Method and system for detecting surface profile of large-aperture plane mirror in vacuum environment

Abstract

The present application relates to the technical field of surface detection, in particular to a surface detection method and system for a large-aperture plane mirror in a vacuum environment, the method comprising constructing a full-aperture spatial discrete mapping model, layering full-aperture surface parameters according to spatial frequency, extracting common modal parameters corresponding to low-frequency surface components in each sub-aperture measurement result, explicitly introducing the common modal parameters into a stitching equation as a global constraint term, and constructing a stitching matrix; and performing block reconstruction processing on the stitching matrix. The present application effectively solves the problem of insufficient surface stitching stability under the condition of reducing the sub-aperture overlap ratio without relying on a super-large-aperture interferometer and without interrupting the existing detection system of the Ritchey-Corman method, realizes the consideration of detection efficiency and surface reconstruction accuracy, and has significant engineering practical value and promotional significance.

Description

Technical Field

[0001] This invention relates to the field of surface shape detection technology, specifically to a method and system for detecting the surface shape of a large-aperture plane mirror under vacuum conditions. Background Technology

[0002] With the development of space optics, extreme ultraviolet lithography, and high-precision remote sensing systems, the surface accuracy requirements for large-aperture plane mirrors in vacuum environments are constantly increasing. Due to the influence of manufacturing processes, transportation and assembly, and service conditions, large-aperture plane mirrors must undergo high-precision surface shape inspection before final application. Limited by the high difficulty and cost of manufacturing and calibrating ultra-large aperture interferometers, existing technologies are increasingly adopting the Richter-Command method based on small-aperture standard spherical mirrors for the inspection of large-aperture plane mirrors. This method achieves full-aperture surface shape reconstruction through multi-angle sub-aperture scanning combined with phase stitching algorithms, and has attracted widespread attention due to its low equipment requirements and wide applicability range.

[0003] However, in practical engineering applications, the inspection of large-aperture plane mirrors is often constrained by factors such as inspection cycle, vacuum stabilization time, and system drift. To shorten the overall inspection cycle, existing technologies typically improve inspection efficiency by reducing the number of sub-aperture scans or decreasing the overlap ratio between adjacent sub-apertures. While these approaches can reduce inspection time costs, they directly weaken the spatial correlation between sub-aperture data, resulting in insufficient constraints in the phase reconstruction matrix constructed during the stitching process. This leads to a deterioration of the stitching matrix condition number. When the stitching matrix condition number deteriorates, the surface reconstruction process becomes highly sensitive to measurement noise, attitude perturbations, and time drift. Small errors can be amplified into full-aperture low-frequency distortion or overall curvature drift, causing the inspection results to appear continuous on the surface but distort their physical meaning. Especially in the inspection of large-aperture plane mirrors, such errors are difficult to eliminate effectively through repeated measurements or post-processing. They are easily misjudged as real surface defects, thus misleading subsequent optical reshaping, system assembly, and engineering applications, leading to quality and reliability risks.

[0004] Therefore, existing large-aperture plane mirror detection methods based on sub-aperture stitching generally lack effective control over the stability of the stitching matrix and global constraint capabilities when reducing the sub-aperture overlap ratio, making it difficult to achieve a balance between detection efficiency and surface reconstruction accuracy. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions.

[0006] This invention employs the following technical solution: a method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions, comprising:

[0007] A full-aperture spatial discrete mapping model is constructed, and the full-aperture surface parameters are represented in layers according to spatial frequency, and a minimum observation constraint relationship is set.

[0008] Under the constraints of the full-aperture spatial discrete mapping model, the scanning positions of each sub-aperture are globally optimized and sorted so that adjacent sub-apertures form a coupled relationship in the low-frequency surface component dimension and maintain independent sampling in the high-frequency surface component dimension.

[0009] Extract the common modal parameters corresponding to the low-frequency surface shape components from the measurement results of each sub-aperture, and explicitly introduce the common modal parameters into the splicing equation as global constraint terms to construct the splicing matrix;

[0010] The splicing matrix is ​​processed by block reconstruction, and the full aperture surface reconstruction problem is decomposed into a low-frequency constraint subsystem and a mid-to-high frequency local correction subsystem. The solution of the low-frequency constraint subsystem is used as the boundary condition of the mid-to-high frequency local correction subsystem.

[0011] Based on the results of block reconstruction, a consistency inversion analysis is performed on the measurement residuals of each sub-aperture to identify sub-aperture combinations that contribute more than a preset threshold to the condition number deterioration, and an adaptive weight adjustment mechanism is introduced for the corresponding sub-aperture data.

[0012] The full-aperture surface profile results are back-substituted for verification. The reconstructed surface profile is back-projected onto the measurement domain of each sub-aperture. The consistency between the common modal parameters corresponding to the low-frequency surface profile components and the original measurements is checked. The common modal parameters are then corrected to form a closed-loop stitching process.

[0013] As a further description of the above technical solution: the method for constructing a full-aperture spatial discrete mapping model includes:

[0014] The effective aperture size of the large-aperture plane mirror under test is obtained, and the single effective sub-aperture range of the standard spherical mirror under the Rickie-Comman test configuration is obtained. Taking the geometric center of the large-aperture plane mirror under test as the reference origin, the full aperture region is discretized by regular grid in the mirror coordinate system. The full aperture is divided into multiple surface sampling nodes with fixed spatial sampling intervals. A full aperture spatial discretization mapping model is established so that each surface sampling node corresponds to a surface height parameter to be reconstructed.

[0015] As a further description of the above technical solution: the method of representing the full aperture surface parameters in layers according to spatial frequency and setting minimum observation constraint relationships includes:

[0016] By using a pre-defined set of spatial basis functions, the surface height parameter is decomposed into low-frequency surface components, mid-frequency surface components, and high-frequency surface components. The low-frequency surface components are used to characterize the overall tilt, overall curvature, and large-scale deformation characteristics of the spatial wavelength, which is greater than the feature size of a single effective detection sub-aperture. The mid-frequency surface components are used to characterize the slow undulation changes across the sub-aperture when the spatial wavelength is close to the coverage scale of the sub-aperture. The high-frequency surface components are used to characterize the local processing errors and small surface undulations when the spatial wavelength is smaller than the feature size inside the sub-aperture.

[0017] Minimum observation constraints are set for different spatial frequency surface components under a single sub-aperture and a combination of multiple sub-apertures. The low-frequency surface component forms a joint coverage across multiple sub-apertures, the mid-frequency surface component forms a continuous coverage between adjacent sub-apertures, and the high-frequency surface component is limited to observation within a single sub-aperture.

[0018] As a further description of the above technical solution: the method for globally optimizing and sorting the scanning positions of each sub-aperture includes:

[0019] Each sub-aperture scanning position is mapped in the full-aperture spatial discrete mapping model to determine the set of discrete sampling nodes covered by the corresponding sub-aperture scanning position. The projection weight distribution of the covered set of discrete sampling nodes in the basis function space corresponding to the low-frequency surface component is calculated to obtain the observation contribution characteristics of the corresponding sub-aperture to the low-frequency surface component.

[0020] A global correlation graph is constructed with sub-aperture scanning positions as nodes. The connection weight between nodes is determined by the similarity of the observation contribution features of their low-frequency surface components. By traversing and analyzing the global correlation graph, combinations of sub-aperture scanning positions that are correlated in the dimension of low-frequency surface components are identified, and a global optimized sorting sequence of sub-aperture scanning positions is formed.

[0021] While forming the global optimized sorting sequence, local independence analysis is performed on the discrete node set covered by each sub-aperture scanning position for high-frequency surface components.

[0022] Based on the constraints, the scanning position is iteratively adjusted to minimize the physical overlap ratio between adjacent sub-apertures while ensuring the global observability of low-frequency surface components, thus obtaining the optimized global sorting sequence.

[0023] As a further description of the above technical solution: the method for extracting the common modal parameters corresponding to the low-frequency surface shape components in the measurement results of each sub-aperture includes:

[0024] Modal projection processing is performed on the measurement results of each sub-aperture to map the surface shape measurement data within the sub-aperture to the basis function space corresponding to the low-frequency surface shape component, thereby obtaining the low-frequency modal parameter vector corresponding to each sub-aperture.

[0025] Based on the sub-aperture layout after global optimization and sorting, a consistency analysis is performed on the low-frequency modal parameter vectors between adjacent sub-apertures.

[0026] Extract the low-frequency modal parameter vectors that repeat in multiple sub-apertures and have a consistent trend of change, and define the corresponding low-frequency modal parameter vectors as the common modal parameters corresponding to the low-frequency surface components.

[0027] As a further description of the above technical solution: the method for performing block reconstruction processing on the spliced ​​matrix includes:

[0028] The unknown parameters in the splicing matrix are rearranged according to the frequency dimension. The unknown parameters and common modal parameters corresponding to the low-frequency surface components are divided into a set of low-frequency constraint parameters, and the unknown parameters corresponding to the mid-frequency surface components and high-frequency surface components are divided into a set of mid-high frequency local correction parameters, thus forming a frequency partitioning structure in the parameter space.

[0029] Based on the frequency partitioning structure, the splicing matrix is ​​reconstructed in blocks, and the original splicing matrix is ​​split into a low-frequency constraint submatrix, a mid-to-high frequency local correction submatrix, and a connection submatrix describing the coupling relationship between the low-frequency constraint parameter set and the mid-to-high frequency local correction parameter set.

[0030] After completing the block reconstruction of the splicing matrix, the low-frequency constraint subsystem is solved independently first. The full-aperture low-frequency surface shape solution is obtained through the joint constraints between the common modal parameters and the low-frequency surface shape components.

[0031] After obtaining the full-aperture low-frequency surface shape solution of the low-frequency constraint subsystem, the full-aperture low-frequency surface shape solution is explicitly introduced as a boundary condition into the mid-to-high frequency local correction subsystem.

[0032] The low-frequency constraint subsystem consists of a low-frequency constraint submatrix and a low-frequency constraint parameter set; the mid-to-high frequency local correction subsystem consists of a mid-to-high frequency local correction submatrix and a mid-to-high frequency local correction parameter set.

[0033] As a further description of the above technical solution: the method of performing consistency inversion analysis on the measurement residuals of each sub-aperture, identifying sub-aperture combinations whose contribution to condition number deterioration exceeds a preset threshold, and introducing an adaptive weight adjustment mechanism for the corresponding sub-aperture data includes:

[0034] The measurement value of each sub-aperture is differentially divided with its corresponding block reconstruction prediction value to obtain the prediction residual vector;

[0035] By constructing a residual covariance matrix, the residual contribution value of each sub-aperture or sub-aperture combination in the parameter space is calculated, and the sub-apertures or sub-aperture combinations that exceed the preset contribution value threshold are marked according to the residual contribution value.

[0036] For the labeled sub-aperture measurement data, an adaptive weight adjustment mechanism is introduced to determine the weight of each sub-aperture based on its residual contribution value. The larger the residual contribution value, the smaller the weight of the corresponding sub-aperture.

[0037] After completing the adaptive weight adjustment, the splicing matrix is ​​reconstructed and solved jointly.

[0038] As a further description of the above technical solution: the method for back-substitution verification of the full-aperture surface profile results includes:

[0039] Step S01: Based on the spatial position of the sub-aperture in the full aperture, map the corresponding full aperture surface shape result to the discrete sampling nodes covered by each sub-aperture to form sub-aperture predicted surface shape data.

[0040] Step S02: Difference the predicted sub-aperture surface data with the original sub-aperture measurement results and calculate the original residual vector;

[0041] Step S03: For the low-frequency surface component, calculate the projection amplitude of the original residual vector of each sub-aperture in the common modal space, and obtain the global consistency index by statistically analyzing the projection amplitudes of all sub-apertures.

[0042] Step S04: The mean or weighted average value of the original residual vector projected onto the common modal space is used as the correction value to update the common modal parameters. The updated common modal parameters are then re-embedded into the splicing matrix, and the splicing and solving are performed again to generate a new full-aperture surface shape result.

[0043] Step S05: Repeat steps S01-S04 until the global consistency index reaches the preset consistency threshold, and obtain the final full-aperture surface reconstruction result.

[0044] As a further description of the above technical solution: the global consistency index is the mean square residual or the maximum residual of the projected amplitude of all sub-apertures.

[0045] A surface profile detection system for a large-aperture plane mirror under vacuum conditions, the system comprising:

[0046] The full-aperture discrete modeling module constructs a full-aperture spatial discrete mapping model, represents the full-aperture surface parameters in layers according to spatial frequency, and sets minimum observation constraint relationships;

[0047] The sub-aperture layout optimization module, under the constraints of the full-aperture spatial discrete mapping model, performs global optimization and sorting of the scanning positions of each sub-aperture, so that adjacent sub-apertures form a coupled relationship in the low-frequency surface component dimension, while maintaining independent sampling in the high-frequency surface component dimension.

[0048] The low-frequency common mode module extracts the common mode parameters corresponding to the low-frequency surface shape components from the measurement results of each sub-aperture, and explicitly introduces the common mode parameters into the splicing equation as global constraint terms to construct the splicing matrix;

[0049] The splicing matrix block module performs block reconstruction processing on the splicing matrix, decomposes the full aperture surface reconstruction problem into a low-frequency constraint subsystem and a mid-to-high frequency local correction subsystem, and uses the solution of the low-frequency constraint subsystem as the boundary condition of the mid-to-high frequency local correction subsystem.

[0050] The hierarchical stability solution module, combined with the results of block reconstruction, performs consistency inversion analysis on the measurement residuals of each sub-aperture, identifies sub-aperture combinations whose contribution to condition number deterioration exceeds a preset threshold, and introduces an adaptive weight adjustment mechanism for the corresponding sub-aperture data.

[0051] The closed-loop consistency correction module performs back-substitution verification on the full-aperture surface profile results, back-projects the reconstructed surface profile to each sub-aperture measurement domain, examines the consistency between the common modal parameters corresponding to the low-frequency surface profile components and the original measurements, corrects the common modal parameters, and forms a closed-loop stitching process.

[0052] The beneficial effects of this invention are as follows:

[0053] This invention addresses the problem of insufficient stability in surface stitching under reduced sub-aperture overlap ratios in the existing Richie-Comman method. By introducing a full-aperture spatial discrete mapping and a surface spatial frequency hierarchical modeling mechanism, it structurally constrains the surface components at different spatial scales at the parameter level of surface reconstruction. This ensures that the full-aperture surface has clear and observable boundary conditions in the low-frequency, mid-frequency, and high-frequency dimensions, fundamentally avoiding the problem of global degree of freedom loss caused by the weakening of the factor aperture coverage relationship, and improving the physical reliability of the stitching process.

[0054] The splicing matrix is ​​further reconstructed in blocks, and the full-aperture surface reconstruction process is divided into a low-frequency constraint subsystem and a mid-to-high-frequency local correction subsystem. A solution strategy of prioritizing low frequencies and passing them step by step is adopted, so that the low-frequency solution can be used as the boundary condition for mid-to-high-frequency reconstruction in subsequent solutions. This avoids mid-to-high-frequency local noise or measurement instability factors from back-contaminating the overall surface reference, thereby reducing the condition number of the splicing matrix at the overall level and improving the stability of the numerical solution process. Attached Figure Description

[0055] The present invention will be further explained below with reference to the accompanying drawings and embodiments:

[0056] Figure 1 This is a flowchart of a method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions, provided in Embodiment 1 of the present invention.

[0057] Figure 2 This is a flowchart of the method for constructing a full-aperture spatial discrete mapping model provided in Embodiment 1 of the present invention;

[0058] Figure 3 This is a flowchart of the method for back-substitution verification of full-aperture surface profile results provided in Embodiment 1 of the present invention;

[0059] Figure 4 This is a module connection diagram of the surface shape detection system for a large-aperture plane mirror in a vacuum environment provided in Embodiment 2 of the present invention. Detailed Implementation

[0060] To make the technical means, creative features, objectives, and effects of this invention readily understandable, the invention is further described below with reference to specific illustrations. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0061] Example 1:

[0062] Please see Figures 1-3 This invention provides a technical solution: a method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions, comprising:

[0063] Based on the effective aperture size of the large-aperture plane mirror under test and the effective detection sub-aperture range of the standard spherical mirror, a full-aperture spatial discrete mapping model is constructed. In this full-aperture spatial discrete mapping model, the full-aperture surface parameters are represented in layers according to spatial frequency, and the minimum observation constraint relationship of low-frequency, mid-frequency and high-frequency surface components in sub-aperture coverage is clarified, providing a structured prior basis for subsequent splicing stability control.

[0064] Specifically, the effective aperture size of the large-aperture plane mirror under test is first obtained, and the single effective detection sub-aperture range of the standard spherical mirror under the Rickie-Comman detection configuration is obtained. A mirror coordinate system is established, where the X / Y axes are the mirror plane and the Z axis is the mirror normal. The geometric center of the large-aperture plane mirror under test is used as the reference origin. The full aperture area is discretized by regular grid in the mirror coordinate system, and the full aperture is divided into multiple surface sampling nodes with fixed spatial sampling intervals. Thus, a full aperture spatial discrete mapping model is established, so that each surface sampling node corresponds to a surface height parameter to be reconstructed.

[0065] Based on the aforementioned full-aperture spatial discrete mapping model, the full-aperture surface profile parameters are represented hierarchically according to spatial frequency characteristics. Specifically, through a preset set of spatial basis functions, the surface profile height parameter is decomposed into low-frequency, mid-frequency, and high-frequency surface profile components. The low-frequency components characterize overall tilt, overall curvature, and large-scale deformation features; the mid-frequency components characterize slow fluctuations across sub-aperture scales; and the high-frequency components characterize local processing errors or minute surface profile undulations. The basis functions corresponding to each frequency layer have different spatial support scales on the discrete sampling grid, thus achieving a hierarchical representation of surface profile information.

[0066] It should be noted that the set of spatial basis functions refers to a set of two-dimensional spatial functions predefined on the full-aperture discrete sampling grid, which are used to represent the height distribution of the measured optical surface as a linear combination of components of different spatial scales, so that the full-aperture surface parameters can be described in layers according to spatial frequency characteristics.

[0067] The set of spatial basis functions includes at least three categories: low-frequency spatial basis functions, mid-frequency spatial basis functions, and high-frequency spatial basis functions. Specifically: low-frequency spatial basis functions are used to describe overall surface shape changes covering the entire aperture range, and their spatial support region is not smaller than the effective detection area of ​​the measured aperture; mid-frequency spatial basis functions are used to describe slow surface shape undulations across multiple adjacent sub-apertures, and their spatial support region covers the measurement range of at least two sub-apertures; high-frequency spatial basis functions are used to describe minute surface shape undulations within a local sub-aperture, and their spatial support region is limited to the measurement range of a single sub-aperture or its local area.

[0068] The low-frequency spatial basis functions can be selected from low-order Zernike polynomials, two-dimensional orthogonal polynomials, or their equivalent functional forms; the mid-frequency spatial basis functions can be selected from piecewise polynomial functions, B-spline basis functions, or mesoscale wavelet basis functions; the high-frequency spatial basis functions can be selected from high-order wavelet basis functions, local pixel basis functions, or other functional forms with local spatial support characteristics.

[0069] Subsequently, based on the effective detection sub-aperture range of the standard spherical mirror, each sub-aperture measurement is mapped to the full-aperture spatial discrete mapping model, and the corresponding covered sampling nodes are marked as observable nodes. By statistically analyzing the integrity of the basis functions of each frequency layer within the sub-aperture coverage area, the minimum observation constraints of different spatial frequency surface shape components under a single sub-aperture and multiple sub-aperture combinations are clarified. Among them, the low-frequency surface shape component needs to form a cross-regional joint coverage at least among multiple sub-apertures, the mid-frequency surface shape component needs to form a continuous coverage between adjacent sub-apertures, and the high-frequency surface shape component is limited to observation within a single sub-aperture.

[0070] After establishing the minimum observation constraint relationship, this constraint relationship is embedded as a priori condition for full-aperture surface reconstruction in the subsequent sub-aperture scanning layout and stitching solution process. This ensures that the stitching matrix remains fully constrained in the parameter space corresponding to the low-frequency and mid-frequency surface components, thereby avoiding the problem of uncontrolled degrees of freedom or deterioration of the condition number in the stitching matrix while reducing the overlap ratio of physical sub-apertures.

[0071] Under the constraints of the full-aperture spatial discrete mapping model, the scanning positions of each sub-aperture are globally optimized and sorted, so that adjacent sub-apertures form a coupled relationship in the low-frequency surface component dimension and maintain relatively independent sampling in the high-frequency surface component dimension. This reduces the physical overlap ratio while maintaining the observability of the splicing matrix in the key low-frequency subspace.

[0072] Specifically, based on the constructed full-aperture spatial discrete mapping model and the surface shape spatial frequency layering results as input, each sub-aperture scanning position is mapped in the full-aperture spatial discrete mapping model to determine the set of discrete sampling nodes covered by the sub-aperture scanning position. Furthermore, the projection weight distribution of the covered set of discrete sampling nodes in the basis function space corresponding to the low-frequency surface shape component is calculated to obtain the observation contribution characteristics of the sub-aperture to the low-frequency surface shape component.

[0073] After obtaining the low-frequency observation contribution features of each sub-aperture scanning position, a global correlation graph with sub-aperture scanning positions as nodes is constructed. The connection weight between nodes is determined by the similarity of their low-frequency observation contribution features. By traversing and analyzing this global correlation graph, combinations of sub-aperture scanning positions that are correlated in the low-frequency surface component dimension are identified, and a global optimized sorting sequence of sub-aperture scanning positions is formed accordingly. This ensures that adjacent sub-aperture scanning positions in time or space maintain a continuous and stable constraint relationship in the low-frequency observation dimension.

[0074] While forming the globally optimized sorting sequence, local independence analysis is performed on the discrete node set covered by the scanning position of each sub-aperture for the high-frequency surface component. This ensures that adjacent sub-apertures do not form excessive re-sampling within the basis function support region corresponding to the high-frequency surface component in the globally optimized sorting sequence, thereby avoiding redundant constraints or mutual coupling introduced by high-frequency information during the stitching process. In this way, the high-frequency surface component maintains its locally independent sampling characteristics in different sub-apertures.

[0075] Subsequently, based on the constraints of low-frequency coupling and relatively independent high-frequency components, the scanning positions were iteratively adjusted to minimize the physical overlap between adjacent sub-apertures while ensuring the global observability of the low-frequency surface component, resulting in an optimized global sorting sequence. During this adjustment, the associated order of sub-apertures that contribute significantly to the observation of the low-frequency surface component was retained first, while the order of sub-apertures with highly overlapping contributions to the high-frequency surface component was decoupled and rearranged.

[0076] After completing the optimization of the scanning position sorting, the final sub-aperture scanning sequence is input into the detection system as the execution order of surface detection. This ensures that during the actual detection process, the measurement data of adjacent sub-apertures form a stable joint constraint in the low-frequency surface component parameter space, thereby maintaining the necessary independence in the high-frequency surface component parameter space. This maintains the observability and numerical stability of the splicing matrix in the key low-frequency subspace under the condition of reduced physical overlap ratio.

[0077] In this embodiment, by globally optimizing and sorting the scanning positions of each sub-aperture under the spatial frequency layer constraint, adjacent sub-apertures form a stable and continuous joint observation relationship in the low-frequency surface component dimension, while maintaining the necessary independent sampling characteristics in the high-frequency surface component dimension. Without relying on large-area physical overlap, sufficient constraints on the low-frequency surface parameters of the entire aperture can still be maintained. Thus, while shortening the detection cycle, the unconstrained drift of low-frequency distortions such as overall tilt and overall curvature during the stitching process is effectively suppressed.

[0078] For example, when inspecting a plane mirror with a diameter of two meters, a candidate set of sub-aperture scanning is constructed using a standard spherical mirror with an effective detection diameter of three hundred millimeters. After the candidate scanning positions are globally optimized and sorted using the above method, the physical overlap ratio of adjacent sub-apertures is reduced from the original thirty percent to less than ten percent, while the rank of the stitching matrix in the subspace corresponding to the low-frequency surface component remains unchanged, and the condition number is significantly reduced. This verifies that the implementation method can ensure the stability of surface reconstruction while reducing the detection cycle.

[0079] Based on the sub-aperture layout after global optimization and sorting, common modal parameters corresponding to low-frequency surface components are extracted from the measurement results of each sub-aperture. These common modal parameters are then explicitly introduced into the splicing equation as global constraint terms to construct a splicing matrix. This ensures that the splicing matrix has stable reference anchor points during the solution process, thereby suppressing free drift caused by insufficient overlap.

[0080] In this embodiment, by extracting common modal parameters from the sub-aperture measurement results and explicitly introducing these common modal parameters into the splicing equation as global constraint terms, a unified reference benchmark is established in the low-frequency surface component parameter space of the splicing matrix. This avoids the splicing solution from having arbitrary translational or rotational degrees of freedom in the low-frequency subspace due to the reduced overlap ratio of factor apertures, thereby significantly enhancing the rank stability and numerical controllability of the splicing matrix.

[0081] Specifically, firstly, based on the definition range of the low-frequency surface shape component in the full-aperture spatial discrete mapping model, the measurement results of each sub-aperture are processed by low-frequency modal projection, and the surface shape measurement data in the sub-aperture is mapped to the basis function space corresponding to the low-frequency surface shape component to obtain the low-frequency modal parameter vector corresponding to the sub-aperture, which is used to characterize the measurement results of the sub-aperture in the dimensions of overall tilt, overall curvature and large-scale deformation.

[0082] After obtaining the low-frequency modal parameter vectors of each sub-aperture, based on the sub-aperture layout relationship after global optimization and sorting, a consistency analysis is performed on the low-frequency modal parameter vectors between adjacent sub-apertures. Low-frequency modal parameter vectors that appear repeatedly in multiple sub-apertures and have the same trend of change are extracted, and this part of the low-frequency modal parameter vectors is defined as the common modal parameters corresponding to the low-frequency surface components.

[0083] The common modal parameters are used to characterize the common low-frequency surface features of the large-aperture plane mirror under the full aperture scale, and they have stability and repeatability in the measurement results of different sub-apertures.

[0084] After determining the common modal parameter, it is explicitly introduced into the full-aperture surface shape splicing equation. Specifically, based on the original splicing equation with the sub-aperture surface shape parameters as unknowns, a global constraint term with the common modal parameter as an independent unknown is added, and a uniform action weight across sub-apertures is assigned to the common modal parameter in the splicing matrix, so that the low-frequency modal parameters of each sub-aperture are all associated with the global surface shape model through the common modal parameter;

[0085] Subsequently, during the solution process of the spliced ​​matrix, common modal parameters are used as global reference anchors in the joint solution, enabling the spliced ​​matrix to form a clear reference constraint in the low-frequency subspace. This limits the overall tilt drift or curvature free drift caused by the reduction in the physical overlap ratio of the limiting aperture. In this way, the spliced ​​matrix maintains a stable rank structure and controlled condition number during the numerical solution process.

[0086] After completing the joint solution, based on the common modal parameters obtained from the solution, the low-frequency surface shape components of each sub-aperture are subjected to consistency correction, so that the corrected sub-aperture data are consistent with the global common mode in the dimension of low-frequency surface shape components, providing a stable benchmark for subsequent fine splicing of mid- and high-frequency surface shape components.

[0087] For example, when inspecting a 1.5-meter-diameter plane mirror, sixteen sub-aperture measurement positions are used and optimized and sorted using the aforementioned method. By performing low-frequency modal projection on the measurement results of each sub-aperture, low-frequency modal parameters corresponding to the overall tilt and second-order curvature are extracted, and stable and consistent common modal parameters are identified among adjacent sub-apertures. After incorporating these common modal parameters into the stitching equation, the overall tilt direction drift no longer occurs during the full-aperture surface reconstruction process, and the stitching result maintains good stability and consistency even when the sub-aperture overlap ratio is reduced to half of its original level.

[0088] Based on the introduction of common modal parameters, the splicing matrix is ​​reconstructed in blocks, and the full aperture surface reconstruction problem is split into a low-frequency constraint subsystem and a mid-to-high frequency local correction subsystem. The solution of the low-frequency constraint subsystem is used as the boundary condition of the mid-to-high frequency local correction subsystem, and the stability is transferred step by step to reduce the overall condition number.

[0089] Specifically, in this embodiment, the full-aperture splicing matrix containing common modal parameters constructed in the previous embodiment is used as the initial input. First, based on the spatial frequency stratification results, the unknown parameters in the splicing matrix are rearranged in the frequency dimension. The unknown parameters corresponding to the low-frequency surface components and the common modal parameters are divided into a low-frequency constraint parameter set, and the unknown parameters corresponding to the mid-frequency surface components and the high-frequency surface components are divided into a mid-high frequency local correction parameter set, thereby forming a clear frequency partitioning structure in the parameter space.

[0090] After parameter partitioning, the splicing matrix is ​​reconstructed in blocks based on the frequency partitioning structure. The original splicing matrix is ​​split into a low-frequency constraint submatrix, a mid-to-high-frequency local correction submatrix, and a connection submatrix describing the coupling relationship between the low-frequency constraint parameter set and the mid-to-high-frequency local correction parameter set. The low-frequency constraint submatrix contains only the constraint relationships between low-frequency surface shape components and common modal parameters, and is used to describe the overall surface shape behavior at the full aperture scale. The mid-to-high-frequency local correction submatrix is ​​used to describe the local surface shape variation characteristics within each sub-aperture.

[0091] After completing the block reconstruction of the splicing matrix, the low-frequency constrained subsystem is first solved independently. A stable full-aperture low-frequency surface shape solution is obtained through joint constraints between common modal parameters and low-frequency surface shape components. This low-frequency surface shape solution does not rely on mid-to-high frequency local correction parameters during the solution process, thus avoiding interference from high-frequency noise and local instability factors on the overall solution. This results in the low-frequency constrained subsystem possessing good numerical stability and a low condition number.

[0092] The low-frequency constraint subsystem consists of a low-frequency constraint submatrix and a set of low-frequency constraint parameters.

[0093] The mid-to-high frequency local correction subsystem consists of a mid-to-high frequency local correction submatrix and a mid-to-high frequency local correction parameter set.

[0094] After obtaining the full-aperture low-frequency surface shape solution of the low-frequency constraint subsystem, the full-aperture low-frequency surface shape solution is explicitly introduced as a boundary condition into the mid-to-high frequency local correction subsystem.

[0095] Specifically, in the splicing equation of the mid-to-high frequency local correction subsystem, the corresponding low-frequency surface component is fixed as a known term, and only the mid-frequency and high-frequency local correction parameters are solved, so that the mid-to-high frequency surface reconstruction is carried out on the predetermined low-frequency reference, thereby effectively suppressing the overall drift of the local solution or low-frequency distortion.

[0096] Finally, by adopting the solution strategy of prioritizing low frequencies and passing the solution step by step, the stability of the low-frequency constraint subsystem is gradually transferred to the mid-to-high-frequency local correction subsystem, which significantly reduces the degree of freedom and the number of ill-conditioned directions in the overall splicing problem. Thus, while reducing the physical overlap ratio of sub-apertures, the numerical stability and reliability of the full-aperture surface reconstruction process are still maintained.

[0097] Based on the results of block reconstruction, a consistency inversion analysis is performed on the measurement residuals of each sub-aperture to identify sub-aperture combinations whose contribution to condition number deterioration exceeds a preset threshold. Accordingly, an adaptive weight adjustment mechanism is introduced for the corresponding sub-aperture data to automatically suppress the error amplification effect of ill-conditioned directions during the numerical solution process of the splicing matrix.

[0098] For each sub-aperture measurement data, the residual is calculated under the low-frequency common mode and the mid-to-high frequency local correction block results. That is, the measurement value of each sub-aperture is differentiated from its corresponding block reconstruction prediction value to obtain the prediction residual vector, which is used to characterize the error distribution characteristics of each sub-aperture that is not fully constrained during the splicing process.

[0099] Subsequently, a consistency inversion analysis was performed on the residual vectors of each sub-aperture. Specifically, by constructing a residual covariance matrix, the residual contribution value of each sub-aperture or sub-aperture combination in the low-frequency or mid-to-high-frequency surface profile parameter space was calculated. Based on the residual contribution values, sub-apertures or sub-aperture combinations with residual contribution values ​​exceeding a preset contribution threshold were marked as key adjustment targets. This clarified their impact on the condition number of the splicing matrix, i.e., which sub-aperture residual amplification effects are prone to causing instability in the full-aperture surface profile reconstruction. Based on the analysis results, sub-apertures with higher residual contribution values ​​were marked as key adjustment targets.

[0100] The residual contribution value is used to characterize the relative magnitude of the numerical instability caused by the sub-aperture residual in the corresponding parameter subspace of the splicing matrix. It can be quantitatively characterized by the statistical results of the changes in the eigenvalues ​​of the residual covariance matrix.

[0101] For the labeled sub-aperture measurement data, an adaptive weight adjustment mechanism is introduced. This mechanism dynamically adjusts the weight coefficients of the corresponding sub-aperture measurements in the splicing matrix solution based on the residual contribution value: sub-apertures with higher residual contribution values ​​are assigned lower weights to reduce their direct impact on the overall low-frequency and mid-to-high-frequency surface parameter solutions; sub-apertures with lower residual contribution values ​​maintain or moderately increase their weights to strengthen their constraint effect. The weight adjustment coefficients can be obtained through iterative optimization or calculated based on residual amplitude and covariance characteristics.

[0102] After adaptive weight adjustment, the stitching matrix is ​​reconstructed and jointly solved, allowing each sub-aperture data to receive different levels of constraint contribution in the numerical solution, thereby automatically suppressing the error amplification effect caused by ill-conditioned orientation. In this way, even if the physical overlap ratio of sub-apertures decreases or local measurement noise exists, the stitching matrix can still maintain a low condition number, ensuring the stability and reliability of the full-aperture surface reconstruction.

[0103] For example, when performing surface profile detection on a large-aperture plane mirror with a diameter of two meters, the residuals of the sub-aperture data after block reconstruction were projected onto the low-frequency and mid-to-high-frequency subspaces. It was found that the residuals of sub-apertures 3, 7, and 12 contributed significantly to the low-frequency subspace. Through an adaptive weight adjustment mechanism, the weights of the measurements of sub-apertures 3, 7, and 12 in the stitching matrix solution were adjusted from the default 1.0 to 0.6–0.7, while the weights of other sub-apertures remained at 1.0, and the stitching solution was re-performed. The results showed that the low-frequency drift of the full-aperture surface profile was significantly reduced, the condition number of the stitching matrix decreased from the original 450 to 220, and the surface profile reconstruction results maintained high stability under low overlap conditions.

[0104] Based on the stitching solution after weight adjustment, the full-aperture surface profile results are back-substituted for verification. The reconstructed surface profile is back-projected to each sub-aperture measurement domain to check the consistency between the common modal parameters corresponding to the low-frequency surface profile components and the original measurements. The aforementioned common modal parameters are then back-corrected using the consistency index to form a closed-loop stable stitching process, ensuring that reliable full-aperture surface profile reconstruction results are obtained even under low overlap conditions.

[0105] Step S01: The full-aperture surface profile results are back-projected to the measurement domain of each sub-aperture according to the full-aperture spatial discrete mapping model. That is, according to the spatial position of the sub-aperture in the full aperture, the corresponding full-aperture surface profile results are mapped to the discrete sampling nodes covered by each sub-aperture to form the sub-aperture predicted surface profile data.

[0106] Step S02: Difference the predicted sub-aperture surface data with the original sub-aperture measurement results and calculate the original residual vector to quantify the consistency between the low-frequency common mode and the original measurement in each sub-aperture.

[0107] Step S03: For the low-frequency surface shape component, further calculate the projection amplitude of the original residual vector of each sub-aperture in the low-frequency common mode space, and obtain a global consistency index, such as mean square residual or maximum residual, by statistically analyzing the projection amplitudes of all sub-apertures, to evaluate the degree of matching between the full-aperture common mode parameters and the actual measurement.

[0108] Step S04: Based on the global consistency index, the common modal parameters are reverse-corrected. Specifically, the mean or weighted average of the original residual vector projected onto the low-frequency common modal space is used as the correction value to update the common modal parameters. The updated common modal parameters are then re-embedded into the splicing matrix, and the splicing and solving are performed again to generate a new full-aperture surface shape result.

[0109] Step S05: Repeat steps S01-S04 until the global consistency index reaches the preset consistency threshold, ensuring that the low-frequency common mode remains stable and consistent in each sub-aperture measurement domain. After completing the closed-loop correction, the final full-aperture surface reconstruction result is obtained.

[0110] It should be noted that the consistency threshold is set by those skilled in the art based on the actual situation or obtained through simulation with a large amount of data.

[0111] Through this iterative verification and closed-loop adjustment process, even when the physical overlap ratio of sub-apertures is significantly reduced, the global drift caused by insufficient overlap of factor apertures or local measurement errors can still be effectively suppressed, ensuring the reliability and repeatability of the full aperture surface reconstruction results.

[0112] In this embodiment, the present invention effectively solves the problem of insufficient surface splicing stability under the condition of reducing the sub-aperture overlap ratio without relying on ultra-large aperture interferometers or interrupting the existing detection system of the Richter-Comman method. It achieves a balance between detection efficiency and surface reconstruction accuracy, and has significant engineering practical value and promotion significance.

[0113] Example 2:

[0114] Please see Figure 4 This invention provides a technical solution: a surface shape detection system for a large-aperture plane mirror in a vacuum environment, which is used to implement the aforementioned method for detecting the surface shape of a large-aperture plane mirror in a vacuum environment. The system includes:

[0115] The full-aperture discrete modeling module constructs a full-aperture spatial discrete mapping model, represents the full-aperture surface parameters in layers according to spatial frequency, and sets minimum observation constraint relationships;

[0116] The sub-aperture layout optimization module, under the constraints of the full-aperture spatial discrete mapping model, performs global optimization and sorting of the scanning positions of each sub-aperture, so that adjacent sub-apertures form a coupled relationship in the low-frequency surface component dimension, while maintaining independent sampling in the high-frequency surface component dimension.

[0117] The low-frequency common mode module extracts the common mode parameters corresponding to the low-frequency surface shape components from the measurement results of each sub-aperture, and explicitly introduces the common mode parameters into the splicing equation as global constraint terms to construct the splicing matrix;

[0118] The splicing matrix block module performs block reconstruction processing on the splicing matrix, decomposes the full aperture surface reconstruction problem into a low-frequency constraint subsystem and a mid-to-high frequency local correction subsystem, and uses the solution of the low-frequency constraint subsystem as the boundary condition of the mid-to-high frequency local correction subsystem to pass stability step by step to reduce the overall condition number.

[0119] The hierarchical stability solution module, in conjunction with the block reconstruction results, performs consistency inversion analysis on the measurement residuals of each sub-aperture to identify sub-aperture combinations whose contribution to condition number deterioration exceeds a preset threshold, and introduces an adaptive weight adjustment mechanism for the corresponding sub-aperture data accordingly.

[0120] The closed-loop consistency correction module performs back-substitution verification on the full-aperture surface profile results, back-projects the reconstructed surface profile to each sub-aperture measurement domain, examines the consistency between the common modal parameters corresponding to the low-frequency surface profile components and the original measurements, corrects the common modal parameters, and forms a closed-loop stitching process.

[0121] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions, characterized in that, include: A full-aperture spatial discrete mapping model is constructed, and the full-aperture surface parameters are represented in layers according to spatial frequency, and a minimum observation constraint relationship is set. Under the constraints of the full-aperture spatial discrete mapping model, the scanning positions of each sub-aperture are globally optimized and sorted so that adjacent sub-apertures form a coupled relationship in the low-frequency surface component dimension and maintain independent sampling in the high-frequency surface component dimension. The method for globally optimizing and sorting the scanning positions of each sub-aperture includes: Each sub-aperture scanning position is mapped in the full-aperture spatial discrete mapping model to determine the set of discrete sampling nodes covered by the corresponding sub-aperture scanning position. The projection weight distribution of the covered set of discrete sampling nodes in the basis function space corresponding to the low-frequency surface component is calculated to obtain the observation contribution characteristics of the corresponding sub-aperture to the low-frequency surface component. A global correlation graph is constructed with sub-aperture scanning positions as nodes. The connection weight between nodes is determined by the similarity of the observation contribution features of their low-frequency surface components. By traversing and analyzing the global correlation graph, combinations of sub-aperture scanning positions that are correlated in the dimension of low-frequency surface components are identified, and a global optimized sorting sequence of sub-aperture scanning positions is formed. Extract the common modal parameters corresponding to the low-frequency surface shape components from the measurement results of each sub-aperture, and explicitly introduce the common modal parameters into the splicing equation as global constraint terms to construct the splicing matrix; The splicing matrix is ​​processed by block reconstruction, and the full aperture surface reconstruction problem is decomposed into a low-frequency constraint subsystem and a mid-to-high frequency local correction subsystem. The solution of the low-frequency constraint subsystem is used as the boundary condition of the mid-to-high frequency local correction subsystem. The method for performing block reconstruction processing on the spliced ​​matrix includes: The unknown parameters in the splicing matrix are rearranged according to the frequency dimension. The unknown parameters and common modal parameters corresponding to the low-frequency surface components are divided into a set of low-frequency constraint parameters, and the unknown parameters corresponding to the mid-frequency surface components and high-frequency surface components are divided into a set of mid-high frequency local correction parameters, thus forming a frequency partitioning structure in the parameter space. The splicing matrix is ​​reconstructed in blocks based on the frequency partitioning structure. Based on the results of block reconstruction, a consistency inversion analysis is performed on the measurement residuals of each sub-aperture to identify sub-aperture combinations that contribute more than a preset threshold to the condition number deterioration, and an adaptive weight adjustment mechanism is introduced for the corresponding sub-aperture data. The full-aperture surface profile results are back-substituted for verification. The reconstructed surface profile is back-projected onto the measurement domain of each sub-aperture. The consistency between the common modal parameters corresponding to the low-frequency surface profile components and the original measurements is checked. The common modal parameters are then corrected to form a closed-loop stitching process.

2. The method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions according to claim 1, characterized in that, The method for constructing a full-aperture spatial discrete mapping model includes: The effective aperture size of the large-aperture plane mirror under test is obtained, and the single effective sub-aperture range of the standard spherical mirror under the Rickie-Comman test configuration is obtained. Taking the geometric center of the large-aperture plane mirror under test as the reference origin, the full aperture region is discretized by regular grid in the mirror coordinate system. The full aperture is divided into multiple surface sampling nodes with fixed spatial sampling intervals. A full aperture spatial discretization mapping model is established so that each surface sampling node corresponds to a surface height parameter to be reconstructed.

3. The method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions according to claim 2, characterized in that, The method for representing the full aperture surface parameters in layers according to spatial frequency and setting minimum observation constraints includes: The surface height parameter is decomposed into low-frequency surface components, mid-frequency surface components, and high-frequency surface components using a preset set of spatial basis functions. Minimum observation constraints are set for different spatial frequency surface components under a single sub-aperture and a combination of multiple sub-apertures. The low-frequency surface component forms a joint coverage across multiple sub-apertures, the mid-frequency surface component forms a continuous coverage between adjacent sub-apertures, and the high-frequency surface component is limited to observation within a single sub-aperture.

4. The method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions according to claim 2, characterized in that, The method for globally optimizing and sorting the scanning positions of each sub-aperture includes: While forming the global optimized sorting sequence, local independence analysis is performed on the discrete node set covered by each sub-aperture scanning position for high-frequency surface components. Based on the constraints, the scanning position is iteratively adjusted to minimize the physical overlap ratio between adjacent sub-apertures while ensuring the global observability of low-frequency surface components, thus obtaining the optimized global sorting sequence.

5. The method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions according to claim 1, characterized in that, The method for extracting the common modal parameters corresponding to the low-frequency surface shape components from the measurement results of each sub-aperture includes: Modal projection processing is performed on the measurement results of each sub-aperture to map the surface shape measurement data within the sub-aperture to the basis function space corresponding to the low-frequency surface shape component, thereby obtaining the low-frequency modal parameter vector corresponding to each sub-aperture. Based on the sub-aperture layout after global optimization and sorting, a consistency analysis is performed on the low-frequency modal parameter vectors between adjacent sub-apertures. Extract the low-frequency modal parameter vectors that repeat in multiple sub-apertures and have a consistent trend of change, and define the corresponding low-frequency modal parameter vectors as the common modal parameters corresponding to the low-frequency surface components.

6. The method for detecting the surface shape of a large-aperture plane mirror under vacuum environment according to claim 3, characterized in that, The method for performing block reconstruction processing on the spliced ​​matrix includes: The original splicing matrix is ​​split into a low-frequency constraint submatrix, a mid-to-high frequency local correction submatrix, and a connection submatrix describing the coupling relationship between the low-frequency constraint parameter set and the mid-to-high frequency local correction parameter set. After completing the block reconstruction of the splicing matrix, the low-frequency constraint subsystem is solved independently first. The full-aperture low-frequency surface shape solution is obtained through the joint constraints between the common modal parameters and the low-frequency surface shape components. After obtaining the full-aperture low-frequency surface shape solution of the low-frequency constraint subsystem, the full-aperture low-frequency surface shape solution is explicitly introduced as a boundary condition into the mid-to-high frequency local correction subsystem. The low-frequency constraint subsystem consists of a low-frequency constraint submatrix and a low-frequency constraint parameter set; the mid-to-high frequency local correction subsystem consists of a mid-to-high frequency local correction submatrix and a mid-to-high frequency local correction parameter set.

7. The method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions according to claim 1, characterized in that, The method of performing consistency inversion analysis on the measurement residuals of each sub-aperture, identifying sub-aperture combinations whose contribution to condition number deterioration exceeds a preset threshold, and introducing an adaptive weight adjustment mechanism for the corresponding sub-aperture data includes: The measurement value of each sub-aperture is differentially divided with its corresponding block reconstruction prediction value to obtain the prediction residual vector; By constructing a residual covariance matrix, the residual contribution value of each sub-aperture or sub-aperture combination in the parameter space is calculated, and the sub-apertures or sub-aperture combinations that exceed the preset contribution value threshold are marked according to the residual contribution value. For the labeled sub-aperture measurement data, an adaptive weight adjustment mechanism is introduced to determine the weight of each sub-aperture based on its residual contribution value. The larger the residual contribution value, the smaller the weight of the corresponding sub-aperture. After completing the adaptive weight adjustment, the splicing matrix is ​​reconstructed and solved jointly.

8. The method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions according to claim 1, characterized in that, The method for back-substitution verification of the full-caliber surface profile results includes: Step S01: Based on the spatial position of the sub-aperture in the full aperture, map the corresponding full aperture surface shape result to the discrete sampling nodes covered by each sub-aperture to form sub-aperture predicted surface shape data. Step S02: Difference the predicted sub-aperture surface data with the original sub-aperture measurement results and calculate the original residual vector; Step S03: For the low-frequency surface component, calculate the projection amplitude of the original residual vector of each sub-aperture in the common modal space, and obtain the global consistency index by statistically analyzing the projection amplitudes of all sub-apertures. Step S04: The mean or weighted average value of the original residual vector projected onto the common modal space is used as the correction value to update the common modal parameters. The updated common modal parameters are then re-embedded into the splicing matrix, and the splicing and solving are performed again to generate a new full-aperture surface shape result. Step S05: Repeat steps S01-S04 until the global consistency index reaches the preset consistency threshold, and obtain the final full-aperture surface reconstruction result.

9. The method for detecting the surface shape of a large-aperture plane mirror under vacuum conditions according to claim 8, characterized in that, The global consistency index is the mean square residual or the maximum residual of the projected amplitudes of all sub-apertures.

10. A surface profile detection system for a large-aperture plane mirror under vacuum conditions, used to implement the surface profile detection method for a large-aperture plane mirror under vacuum conditions as described in any one of claims 1-9, characterized in that, The system includes: The full-aperture discrete modeling module constructs a full-aperture spatial discrete mapping model, represents the full-aperture surface parameters in layers according to spatial frequency, and sets minimum observation constraint relationships; The sub-aperture layout optimization module, under the constraints of the full-aperture spatial discrete mapping model, performs global optimization and sorting of the scanning positions of each sub-aperture, so that adjacent sub-apertures form a coupled relationship in the low-frequency surface component dimension, while maintaining independent sampling in the high-frequency surface component dimension. The low-frequency common mode module extracts the common mode parameters corresponding to the low-frequency surface shape components from the measurement results of each sub-aperture, and explicitly introduces the common mode parameters into the splicing equation as global constraint terms to construct the splicing matrix; The splicing matrix block module performs block reconstruction processing on the splicing matrix, decomposes the full aperture surface reconstruction problem into a low-frequency constraint subsystem and a mid-to-high frequency local correction subsystem, and uses the solution of the low-frequency constraint subsystem as the boundary condition of the mid-to-high frequency local correction subsystem. The hierarchical stability solution module, combined with the results of block reconstruction, performs consistency inversion analysis on the measurement residuals of each sub-aperture, identifies sub-aperture combinations whose contribution to condition number deterioration exceeds a preset threshold, and introduces an adaptive weight adjustment mechanism for the corresponding sub-aperture data. The closed-loop consistency correction module performs back-substitution verification on the full-aperture surface profile results, back-projects the reconstructed surface profile to each sub-aperture measurement domain, examines the consistency between the common modal parameters corresponding to the low-frequency surface profile components and the original measurements, corrects the common modal parameters, and forms a closed-loop stitching process.

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