Average delay term The global average phase delay of the polarization components is described; the x-direction variation term is also included. The term describes the linear change of phase delay along the x-axis; the term describing the change in the y-direction... , describes the linear change of phase delay along the y-axis.

[0085] For the k-th sub-aperture, perform local coordinate transformation and low-order Zernike basis function calculation:

[0086] Global coordinates of the center of the sub-aperture Using the origin as the coordinate point, calculate the local rectangular coordinates. , Further calculate the local radial distance. Normalized radial distance ( (sub-aperture radius) and azimuth angle .

[0087] Only 0th and 1st order Zernike polynomials are used as the parametric basis, specifically:

[0088] 0th degree polynomial (piston term): ;

[0089] First-order first-degree polynomial (x-direction tilted term): ;

[0090] First-order (-1) polynomial (y-direction slanted term): ;

[0091] The Zernike basis function values ​​in the region outside the sub-aperture are all set to 0 to ensure the spatial constraint of the parameter representation.

[0092] Based on wavefront aberration parameters and Zernike basis functions, a quantitative characterization of the sub-aperture scalar wavefront is achieved:

[0093] The scalar wavefront (unit: length, e.g., nm) of each sub-aperture is a linear combination of each wavefront parameter and the corresponding Zernike basis function, expressed as:

[0094] ,in, , , The Zernike polynomial coefficients for the wavefront phase (unit: length);

[0095] Convert the scalar wavefront, in physical length form, to phase (unit: radians), i.e.: Furthermore, by characterizing the complex amplitude of the light field in the form of a complex exponent, we obtain... , It is the imaginary unit.

[0096] Based on polarization characteristic parameters and Zernike basis functions, the polarization modulation distribution of the sub-aperture is constructed:

[0097] The biaxial attenuation distribution of each sub-aperture is a linear combination of the biaxial attenuation parameter and the Zernike basis function, expressed as: , , = , The Zernike polynomial coefficients for the biaxial attenuation parameters; further calculation of the biaxial attenuation exponent. and .

[0098] The phase delay distribution of each sub-aperture is a linear combination of the phase delay parameter and the Zernike basis function, expressed as: , , , where are the Zernike polynomial coefficients for the phase delay parameter.

[0099] By integrating geometric aperture, wavefront phase, and polarization modulation characteristics, an independent Jones matrix is ​​generated for each sub-aperture:

[0100] Aperture function combined with sub-aperture (also known as a light transmission mask) With wavefront complex amplitude The scalar geometry-phase matrix is ​​formed as follows: , It is a 2×2 identity matrix. For a bivariate function: when When the corresponding position is inside the sub-aperture (effective light-transmitting area), This indicates that the location allows the light field to pass through; when When the corresponding position is outside the sub-aperture (the light-blocking area), This indicates that the location blocks the passage of the light field.

[0101] Based on the calculation results of bidirectional attenuation and phase delay, a polarization modulation matrix is ​​constructed: .

[0102] By fusing the geometry-phase matrix and the polarization modulation matrix through matrix multiplication, the total Jones matrix of the sub-aperture is obtained: This matrix fully characterizes the combined properties of the sub-aperture's geometric constraints, wavefront distortion, and polarization modulation.

[0103] Based on the principle of coherent superposition between sub-apertures, the Jones matrices of the three sub-apertures are vector-superimposed on the pupil plane to obtain the system-level Jones pupil matrix: This matrix comprehensively integrates the optical properties of all sub-apertures, accurately describing the propagation modulation and polarization interaction laws of sparse aperture polarization optical systems on the incident light field, providing core model support for subsequent point spread function calculations and parameter inversion.

[0104] Furthermore, in step S2, based on preset real optical parameters and combined with the Jones pupil matrix model, the method for simulating the propagation, polarization interaction, and imaging process of the light field in the system, and calculating and generating multiple sets of real point spread function data is as follows:

[0105] S21: Substitute the preset real optical parameters into the Jones pupil matrix model to complete the parameter configuration of the model; at the same time, define the incident light field as a column vector. The x-polarization component of this light field With y-polarization component With amplitudes all equal to 1 and phases consistent, the system's response characteristics to orthogonal polarization directions can be uniformly excited, allowing for the complete extraction of polarization-related information.

[0106] S22: The incident light field The Jones pupil matrix model with configured input parameters is used to calculate the outgoing light field through matrix multiplication. The x-direction emission component is The emission component in the y-direction is ; , , , The elements of the Jones pupil matrix model are used in this calculation process, which fully integrates the wavefront distortion modulation and polarization coupling of the system. The outgoing light field retains amplitude and phase information in complex form.

[0107] S23: Configure polarizers with two orthogonal target polarization states: a 0° polarizer (allowing only x-direction polarized light to pass through) and a 90° polarizer (allowing only y-direction polarized light to pass through), with their Jones matrices as follows: and The emitted light field The two polarizers are respectively passed through, according to the formula Calculate the filtered light field corresponding to the polarization directions of 0° and 90° under the undefocused state. Where P is the Jones matrix of the polarizer, and we take... or ;

[0108] S24: Based on the Jones pupil matrix model with parameter configuration, superimpose the global defocus phase to generate a Jones pupil matrix model with defocus characteristics. Repeat the light field propagation and polarization filtering process of steps S22-S23 to obtain the filtered light field corresponding to the 0° and 90° polarization directions under the defocus state.

[0109] S25: Based on the filtered light fields in both the non-defocused and defocused states, extract their x and y components and combine them with the system pupil mask to construct an effective pupil function according to the following rules. :

[0110] Extracting the x-component of any filtered light field With y component And summing them up, since the polarizer has already achieved single polarization direction screening, the summation is essentially the effective complex amplitude of the target polarization direction;

[0111] The superimposed effective complex amplitude and the system pupil mask (Values ​​are 1 inside the aperture and 0 outside the aperture) Multiplying these values ​​shields the ineffective light field outside the aperture, ultimately yielding the effective pupil function. This function fully characterizes the light field distribution (including amplitude, phase, and spatial range information) in the polarization direction of the target within the pupil plane.

[0112] S26: Based on Fourier optical imaging theory, perform a two-dimensional Fourier transform on the effective pupil function, and then take the square of the modulus of the transformation result (i.e., ,in (representing a two-dimensional Fourier transform), converting the complex amplitude distribution in the pupil plane into the real intensity distribution in the image plane, and obtaining the preliminary point spread function under different polarization states (0°, 90°) and different defocus states (no defocus, defocus);

[0113] S27: Perform peak normalization processing on the preliminary point spread function: Divide each preliminary point spread function by its own maximum intensity value to normalize the peak value of all point spread functions to 1, eliminate the absolute intensity difference caused by irrelevant factors such as incident light intensity and system transmittance, and finally form 4 sets of standardized real point spread function data, including 0° non-defocus spread function, 0° defocus spread function, 90° non-defocus spread function, and 90° defocus spread function.

[0114] Furthermore, in S24, the method for generating a Jones pupil matrix model with defocus characteristics by superimposing a global defocus phase on the Jones pupil matrix model with configured parameters is as follows:

[0115] Defocus characterization method based on Zernike polynomials, defining global defocus phase Its mathematical expression is:

[0116] ,in, The global defocus phase, measured in radians (rad), characterizes the additional phase distortion caused by defocusing after the light field passes through the system. It is a key quantitative indicator of the defocus effect that leads to image blurring, and its distribution is related to the rectangular coordinates of the pupil plane. Related; Indicates the system's operating wavelength; Defocusing amount, usually related to wavelength For the same magnitude, specific values ​​can be preset according to simulation requirements (such as...). , wait); It is a 2nd-order Zernike polynomial of degree 0, i.e., a defocus term. ; Represents the normalized radial distance of the pupil plane. R is the radius of the circumcircle of the system pupil, and its value ranges from [0,1].

[0117] Jones' pupil matrix configured with parameters Based on this, the global defocus phase is incorporated into the matrix in a complex exponential form to generate the Jones pupil matrix model with defocus characteristics. Its mathematical expression is:

[0118] ,

[0119] in, The total Jones pupil matrix of the system containing defocus characteristics is a 2×2 complex matrix. The complex exponential factor representing the defocus phase, express Exponentiation. It represents the imaginary unit.

[0120] Furthermore, in step S3, a Jones pupil prediction model is constructed that is completely consistent with the Jones pupil matrix model structure in step S1. The core components of the model (sub-aperture matrix form, Zernike polynomial representation method, global defocus superposition logic, etc.) are kept in the same origin as the benchmark model, ensuring that the prediction process can accurately reproduce the light field propagation and polarization interaction law of the real system.

[0121] Nine core optical parameters for each sub-aperture are set as model-optimizable variables, specifically including: wavefront aberration parameters (piston term). x-direction tilt term y-direction tilt term ), bidirectional attenuation parameters (average attenuation term) Changes in the x-direction Changes in the y-direction Phase delay factor (average delay) Changes in the x-direction Changes in the y-direction This forms a trainable vector with 27 parameters (3 sub-apertures × 9 parameters), while fixing the first sub-aperture. The parameter is set to 0, serving as a global reference baseline.

[0122] A multi-dimensional mean squared error (MSE) superposition loss function is constructed based on the difference between the predicted point spread function and the true point spread function. The mathematical expression is as follows:

[0123] ,

[0124] Where L represents the loss function value, This represents the mean squared error, used to calculate the average squared difference between the pixel intensity values ​​corresponding to the predicted point spread function and the true point spread function. The point spread function with no defocus at 0° polarization refers to the point spread function generated after incident light propagates through the system, is filtered by a 0° polarizer, and the system is in a state of no defocus. The 0° polarization defocus spread function refers to the point spread function generated after the incident light propagates through the system, is filtered by a 0° polarizer, and the system is in a preset defocus state. The point spread function for 90° polarization without defocus refers to the point spread function generated after incident light propagates through the system, is filtered by a 90° polarizer, and the system is in a state of no defocus. The 90° defocusing diffusion function refers to the point spread function generated after incident light propagates through the system, is filtered by a 90° polarizer, and the system is in a preset defocused state.

[0125] The above four sets of point spread functions cover the 0° / 90° polarization states and the non-defocus / defocus conditions, respectively, ensuring that the model optimization can fully constrain the polarization characteristics and wavefront aberrations of the system.

[0126] To eliminate the interference of absolute intensity differences on loss calculation, the predicted point spread function adopts a normalization method that is completely consistent with the true point spread function: the 0° non-defocus spread function is normalized according to its own peak value, and the 90° non-defocus spread function is normalized according to the peak value of the 0° non-defocus spread function; the 0° defocus spread function is normalized according to its own peak value, and the 90° defocus PSF is normalized according to the peak value of the 0° defocus spread function, ensuring that the two sets of data are compared on the same scale.

[0127] Furthermore, in step S4, multiple initial parameter points are generated within the preset constraints of the optimizable variables: the wavefront aberration coefficient is limited to a range of [-1, 1] (wavelength units), and the biaxial attenuation coefficient and phase delay coefficient are limited to a range of [-0.2, 0.2] (wavelength units). The initial points include one all-zero starting point and eight random initialization starting points, covering the key regions of the parameter space and reducing the risk of getting trapped in local optima.

[0128] The optimization iterations are performed independently for each initial parameter point using either a serial or parallel approach: the Adam optimizer is selected, with an initial learning rate of 0.01, and a predetermined number of iterations are performed at each starting point (ensuring initial parameter convergence). During the iteration process, physical constraints are automatically applied after each parameter update to force all parameters to remain within a preset range and to always maintain the first sub-aperture. Fixed constraints.

[0129] After all initial points have been iterated, the loss function value corresponding to the optimization result of each starting point is calculated. The set of parameters with the smallest loss value is selected as the preliminary optimization result. This result has initially approximated the true parameters, providing high-quality initial values ​​for subsequent fine optimization.

[0130] Furthermore, in step S5, using the preliminary optimization results selected in step S4 as initial parameters, a fine-grained optimization framework is constructed: the learning rate is adjusted to 5×10. -4 The ReduceLROnPlateau learning rate scheduler is used to automatically reduce the learning rate when the loss function enters a plateau period (no significant decrease for several consecutive rounds), achieving a smooth transition from "coarse tuning" to "fine tuning". At the same time, gradient pruning technology is implemented, and a gradient magnitude threshold is set to prevent gradient explosion during the optimization process and ensure the stability of parameter updates.

[0131] During the optimization process, the loss function value and the number of iterations are monitored in real time: when the loss function first falls below the preset target threshold (e.g., 1×10⁻⁶), the loss function value and the number of iterations are monitored. -21 If the number of iterations reaches a preset maximum threshold, the optimization will be terminated immediately to avoid wasting computing resources due to invalid iterations.

[0132] After optimization is completed, the wavefront aberration parameters, biaxial attenuation parameters, and phase delay parameters corresponding to each sub-aperture are output to complete the full-process parameter inversion. The results can be directly used for subsequent system aberration correction and imaging quality optimization.

[0133] To improve model computation efficiency and iterative optimization speed, the entire parameter inversion process adopts a GPU-accelerated computing solution, the specific technical implementation of which is as follows:

[0134] The computational architecture is built based on the PyTorch deep learning framework. The forward computation process of the Jones pupil prediction model (including sub-aperture matrix construction, light field propagation simulation, polarization filtering, etc.) is encapsulated into tensor operations that can be executed in parallel, which fully adapts to the parallel computing characteristics of GPUs.

[0135] With the help of PyTorch’s built-in automatic differentiation technology, the gradient information of each optimizable variable can be automatically calculated based on the constructed loss function without the need to manually derive the gradient formula, providing efficient support for the optimizer’s parameter updates.

[0136] For the two-dimensional Fourier transform stage in PSF calculation, the CUDA parallel computing interface is called to significantly shorten the calculation time of the Fourier transform by leveraging the multi-core parallel processing capability of the GPU. This ensures the rapid generation of multiple sets of PSF data and the efficient iteration of the loss function, thereby significantly improving the overall computational efficiency of parameter inversion.

[0137] To verify the effectiveness of the technical solution proposed in this invention, this experiment uses a Golay3 sparse aperture polarization optical system as the object for targeted verification. The core parameters of this system are as follows:

[0138] The center wavelength λ = 550 nm, focal length f = 1.04302 m, and F number = 5.22157. The sparse aperture consists of three circular sub-apertures with a diameter of 73.2 mm and center coordinates of (54.9 mm, -31.7 mm), (-54.9 mm, -31.7 mm), and (0, 63.4 mm), respectively. A 512×512 two-dimensional grid is constructed in the interval [-R, R] using the circumcircle of the three sub-apertures as the circumcircle of the system to represent the aperture plane coordinates.

[0139] The experiment used nine core optical parameters for each sub-aperture as inversion targets, including wavefront aberration parameters ( , , ), biaxial attenuation parameters ( , , ) and phase delay parameter ( , , All parameters are in wavelength λ. The first sub-aperture was fixed in the experiment. As a reference benchmark, the true point spread function (PSF) under four working conditions is calculated by pre-setting real optical parameters, including 0° no defocus, 0° 1λ defocus, 90° no defocus, and 90° 1λ defocus. These are used as benchmark data to evaluate the effectiveness of this method in parameter inversion.

[0140] The experimental optimization process is divided into two stages: preliminary optimization with multiple starting points and fine optimization. The learning rate changes are as follows: Figure 2 As shown. The first stage uses the Adam optimizer with a learning rate of 0.01, iterating through nine starting points: zero initial point and eight random initial points, to avoid local optima. The second stage uses the optimal parameters obtained in the first stage as initial values ​​and reduces the learning rate to 5 × 10. -4 Furthermore, the ReduceLROnPlateau learning rate scheduler and gradient pruning technique were introduced to ensure stable convergence of the optimization process. The loss function decreased rapidly in the initial stage of optimization, then gradually leveled off, and finally decreased to 1×10⁻⁶ after approximately 3000 iterations. -21 The preset goals were achieved, fully demonstrating the efficiency and stability of the optimization strategy.

[0141] The comparison results of the actual optical parameters and inverted optical parameters of the three sub-apertures are as follows: Figures 3 to 5 As shown, the quantitative error analysis data are detailed in Tables 1 to 3.

[0142] Table 1

[0143]

[0144] Table 2

[0145]

[0146] Table 3

[0147]

[0148] Experimental results show that, except for the sub-aperture diameter 2 Apart from the wavefront aberration parameters, all other parameters to be inverted exhibit extremely high inversion accuracy: among the wavefront aberration parameters... , biaxial attenuation parameters , , and phase delay parameters , , The absolute errors are all within 10 -8 ~10 -7 On the order of λ, the relative error approaches 0%; even for parameters with relatively small values ​​(such as... The relative error is only 0.01%, which fully verifies the high accuracy of the method of the present invention in inverting polarization aberration and co-phase error.

[0149] Sub-aperture 2 The absolute error of order 1λ in the parameters (true value 0.80608λ, estimated value -0.19392λ) is not a method defect, but rather stems from the inherent physical characteristics of the Golay3 sparse aperture structure: piston error exhibits ambiguity with a wavelength period, causing image sharpness to vary periodically. The parameters exhibit ambiguity in the solution space at multiples of 1λ. This phenomenon is a periodic fuzziness at the principle level and is unrelated to the accuracy of the inversion method itself.

[0150] Comparison and residual analysis of the real PSF and the inverted PSF, as follows: Figures 6 to 8 As shown, under the four operating conditions, the inverted PSF and the true PSF are highly consistent in key features such as intensity distribution, peak position, and sidelobe structure. The residual plots show that the residual amplitudes for all operating conditions are at extremely low levels and do not exhibit systematic deviations, indicating that the Jones pupil model constructed based on the inversion parameters can accurately reproduce the optical field propagation and modulation characteristics of the system, further confirming the reliability of the inversion results.

[0151] In summary, through multi-dimensional experimental verification, the sparse aperture polarization optics system parameter inversion method proposed in this invention can synchronously and accurately invert the system's polarization aberrations (biaxial attenuation, phase delay) and co-phase errors (wavefront aberrations). Except for piston parameter ambiguity caused by the inherent periodicity of the sparse aperture, the inversion errors of other parameters all reach the nanometer-scale wavelength level, meeting the accuracy requirements of high-resolution imaging systems. The optimization process is stable and efficient, and the inverted PSF closely matches the true PSF, demonstrating the method's good practicality and reliability, and providing accurate parameter basis for subsequent image restoration and system performance optimization.

[0152] Example 2:

[0153] like Figure 9 As shown, the present invention also provides an aberration coefficient inversion system for sparse aperture polarization optical systems, comprising: a model building module 100, a multi-state true point spread function generation module 200, a prediction model building and loss function definition module 300, a multi-starting point global optimization solution module 400, and an optimization result output module 500; wherein,

[0154] The model building module 100 is used to establish an independent Jones matrix model for each sub-aperture in the sparse aperture polarization optical system. The model parameters of each sub-aperture include wavefront aberration parameters characterizing wavefront distortion, biaxial attenuation parameters characterizing polarization component amplitude differences, and phase delay parameters reflecting polarization component phase differences. The Jones matrices of each sub-aperture are coherently synthesized on the pupil plane to obtain the Jones pupil matrix model of the system.

[0155] The multi-state real point spread function generation module 200 is used to calculate multiple sets of real point spread functions generated after passing through different polarization directions and different defocus states when the incident light is in a specified polarization state, based on preset real optical parameters and the Jones pupil matrix model.

[0156] The prediction model construction and loss function definition module 300 is used to construct a Jones pupil prediction model with the same structure as the Jones pupil matrix model, set the optical parameters of the sub-aperture as the optimizable variables of the model, and construct a loss function based on the difference between the point spread function predicted by the model and the actual point spread function.

[0157] The multi-starting point global optimization solution module 400 is used to adopt a multi-starting point optimization strategy, set multiple different initial parameter points within the preset value range of the optimizable variable, and iteratively optimize the optimizable variable corresponding to each initial parameter point in parallel or serial manner, and select the parameter with the smallest loss function value among all the optimization results corresponding to the initial parameter points as the preliminary optimization result.

[0158] The optimization result output module 500 is used to perform fine-grained optimization with the preliminary optimization result as the initial value. During the optimization process, the learning rate is dynamically adjusted and the gradient magnitude is controlled. When the loss function is lower than the preset target threshold or the maximum number of iterations is reached, the wavefront aberration parameters, biaxial attenuation parameters and phase delay parameters corresponding to each sub-aperture obtained by optimization are output.

[0159] This embodiment proposes an aberration coefficient inversion system for sparse aperture polarized optical systems, which is used to implement the aforementioned aberration coefficient inversion method for sparse aperture polarized optical systems. Therefore, the specific implementation of the aberration coefficient inversion system for sparse aperture polarized optical systems can be found in the embodiment section of the aforementioned aberration coefficient inversion method for sparse aperture polarized optical systems. For example, the model building module 100, the multi-state true point spread function generation module 200, the prediction model building and loss function definition module 300, the multi-starting point global optimization solution module 400, and the optimization result output module 500 are respectively used to implement steps S1, S2, S3, S4, and S5 in the aberration coefficient inversion method for sparse aperture polarized optical systems described in Embodiment 1. Therefore, its specific implementation can be referred to the description of the corresponding embodiment. To avoid redundancy, it will not be repeated here.

[0160] Example 3:

[0161] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the aberration coefficient inversion method for sparse aperture polarization optical systems described in Embodiment 1.

[0162] Example 4:

[0163] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the aberration coefficient inversion method for sparse aperture polarization optical systems described in Embodiment 1.

[0164] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied 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.

[0165] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0166] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0167] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0168] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for inverting aberration coefficients in sparse aperture polarization optical systems, characterized in that, include: Step S1: Establish an independent Jones matrix model for each sub-aperture in the sparse aperture polarization optical system. The model parameters for each sub-aperture include wavefront aberration parameters characterizing wavefront distortion, biaxial attenuation parameters characterizing the amplitude difference of polarization components, and phase delay parameters reflecting the phase difference of polarization components. The Jones matrices of each sub-aperture are coherently synthesized on the pupil plane to obtain the Jones pupil matrix model of the system. Step S2: Based on preset real optical parameters, calculate multiple sets of real point spread functions generated after passing through different polarization directions and different defocus states when the incident light is in a specified polarization state using the Jones pupil matrix model; Step S3: Construct a Jones pupil prediction model with the same structure as the Jones pupil matrix model, set the optical parameters of the sub-aperture as the optimizable variables of the model, and construct a loss function based on the difference between the point spread function predicted by the model and the actual point spread function; Step S4: Adopt a multi-starting point optimization strategy, set multiple different initial parameter points within the preset value range of the optimizable variable, and iteratively optimize the optimizable variable corresponding to each initial parameter point in parallel or serial manner, and select the parameter with the smallest loss function value among all the optimization results corresponding to the initial parameter points as the preliminary optimization result. Step S5: Using the preliminary optimization result as the initial value, perform fine-grained optimization. During the optimization process, the learning rate is dynamically adjusted and the gradient magnitude is controlled. When the loss function is lower than the preset target threshold or the maximum number of iterations is reached, the wavefront aberration parameters, biaxial attenuation parameters and phase delay parameters corresponding to each sub-aperture obtained by optimization are output.

2. The aberration coefficient inversion method for sparse aperture polarization optical systems according to claim 1, characterized in that: In step S1, the method for establishing an independent Jones matrix model for each sub-aperture in a sparse aperture polarization optical system is as follows: The Jones matrix model for each sub-aperture is represented as follows: ， in, Jones' pupil matrix represents the sub-aperture. Represents the polar coordinates of the pupil plane. For normalized radial distance, It is the azimuth angle; The aperture function representing the sub-aperture. The wavefront phase of the sub-aperture, Indicates the operating wavelength; Represents the polarization modulation matrix; The calculation formulas for each element of the polarization modulation matrix are as follows: ， ， ， ， in For bidirectional attenuation parameters, For phase delay parameters, It is the imaginary unit.

3. The aberration coefficient inversion method for sparse aperture polarization optical systems according to claim 2, characterized in that: wavefront phase The bidirectional attenuation parameter The phase delay parameter Parametric representations are performed using low-order Zernike polynomials: ， ， ， in, , , These are the Zernike polynomials for the piston term, the x-direction tilt term, and the y-direction tilt term, respectively. , , The Zernike polynomial coefficients represent the wavefront phase. , , The Zernike polynomial coefficients are the biaxial attenuation parameters; , , where are the Zernike polynomial coefficients for the phase delay parameter.

4. The aberration coefficient inversion method for sparse aperture polarization optical systems according to claim 1, characterized in that: In step S2, based on preset real optical parameters, the method for calculating multiple sets of real point spread functions generated after passing through different polarization directions and different defocus states when the incident light is in a specified polarization state using the Jones pupil matrix model is as follows: S21: Substitute the preset real optical parameters into the Jones pupil matrix model to complete the parameter configuration of the model; at the same time, define the incident light field as a column vector. The x-polarization component of this light field With y-polarization component The amplitudes are all 1, and the phases are consistent; S22: The incident light field The Jones pupil matrix model with configured input parameters is used to calculate the outgoing light field through matrix multiplication. The x-direction emission component is The emission component in the y-direction is ; , , , For elements of the Jones pupil matrix model; S23: Configure polarizers with multiple target polarization states to polarize the emitted light field. Multiple polarizers are respectively fed into the polarizers, according to the formula Calculate the filtered optical field corresponding to different polarization directions under the undefocused state. , where P is the Jones matrix of the polarizer; S24: Based on the Jones pupil matrix model with parameter configuration, superimpose the global defocus phase to generate a Jones pupil matrix model with defocus characteristics. Repeat the light field propagation and polarization filtering process of steps S22-S23 to obtain the filtered light field corresponding to different polarization directions under the defocus state. S25: Based on the filtered light fields in the non-defocused or defocused state, extract their x and y components and combine them with the system pupil mask to obtain the effective pupil function; S26: Perform a two-dimensional Fourier transform on the effective pupil function, and then take the square of the modulus of the transformation result to convert the complex amplitude distribution of the pupil plane into the light intensity distribution of the image plane, thereby obtaining the preliminary point spread function under different polarization and defocus states. S27: Perform peak normalization processing on the preliminary point spread function. By dividing it by its own maximum intensity value, the peak value of the preliminary point spread function is unified to 1, eliminating the absolute intensity difference, and finally forming multiple sets of standardized real point spread functions.

5. The aberration coefficient inversion method for sparse aperture polarization optical systems according to claim 4, characterized in that: In S24, the method for generating a Jones pupil matrix model with defocus characteristics by superimposing a global defocus phase on the Jones pupil matrix model with configured parameters is as follows: Global defocus phase is superimposed on the Jones pupil matrix model with the parameters configured. The expression for generating the Jones pupil matrix model with defocus characteristics is as follows: ， in, Indicates the system's operating wavelength. This is the defocus amount. It is a 2nd-order Zernike polynomial of degree 0, i.e., a defocus term. ; This represents the normalized radial distance of the pupil plane; express Exponentiation. Represents the imaginary unit. Represents the rectangular coordinates of the pupil plane. This indicates the total Jones pupil matrix of the basic system after parameter configuration is complete.

6. The aberration coefficient inversion method for sparse aperture polarization optical systems according to claim 5, characterized in that: In S25, the effective pupil function is obtained. The calculation formula is as follows: ， in, Indicates the system's pupil mask. This represents the x-component of the filtered light field in either a non-defocused or defocused state. This represents the y-component of the filtered light field in either out-of-focus or defocused state.

7. The aberration coefficient inversion method for sparse aperture polarization optical systems according to claim 1, characterized in that: The loss function is defined as: ， Where L represents the loss function value, This represents the mean squared error, used to calculate the average squared difference between the pixel intensity values ​​corresponding to the predicted point spread function and the true point spread function. The point spread function with no defocus at 0° polarization refers to the point spread function generated after incident light propagates through the system, is filtered by a 0° polarizer, and the system is in a state of no defocus. The 0° polarization defocus spread function refers to the point spread function generated after the incident light propagates through the system, is filtered by a 0° polarizer, and the system is in a preset defocus state. The point spread function for 90° polarization without defocus refers to the point spread function generated after incident light propagates through the system, is filtered by a 90° polarizer, and the system is in a state of no defocus. The 90° defocusing diffusion function refers to the point spread function generated after incident light propagates through the system, is filtered by a 90° polarizer, and the system is in a preset defocused state.

8. An aberration coefficient inversion system for sparse aperture polarization optical systems, characterized in that, include: The model building module is used to establish an independent Jones matrix model for each sub-aperture in a sparse aperture polarization optical system. The model parameters of each sub-aperture include wavefront aberration parameters characterizing wavefront distortion, biaxial attenuation parameters characterizing the amplitude difference of polarization components, and phase delay parameters reflecting the phase difference of polarization components. The Jones matrices of each sub-aperture are coherently synthesized on the pupil plane to obtain the Jones pupil matrix model of the system. The multi-state real point spread function generation module is used to calculate multiple sets of real point spread functions generated after passing through different polarization directions and different defocus states when the incident light is in a specified polarization state, based on preset real optical parameters and the Jones pupil matrix model. The prediction model construction and loss function definition module is used to construct a Jones pupil prediction model with the same structure as the Jones pupil matrix model, set the optical parameters of the sub-aperture as the optimizable variables of the model, and construct a loss function based on the difference between the point spread function predicted by the model and the actual point spread function. The multi-starting-point global optimization solution module is used to adopt a multi-starting-point optimization strategy, set multiple different initial parameter points within the preset value range of the optimizable variable, and iteratively optimize the optimizable variable corresponding to each initial parameter point in parallel or serial manner, and select the parameter with the smallest loss function value among all the optimization results corresponding to the initial parameter points as the preliminary optimization result. The optimization result output module is used to perform fine-grained optimization with the preliminary optimization result as the initial value. During the optimization process, the learning rate is dynamically adjusted and the gradient magnitude is controlled. When the loss function is lower than the preset target threshold or the maximum number of iterations is reached, the wavefront aberration parameters, biaxial attenuation parameters and phase delay parameters corresponding to each sub-aperture obtained by optimization are output.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the aberration coefficient inversion method for sparse aperture polarization optical systems as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the aberration coefficient inversion method for sparse aperture polarization optical systems as described in any one of claims 1 to 7.

Images