CN-122021064-A - Spline modeling-based complex surface shape CGH gauge design method

CN122021064ACN 122021064 ACN122021064 ACN 122021064ACN-122021064-A

Abstract

The invention relates to the technical field of precision detection, in particular to a design method of a complex surface shape CGH gauge based on spline modeling, which comprises the steps of determining sampling points in the range of an effective aperture of the CGH, determining a target phase of each sampling point, constructing a current node model by adopting a B spline function as mathematical representation of the target phase, optimizing the current node model by utilizing the sampling points and the target phases thereof to obtain an optimal node model and an optimal node matrix corresponding to the optimal node model, and outputting data for CGH coding manufacturing based on the optimal node matrix. According to the invention, through an error-driven hierarchical node generation strategy, the problems of geometric mismatch and poor local adaptability of the traditional global basis function in complex surface shape fitting are solved, and design accuracy of sub picometer level is realized with a very small parameter quantity.

Inventors

WANG XIAOKUN
CAI MINGXUAN
CAI MENGXUE
GUO SHUTONG
ZHANG XUEJUN

Assignees

中国科学院长春光学精密机械与物理研究所

Dates

Publication Date: 20260512
Application Date: 20260407

Claims (9)

1. A design method of a complex surface shape CGH gauge based on spline modeling is characterized by comprising the following steps: s1, determining sampling points in the range of the CGH effective aperture, and determining a target phase of each sampling point; s2, constructing a current node model by using the B spline function as the mathematical representation of the target phase, and optimizing the current node model by using the sampling points and the target phase thereof obtained in the step S1 to obtain an optimal node model and an optimal node matrix corresponding to the optimal node model; And S3, outputting data for CGH coding manufacturing based on the optimal node matrix obtained in the step S2.
2. The spline modeling-based complex surface shape CGH gauge design method according to claim 1, wherein in step S1: the target phase for each sample point is determined by: ; Wherein, the i Representing the target phase of the i-th sample point, λ representing the wavelength of the reference light emitted to the CGH, OPD i representing the optical path difference between the reference light and the ray trace of the target light at the i-th sample point.
3. The spline modeling-based complex surface shape CGH gauge design method according to claim 1, wherein the process of constructing the current node model in step S2 comprises: s21, uniformly selecting a small number of sampling points from all the sampling points in the selection step S1 to serve as nodes, and constructing an initial spline function of the nodes by taking the phase as output and the coordinates of the sampling points as input; S22, calculating the difference value of the target phases corresponding to the initial spline function and all sampling points in the step S21 to obtain initial global residual distribution mapped to each node interval; S23, finding intervals to be optimized according to residual error distribution in each node interval obtained in the step S22, and dynamically inserting new nodes into all the intervals to be optimized; S24, merging the new node inserted in the step S23 with the original node, and maintaining the node density unchanged; S25, constructing an overdetermined equation set which takes all target phases as targets and takes spline coefficients as unknowns according to the current spline function obtained in the step S24; S26, solving the minimum norm solution of the overdetermined equation set in the step S25, obtaining a spline coefficient with the minimum global residual square sum under the current node distribution, and obtaining a current node model, wherein the corresponding current node distribution is the current node matrix.
4. The spline modeling-based complex surface shape CGH gauge design method according to claim 3, wherein the process of dynamically inserting new nodes into all intervals to be optimized in step S23 comprises: S231, arranging all intervals to be optimized in descending order according to the maximum residual error value of the intervals to be optimized to obtain a sequencing index sequence; S232, selecting the first eta percent of intervals to be optimized from the intervals sequenced in the step S231 as a set to be encrypted of the round, and inserting a new node at the geometric midpoint of the eta percent of intervals to be optimized to obtain a plurality of new node intervals; And S233, calculating the interval width of each new node interval in the step S232, repeating the operations from the step S231 to the step S232 by using the new node interval with all the interval widths being greater than or equal to the preset minimum node interval threshold.
5. The spline modeling-based complex surface shape CGH gauge design method according to claim 3, wherein the system of overdetermined equations in step S25 is: ; wherein J (c) represents an overdetermined equation set for solving spline coefficients c of the spline function, mu k represents the shape of the surface of the kth sampling point, target (μ k ) Representing the target phase corresponding to the kth sampling point, M representing the total number of sampling points, c i representing the ith spline coefficient in the spline function, N representing the total number of spline coefficients, and N i,p representing the ith term p times of the B spline basis function in the spline function.
6. The spline modeling-based complex surface shape CGH gauge design method according to claim 1, wherein the stopping condition optimized in step S2 is that the maximum residual of the node matrix currently obtained is smaller than a preset residual threshold.
7. The spline modeling-based complex surface shape CGH gauge design method according to claim 1, wherein the step S2 further comprises verifying the obtained optimal node matrix by using the analysis property and the numerical iterative algorithm of the B spline.
8. The spline modeling based complex surface shape CGH gauge design method according to claim 7, wherein the verification process comprises: determining a plurality of sampling points mutually exclusive with those in the step S1 in the CGH effective aperture range, and constructing a verification point set; Based on the obtained optimal node model, directly analyzing and calculating the phase gradient at any verification point in the CGH effective aperture by utilizing the derivative property of the B spline; according to the calculated phase gradient, determining a reverse vector of light emitted from the CGH, and establishing a surface light parameter equation from the CGH plane to the optical element to be measured based on the reverse vector to obtain an emitting point of the light emitted from the CGH: ; Wherein, the Represents the reverse vector, t represents the optical path parameter, Representing the spatial position coordinates of the light corresponding to the optical path parameter t, Representing an initial space coordinate point of the light ray on the CGH plane, namely coordinates of an emergent point of the light ray on the CGH plane; The CGH emits light rays from the emergent point to the surface of the optical element to be detected, and a normal vector at the intersection point of the surface of the optical element to be detected and the light rays is determined; Constructing a forward ray path returning to the CGH plane from the surface of the optical element to be detected based on the normal vector, and obtaining a return point of the return ray and the CGH plane; and calculating the geometric position deviation and the light angle deviation between the emergent point and the return point.
9. The spline modeling based complex surface shape CGH gauge design method according to claim 8, wherein the optical path parameters are obtained by iterative solution of: ; wherein t j represents an optical path parameter obtained by the jth iteration, F represents a surface shape equation of the optical element to be measured, and alpha represents an under-relaxation factor.

Description

Spline modeling-based complex surface shape CGH gauge design method Technical Field The invention belongs to the technical field of precision detection, and particularly relates to a design method of a complex surface shape CGH gauge based on spline modeling. Background In modern optical manufacturing, off-axis aspheric surfaces, cylindrical mirrors, free-form surfaces and other complex surface shapes are increasingly widely used. The CGH (Computer Generated Hologram, hologram) is a core compensator that enables such surface-shaped high-precision null detection as a kind of diffractive optical element capable of producing arbitrarily complex wave fronts. The design goal of CGH is to convert a standard reference wave (such as a plane wave or spherical wave) output by an interferometer into a target wavefront that exactly matches the theoretical shape of the surface being measured. Existing CGH design methods mainly employ global polynomial fitting (e.g., zernike polynomials, XY polynomials) or fixed grid sampling (GRID PHASE). In the detection of complex surface shapes facing large caliber, large off-axis quantity or non-rotational symmetry (such as cylindrical surface), the prior art has the following remarkable defects: (1) Geometry mismatch problem Zernike polynomials are defined on unit circle fields with rotational symmetry. While the aperture of many complex optical elements is elongated or rectangular and the shape of the face exhibits unidirectional bending characteristics. Forcibly fitting the cylindrical phase of the rectangular domain with the Zernike of the circular domain can result in severe mathematical mismatch; (2) When the target phase is in a local change violent (such as off-axis, free-form surface edge and local steep area), the global polynomial/fixed basis function with fixed order may have local residual increase or oscillation phenomenon, and the order needs to be increased to cause unstable model and expansion of parameter quantity; (3) In order to achieve the nano-scale detection precision, the traditional direct sampling method needs extremely high sampling rate, so that data files are huge and optimization is difficult; (4) The local adaptability is poor, and the complex curved surface tends to be in a region with severe local curvature change (such as a region with large off-axis quantity), and other regions are gentle. The traditional global polynomial or uniform sampling can not allocate computing resources according to local characteristics as required, undersampling or oversampling easily occurs, and the method is unfavorable for the generation of subsequent manufacturing files, the analysis of spatial frequency and the control of errors. Disclosure of Invention In view of the above, the invention aims to provide a design method of a complex surface shape CGH gauge based on spline modeling, which constructs a spline phase model through an error-driven hierarchical node self-adaptive refinement strategy, outputs phase data which can be used for CGH coding manufacturing and checking, solves the problems of geometric mismatch and poor local adaptability of the traditional global basis function in complex surface shape fitting, and realizes sub-picometer design precision with a small amount of parameters. In order to achieve the above purpose, the technical scheme of the invention is realized as follows: a design method of a complex surface shape CGH gauge based on spline modeling comprises the following steps: s1, determining sampling points in the range of the CGH effective aperture, and determining a target phase of each sampling point; s2, constructing a current node model by using the B spline function as the mathematical representation of the target phase, and optimizing the current node model by using the sampling points and the target phase thereof obtained in the step S1 to obtain an optimal node model and an optimal node matrix corresponding to the optimal node model; And S3, outputting data for CGH coding manufacturing based on the optimal node matrix obtained in the step S2. Further, in step S1, the target phase for each sample point is determined by: ; Wherein, the i Representing the target phase of the i-th sample point, λ representing the wavelength of the reference light emitted to the CGH, OPD i representing the optical path difference between the reference light and the ray trace of the target light at the i-th sample point. Further, the process of constructing the current node model in step S2 includes: s21, uniformly selecting a small number of sampling points from all the sampling points in the selection step S1 to serve as nodes, and constructing an initial spline function of the nodes by taking the phase as output and the coordinates of the sampling points as input; S22, calculating the difference value of the target phases corresponding to the initial spline function and all sampling points in the step S21 to obtain initial global residual distribution m