Subaperture splicing detection method based on frequency domain and space domain cooperation strategy

Abstract

The invention relates to the field of optical precision detection, in particular to a sub-aperture splicing detection method based on a frequency domain and space domain cooperative strategy, which comprises the following steps: collecting discrete phase data of sub-apertures; constructing a continuous physical field model; performing coarse alignment on the adjacent sub-apertures by using a frequency domain phase correlation technology to obtain integer pixel displacement between the adjacent sub-apertures; performing sub-pixel fine alignment through a numerical gradient method based on a normalized cross-correlation function of a continuous physical field model and an embedded geometric error elimination operator; constructing a global robust energy functional to carry out global optimization; and solving the zero-rotation pose under the floating reference, and performing Gaussian gradient weighted fusion and adaptive orthogonal substrate surface shape reconstruction to obtain the full-aperture surface shape of the large-aperture optical element. According to the method, the problems of high initial value dependence, displacement-inclination degeneracy, accumulative error warping, abnormal value sensitivity and the like of a traditional sub-aperture splicing detection method are solved, and ultrahigh precision and high robustness of large-aperture optical element sub-aperture splicing detection are realized.

Description

Technical Field

[0001] This invention belongs to the field of optical precision detection technology, and particularly relates to a sub-aperture stitching detection method based on a frequency domain and spatial domain collaborative strategy. Background Technology

[0002] Large-aperture optical elements are core components in high-end technology fields such as astronomical observation, high-energy laser systems, extreme ultraviolet lithography, and space exploration. As the performance requirements of optical systems continue to increase, the aperture of optical elements continues to grow, while the requirements for surface accuracy become increasingly stringent, often needing to reach sub-nanometer levels. However, traditional full-aperture interferometric testing methods face technical bottlenecks when dealing with large-aperture optical elements, including high manufacturing costs, difficulty in fabricating reference mirrors, and limited dynamic range, making it difficult to meet the demands of high-precision testing.

[0003] The sub-aperture stitching interferometry method has emerged as a crucial means to overcome the aforementioned bottlenecks. This method utilizes a small-aperture interferometer to collect local surface shape data of a large-aperture optical element in sections, and then uses algorithms to eliminate relative positional errors between sub-apertures, ultimately reconstructing the full-aperture surface shape. Compared to the full-aperture interferometry method, the sub-aperture stitching interferometry method offers advantages such as lower cost, greater flexibility, and higher resolution, making it particularly suitable for high-precision measurements of steep aspherical surfaces and freeform surfaces.

[0004] However, existing sub-aperture splicing detection methods still have the following technical shortcomings: (1) Spatial domain optimization is highly dependent on initial values ​​and is prone to getting trapped in local extrema: Most of the current mainstream algorithms are based on minimizing the phase difference in the spatial domain, which is a local optimization strategy. The accuracy of the initial coordinates is highly dependent on the mechanical guide rail, lacks a global perspective, and is prone to convergence failure due to initial value deviation.

[0005] (2) Degeneracy of displacement and tilt: In a smooth surface, lateral displacement and wavefront tilt are mathematically difficult to distinguish. If the tilt term is removed during registration, geometric displacement information will be lost; if the tilt term is retained, mechanical errors will be mixed into the positioning calculation, affecting the splicing accuracy.

[0006] (3) Accumulated error and non-physical warping: Traditional methods often use pairwise registration or least squares optimization with fixed references. The error accumulates with the stitching path, causing non-physical warping of the surface in distant areas, which affects the overall accuracy.

[0007] (4) Sensitive to outliers and lacking robustness: Most existing algorithms are based on L2 norm optimization, which lacks effective suppression of outliers such as airflow disturbance, dust diffraction rings, and edge artifacts, which can easily lead to surface distortion.

[0008] (5) Discretization accuracy limitation: Interpolation and matching methods based on pixel grids are difficult to achieve sub-pixel level high-precision positioning, especially in high curvature regions, the positioning error significantly affects the reconstruction accuracy.

[0009] In summary, existing sub-aperture stitching detection methods have significant shortcomings in terms of initial value dependence, error decoupling, global optimization, and robustness, making it difficult to meet the detection requirements of ultra-high precision optical components. Summary of the Invention

[0010] In view of this, the present invention aims to provide a sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy, in order to solve the problems of existing sub-aperture stitching interferometric detection methods, which rely on pure spatial-domain local optimization, resulting in strong initial value dependence, easy trapping in local extrema, difficulty in achieving sub-pixel accuracy, and lack of global error suppression capability.

[0011] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy includes the following steps: S1: Using an interferometer in conjunction with a precision displacement platform, the sub-aperture scanning measurement of the large-aperture optical element under test is performed in sections according to a preset overlap rate to obtain the phase data of each sub-aperture. The phase correlation method is used to coarsely align adjacent sub-apertures. While preserving the macroscopic contour features, the integer pixel displacement between adjacent sub-apertures is obtained. S2: Interpolate or fit the phase data of each sub-aperture to construct a continuous physical field model; S3: Using integer pixel displacement as the initial value, a normalized cross-correlation objective function with an embedded geometric error elimination operator is constructed on the continuous physical field model. Sub-pixel level micro-motion search is performed by numerical gradient method to solve the relative pose relationship between adjacent sub-apertures. S4: Based on the relative pose relationship between adjacent sub-apertures, a weighted graph Laplacian topology network is constructed with sub-apertures as nodes and the texture confidence of overlapping regions as weights, and a global robust energy functional is established. S5: Based on the global robust energy functional, construct and solve the regularized equation system to obtain the global zero-curvature pose of all sub-apertures under the floating reference. S6: Based on the global zero-curvature pose of all sub-apertures, perform coordinate transformation on the phase data of all sub-apertures to map the phase data of all sub-apertures to the global coordinate system. Use the continuous physics field model to resample the non-integer coordinate points after coordinate transformation to obtain the phase data of the overlapping area under the global grid. Then, perform Gaussian weighted fusion based on distance attenuation to obtain the full-aperture phase data of the large-aperture optical element under test. Adaptively select an orthogonal basis according to the shape of the large-aperture optical element under test to remove system aberrations and obtain the full-aperture surface shape of the large-aperture optical element under test.

[0012] Furthermore, in step S1, the phase correlation method is used to perform coarse alignment of adjacent sub-apertures. The specific process of obtaining the integer pixel displacement between adjacent sub-apertures while preserving macroscopic contour features is as follows: Phase data of the overlapping region of adjacent sub-apertures in ideal coordinates are extracted, and the tilt term of the sub-apertures is retained as a macroscopic contour feature. Calculate the normalized cross-power spectrum of the overlapping region phase data after retaining the tilt term. :

[0013] in, Indicates Fourier transform, and Indicates the sub-aperture i and j The phase data of the overlapping region extracted in ideal coordinates, Denotes the minimum regularization constant. Indicates complex conjugation; Performing an inverse Fourier transform on the normalized cross-power spectrum yields the correlation peak matrix. The peak position of the correlation peak matrix is ​​used as the integer pixel displacement between adjacent sub-apertures.

[0014] Furthermore, in step S3, the specific process of constructing the normalized cross-correlation objective function with embedded geometric error elimination operator is as follows: Sub-aperture i As a reference standard, with sub-aperture j As a floating sub-aperture; Define the embedded geometric error culling operator as the projection operator. Through the projection operator Remove sub-aperture i and j Mechanical errors in the phase data are used to obtain the sub-aperture. i and j Texture residual field and : ; ; in, A Represents the geometric basis matrix. T To represent the transpose of a matrix, Indicates sub-aperture i The original phase data, Indicates sub-aperture j raw phase data After rigid body transformation, in the sub-aperture i Phase data obtained by resampling in the reference coordinate system; The constructed normalized cross-correlation objective function is: ; in, NCC Indicates sub-aperture i and j The degree of matching of the texture residual field.

[0015] Furthermore, in step S3, the specific process of solving the relative pose relationship between adjacent sub-apertures by performing sub-pixel-level micro-motion search using the numerical gradient method is as follows: In the continuous physics model, with sub-aperture i and j Pose determined by integer pixel displacement between p Starting from the aperture, j Apply small perturbation Calculate the normalized cross-correlation objective function values ​​before and after the perturbation. and The gradient is calculated using the numerical difference method. :

[0016] Along gradient Iterative pose update in the direction The process continues until convergence, obtaining the relative pose relationship between adjacent sub-apertures. Indicates the current pose. This represents the pose after the iterative update. This represents the step size factor.

[0017] Furthermore, in step S4, the constructed global robust energy functional :

[0018] in, This represents all adjacent sub-aperture pairs. and Indicates sub-aperture i and j The pose to be optimized Indicates sub-aperture i and j The relative pose relationship between them. This represents the adaptive weights calculated based on the texture confidence of the overlapping region. This represents the Huber kernel function; Furthermore, adaptive weights The Hessian matrix at the peak of the overlapping region is calculated. H get: ; in, Representing the Hessian matrix H The determinant, The sign indicates proportionality.

[0019] Furthermore, the Huber kernel function Defined as: ; in, Represents the residual. , This represents the residual threshold.

[0020] Furthermore, the regularized equation set constructed in step S5 is as follows: ; in, This represents the weighted graph Laplacian matrix constructed based on the weighted graph Laplacian topology network. This represents the Tikhonov regularization term. This indicates the pose to be optimized. Indicates based on and The right-hand side of the construction.

[0021] Furthermore, in step S6, the specific process of performing distance-attenuation-based Gaussian weighted fusion on the phase data of overlapping regions in the global grid is as follows: For any pixel within the overlapping region of adjacent sub-apertures Calculate its distance to the center of its sub-aperture. Euclidean distance d Construct a Gaussian decay weight function :

[0022] in, The smoothing factor that controls the width of the fused region; Smooth fusion is achieved through weighted averaging:

[0023] in, This represents the fused phase data. Indicates the sub-aperture index. Indicates the first Weight of individual apertures, Indicates the first Phase values ​​of each aperture after coordinate transformation and resampling of non-integer coordinate points This indicates that all covered pixels... The sub-apertures are accumulated.

[0024] Furthermore, in step S6, the adaptive selection of orthogonal substrates to remove system aberrations based on the shape of the large-aperture optical element under test is specifically as follows: When the large-aperture optical element under test is a rectangular or square full-aperture, the normalized Legendre orthogonal polynomial is used as the orthogonal basis. When the large-aperture optical element under test is a circular full-aperture, Zernike polynomials are used as orthogonal basis. By using a linear combination of selected orthogonal bases, the system aberrations are reconstructed through least-squares fitting, and the system aberrations are removed from the full-aperture phase data of the large-aperture optical element under test.

[0025] Compared with the prior art, the present invention can achieve the following beneficial effects: 1. This invention abandons the limitations of traditional methods that rely solely on local spatial domain searches. It introduces frequency domain phase correlation technology in the coarse alignment stage and utilizes its global cross-correlation characteristics to quickly solve large-scale mechanical positioning errors. This effectively avoids interference from local extrema and edge pseudo-peaks common in spatial domain optimization, ensuring that the subsequent fine alignment stage is always within the attraction domain of the global optimal solution, thus significantly improving the stitching success rate and stability.

[0026] 2. This invention constructs a differentiable continuous physical field model, reconstructing the discrete phase matrix into a spatially continuous manifold, supporting accurate sampling and numerical differentiation operations at non-integer coordinates. Combined with an embedded geometric error culling operator, it achieves physical-level decoupling of translation and tilt errors, completely cutting off the propagation path of mechanical errors such as guide rail straightness and angular runout, thus improving registration accuracy from the traditional pixel level to the sub-pixel level.

[0027] 3. This invention constructs a global robust energy functional of a weighted graph Laplacian topology network and utilizes the Hessian matrix to quantify the texture confidence of overlapping regions, achieving adaptive weight allocation and avoiding the degradation of overall accuracy by low-texture regions. Simultaneously, it introduces the Huber kernel function to replace the traditional L2 norm, suppressing abnormal measurements such as airflow disturbances, dust diffraction rings, and edge artifacts, significantly improving the robustness of the algorithm and the reliability of the measurement data.

[0028] 4. This invention constructs a set of regularized equations to achieve automatic equilibrium solution of the entire mesh under a floating reference without forcibly fixing any sub-aperture. It forces the zero curl of the geometric closed loop and dissipates local measurement noise and system errors uniformly across the entire aperture range. This fundamentally solves the problem of surface warping in long-distance regions caused by error accumulation in traditional methods and reconstructs the surface shape to be closer to the true shape of the large-aperture optical element under test.

[0029] 5. This invention employs a Gaussian attenuation weighting function based on distance attenuation for fusion, assigning higher weights to the central region and lower weights to the edge region of the sub-aperture, effectively eliminating steps and artifacts at the splicing boundary. Simultaneously, it adaptively selects a normalized Legendre orthogonal polynomial or a Zernike polynomial as the orthogonal basis according to the shape of the large-aperture optical element under test, performing system aberration removal, significantly improving measurement accuracy, and ensuring that the detection results truly reflect the intrinsic morphology of the large-aperture optical element under test. Attached Figure Description

[0030] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic flowchart of the sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy as described in the embodiments of the present invention; Figure 2 A schematic diagram of the sub-aperture layered layout described in an embodiment of the present invention; Figure 3 A schematic diagram of the sub-aperture grid layout described in an embodiment of the present invention; Figure 4 A schematic diagram illustrating the construction of the continuous physical field model described in the embodiments of the present invention; Figure 4 In this context, (a) represents a discrete pixel. Figure 4 (b) in the figure represents the continuous physical field model. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0032] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0033] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0034] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "assembly," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0035] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0036] like Figure 1 As shown in the figure, an embodiment of the present invention provides a sub-aperture stitching detection method based on a frequency domain-spatial domain collaborative strategy, comprising the following steps: S1: Using an interferometer in conjunction with a precision displacement platform, the large-aperture optical element under test is scanned and measured in sections according to a preset overlap rate to obtain the phase data of each sub-aperture. The phase correlation method is used to coarsely align adjacent sub-apertures, and the integer pixel displacement between adjacent sub-apertures is obtained while preserving the macroscopic contour features.

[0037] Using a small-aperture interferometer in conjunction with a precision displacement platform, sub-aperture scanning measurements are performed on the large-aperture optical element (planar, spherical, aspherical, or freeform surface) under test, according to a preset overlap ratio. The scanning path of the sub-aperture adopts the following... Figure 2 The layered layout shown or as Figure 3 The grid layout shown ensures sufficient overlap between adjacent sub-apertures.

[0038] Obtained through measurement N Discrete phase data set of individual apertures Phase data for each sub-aperture Record as The pixel matrix, where Depending on the resolution of the interferometer camera, this pixel matrix serves as the initial data source for subsequent optimization.

[0039] This invention utilizes the phase correlation method to achieve coarse alignment of adjacent sub-apertures, obtaining integer pixel displacements between adjacent sub-apertures. The specific process is as follows: Based on the ideal coordinates (i.e. theoretical expected coordinates, which contain mechanical errors) provided by the precision displacement platform, the phase data of the overlapping area of ​​adjacent sub-apertures under the ideal coordinates are extracted, and the tilt term of the sub-apertures is retained as macroscopic contour features.

[0040] Unlike traditional methods, the tilt term of the sub-aperture is not removed during the coarse alignment stage. Instead, the low-frequency large-profile features are retained as macroscopic alignment signals to make full use of the frequency domain cross-correlation characteristics.

[0041] Calculate the normalized cross-power spectrum of the overlapping region phase data after retaining the tilt term. :

[0042] in, Indicates Fourier transform, and Indicates the sub-aperture i and j The phase data of the overlapping region extracted in ideal coordinates, This represents a minimal regularization constant to prevent division by zero errors. Indicates complex conjugation.

[0043] Normalized cross-power spectrum The numerator in the formula is used to calculate the diameter of two adjacent sub-pores. i and j The cross-power spectrum is then used to extract the cross-power spectrum of two adjacent sub-apertures. i and j Phase difference information between them.

[0044] Normalized cross-power spectrum The denominator in the formula is used to achieve spectral whitening. By dividing by the respective amplitude spectrum, the amplitude of each frequency component is normalized, resulting in a normalized cross-power spectrum. It retains only phase information and is unaffected by factors such as image lighting and contrast.

[0045] Performing an inverse Fourier transform on the normalized cross-power spectrum yields the correlation peak matrix. The position of the peak in the correlation peak matrix is ​​the position of the two adjacent sub-apertures. i andj Integer pixel displacement between .

[0046] This invention utilizes the global cross-correlation characteristics in the frequency domain to effectively suppress high-frequency pseudo-peak interference caused by the non-periodic truncation of overlapping region edges, ensuring that subsequent fine alignment algorithms are within the attraction domain of the global optimal solution.

[0047] S2: Interpolate or fit the phase data of each sub-aperture to construct a continuous physical field model.

[0048] To address the issue of truncation errors in sub-pixel accuracy caused by the limitations of detector pixel grid in traditional algorithms, this invention utilizes scatter interpolation or spline functions to analyze the discrete phase data for each sub-aperture. Perform interpolation or fitting to construct a continuous physics model. This continuous physics model This method reconstructs discrete pixel matrices into spatially continuous and differentiable optical phase field manifolds, supporting sampling and gradient calculation at non-integer coordinates. The construction of continuous physics models is as follows... Figure 4 As shown in (a) and (b), discrete pixels are reconstructed into a smooth, continuous surface.

[0049] Continuous Physics Model It supports phase value sampling and calculation of its first and second-order partial derivatives at non-integer coordinates, providing a foundation for subsequent numerical gradient optimization.

[0050] S3: Displacement in integer pixels Using the initial value, a normalized cross-correlation objective function with an embedded geometric error elimination operator is constructed on the continuous physical field model. The sub-pixel level micro-motion search is performed by numerical gradient method to solve the relative pose relationship between adjacent sub-apertures.

[0051] The integer pixel displacement between adjacent sub-apertures obtained in step S2 With the initial value as the starting point, the process proceeds to the sub-pixel fine alignment stage. The core of step S3 lies in constructing a normalized cross-correlation objective function with an embedded geometric error culling operator, and using a continuous physics model to perform numerical micro-motion search, thereby achieving physical-level decoupling between mechanical errors and real textures.

[0052] The specific process of constructing the normalized cross-correlation objective function with an embedded geometric error removal operator is as follows: Define the embedded geometric error culling operator as the projection operator. For any input sub-aperture phase data W, based on the geometric basis matrix A Constructing low-order geometric components And it is forcibly stripped to obtain a texture residual field with pure sub-aperture. : ; in, A This represents the geometric basis matrix containing translation and tilt components.

[0053] Texture residual field refers to the field obtained by using projection operators in sub-aperture stitching detection. After removing low-order geometric errors such as translation and tilt from the original phase data, the remaining pure high-frequency texture information reflects the real microstructure (such as scratches, dust, and feature patterns) on the surface of the large-aperture optical element under test. This information is then used for subsequent sub-pixel alignment and similarity comparison on the real optical texture.

[0054] Sub-aperture i and j For example, the sub-aperture i As a reference standard, the sub-aperture j As a floating sub-aperture; via projection operator Remove sub-aperture i and j Mechanical errors in the phase data are used to obtain the sub-aperture. i and j Pure texture residual field and : ; ; in, T To represent the transpose of a matrix, Indicates sub-aperture i The original phase data, Indicates sub-aperture j raw phase data After rigid body transformation, in the sub-aperture i The phase data is obtained by resampling in the reference coordinate system.

[0055] The normalized cross-correlation objective function constructed based on the embedded geometric error elimination operator is: ; in, NCC Indicates sub-aperture i and j The degree of matching of the texture residual field.

[0056] Normalized cross-correlation objective function It is a mathematical expression used to quantify the current pose. The alignment quality of the next two sub-apertures. In this invention, the normalized cross-correlation objective function... It is based on the normalized cross-correlation (NCC) of the texture residual field, and the objective function of the normalized cross-correlation is... A higher value indicates better alignment.

[0057] The specific process of solving the relative pose relationship between adjacent sub-apertures by performing sub-pixel-level micro-motion search using the numerical gradient method is as follows: In the continuous physics model, with sub-aperture i and j Integer pixel displacement between Determined pose p Starting from the aperture, j Apply small perturbation Calculate the normalized cross-correlation objective function values ​​before and after the perturbation. and The gradient is calculated using the numerical difference method. :

[0058] Along gradient Iterative pose update in the direction This process continues until convergence, at which point the pose represents the high-precision relative pose relationship between adjacent sub-apertures. , Indicates the current pose. This represents the pose after the iterative update. This represents the step size factor.

[0059] By filtering out low-order geometric terms in real time during iteration, the propagation path of mechanical errors such as guide rail straightness and angular runout into the final result is completely cut off, improving the registration accuracy from the traditional pixel level to the sub-pixel level.

[0060] S4: Based on the relative pose relationship between adjacent sub-apertures We construct a weighted graph Laplacian topology network with sub-apertures as nodes and overlapping region texture confidence as weights, and establish a global robust energy functional.

[0061] The high-precision relative pose relationship of each adjacent sub-aperture (i.e., sub-aperture pairs with overlapping regions) obtained in step S4. As observations (representing local optimal relative relationships), a global robust energy functional is constructed. This invention abandons the traditional serial splicing mode or fixed benchmark mode (least squares), and reconstructs the splicing of sub-apertures into a weighted graph Laplace topology network optimization problem, with sub-apertures as nodes and overlapping regions as edges.

[0062] Global robust energy functional Defined as:

[0063] in, This represents all adjacent sub-aperture pairs. and Indicates sub-aperture i and j The pose to be optimized Indicates sub-aperture i and j The relative pose relationship between them. This represents the adaptive weights calculated based on the texture confidence of the overlapping region. This represents the Huber kernel function.

[0064] Uncertainty perception weighting mechanism: Calculate the Hessian matrix at the peak of the overlapping region. H (Second derivative matrix), its determinant This reflects the sharpness of the matching peak. Define adaptive weights. In other words, regions with rich textures and sharp peaks (high confidence) are given high weights, while regions with smooth textures and flat peaks (low confidence) are automatically downweighted to avoid random matching of smooth regions that would lower the overall accuracy.

[0065] Huber kernel function immune mechanism: The Huber kernel function is defined as follows: ; in, Represents the residual. , This represents the residual threshold.

[0066] The Huber kernel function is effective against small errors ( Square optimization is performed on large errors () The Huber kernel function automatically degrades to linear, effectively isolating outliers from disrupting the global results. This demonstrates that the Huber kernel can automatically identify and isolate outliers. When a pair of sub-apertures experiences excessive error due to airflow or spurious peaks, the loss function automatically degrades to linear, preventing it from corrupting the global surface shape.

[0067] This invention constructs a global robust energy functional of a weighted graph Laplacian topology network and utilizes the Hessian matrix to quantify the texture confidence of overlapping regions, achieving adaptive weight allocation and avoiding the degradation of overall accuracy by low-texture regions. Simultaneously, it introduces the Huber kernel function to replace the traditional L2 norm, suppressing abnormal measurements such as airflow disturbances, dust diffraction rings, and edge artifacts, significantly improving the robustness of the algorithm and the reliability of the measurement data.

[0068] S5: Construct a set of regularized equations based on the global robust energy functional, and solve the set of regularized equations to obtain the global zero-curvature pose of all sub-apertures under the floating reference.

[0069] Based on a weighted graph Laplacian topology network (nodes are sub-apertures, edges are overlapping regions, and adaptive weights are used). Construct the weighted graph Laplace matrix L Its construction rule is: diagonal elements Off-diagonal elements The Laplace matrix of this graph L The network topology and confidence information are fully encoded.

[0070] The constructed regularized system of equations is as follows: ; in, This represents the Tikhonov regularization term. This indicates the pose to be optimized. Indicates based on and The right-hand side of the construction.

[0071] Introduction The significance lies in achieving floating datum solution: instead of forcibly fixing any sub-apertures, it prevents overall drift through extremely weak damping terms, allowing the entire mesh to automatically find the equilibrium state with minimum internal stress in space. This is due to the weighted graph Laplace matrix... L The solution to this system of equations satisfies zero curl, which forces the realization of zero curl, meaning that the cumulative displacement of any closed path is zero. This completely eliminates the problem of surface warping in distant regions caused by cumulative errors, and reconstructs the surface shape to be closer to the true shape of the large-aperture optical element under test.

[0072] S6: Based on the global zero-curvature pose of all sub-apertures, perform coordinate transformation on the phase data of all sub-apertures to map the phase data of all sub-apertures to the global coordinate system. Use the continuous physics field model to resample the non-integer coordinate points after coordinate transformation to obtain the phase data of the overlapping area under the global grid. Then, perform Gaussian weighted fusion based on distance attenuation to obtain the full-aperture phase data of the large-aperture optical element under test. Adaptively select an orthogonal basis according to the shape of the large-aperture optical element under test to remove system aberrations and obtain the full-aperture surface shape of the large-aperture optical element under test.

[0073] Based on the global zero-curvature poses of all sub-apertures obtained in step S5, the phase data of each sub-aperture are transformed from the local coordinate system to the global coordinate system for fusion and reconstruction. To eliminate stitching marks in overlapping areas and remove systematic errors, step S6 implements the following dual optimization strategy: 1. Gaussian gradient weighted fusion based on distance decay To address potential stitching artifacts in overlapping regions, a distance-dependent flexible fusion mechanism is proposed. This mechanism is applied to any pixel within the overlapping region under a global mesh. Calculate the pixel point ( x , y To the center of its sub-aperture Euclidean distance d : ; Based on Euclidean distance d Constructing a Gaussian decay weight function :

[0074] in, This represents the smoothing factor that controls the width of the fused region.

[0075] Smooth fusion is achieved through weighted averaging:

[0076] in, This represents the fused phase data. Indicates the sub-aperture index. Indicates the first Weight of individual apertures, Indicates the first Phase values ​​of each aperture after coordinate transformation and resampling of non-integer coordinate points This indicates that all covered pixels... The sub-apertures are accumulated.

[0077] This weighted averaging strategy assigns high weights to the central region of the sub-aperture (which has high data quality and low distortion) and low weights to the peripheral region (which is susceptible to diffraction effects), thus achieving a smooth transition from one sub-aperture to another and eliminating seams.

[0078] 2. Adaptive orthogonal basis surface reconstruction After obtaining the full-aperture fused data, it is necessary to remove the systematic low-order aberrations introduced by the detection optical path. For the different shapes of the large-aperture optical element under test, this invention proposes an adaptive substrate selection strategy: When the large-aperture optical element under test is rectangular or square full-aperture, the coordinates are mapped to a normalized Legendre orthogonal polynomial. Intervals, construct orthogonal basis; When the large-aperture optical element under test is a circular full-aperture, Zernike polynomials are used as orthogonal basis, which directly correspond to the physical meaning of optical aberrations (such as astigmatism and coma), and facilitate optical processing guidance. By using a linear combination of selected orthogonal bases, the system aberrations are reconstructed through least-squares fitting, and the system aberrations are removed from the full-aperture phase data of the large-aperture optical element under test.

[0079] This adaptive selection strategy ensures that regardless of whether the large-aperture optical element under test is elongated, square, or circular, the orthogonal basis with the best mathematical properties can be selected for systematic error removal, which significantly improves the measurement accuracy and makes the test results truly reflect the intrinsic morphology of the large-aperture optical element under test.

[0080] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0081] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy, characterized in that, Includes the following steps: S1: Using an interferometer in conjunction with a precision displacement platform, the sub-aperture scanning measurement of the large-aperture optical element under test is performed in sections according to a preset overlap rate to obtain the phase data of each sub-aperture. The phase correlation method is used to coarsely align adjacent sub-apertures. While preserving the macroscopic contour features, the integer pixel displacement between adjacent sub-apertures is obtained. S2: Interpolate or fit the phase data of each sub-aperture to construct a continuous physical field model; S3: Using integer pixel displacement as the initial value, a normalized cross-correlation objective function with an embedded geometric error elimination operator is constructed on the continuous physical field model. Sub-pixel level micro-motion search is performed by numerical gradient method to solve the relative pose relationship between adjacent sub-apertures. S4: Based on the relative pose relationship between adjacent sub-apertures, a weighted graph Laplacian topology network is constructed with sub-apertures as nodes and the texture confidence of overlapping regions as weights, and a global robust energy functional is established. S5: Based on the global robust energy functional, construct and solve the regularized equation system to obtain the global zero-curvature pose of all sub-apertures under the floating reference. S6: Based on the global zero-curvature pose of all sub-apertures, perform coordinate transformation on the phase data of all sub-apertures to map the phase data of all sub-apertures to the global coordinate system. Use the continuous physics field model to resample the non-integer coordinate points after coordinate transformation to obtain the phase data of the overlapping area under the global grid. Then, perform Gaussian weighted fusion based on distance attenuation to obtain the full-aperture phase data of the large-aperture optical element under test. Adaptively select an orthogonal basis according to the shape of the large-aperture optical element under test to remove system aberrations and obtain the full-aperture surface shape of the large-aperture optical element under test.

2. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 1, characterized in that, In step S1, the phase correlation method is used to coarsely align adjacent sub-apertures. The specific process of obtaining the integer pixel displacement between adjacent sub-apertures while preserving the macroscopic contour features is as follows: Phase data of the overlapping region of adjacent sub-apertures in ideal coordinates are extracted, and the tilt term of the sub-apertures is retained as a macroscopic contour feature. Calculate the normalized cross-power spectrum of the overlapping region phase data after retaining the tilt term. : in, Indicates Fourier transform, and Indicates the sub-aperture i and j The phase data of the overlapping region extracted in ideal coordinates, Denotes the minimum regularization constant. Indicates complex conjugation; Performing an inverse Fourier transform on the normalized cross-power spectrum yields the correlation peak matrix. The peak position of the correlation peak matrix is ​​used as the integer pixel displacement between adjacent sub-apertures.

3. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 1, characterized in that, In step S3, the specific process of constructing the normalized cross-correlation objective function with embedded geometric error elimination operator is as follows: Sub-aperture i As a reference standard, with sub-aperture j As a floating sub-aperture; Define the embedded geometric error culling operator as the projection operator. Through the projection operator Remove sub-aperture i and j Mechanical errors in the phase data are used to obtain the sub-aperture. i and j Texture residual field and : ； ； in, A Represents the geometric basis matrix. T To represent the transpose of a matrix, Indicates sub-aperture i The original phase data, Indicates sub-aperture j raw phase data After rigid body transformation, in the sub-aperture i Phase data obtained by resampling in the reference coordinate system; The constructed normalized cross-correlation objective function is: ； in, NCC Indicates sub-aperture i and j The degree of matching of the texture residual field.

4. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 3, characterized in that, In step S3, the specific process of solving the relative pose relationship between adjacent sub-apertures by performing sub-pixel-level micro-motion search using the numerical gradient method is as follows: In the continuous physics model, with sub-aperture i and j Pose determined by integer pixel displacement between p Starting from the aperture, j Apply small perturbation Calculate the normalized cross-correlation objective function values ​​before and after the perturbation. and The gradient is calculated using the numerical difference method. : Along gradient Iterative pose update in the direction The process continues until convergence, obtaining the relative pose relationship between adjacent sub-apertures. Indicates the current pose. This represents the pose after the iterative update. This represents the step size factor.

5. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 1, characterized in that, In step S4, the constructed global robust energy functional : in, This represents all adjacent sub-aperture pairs. and Indicates sub-aperture i and j The pose to be optimized Indicates sub-aperture i and j The relative pose relationship between them. This represents the adaptive weights calculated based on the texture confidence of the overlapping region. This represents the Huber kernel function.

6. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 5, characterized in that, Adaptive weights The Hessian matrix at the peak of the overlapping region is calculated. H get: ； in, Representing the Hessian matrix H The determinant, The sign indicates proportionality.

7. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 5, characterized in that, Huber kernel function Defined as: ； in, Represents the residual. , This represents the residual threshold.

8. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 1, characterized in that, The regularized equation set constructed in step S5 is as follows: ； in, This represents the weighted graph Laplacian matrix constructed based on the weighted graph Laplacian topology network. This represents the Tikhonov regularization term. This indicates the pose to be optimized. Indicates based on and The right-hand side of the construction.

9. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 1, characterized in that, In step S6, the specific process of performing distance-attenuation-based Gaussian weighted fusion on the phase data of the overlapping regions in the global grid is as follows: For any pixel within the overlapping region of adjacent sub-apertures Calculate its distance to the center of its sub-aperture. Euclidean distance d Construct a Gaussian decay weight function : in, The smoothing factor that controls the width of the fused region; Smooth fusion is achieved through weighted averaging: in, This represents the fused phase data. Indicates the sub-aperture index. Indicates the first Weight of individual apertures, Indicates the first Phase values ​​of each aperture after coordinate transformation and resampling of non-integer coordinate points This indicates that all covered pixels... The sub-apertures are accumulated.

10. The sub-aperture stitching detection method based on a frequency-domain and spatial-domain collaborative strategy according to claim 1, characterized in that, In step S6, the orthogonal substrate is adaptively selected to remove system aberrations based on the shape of the large-aperture optical element under test, specifically as follows: When the large-aperture optical element under test is a rectangular or square full-aperture, the normalized Legendre orthogonal polynomial is used as the orthogonal basis. When the large-aperture optical element under test is a circular full-aperture, Zernike polynomials are used as orthogonal basis. By using a linear combination of selected orthogonal bases, the system aberrations are reconstructed through least-squares fitting, and the system aberrations are removed from the full-aperture phase data of the large-aperture optical element under test.

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