A method, system, and medium for curved layered jones stress birefringence analysis

Abstract

The present disclosure relates to a curved surface layered Jones stress birefringence analysis method, system and medium, relating to the field of optics. The method establishes a curved surface along the shape layering between the incident side surface and the exit side surface, maps the finite element stress tensor to the layer center sampling point with the global Z axis as the fast approximate propagation direction and the global X-Y coordinate base as the unified transverse representation base; calculates the two principal axis refractive index perturbation, slow axis and layer phase delay according to the transverse principal stress algebraic order, constructs and sequentially accumulates each layer Jones matrix; removes the common phase to form the principal value phase delay, slow intrinsic polarization state azimuth angle, slow intrinsic polarization state ellipticity angle and equivalent birefringence aperture field, and independently accumulates the average refractive index perturbation to obtain the photoelastic optical path difference field. The present disclosure is used for the engineering fast screening of the stress birefringence of the curved surface optical element, and has the advantages of small calculation amount and high efficiency.

Description

Technical Field

[0001] This disclosure relates to the field of optics, and in particular to a method, system, and medium for analyzing birefringence of layered Jones stress on curved surfaces. Background Technology

[0002] Curved optical elements are widely used in imaging, measurement, detection, window protection, and beam transmission systems, such as curved lenses, optical windows, and transparent optical plates with curved incident and exit surfaces. During assembly, support, clamping, or service, these elements are typically subjected to pressure ring preload, edge support, positioning clamping, adhesive curing, and environmental loads.

[0003] The aforementioned mechanical loads and boundary constraints create a spatially uneven stress field within the component. For transparent optical materials, this stress field alters the local refractive index through stress optics, causing a direction-dependent refractive index change in the originally approximately isotropic material, resulting in stress birefringence. When a light beam passes through a stress-affected component, its polarization state, phase delay, intrinsic polarization azimuth angle, birefringence distribution, and photoelastic path difference may all change, further affecting the system's imaging quality, polarization preservation performance, and measurement stability.

[0004] For curved lenses and window-like components, the stress birefringence response is not solely determined by the magnitude of stress at a single point. The local thickness varies at different locations within the aperture, the surface shapes on the incident and exit sides differ, and the propagation paths of light within the component may also differ. Therefore, the final polarization response is simultaneously influenced by the surface geometry, the three-dimensional stress field, and the light propagation path, requiring a combined analysis of mechanical results and polarization transmission calculations.

[0005] Existing technologies typically employ a Jones reference-based approach for refracted rays. This approach samples the local stress state along the actual propagation path of the refracted ray, projects the stress tensor onto the local ray coordinates, calculates the local birefringence parameters based on stress-optics relationships, and accumulates the Jones matrix segment by segment along the path, ultimately obtaining aperture-resolved phase delay, intrinsic polarization azimuth angle, birefringence distribution, and photoelastic path difference. The Jones reference solution for refracted rays can adequately consider actual refraction propagation, local ray coordinate projection, and three-dimensional stress field sampling, making it suitable as a high-fidelity reference scheme. However, its processing efficiency is low, hindering rapid engineering selection, specifically in the following ways: Determining the propagation path of refracted rays is complex. For curved surface elements, the incident angle, refraction direction, and internal propagation path of light rays may differ at different aperture positions, requiring the path to be determined for each ray and a spatial correspondence established with the three-dimensional stress field. Local ray coordinate projection and path sampling are costly processes. Each path sampling point requires obtaining the local stress state, transforming it into a transverse plane related to the ray propagation direction, and then performing stress optical transformation. This process is beneficial for precise calculations but not for the rapid, repeated execution of a large number of candidate solutions. The computation time is relatively long after the path sampling and Jones matrix accumulation are coupled. Multiple sampling segments are set up along the path for each ray, and each segment needs to complete stress interpolation, local birefringence calculation and matrix accumulation. When the number of working conditions, support schemes or assembly states increases, the efficiency of repeated calculations becomes insufficient.

[0006] Based on this, a rapid Jones analysis method for stress birefringence curved surfaces of curved optical elements is proposed to improve analysis efficiency and facilitate rapid screening of multiple engineering options. Summary of the Invention

[0007] Therefore, it is necessary to provide a method, system, and medium for layered Jones stress birefringence analysis of curved optical elements, which addresses the problems of large computational load and difficulty in rapid screening of multiple schemes in high-fidelity analysis of stress birefringence.

[0008] To solve the above problems, the present disclosure adopts the following technical solution: In a first aspect, this disclosure provides a method for analyzing the birefringence of layered Jones stress on curved surfaces, including: Step 1: Obtain the operating wavelength, material parameters, geometric information, and finite element stress field of the curved optical element; Step 2: Determine the incident side surface and the exit side surface; Step 3: Establish at least two conformal surface layers between the two surfaces; using the global Z-axis as the approximate propagation direction and the fixed global XY coordinate base as the unified lateral representation base, determine the layer center and effective propagation length of each conformal surface layer; Step 4: Map and interpolate the finite element stress field to the layer center to obtain the local stress tensor; Step 5: Construct transverse stress blocks, sort the transverse principal stresses by algebraic values, and calculate the refractive index perturbation of the two principal axes, the average refractive index perturbation, and the slow axis direction based on the stress-optic relationship. Step 6: Construct the Jones matrix for each layer based on the difference in refractive index perturbation between the two principal axes, the effective propagation length, and the slow axis direction; Step 7: Multiply the Jones matrices of each layer in the order of propagation to obtain the total Jones matrix; Step 8: Remove the common phase of the total Jones matrix, obtain the principal phase delay, slow intrinsic polarization azimuth angle and slow intrinsic polarization ellipticity angle based on matrix invariants and eigenvalue decomposition, and calculate the equivalent birefringence; obtain the photoelastic path difference by multiplying the cumulative average refractive index perturbation by the effective propagation length, and form an aperture output field at multiple aperture sampling positions.

[0009] In a preferred embodiment, the finite element stress field information is discrete stress data; the incident side surface and the exit side surface are both described by geometric equations and discrete surface points, or by geometric equations and finite element mesh boundaries.

[0010] In a preferred embodiment, the position of each conformal layer on the surface is determined by the incident side surface, the exit side surface, and a layer sequence parameter, wherein the layer sequence parameter represents the relative position of the layer in the local thickness direction of the global Z-axis. No. The sampling position of the center of each conformal layer of the surface is: The conformal layering of the curved surface can be either equidistant or non-equidistant. When using equidistant stratification, , ; When using non-equidistant stratification, , or Each node according to The increasing direction is consistent with the order of light propagation; in, The aperture is the X-axis coordinate. The aperture is the Y-axis coordinate. For aperture coordinates, This represents the total number of conformal layers on the surface. This refers to the numbering of the conformal layering of the surface. For the first The center position vector of each conformal layer of the surface The height of the incident side surface. The height of the exit side surface. For the first A normalized sequence coordinate, The height of the incident side surface. The height of the exit side surface. For local thickness, , For the first The effective propagation length of a surface conforming to layering For the Gauss-Legendal node, As weight, For summation index.

[0011] In a preferred embodiment, step 4 includes: for swept finite element meshes, first interpolating along the aperture direction within each swept finite element layer, and then interpolating between adjacent swept finite element layers according to normalized thickness coordinates; for non-swept finite element meshes, obtaining the local stress tensor at the sampling point at the layer center through three-dimensional element search and finite element shape function interpolation. The material parameters in step 1 include the unstressed refractive index. First stress optical coefficient Second stress optical coefficient ; Step 5 specifically includes: Extract global XY transverse stress blocks from the local stress tensor and sort the transverse principal stresses in descending order of their algebraic values; when the difference between transverse principal stresses is lower than a preset stress threshold, the sampling point is excluded from the statistics of the optical axis direction. according to and Calculate the refractive index perturbations along the two principal axes, and calculate the difference between the two principal axis perturbations; As a local birefringence optical path delay, with As the average refractive index perturbation of the photoelastic path difference, the principal axis with larger refractive index perturbation is designated as the slow axis, and the principal axis with smaller refractive index perturbation is designated as the fast axis; in, For a principal axis refractive index perturbation, For the refractive index perturbation of the other principal axis, The refractive index is the unstressed refractive index. and All are transverse principal stresses. , For axial stress components, For the first The effective propagation length of a curved, conformal layer.

[0012] In a preferred embodiment, the first The Jones matrix for each conformal layer of the surface is: in, For the first Layer Jones matrix, In the direction of the slow axis, It is a two-dimensional rotation matrix along the slow axis. For layer phase delay, It is the imaginary unit.

[0013] In a preferred embodiment, the method further includes: forming a principal phase delay field, a slow intrinsic polarization state azimuth angle field, a slow intrinsic polarization state ellipticity angle field, an equivalent birefringence field, and a photoelastic path difference field at multiple aperture sampling positions; obtaining evaluation indicators by comparing the corresponding aperture fields of the layered Jones bridging solution or the refracted ray Jones reference solution in step 8; the slow intrinsic polarization state azimuth angle residual is calculated using a dual-angle period, and only satisfies the condition simultaneously in the refracted ray Jones reference solution. and Statistics within the mask; among which, For reference, the ellipticity angle of the slow intrinsic polarization state, The ellipticity angle threshold. As a reference solution principal value phase delay, This is the phase delay threshold.

[0014] In a preferred embodiment, the method further includes: using the refracted ray Jones reference solution and / or the ray path layered Jones bridging solution to perform result verification and / or error attribution on the aperture output field obtained in step 8.

[0015] In a preferred embodiment, the error attribution of the aperture output field obtained in step 8 specifically involves: the ray path layered Jones bridging solution maintains the same total number of conformal layering layers as in step 3, while restoring the refraction propagation path, local ray coordinate projection, and finite element element-sensing stress sampling; by comparing the corresponding aperture output fields of step 8, the ray path layered Jones bridging solution, and the refracted ray Jones reference solution, the relative dominance of the joint simplification error and the Jones layering update number error is determined.

[0016] Secondly, this disclosure provides a surface-layered Jones stress birefringence analysis system, comprising: The acquisition module is used to acquire the operating wavelength, material parameters, geometric information, and finite element stress field information of the curved optical element. A determination module is used to determine the incident side surface and the exit side surface; A module is established to create at least two conformal surface layers between the incident and exit surfaces. The global Z-axis direction is used as the fast approximate propagation direction, and the fixed global XY coordinate base is used as the unified lateral representation base to determine the layer center sampling position and effective propagation length of each conformal surface layer. The mapping and interpolation module is used to map and interpolate the finite element stress field to the layer center to obtain the local stress tensor. The stress optics calculation module is used to construct transverse stress blocks, sort transverse principal stresses by algebraic values, and calculate the refractive index perturbations of the two principal axes, the average refractive index perturbation, and the slow axis direction based on stress optics relationships. The matrix construction module constructs Jones matrices for each layer based on the difference in refractive index perturbation between the two principal axes, the effective propagation length, and the slow axis direction. The cumulative module multiplies the Jones matrices of each layer in the order of propagation to obtain the total Jones matrix. The calculation module is used to remove the common phase of the total Jones matrix, obtain the principal phase delay, slow intrinsic polarization azimuth angle, and slow intrinsic polarization ellipticity angle based on matrix invariants and eigenvalue decomposition, calculate the equivalent birefringence, and obtain the photoelastic path difference by multiplying the accumulated average refractive index perturbation of each layer with the effective propagation length, forming an aperture output field at multiple aperture sampling positions.

[0017] Thirdly, this disclosure provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the surface layered Jones stress birefringence analysis method described in the first aspect.

[0018] The aforementioned method, system, and medium for analyzing the stress birefringence of curved surfaces using layered Jones stress are achieved through conformal layering of the curved surface, structured mapping of the finite element stress field, unified transverse stress processing, local stress optical transformation, and ordered accumulation of the Jones matrix. This results in an aperture-resolved polarization output field and a photoelastic path difference field, simplifying the optical post-processing of stress birefringence in curved optical elements. The analysis involves less computation, shorter analysis time, and higher computational efficiency, thus improving the efficiency of multi-condition engineering screening and making it suitable for problems involving rapid screening of multiple solutions. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating a method in one embodiment of the present disclosure; Figure 2 This is a schematic diagram of a layered curved surface structure. Figure 3 This is a schematic diagram of finite element stress field mapping and structured sampling; Figure 4 For reference path verification diagram; Figure 5 This is a schematic diagram of the system structure in one embodiment of the present disclosure. Detailed Implementation

[0020] The technical solutions of this disclosure will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0021] See Figure 1 A method for analyzing birefringence of layered Jones stress on curved surfaces is provided, including: Step 1: Obtain the operating wavelength, material parameters, geometric information, and finite element stress field information of the curved optical element; Step 2: Determine the incident and exit surfaces of the curved optical element; Step 3, establish at least two conformal surface layers between the incident and exit surfaces ( (Each surface is shaped into layers), with the global Z-axis direction as the fast approximate propagation direction, a fixed global XY coordinate base as the unified lateral representation base, and the layer center sampling position and effective propagation length of each layer are determined; Step 4: Map the discrete stress field of the finite element to the sampling point at the center of each conformal layer of the surface, and obtain the local stress tensor through structured layer interpolation or finite element shape function interpolation. Step 5: Construct transverse stress blocks from the local stress tensor, perform algebraic sorting of the transverse principal stresses, and calculate the refractive index perturbation of the two principal axes, the average refractive index perturbation, the slow axis direction, the local phase delay, and the local birefringence optical path delay based on the material stress-optic relationship. Step 6: In the unified transverse representation basis, construct the Jones matrix of each layer according to the local phase delay and slow axis direction of each layer; Step 7: Perform ordered matrix multiplication on the Jones matrices of each layer in the order of light propagation from the incident side to the exit side to obtain the total Jones matrix at each aperture sampling position. Step 8: Remove the common phase of the total Jones matrix and calculate the principal phase delay using matrix invariants; perform eigenvalue decomposition on the matrix, and under the same principal phase delay convention, determine the eigenmode corresponding to the positive delay phase as the slow intrinsic polarization state, and extract the azimuth angle, ellipticity angle, and equivalent birefringence of the slow intrinsic polarization state; separately accumulate the product of the average refractive index perturbation of each layer and the effective propagation length to obtain the photoelastic path difference, and form the corresponding aperture output field at multiple aperture sampling positions.

[0022] The fast approximation embodiment of this disclosure is referred to as the surface layered Jones fast approximation method, and its computation chain is described in detail below.

[0023] First, a unified explanation of all symbols and terms used in the text will be provided.

[0024] To avoid different interpretations due to repeated formulas, the meaning of the same symbol remains consistent throughout the text: The subscript indicates the number of the conformal layer of the surface. Indicates the first The surface is layered according to its shape, subscript Indicates the summation index, subscript Indicates the total amount accumulated along the direction of propagation, subscript Indicates equivalent quantity, subscript and Representing slow and fast models respectively, subscripts , and These represent the incident side, the exit side, and the reference solution, respectively; superscript The symbol indicates transpose, the superscript asterisk indicates complex conjugate, and the cap above the symbol indicates that the common phase has been removed.

[0025] Geometric and layered notation: X, Y, and Z are fixed global coordinate axes. For aperture coordinates, The aperture is the X-axis coordinate. The aperture is the Y-axis coordinate. For the first Layer center position vector and The height of the two sides of the surface, For the global Z-axis local thickness, The total number of layers, Normalized sequence coordinates, For effective propagation length, and These are Gauss-Legendre nodes and weights, and the intervals are... This is the standard domain of the node.

[0026] Stress optical symbols: It is a transverse stress block. These are the two normal stress components and the shear stress components of the transverse plane of the transverse stress block. Clearly... The normal stress component is located in the X-axis direction. The normal stress component is located in the Y-axis direction. To satisfy the algebraic values The transverse principal stress, For the axial stress components of the transverse plane used, To and The corresponding principal axis angle, The refractive index is the unstressed refractive index. These are the optical coefficients for the first and second stresses. For a principal axis refractive index perturbation, For the refractive index perturbation of the other principal axis, the two principal axes correspond to the subsequently determined fast axis and slow axis. Due to the difference in refractive index due to anisotropy, For the average refractive index perturbation, In the direction of the slow axis, In the direction of the fast axis, Indicates by The periodic angle is wrapped. The stress unit is Pascal, the refractive index and its perturbation are dimensionless, and the stress optical coefficient is in Pascal to the negative first power.

[0027] Local Jones symbol: For the operating wavelength, For the first Layer phase delay, For the first Birefringence optical path delay It is a two-dimensional rotation matrix along the slow axis. For the first Layer Jones matrix, The total Jones matrix is ​​an ordered cumulative matrix. The total Jones matrix after removing the common phase. The imaginary unit, Angular frequency, For time variables, It is an exponential function; in the matrix It is a zero element.

[0028] Total amount and eigenstate symbols: , and Represent the determinant, matrix trace, and truncation to a closed interval, respectively. , Principal value phase delay, For equivalent birefringence optical path delay, For the total effective propagation length, For equivalent birefringence, For normalized slow eigenstates, Let its complex components in the X and Y axes be defined in the global XY aperture basis. For the azimuth angle of the slow intrinsic polarization state, For the azimuth angle of the fast intrinsic polarization state, For the ellipticity angle of the slow intrinsic polarization state, The ellipticity angle threshold. This is the phase delay threshold.

[0029] Optical path difference and operation symbols: To avoid the optical path difference of the piston-electro-optical-elastic composite, To eliminate the optical path difference of the piston-electro-optical system, To evaluate the aperture, For average aperture, For the result With results The residual optical path difference between the piston-de-optical-elastic surfaces; To express summation, Represents the absolute value or the modulus of a complex number. Indicates the real part, Indicates the imaginary part. Represents the bivariate arctangent function. Represents the arccosine and arcsine functions. The value is pi. Length quantities use units consistent with the input geometry and wavelength, while phase delay, azimuth, and ellipticity angles are expressed in radians.

[0030] Step 1: Obtain the operating wavelength, material parameters, geometric information, and finite element stress field information of the curved optical element.

[0031] The material parameters include stress optical coefficients and the refractive index when unstressed. The geometric information includes the incident side surface, the exit side surface, the element thickness variation, and the aperture range. The finite element stress field information includes the spatial stress distribution formed by the element under assembly, support, clamping, or service loads. The finite element stress field can be discrete stress data such as nodal stress, element stress, or integration point stress, or it can be a spatial stress field obtained by reconstructing and interpolating from these discrete data. This finite element stress field typically originates from three-dimensional finite element calculations and is represented as discrete stress data at nodes, elements, or integration points, rather than a regular table that can be directly used for optical accumulation calculations. In other words, the finite element stress field information is discrete stress data.

[0032] Preferably, this step also involves obtaining relevant parameters for evaluating the results.

[0033] Since stress birefringence calculation requires continuous reading of local stress states along the optical propagation path or at layered locations, this method specifies fundamental quantities such as geometric information, aperture range, material parameters, and operating wavelength during the input stage, and uses discrete mechanics results as the raw data for subsequent structured processing. This step 1 provides a unified data foundation for surface layering, stress field mapping, local birefringence parameter calculation, and global polarization response determination.

[0034] Step 2: Determine the incident side surface and the exit side surface of the curved optical element.

[0035] Before determining the surface layering, it is necessary to first determine the incident side surface corresponding to the entry of light into the element and the exit side surface corresponding to the exit of light from the element. For all curved optical elements (which can be curved lenses, curved windows, or similar curved elements), the incident side surface and the exit side surface can be described by geometric equations and discrete surface points, or by geometric equations and finite element mesh boundaries. Each aperture position within the aperture range corresponds to a point on the incident side surface and a point on the exit side surface. The spatial distance and direction between the two points reflect the local thickness and surface morphology at that aperture position.

[0036] This method utilizes the optical surfaces on both sides to establish a unified aperture coordinate relationship, enabling subsequent layering positions, stress sampling positions, and optical output positions to correspond under the same aperture grid. In this way, the three-dimensional spatial information in the finite element stress field can be organized into aperture-resolved data oriented towards optical evaluation, facilitating comparable analysis under different support methods, clamping loads, or variations in structural parameters.

[0037] Step 3, establish a connection between the incident side surface and the exit side surface. The surface is layered according to its shape. In this embodiment, the global Z-axis direction is used as the approximate propagation direction, and the fixed global XY coordinate base is used as the unified transverse representation base, that is, as the unified representation base for the transverse stress plane and the Jones matrix. A number greater than or equal to 2. Determine the layer center and effective propagation length for each layer.

[0038] The XYZ coordinate system is fixed, with the XY plane perpendicular to the Z-axis. Understandably, although the actual surface is curved and the light path may also be curved, for computational convenience (fast approximation), light is presumably defined to primarily propagate along this fixed Z-axis direction, hence it's called the approximate propagation direction, or simply the propagation direction. The global representation coordinate axes are fixed.

[0039] The surface conformal layering is either equidistant or non-equidistant.

[0040] Multiple aperture sampling points are determined within the light-transmitting aperture, and the local thickness range is defined by the incident and exit surfaces. For the same aperture location... Define the global Z-axis local thickness .use When the equidistant layer is reached, the first The normalized center coordinates of each layer are , No. The sampling position of the center of each conformal layer of the surface is , No. The effective propagation length of the conformal layering of the surface is: .

[0041] The fixed global XY coordinate basis ensures that the Jones matrices of each layer are in the same representation basis, thus the coordinate basis transformation matrix between adjacent layers is the identity matrix. For non-equidistant layers, Take the actual length of the corresponding hierarchical interval; for those defined in Gauss-Legendre node and weight ,use and If other normalization methods are used for the weights, then use , For summation indexing; each node is arranged in order according to the direction of light propagation, and dimensionless weights must not be directly used as propagation lengths. Thus, each layer varies with the surface morphology on both sides, rather than being a fixed planar layer; each layer serves as a computational unit for subsequent stress sampling, propagation length determination, and the construction of the Jones increment matrix.

[0042] The central curved surface of each layer varies with the morphology of the incident and exit surfaces, rather than being a fixed planar slice of the element. This surface-following layering preserves the aperture-related surface morphology and local thickness variations, but does not perform true refraction ray tracing per aperture point. Its applicability depends on the closeness between the layered sampling stress history and the actual refraction path stress history.

[0043] Step 4: Map the discrete stress field of the finite element method to the sampling points at the center of each conformal layer of the surface, and perform stress interpolation to obtain the local stress tensor.

[0044] The finite element stress field used in this step is a discrete finite element stress field.

[0045] For swept finite element meshes, the nodal stresses are first interpolated along the aperture direction within each swept finite element layer, and then interpolated between adjacent swept finite element layers according to normalized thickness coordinates, thereby obtaining the local stress tensor at the sampling point at the center of each conformal layer. For non-swept finite element meshes, a three-dimensional finite element containing the sampling point can be searched, and the nodal stresses can be interpolated using the shape function of the element.

[0046] After the above processing, the irregular finite element discrete stress results are transformed into structured stress data of "aperture location × conformal surface layering". Each aperture location corresponds to a column of layered stress states arranged in an approximate propagation direction. The finite element stress field mapping and structured sampling are as follows: Figure 3 As shown, where Figure 3 (a) is a finite element mesh. Figure 3 (b) represents the conformal layering of the surface and the sampling points at the center of each layer.

[0047] The finite element stress field can include nodal stress, element stress, integral point stress, or the spatial stress field recovered from them. For swept finite element meshes, a two-dimensional aperture-thickness index or a structured sampling table can be established to store the stress tensor at the center of each layer; for other meshes, three-dimensional element search and shape function interpolation are used. Throughout this text, "swept finite element layer" refers to the finite element mesh structure, "conformal surface layering" refers to the optical computation layer, and "sampling point" refers to the spatial location where the local stress tensor is read.

[0048] Step 5: Construct transverse stress blocks, sort transverse principal stresses by algebraic values, and calculate the refractive index perturbations of the two principal axes, the average refractive index perturbation, and the slow axis direction based on stress-optics relations. Specifically, convert the local stress tensor into the refractive index perturbations of the two principal axes, the average refractive index perturbation, the slow axis direction, the local phase delay, and the local birefringence optical path delay.

[0049] The material parameters in step 1 include the unstressed refractive index. First stress optical coefficient Second stress optical coefficient First stress optical coefficient The second stress optical coefficient is a proportionality coefficient describing the change of the material's refractive index with normal stress along the direction of stress, reflecting the linear correlation between the refractive index and stress of the optical vibration component parallel to the principal stress direction. This refers to the proportionality coefficient describing the change of a material's refractive index with normal stress perpendicular to the direction of stress, reflecting the linear correlation between the refractive index of the optical vibration component perpendicular to the principal stress direction and stress. The local birefringence parameters include the two principal axis refractive index perturbations, the average refractive index perturbation, the slow axis direction, the local phase retardation, and the local birefringence optical path retardation. The material is optically isotropic in its unstressed state and satisfies the linear stress-optical relationship within the considered load range. All are transverse principal stresses.

[0050] The birefringence optical path delay and the photoelastic optical path difference are defined by different physical quantities: the former is determined by the difference in refractive index perturbations of the two orthogonal principal axes, while the latter is obtained by accumulating the average value of the refractive index perturbations of the two principal axes along the propagation direction.

[0051] For the fast approximation embodiment, it is constructed from local stress tensors in the global XY transverse plane. ,right Find the eigenvalues ​​and eigenvectors, and sort the two transverse principal stresses by their algebraic values. The reference solution and the bridging solution are processed in the same way in a transverse plane perpendicular to the locally refracted ray.

[0052] and The corresponding principal axis angle is denoted as , and according to Apply the wrapping at two angles periodically. Do not follow the instructions. The magnitude relationship should be swapped along the principal axis to avoid non-physical issues arising under a mixed tension and compression state. Axial jump. When the transverse principal stress difference is lower than the preset stress threshold or the total phase delay is lower than the preset delay threshold, this point can still participate in the calculation of scalar phase delay and photoelastic path difference, but should be excluded from the statistics of the optical axis direction.

[0053] exist When representing the axial stress components of the transverse plane used, according to , Calculate the refractive index perturbation along the two principal axes. The anisotropic refractive index difference is... The average refractive index perturbation is .like ,but ;otherwise The direction of the fast axis is .

[0054] Extract the global XY transverse stress blocks from the local stress tensor, and sort the transverse principal stresses in descending order of their algebraic values. Not adopted The magnitude relationship determines the optical axis; when the transverse principal stress difference If the stress level is below the preset stress threshold, the sampling point will be excluded from the statistics along the optical axis. according to and Calculate the refractive index perturbations along the two principal axes, and calculate the difference between the two principal axis perturbations; As a local birefringence optical path delay, with As the average refractive index perturbation of the photoelastic path difference, the principal axis with larger refractive index perturbation is designated as the slow axis, and the principal axis with smaller refractive index perturbation is designated as the fast axis; in, For a principal axis refractive index perturbation, For the refractive index perturbation of the other principal axis, The refractive index is the unstressed refractive index. All are transverse principal stresses. , For axial stress components, For the average refractive index perturbation, For the first The effective propagation length of a curved, conformal layer.

[0055] and These are the two principal stresses calculated from the plane stress state when light propagates along the Z-axis in the XY transverse plane perpendicular to the Z-axis; they are the two eigenvalues ​​of the plane stress matrix. The first transverse principal stress, Let be the second transverse principal stress, and follow the algebraic numerical convention. ≥ The calculation formula is as follows: The meanings of the symbols in the formula are as follows: This is the first transverse principal stress, i.e., the principal stress with the larger value in the XY transverse plane; This is the second transverse principal stress, which is the principal stress with the smaller value in the XY transverse plane. The normal stress component is in the X direction; The normal stress component is in the Y direction; Let X and Y represent the shear stress components in the XY plane. The X and Y directions represent the transverse coordinate directions perpendicular to the Z-axis, which is approximately the direction of ray propagation. , , , and The units for all values ​​are Pa. Transverse principal stress is also known as transverse plane principal stress.

[0056] Step 6: Construct the Jones matrix for each layer based on the two principal axis refractive index perturbations, effective propagation length, and slow axis direction.

[0057] No. The phase delay of the layer is The local birefringence optical path delay is . It is a length quantity, not the photoelastic path difference caused by the perturbation of the average refractive index.

[0058] Using field time factor Under the agreement, the first The Jones matrix of a surface conformally layered is: ,in, The imaginary unit, Angular frequency, As a time variable, the slower modes with higher refractive indices correspond to the forward propagation phase.

[0059] When adjacent surfaces are layered according to different transverse representation bases, a corresponding coordinate base transformation matrix is ​​inserted between the adjacent layered Jones matrices.

[0060] Step 7: Perform ordered matrix multiplication according to the order in which light propagates from the incident surface to the exit surface. . Indicates the order of propagation. A surface conformally layered with conformal structure. Indicates the order of propagation. A surface conformally layered with conformal structure. Indicates the order of propagation. A surface conformally layered with conformal structure. Indicates the order of propagation. The surface is layered according to its shape. Since this fast approximation embodiment uses a fixed global XY coordinate base, no additional coordinate base transformation is required between layers; if the extended embodiment uses different lateral coordinate bases in adjacent layers, then the corresponding coordinate base transformation matrix must be inserted between the Jones matrices of adjacent layers.

[0061] A total Jones matrix is ​​obtained at each aperture sampling position. This matrix represents the deterministic, non-depolarization polarization transmission result after the local polarization transmission effects of each layer act together in the propagation sequence.

[0062] The total phase delay and total intrinsic polarization state are obtained by matrix invariants and eigenvalue decomposition of the total Jones matrix, and cannot be replaced by a simple arithmetic mean of the phase delay or optical axis angle of each layer.

[0063] By performing the above ordered matrix multiplication at multiple aperture sampling locations, a total Jones matrix aperture field can be formed, which in turn forms a principal phase delay field, a slow intrinsic polarization azimuth angle field, a slow intrinsic polarization ellipticity angle field, and an equivalent birefringence field.

[0064] Step 8, first through Remove the common phase of the total Jones matrix; the complex square root branch should be selected consistently with the aperture position or continuous parameters to avoid artificial phase jumps.

[0065] Calculated from the total Jones matrix after removing the common phase. and will Limited to The principal phase delay referred to in this disclosure is the non-negative principal value obtained from the invariants of the total Jones matrix according to the formula, and is not the arithmetic sum of the phase delays of each layer. The principal phase delay represents the phase difference between two equivalent intrinsic polarization states after light passes through the entire element; due to the periodicity of the phase, this phase difference is uniformly converted into a unique non-negative representative value in the range of 0 to π, so as to allow for consistent comparison between different aperture positions. The equivalent birefringence optical path delay is defined. Total effective propagation length and equivalent birefringence The equivalent birefringence is a scalar calculated from the total principal phase delay, not the arithmetic mean of the local birefringence.

[0066] right Perform eigenvalue decomposition, and under the phase convention of having the same delay as the principal phase, determine the eigenmode corresponding to the positive delay phase as the slow eigenpolarization state. The slow eigenstate azimuth angle, as referred to in this disclosure, is the azimuth angle of the major axis of the polarization ellipse of the normalized eigenvector in the global XY aperture basis used for reporting, defined as follows: , and according to Periodic interpretation; the azimuth angle of the fast eigenstate orthogonal to it is Superscript This is the complex conjugate operator.

[0067] The ellipticity angle of the slow intrinsic polarization state is defined as Its value range is The sign follows the chirality convention given in the formula. This disclosure uses the ellipticity angle. Not the undefined minor-to-major axis ratio; only when Below the preset threshold and Only when the azimuth angle of the intrinsic polarization state is higher than the preset threshold will it be approximately interpreted as the direction of the linear slow axis or fast axis.

[0068] The optical path difference of the photoelasticity is calculated independently as follows: The depiston field used for display or Zernike fitting is... Solution results and The piston-residual between them is .in, To evaluate aperture, angle brackets indicate the average aperture. , These are two solutions to be compared. To avoid the optical path difference of the piston-electro-optical-elastic composite, To eliminate the optical path difference of the piston-electro-optical system, Right now , for the result The optical path difference of the unremoved piston photoelastic for , for the result The optical path difference of the unremoved piston photoelastic.

[0069] The method further includes: The principal phase delay field, slow intrinsic polarization azimuth angle field, slow intrinsic polarization ellipticity angle field, equivalent birefringence field, and photoelastic path difference field are formed at multiple aperture sampling positions. Evaluation indexes are obtained by comparing the corresponding aperture fields of the fast approximation solution (the fast approximation method is the method of steps 1 to 8 of this invention, and the fast approximation solution is the relevant result of the method of steps 1 to 8), the bridging solution, or the Jones reference solution of the refracted ray. Evaluation metrics are calculated by source: Zernike coefficients are obtained by fitting the depiston-free photoelastic path difference aperture field; the Zernike fitting referred to in this disclosure means using a set of standard Zernike polynomials to approximate the depiston-free photoelastic path difference distribution within the aperture, and the fitted coefficients reflect typical spatial variation components such as defocus, astigmatism, and spherical aberration; path deviation is obtained by geometric comparison between the surface layer sampling position and the refracted ray path; phase delay residual, slow intrinsic polarization state azimuth residual, photoelastic path difference residual, root mean square residual, correlation coefficient, and regional overlap are obtained by comparing the corresponding aperture fields of the fast approximation solution, bridging solution, or reference solution. Among them, the slow intrinsic polarization state azimuth residual is calculated using a dual-angle period and is only satisfied in the reference solution. and Statistics within the preset threshold mask. For reference, the ellipticity angle of the slow intrinsic polarization state, The principal value phase delay is used as the reference solution.

[0070] Therefore, the outputs are divided into three categories: the polarization output field generated by the total Jones matrix and its eigenvalue decomposition; the photoelastic path difference field generated by the independent accumulation of the average refractive index perturbation; and the evaluation index generated by comparing the aperture fields of different geometric paths or different solution results. These three types of outputs can be used together for engineering comparisons of support schemes, installation loads, clamping loads, structural parameters, or layered configurations.

[0071] Step 9, Reference path verification and / or error attribution: Using the refracted ray Jones reference solution and / or the layered Jones bridging solution of the ray path, the aperture output field obtained in step 8 is verified and / or error is attributed.

[0072] To assess the applicability of the layered Jones fast approximation method for surfaces under specific surface conditions, stress levels, and support conditions, a refracted ray Jones reference solution and / or a ray path layered Jones bridging solution can be introduced. The refracted ray Jones reference solution performs finite element-sensing stress sampling along the actual refracted ray path and accumulates a finer Jones matrix in the local ray coordinate base as a high-fidelity numerical reference.

[0073] The layered Jones bridging solution for ray path maintains the same Jones update layer number as the fast approximation solution. Simultaneously, the refraction propagation path, local ray coordinate projection, and finite element element-sensing stress sampling are restored. This bridging solution belongs to joint attribution control, not item-by-item ablation; its difference from the fast approximation solution reflects the effect of joint simplification of propagation, projection, and sampling, and its difference from the refracted ray reference solution reflects the effect of reducing the number of Jones updates under the same path, projection, and sampling conditions.

[0074] By comparing the corresponding aperture output fields of the fast approximation solution, the ray path layered Jones bridging solution, and the refracted ray Jones reference solution, the relative dominance of the joint simplification error and the Jones update layer error can be determined. The bridging solution is not used to quantify the independent contribution of any single factor in the propagation path, local projection, or unit-sensing sampling; the reference solution is only used as a high-fidelity reference under the numerical model and discrete settings, not the experimental truth.

[0075] Step 10: Rapid project assessment and solution comparison.

[0076] This method is ultimately geared towards early-stage engineering design and multi-scheme comparison scenarios. For different support methods, clamping loads, assembly states, or structural parameters, corresponding finite element stress fields can be obtained, and comparable stress birefringence results are generated following the same process of surface layering, stress mapping, stress optical transformation, and Jones matrix accumulation. Because the rapid approximation process reduces reliance on complete refracted ray tracing and repeated three-dimensional element searches, it is suitable for quickly identifying high-risk support areas, load combinations, or structural parameters under multiple operating conditions.

[0077] In practical applications, steps 1 to 8 of this embodiment can be used to complete a wide range of scheme selection. For schemes with high residual indices, large curvature, strong stress gradients, or strict polarization performance requirements, the Jones reference solution for refracted rays and / or the layered Jones bridging solution for ray paths are then introduced for focused verification. Through this hierarchical analysis method, this disclosure simplifies the calculation process while retaining the main physical factors, improves the efficiency of stress birefringence analysis of curved optical elements, and provides engineering basis for support design, assembly status evaluation, clamping load analysis, and structural parameter optimization.

[0078] In the tested examples of flat plates, representative curved lenses, and high-curvature boundaries, using the same finite element stress field as the mechanical input, the surface-layered Jones fast approximation method, the refracted ray Jones reference solution, and the ray path-layered Jones bridging solution were compared. Phase delay, the azimuth angle of the slow intrinsic polarization state statistically within a mask with preset ellipticity and phase delay threshold, the photoelastic path difference, the root mean square residual, the correlation coefficient, and the overlap of the high phase delay region were used to evaluate the engineering usability of the fast approximation method within the tested range; these examples do not constitute a general convergence proof for all surfaces, loads, and mesh conditions.

[0079] In the extreme case of a flat plate, the surface layering degenerates into parallel layering along the thickness direction. The calculation results show that at a wavelength of 632.8 nm, the maximum phase retardation is 7.89 mRa, and the 95% aperture value is 6.22 mRa; the peak-to-valence value of the photoelastic path difference is 1.02 nm, and the 95% aperture value is 0.879 nm; after wavelength scaling, the maximum phase retardation at wavelengths of 248 nm and 193 nm is approximately 0.0201 Ra and 0.0259 Ra, respectively. This example demonstrates that, in the case of a flat plate, the stress-optical transformation, layered sampling, and Jones matrix accumulation employed in this embodiment can achieve an order of magnitude and spatial distribution consistent with the physical laws of stress birefringence.

[0080] In a representative example of a curved lens mounting support, the surface-layered Jones fast approximation method can preserve the main high phase delay regions caused by the support load, while maintaining the overall distribution characteristics of the weak response center region and the edge enhancement region. Compared to the refracted ray Jones reference solution, the root mean square residual of the phase delay of this fast approximation result is 0.281 milliradians, the relative root mean square residual is 6.45%, the correlation coefficient is 0.984, and the overlap of the region with the highest phase delay of 10% is 0.779. The correlation coefficient of the photoelastic path difference result after depiston processing is 0.995, and the root mean square residual of the photoelastic path difference is 0.0174 nanometers. Under the same finite element stress field and optical parameters, the optical post-processing time is reduced from 441 seconds to 1.09 seconds. These results demonstrate that under the representative curved surface and load conditions, this invention can significantly improve computational efficiency while preserving the main aperture response characteristics, making it suitable for rapid screening in engineering applications.

[0081] To further determine the sources of error in the fast approximation, the layered Jones bridging solution for ray paths maintains the same number of Jones accumulation layers as the fast approximation method, while recovering the refraction propagation path, local ray coordinate projection, and finite element-sensor stress sampling. In a representative curved lens example, the bridging solution reduces the root mean square residual of phase delay from 0.281 milliradians to [missing value]. Milliradian, the root mean square residual of the photoelastic path difference decreased from 0.0174 nanometers to The root mean square difference in the azimuth angle of the slow intrinsic polarization state, statistically measured within a mask with a preset ellipticity and phase retardation threshold, decreased from 3.81 degrees to [missing value]. The results support attributing the major residuals in this example to the joint simplification of propagation, projection, and sweep stratified sampling, rather than quantifying the independent contribution of any single factor.

[0082] Meanwhile, the high-curvature curved lens example demonstrates that the fast approximation method has limitations in its applicability. When the curvature increases, the refraction path shift is significant, or the stress gradient does not match the fast layered sampling, the root mean square residual of the phase delay of the fast approximation solution relative to the Jones reference solution of the refracted ray can increase to 0.786 milliradians, the relative root mean square residual reaches 23.7%, and the overlap of the region with the highest phase delay of 10% decreases to 0.550. The bridging solution can reduce the root mean square residual of the phase delay to 7.36 × 10⁻³ milliradians, the root mean square residual of the photoelastic path difference to 1.21 × 10⁻³ nanometers, and restore the overlap of the region with the highest phase delay to 0.994. This example supports the use of the reference solution or the bridging solution for verification under conditions of high curvature or strong path shift.

[0083] In summary, the tested examples support the application of this method for rapid screening and scheme comparison of stress birefringence in curved optical elements. For cases with large curvature, significant refraction path offset, strong stress gradient, or requiring final high-precision confirmation, the Jones reference solution for the refracted ray or the layered Jones bridging solution for the ray path should be used for further verification; the specific applicable scope should be determined in combination with the material, wavelength, support load, mesh resolution, and evaluation accuracy requirements.

[0084] See Figure 5 A surface-layered Jones stress birefringence analysis system is provided, comprising: The acquisition module is used to acquire the operating wavelength, material parameters, geometric information, and finite element stress field information of the curved optical element. A determination module is used to determine the incident side surface and the exit side surface; A module is established to create at least two conformal surface layers between the incident and exit surfaces. The global Z-axis direction is used as the fast approximate propagation direction, and the fixed global XY coordinate base is used as the unified lateral representation base to determine the layer center sampling position and effective propagation length of each conformal surface layer. The mapping and interpolation module is used to map and interpolate the finite element stress field to the layer center to obtain the local stress tensor. The stress optics calculation module is used to construct transverse stress blocks, sort transverse principal stresses by algebraic values, and calculate the refractive index perturbations of the two principal axes, the average refractive index perturbation, and the slow axis direction based on stress optics relationships. The matrix construction module constructs Jones matrices for each layer based on the difference in refractive index perturbation between the two principal axes, the effective propagation length, and the slow axis direction. The cumulative module multiplies the Jones matrices of each layer in the order of propagation to obtain the total Jones matrix. The calculation module is used to remove the common phase of the total Jones matrix, obtain the principal phase delay, slow intrinsic polarization azimuth angle, and slow intrinsic polarization ellipticity angle based on matrix invariants and eigenvalue decomposition, calculate the equivalent birefringence, and obtain the photoelastic path difference by multiplying the accumulated average refractive index perturbation of each layer with the effective propagation length, forming an aperture output field at multiple aperture sampling positions.

[0085] The modules of the system are sequentially connected according to the data flow of "layering and effective length determination - local stress tensor interpolation - stress optical transformation - layered Jones matrix construction - ordered matrix accumulation - intrinsic output and photoelastic path difference output - aperture field evaluation". The specific calculation rules can be referred to the above method embodiment.

[0086] This disclosure provides an electronic device including: a memory; one or more processors; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing a surface-layered Jones stress birefringence analysis method.

[0087] This disclosure provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the described method for analyzing the birefringence of surface layered Jones stress.

[0088] This disclosure maps the finite element stress field of a curved optical element to structured stress data on a conformal layer of the curved surface, and obtains aperture-resolved polarization transmission results through unified transverse stress processing, stress-optical transformation, and ordered accumulation of layered Jones matrices; the average refractive index perturbation is independently accumulated along the propagation direction as the photoelastic path difference. This fast approximation embodiment does not perform complete tracing of every real refracted ray, making it suitable as a rapid screening method in engineering.

[0089] Furthermore, the applicability of the fast approximation method under the corresponding working conditions can be judged by verifying or attributing errors through the Jones reference solution of the refracted ray, the layered Jones bridging solution of the ray path, and the fast approximation method.

[0090] It is understood that this disclosure can be adapted to the structure, load, accuracy requirements and computational efficiency requirements of curved optical elements.

[0091] The number of conformal layerings on a curved surface can be adjusted according to accuracy and efficiency requirements. For cases with small curvature, gradual stress changes in the thickness direction, or where only initial engineering screening is required, fewer layerings can be used to improve computational efficiency. For cases with large curvature, strong stress gradients, or drastic stress changes near the support or clamping regions, the number of layerings can be increased to improve the resolution of stress sampling in the thickness direction and Jones matrix accumulation. The number of layerings can also be automatically determined based on phase delay convergence, photoelastic-optical path difference convergence, or residual changes with the reference solution.

[0092] The conformal layering method is not limited to uniformly normalized thickness layering. Depending on different engineering needs, layering can employ uniform physical thickness, non-uniform spacing, integral point layering, denser layering near the incident or exit side, denser layering near the area of ​​support load, adaptive layering based on stress gradient, or other conformal layering strategies jointly determined by the parametric surfaces of the incident and exit optical surfaces. For optical plates or window-like elements that are close to flat plates, conformal layering can degenerate into approximately parallel layering; for lenses or window-like elements with large curvature, the layer center position and local thickness information that vary with the aperture position can be preserved.

[0093] The representation of the incident and exit optical surfaces can vary depending on the component type. The surface can be a sphere, aspherical surface, freeform surface, conical surface, surface obtained by fitting a measured point cloud, discrete surface shape given by design data, or an optical surface represented by an analytical function, spline surface, or mesh surface. The aperture is not limited to a circular aperture; it can be an annular aperture, rectangular aperture, irregular aperture, or an effective aperture region defined by obstruction or adjustment boundaries. The layered calculation concept of this invention can be applied as long as an indexable sequence position can be established between the incident and exit surfaces.

[0094] The source and mapping method of the finite element stress field can be replaced. The finite element mesh can use swept hexahedral elements, or tetrahedral elements, wedge elements, hybrid elements, or other discrete structures that can provide spatial stress interpolation; stress data can come from nodes, element centers, integration points, or the spatial stress field after stress recovery. Stress field mapping can be achieved using methods such as nodal interpolation, element shape function interpolation, integration point extrapolation, local least squares recovery, volume weighted recovery, radial basis function interpolation, spline interpolation, layered resampling, or aperture-thickness index tables. For multi-condition calculations, when the geometry remains unchanged, surface layering and sampling indices can be reused, updating only the stress field data under different loads or boundary conditions.

[0095] When using the unstressed refractive index and stress optical coefficient , When calculating the above relationships, the material is limited to transparent materials that are optically isotropic in an unstressed state and satisfy a linear stress-optical relationship within the considered load range, including fused silica, optical glass, transparent ceramics, or polymers that meet the above conditions. For general anisotropic crystals, the above scalar values ​​are not directly used. Instead of relying solely on the relationship between the two coefficients, the refractive index ellipsoid or optical opacity tensor and the corresponding optical pressure coefficient tensor should be used based on the material symmetry to first obtain the local principal refractive index perturbation, average refractive index perturbation, and intrinsic polarization state, and then connect them with the subsequent Jones matrix accumulation process. For different wavelengths or temperatures, material parameters under the corresponding conditions can be used.

[0096] The local transverse principal stresses are always sorted by algebraic values ​​as follows: The optical axis is not determined by stress absolute value sorting. The slow axis and fast axis are calculated... and Then specify according to the magnitude of the refractive index. To avoid unstable directional statistics at near isotropic points or low delay points, a threshold for the transverse principal stress difference and a threshold for the phase delay can be set, and a dual-angle periodic processing can be adopted; the above threshold processing does not change the calculation of scalar phase delay and photoelastic path difference.

[0097] The Jones matrix is ​​used to describe deterministic, non-depolarized fully polarized transmission. Its eigenvalue decomposition provides the principal phase delay, the azimuth angle of the slow eigenstate, and the ellipticity angle of the slow eigenstate. Given a fully polarized input, the output polarization state can be calculated from the total Jones matrix. The photoelastic path difference is obtained by independent integration of the average refractive index perturbation and is not a direct eigenvalue of the total Jones matrix. Non-depolarized Jones results can be converted to an equivalent Mueller-Jones representation; if a true depolarization or statistical mixing effect needs to be described, a coherence matrix or Mueller model should be established separately.

[0098] Reference path verification methods can be used interchangeably or in combination. Besides the Jones reference solution for refracted rays and the layered Jones bridging solution for ray paths, other high-fidelity optical propagation calculations, validated numerical propagation models, experimental measurements, or representative boundary condition results can also be used as verification criteria. For scenarios with small curvature and insignificant path offset, the surface-layered Jones fast approximation method can be primarily used for multi-solution screening. For scenarios with large curvature, significant refraction path offset, or strong stress gradient changes, a fast approximation method can be used for initial screening, followed by verification using the reference solution or bridging solution for key solutions, thus achieving a balance between computational efficiency and result reliability.

[0099] Output evaluation metrics are calculated based on their input data. The Zernike coefficient is obtained by fitting the aperture field of the de-piston photoelastic path difference; path deviation is obtained by comparing geometric paths; residuals, root mean square residuals, correlation coefficients, and overlap in the high phase delay region are obtained by comparing the corresponding aperture fields of different solution methods. For assembly and adjustment support optimization, attention can be paid to the high phase delay region, low-order modes of the photoelastic path difference, and the over-limit area; for polarization performance evaluation, attention can be paid to the principal phase delay, intrinsic polarization state azimuth angle, and ellipticity.

[0100] This invention can be applied to various types of curved optical elements and assembly support structures. Applicable objects include, but are not limited to, curved lenses, plano-convex lenses, biconvex lenses, meniscus lenses, optical windows, protective windows, optical plates, transparent carriers, transmissive optical elements, and optical assemblies with support, pressure rings, adhesive bonding, clamping, or flexible support structures. Load sources may include assembly preload, clamping force, support reaction force, adhesive curing stress, gravity release, temperature changes, and environmental loads during transportation or service.

[0101] This invention can also be applied to various engineering design and evaluation scenarios. For example, it can be used to compare the effects of stress birefringence under different support schemes, clamping loads, assembly and adjustment states, structural parameters, material parameters, or wavelength conditions; it can also be used for support parameter optimization, clamping position optimization, assembly quality assessment, assessment of the impact of machining residual stress, environmental load sensitivity analysis, and rapid screening in the early stages of engineering. For schemes requiring final quantitative confirmation, the rapid screening results of this invention can be used as the basis for ranking candidate schemes, and then combined with high-fidelity reference calculations or experimental measurements for confirmation.

[0102] The effects of this disclosed method, system, and medium for analyzing layered Jones stress birefringence on curved surfaces are as follows: This disclosure utilizes surface conformal layering, finite element stress field structured mapping, algebraic ordering of transverse principal stresses, stress-optical transformation, and ordered accumulation of the Jones matrix to generate aperture-resolved principal phase retardation, slow intrinsic polarization azimuth angle, slow intrinsic polarization ellipticity angle, and equivalent birefringence; and independently accumulates the photoelastic path difference field through average refractive index perturbation. This simplifies the optical post-processing workflow for stress birefringence in curved optical elements, resulting in low analysis cost, minimal computational load, short analysis time, and high computational efficiency, thus improving the efficiency of multi-condition engineering screening and making it suitable for rapid screening of multiple solutions. Within the tested range, this method can reduce optical post-processing time and is suitable for rapid screening in multi-condition engineering.

[0103] Specifically: This invention simplifies the complex process of solving the propagation path of refracted rays; it eliminates the need to obtain the local stress state at each path sampling point, convert the stress state to a transverse plane related to the ray propagation direction, and then perform stress optical transformation. This invention has lower processing costs and facilitates rapid repeated execution of a large number of candidate solutions; it also eliminates the need to set multiple sampling segments along each ray path, and to complete stress interpolation, local birefringence calculation, and matrix accumulation for each segment. This invention improves computational efficiency and reduces computation time.

[0104] Compared to the complete refracted ray Jones reference method, this fast approximation embodiment replaces the tracing of the true refraction path point by aperture with a global Z-axis surface conformal layering, and reduces repeated three-dimensional finite element searches with structured layered stress mapping, thereby simplifying the optical post-processing workflow. This disclosure maps the discrete stress field of the finite element to the sampling point of the conformal layer of the surface, and completes the algebraic sorting of principal stresses, stress optical transformation and layer Jones matrix construction in a unified transverse coordinate base, which facilitates repeated execution of different candidate schemes using a consistent calculation chain. This disclosure accumulates the Jones matrix of each layer in an orderly manner according to the optical propagation sequence, preserving the sequential relationship between the local phase delay and the slow axis direction at different thickness locations; This disclosure clearly distinguishes between the intrinsic output of the total Jones matrix, the photoelastic path difference output generated by the average refractive index perturbation, and the evaluation index generated by the comparison of different aperture fields, thereby achieving a structured connection between the finite element stress field and polarization optics post-processing. This disclosure reduces path-by-path resampling by conformal surface layering and structured stress data, but the fast approximation results should still be verified by reference solution or bridging solution under conditions of high curvature, strong path offset or stress gradient mismatch. The conformal layering of the surface is jointly determined by the optical surfaces on the incident and exit sides, which can preserve the surface geometry and the global Z-axis local thickness variation; Finite element stress field mapping transforms discrete stress data into structured local stress tensors corresponding to aperture positions and conformal surface layering. A fixed global XY representation basis, algebraic sorting of transverse principal stresses, and ordered accumulation of the Jones matrix together ensure consistency in the fast approximation calculation chain. This disclosure is suitable for rapid comparison under multiple working conditions, multiple support schemes, multiple clamping loads, and multiple assembly and adjustment states; The applicability of the fast approximation can be evaluated by using the refracted ray Jones reference solution or the layered Jones bridging solution of the ray path, and the impact of the joint simplification of propagation, projection and sampling on the number of Jones update layers can be attributed. This disclosure is used to make a tiered selection between computational efficiency and result accuracy: first, a fast approximation method is used for batch screening, and then the key solutions are verified using a bridging solution or a refracted ray reference solution.

[0105] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0106] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0107] The embodiments described above are merely illustrative of several implementations of this disclosure, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this disclosure, and these all fall within the protection scope of this disclosure. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A method for analyzing birefringence of layered Jones stress on curved surfaces, characterized in that, include: Step 1: Obtain the operating wavelength, material parameters, geometric information, and finite element stress field of the curved optical element; Step 2: Determine the incident side surface and the exit side surface; Step 3: Create at least two conformal surface layers between the two surfaces; Using the global Z-axis as an approximate propagation direction and the fixed global XY coordinate base as a unified lateral representation base, the layer center and effective propagation length of each surface conformal layer are determined; Step 4: Map and interpolate the finite element stress field to the layer center to obtain the local stress tensor; Step 5: Construct transverse stress blocks, sort the transverse principal stresses by algebraic values, and calculate the refractive index perturbation of the two principal axes, the average refractive index perturbation, and the slow axis direction based on the stress-optic relationship. Step 6: Construct the Jones matrix for each layer based on the difference in refractive index perturbation between the two principal axes, the effective propagation length, and the slow axis direction; Step 7: Multiply the Jones matrices of each layer in the order of propagation to obtain the total Jones matrix; Step 8: Remove the common phase of the total Jones matrix, obtain the principal phase delay, slow intrinsic polarization azimuth angle and slow intrinsic polarization ellipticity angle based on matrix invariants and eigenvalue decomposition, and calculate the equivalent birefringence; obtain the photoelastic path difference by multiplying the cumulative average refractive index perturbation by the effective propagation length, and form an aperture output field at multiple aperture sampling positions.

2. The method for analyzing birefringence of layered Jones stress on curved surfaces according to claim 1, characterized in that, The finite element stress field information is discrete stress data; the incident side surface and the exit side surface are both described by geometric equations and discrete surface points, or by geometric equations and finite element mesh boundaries.

3. The method for analyzing birefringence of layered Jones stress on curved surfaces according to claim 1, characterized in that, The position of each conformal layer on the surface is determined by the incident side surface, the exit side surface, and the layer sequence parameter, which represents the relative position of the layer in the local thickness direction of the global Z-axis. No. The sampling position of the center of each conformal layer of the surface is: The conformal layering of the curved surface can be either equidistant or non-equidistant. When using equidistant stratification, , ; When using non-equidistant stratification, , or Each node according to The increasing direction is consistent with the order of light propagation; in, The aperture is the X-axis coordinate. The aperture is the Y-axis coordinate. For aperture coordinates, This represents the total number of conformal layers on the surface. This refers to the numbering of the conformal layering of the surface. For the first The center position vector of each conformal layer of the surface The height of the incident side surface. The height of the exit side surface. For the first A normalized sequence coordinate, The height of the incident side surface. The height of the exit side surface. For local thickness, , For the first The effective propagation length of a surface conforming to layering For the Gauss-Legendal node, As weight, For summation index.

4. The method for analyzing birefringence of layered Jones stress on curved surfaces according to claim 1, characterized in that, Step 4 includes: for swept finite element meshes, first interpolation is performed along the aperture direction within each swept finite element layer, and then interpolation is performed between adjacent swept finite element layers according to the normalized thickness coordinates; for non-swept finite element meshes, the local stress tensor at the sampling point at the center of the layer is obtained through three-dimensional element search and finite element shape function interpolation. The material parameters in step 1 include the unstressed refractive index. First stress optical coefficient Second stress optical coefficient ; Step 5 specifically includes: Extract global XY transverse stress blocks from the local stress tensor and sort the transverse principal stresses in descending order of their algebraic values; when the difference between transverse principal stresses is lower than a preset stress threshold, the sampling point is excluded from the statistics of the optical axis direction. according to and Calculate the refractive index perturbations along the two principal axes, and calculate the difference between the two principal axis perturbations; As a local birefringence optical path delay, with As the average refractive index perturbation of the photoelastic path difference, the principal axis with larger refractive index perturbation is designated as the slow axis, and the principal axis with smaller refractive index perturbation is designated as the fast axis; in, For a principal axis refractive index perturbation, For the refractive index perturbation of the other principal axis, The refractive index is the unstressed refractive index. and All are transverse principal stresses. , For axial stress components, For the first The effective propagation length of a curved, conformal layer.

5. The method for analyzing birefringence of layered Jones stress on curved surfaces according to claim 4, characterized in that, No. The Jones matrix for each conformal layer of the surface is: in, For the first Layer Jones matrix, In the direction of the slow axis, It is a two-dimensional rotation matrix along the slow axis. For layer phase delay, It is the imaginary unit.

6. The method for analyzing birefringence of layered Jones stress on curved surfaces according to claim 1, characterized in that, The method further includes: forming a principal phase delay field, a slow intrinsic polarization state azimuth angle field, a slow intrinsic polarization state ellipticity angle field, an equivalent birefringence field, and a photoelastic path difference field at multiple aperture sampling positions; obtaining evaluation indicators by comparing the corresponding aperture fields of the layered Jones bridging solution or the refracted ray Jones reference solution in step 8; the slow intrinsic polarization state azimuth angle residual is calculated using a dual-angle period, and only satisfies the condition simultaneously in the refracted ray Jones reference solution. and Statistics within the mask; among which, For reference, the ellipticity angle of the slow intrinsic polarization state, The ellipticity angle threshold. As a reference solution principal value phase delay, This is the phase delay threshold.

7. The method for analyzing birefringence of layered Jones stress on curved surfaces according to claim 1, characterized in that, The method further includes: using the refracted ray Jones reference solution and / or the ray path layered Jones bridging solution to perform result verification and / or error attribution on the aperture output field obtained in step 8.

8. The method for analyzing birefringence of layered Jones stress on curved surfaces according to claim 7, characterized in that, The error attribution of the aperture output field obtained in step 8 is specifically as follows: the ray path layered Jones bridge solution maintains the same total number of conformal layering layers as in step 3, while restoring the refraction propagation path, local ray coordinate projection, and finite element element sensing stress sampling; by comparing the corresponding aperture output fields of step 8, the ray path layered Jones bridge solution, and the refracted ray Jones reference solution, the relative dominance of the joint simplification error and the Jones layer update number error is determined.

9. A layered Jones stress birefringence analysis system for curved surfaces, characterized in that, include: The acquisition module is used to acquire the operating wavelength, material parameters, geometric information, and finite element stress field information of the curved optical element. A determination module is used to determine the incident side surface and the exit side surface; A module is established to create at least two conformal surface layers between the incident and exit surfaces. The global Z-axis direction is used as the fast approximate propagation direction, and the fixed global XY coordinate base is used as the unified lateral representation base to determine the layer center sampling position and effective propagation length of each conformal surface layer. The mapping and interpolation module is used to map and interpolate the finite element stress field to the layer center to obtain the local stress tensor. The stress optics calculation module is used to construct transverse stress blocks, sort transverse principal stresses by algebraic values, and calculate the refractive index perturbation of the two principal axes, the average refractive index perturbation, and the slow axis direction based on the stress optics relationship. The matrix construction module constructs Jones matrices for each layer based on the difference in refractive index perturbation between the two principal axes, the effective propagation length, and the slow axis direction. The cumulative module multiplies the Jones matrices of each layer in the order of propagation to obtain the total Jones matrix. The calculation module is used to remove the common phase of the total Jones matrix, obtain the principal phase delay, slow intrinsic polarization azimuth angle, and slow intrinsic polarization ellipticity angle based on matrix invariants and eigenvalue decomposition, calculate the equivalent birefringence, and obtain the photoelastic path difference by multiplying the accumulated average refractive index perturbation of each layer with the effective propagation length, forming an aperture output field at multiple aperture sampling positions.

10. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for analyzing the birefringence of Jones stress in a layered surface as described in any one of claims 1-8.

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