Curvature self-adaptive curved surface fitting method and system in optical element polishing

Abstract

The invention relates to the technical field of optical precision machining, in particular to a curvature self-adaptive curved surface fitting method and system in optical element polishing, and the method comprises the steps: obtaining a material height difference removal matrix based on interference measurement data before and after polishing of an optical element; traversing the height difference matrix by using a sliding window mode, calculating a Hessian matrix eigenvalue in a local area, forming a curvature sensitivity index (CSI), dividing an optical surface area into a plane area, a gradual change area and a high curvature area, and setting curved surface fitting parameters in the areas respectively; performing curved surface fitting on the region by adopting a weighted least square method to obtain a continuous surface model, and performing adaptive numerical integration calculation on the continuous surface to obtain a material removal volume; according to the method, the process control requirement of high-precision optical manufacturing can be met, the calculation precision is high, the calculation precision and the calculation efficiency can be maximized, the global efficiency is high, the capability of capturing local features can be achieved, the method can be integrated into an existing quality control system, and process decision making is facilitated.

Description

Technical Field

[0001] This invention relates to the field of optical precision machining technology, and in particular to a method and system for adaptive curvature surface fitting in the polishing of optical components. Background Technology

[0002] Fine polishing of optical surfaces is a critical step in the manufacturing process of high-end optical components, affecting imaging, wavefront error, and overall system optical efficiency. Zygo interferometers are commonly used measurement instruments in optical manufacturing, and the final result is a nanoscale three-dimensional surface morphology. In the process of setting executable process parameters from a single measurement, the calculation of material removal volume is quite difficult, which directly affects the polishing path, dwell time, and process iteration efficiency.

[0003] Existing volume calculation methods, such as the Riemann summation method, involve discretely summing pixels. Each pixel is a flat-topped cylinder, and the product of the depth and area of ​​each pixel is its total volume. This method is relatively simple. However, optical surfaces are continuous geometric surfaces, with continuous space and curvature between adjacent pixels. This introduces systematic errors in volume calculations, especially significant in cases of significant local curvature, such as aspherical or free-form surfaces. Experiments have shown that this type of method has a relative error of 15% to 20% compared to typical aspherical polishing scenarios, while high-precision optical manufacturing requires this error to be on the order of 3%. Current technologies use numerical integration methods such as trapezoidal integrals or Simpson's method as fitting methods for optical polishing volume surfaces. These methods suffer from problems such as fixed window sizes and uniform polynomial orders. They adjust the fitting complexity based on the local curvature of the surface, failing to fit surfaces with high curvature and introducing redundancy in surfaces with flat curvature. For data points missing from Zygo interferometric data (mainly due to occlusion areas, noise anomalies, etc.), simple removal or linear interpolation can destroy the geometric features of the local surface. Switching between different algorithms based on experience is necessary, but the resulting volume calculations vary significantly and have poor repeatability. Therefore, a curvature-adaptive surface fitting method is urgently needed to ensure the accuracy and controllability of optical polishing material removal. Summary of the Invention

[0004] To address the problems of large surface fitting errors and computational redundancy in existing optical component manufacturing processes, this invention provides a curvature adaptive surface fitting method and system for optical component polishing. By employing perceptible local surface curvature and adaptive fitting, the curvature adaptive surface fitting for optical polishing volume calculation is achieved, ensuring the accuracy and controllability of optical polishing material removal.

[0005] According to the design scheme provided by the present invention, on one hand, a method for adaptive curvature surface fitting in the polishing of optical elements is provided, comprising:

[0006] Obtain measurement values ​​of the optical element surface before and after polishing, and obtain a height difference matrix of material removal based on the measurement values, wherein the measurement values ​​include height data of the measurement area on the element surface.

[0007] The curvature sensitivity CSI is calculated by traversing the height difference matrix through a sliding window and using the eigenvalues ​​of the Hessian matrix.

[0008] The surface of the optical element is divided into planar region, gradually changing region and high curvature region based on the curvature sensitivity CSI and classification threshold. Fitting parameters are formulated for each region. The fitting parameters corresponding to each pixel in the measurement area are recorded using a parameter mapping matrix. The fitting parameters include window size and polynomial order.

[0009] Based on the fitting parameters and using the least squares method to perform weighted fitting for each region, a continuous surface is generated. The material removal volume is then obtained by adaptive numerical integration of the continuous surface.

[0010] As a curvature adaptive surface fitting method for polishing optical elements in this invention, further, obtaining interference measurement values ​​of the optical element surface before and after polishing includes:

[0011] The optical element was measured twice, before and after polishing, using a Zygo interferometer to obtain the original data of the optical element surface before and after polishing. The original data before and after the measurement included the width (in pixels) of the measurement area, the height (in pixels) of the measurement area, the laser wavelength, and the physical size corresponding to each pixel.

[0012] As a curvature adaptive surface fitting method for polishing optical elements in this invention, further comprising, before traversing the height difference matrix through a sliding window, the following:

[0013] Standardize the units for altitude data;

[0014] A Gaussian filter is used to smooth the height difference matrix so that each element in the smoothed height difference matrix represents the material removal depth at the corresponding pixel.

[0015] As a curvature adaptive surface fitting method in the polishing of optical elements of the present invention, the curvature sensitivity CSI is further calculated using the eigenvalues ​​of the Hessian matrix, including:

[0016] Obtain the second-order partial derivatives of the pixels in the measurement region within the sliding window, and construct the Hessian matrix based on the second-order partial derivatives;

[0017] The eigenvalues ​​of the Hessian matrix at the pixels in the measurement area are calculated. The curvature sensitivity CSI is set using the eigenvalues ​​and then normalized using the known maximum possible curvature of the optical surface.

[0018] As a curvature adaptive surface fitting method for polishing optical elements in this invention, further, fitting parameters are defined for each region, including:

[0019] For the planar region, the window size corresponding to each pixel in the measurement area is set as the first size, and the polynomial order is first order;

[0020] For the gradually varying region, the window size corresponding to each pixel in the measurement area is set to the second size, and the polynomial order is second order;

[0021] For high curvature regions, the window size corresponding to each pixel in the measurement area is set as the third size, the polynomial order is third, and the first size < the second size < the third size;

[0022] The parameter mapping matrix is ​​used to record the window size and polynomial order corresponding to each pixel in the measurement area.

[0023] As a curvature adaptive surface fitting method for polishing optical elements in this invention, further, weighted fitting is performed on each region based on the fitting parameters and using the least squares method, including:

[0024] The pixel fitting region and the pixel fitting region weight function are set according to the window radius and the Euclidean distance from the pixel point in each region to the window center.

[0025] Based on the pixel fitting region weight function, a diagonal weight matrix is ​​set, and a weighted least squares problem is constructed using the diagonal weight matrix, the polynomial coefficient matrix and the observation vector. The observation vector is composed of the measured values ​​of each pixel in the measurement region.

[0026] The continuous surface corresponding to the fitting region is obtained by solving the weighted least squares problem, and the weighted average is used to filter the overlapping parts of each fitting region to obtain the final continuous fitting surface.

[0027] As a curvature adaptive surface fitting method for polishing optical elements in this invention, the material removal volume is further obtained by adaptive numerical integration over a continuous surface, comprising:

[0028] For each fitting parameter, the fitting region is first divided into several sub-regions. The Simpson integral of each sub-region is calculated based on the continuous surface, and the relative error of the Simpson integral of each sub-region is obtained through evaluation.

[0029] If the relative error of the Simpson integral of a sub-region is greater than the threshold, the sub-region is divided again and the Simpson integral of each sub-region is re-acquired. The process of dividing and calculating the Simpson integral of the region is repeated until the relative error of the Simpson integral of all regions is less than the threshold or the maximum number of subdivisions is reached.

[0030] Data outside the fitted region is virtually generated based on the symmetrical points of the boundary of the fitted region. The information outside the region is used to simulate the complete region. The Simpson integral is linearly corrected based on the ratio of the effective region area to the complete region area. The corrected volumes of all local regions are summarized. The geometric relationship of the overlapping parts of the window is used to deduct the duplicated parts to obtain the total volume of material removed.

[0031] As a curvature adaptive surface fitting method for polishing optical elements in this invention, further comprising obtaining the material removal volume by adaptive numerical integration over a continuous surface, and further including:

[0032] The relative error is obtained by comparing the volume of material removed with the result of the volume removed using the pixel summation method.

[0033] The overall fit stability of all current data points is verified using leave-one-out cross-validation.

[0034] If the relative error exceeds the threshold or the current overall fitting stability is not met, the adaptive optimization process of surface fitting is triggered until the adaptive optimization termination condition is met. The adaptive optimization process of surface fitting is to adjust the classification threshold and use the adjusted classification threshold to update the surface region division of the optical element and the fitting parameters of each newly divided region, so as to regenerate the continuous surface using the new fitting parameters. The adaptive optimization termination condition is to meet the maximum number of adaptive optimization iterations or the relative error is less than the threshold.

[0035] As a curvature adaptive surface fitting method for polishing optical elements in this invention, the overall fitting stability of all current data points is further verified using leave-one-out cross-validation, including:

[0036] By masking a single valid data point and re-fitting the material removal volume using the remaining data, the impact of this single valid data point on the overall fitting result is evaluated. The sum of squares of the fitting residuals of all data points is then calculated to assess the overall fitting stability of all current data points in cross-validation based on the sum of squares of the fitting residuals.

[0037] Furthermore, this invention also provides a curvature adaptive surface fitting system for polishing optical elements, comprising: a data acquisition module, an index setting module, a parameter setting module, and a weighted fitting module, wherein...

[0038] The data acquisition module is used to acquire measurement values ​​of the optical element surface before and after polishing, and to obtain a height difference matrix of material removal based on the measurement values. The measurement values ​​include height data of the measurement area on the element surface.

[0039] The index setting module is used to traverse the height difference matrix through a sliding window and calculate the curvature sensitivity CSI using the eigenvalues ​​of the Hessian matrix.

[0040] The parameter setting module is used to divide the surface of the optical element into a planar region, a gradually changing region, and a high curvature region according to the curvature sensitivity CSI and the classification threshold, and to formulate fitting parameters for each region. The parameter mapping matrix is ​​used to record the fitting parameters corresponding to each pixel in the measurement area. The fitting parameters include the window size and the polynomial order.

[0041] The weighted fitting module is used to perform weighted fitting on each region based on the fitting parameters and using the least squares method to generate a continuous surface, so as to obtain the material removal volume by adaptive numerical integration on the continuous surface.

[0042] The beneficial effects of this invention are:

[0043] This invention achieves curvature-adaptive surface fitting for optical polishing volume calculation through perceptible local surface curvature, adaptive fitting, robust data processing, and result verification, ensuring the accuracy and controllability of optical polishing material removal. Experimental data shows that this solution can improve the accuracy of material removal volume calculation to over 97% on typical aspherical optical elements, with calculation errors controlled within 3%. It exhibits regional adaptability, robustness against data anomalies, and reasonable calculation accuracy and efficiency, demonstrating significant engineering value. The experimental results are as follows:

[0044] 1. Volume calculation accuracy reaches over 97%: The calculation error of typical aspherical optical elements is within 3%, with an average absolute error of 1.8%, which is better than the pixel summation method (average absolute error 16.7%), trapezoidal integral method (average absolute error 8.2%) and Simpson method (average absolute error 5.4%), meeting the process control requirements of high-precision optical manufacturing.

[0045] 2. Region-level adaptive capability: Automatically adjusts the fitting window size and polynomial order based on changes in surface CSI values, ensuring computational accuracy in high curvature regions while reducing computational redundancy in planar regions, thus maximizing computational accuracy and efficiency.

[0046] 3. Robust data anomaly handling capability: By using weighted least squares fitting and intelligent data filtering, it can handle common Zygo issues such as missing data points and measurement noise. With a 10% proportion of missing data points, the volume calculation error only increases by 0.5%.

[0047] 4. High engineering practicality: The generated differential data files are fully compatible with mainstream Zygo MetroPro software and can be integrated into existing quality control systems; it provides a visual interface and error reports to facilitate technicians to make quick process decisions.

[0048] 5. Reasonable and controllable computational efficiency: The dynamic parameter adjustment and optimization process means that the overall computation time for typical 2048×2048 pixel data is about 1.15 times that of the traditional pixel summation method. The computational accuracy is high and the computational efficiency is reasonable. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the curvature adaptive surface fitting process in the polishing of optical elements in the embodiment;

[0050] Figure 2 This is a schematic diagram illustrating the core principle of region classification and parameter mapping based on curvature sensitivity index in the embodiment.

[0051] Figure 3 This is a schematic diagram of the logical flow of adaptive surface fitting and volume calculation in the embodiment;

[0052] Figure 4 This is a schematic diagram of the curvature adaptive surface fitting platform architecture for optical polishing volume calculation in this embodiment. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer and more understandable, the invention will be further described in detail below with reference to the accompanying drawings and technical solutions.

[0054] For polishing large aspherical optical lenses, calculating the material removal volume can assess polishing efficiency and control surface accuracy for qualitative reshaping. Commonly used pixel-based and fixed-step-size integration methods cannot utilize local geometric properties when dealing with aspherical problems with high steepness and complex curvature, significantly reducing their computational accuracy. Therefore, this invention provides embodiments, see [link to embodiments]. Figure 1 As shown, a curvature adaptive surface fitting method for polishing optical components is provided, which specifically includes the following:

[0055] S101. Obtain measurement values ​​of the optical element surface before and after polishing, and obtain a height difference matrix of material removal based on the measurement values, wherein the measurement values ​​include height data of the measurement area on the element surface.

[0056] Specifically, the optical element can be measured twice, before and after polishing, using a Zygo interferometer to obtain the original data of the optical element surface before and after polishing. The original data before and after the measurement includes the measurement area width in pixels, the measurement area height in pixels, the laser wavelength, and the physical size corresponding to each pixel.

[0057] The measured width is obtained by parsing the header metadata of the raw Zygo interferometer data (.xyz or .dat format) before and after polishing. ,high Laser wavelength and pixel size Place the data points that are missing in the original data into... The corresponding position is synchronously marked.

[0058] S102. Traverse the height difference matrix through a sliding window and calculate the curvature sensitivity CSI using the eigenvalues ​​of the Hessian matrix.

[0059] Specifically, this can be achieved by unifying the units of the height data and using a Gaussian filter to smooth the height difference matrix so that each element in the smoothed height difference matrix represents the material removal depth at the corresponding pixel.

[0060] By successively reducing the height of the surface after polishing to the height of the surface before polishing, the height difference matrix of material removal amount is obtained. To ensure consistent data units, all heights are measured in micrometers. To eliminate high-frequency noise during measurement, a Gaussian filter is applied to the module. The matrix is ​​smoothed. The filter kernel function is:

[0061]

[0062] Standard deviation The noise level is set to 1.5 pixels based on typical interferometer noise characteristics.

[0063] This operation not only removes random noise while preserving surface morphology, but also allows the module to simultaneously scan for invalid measurement points in the original data. Marked on the matrix The matrix is ​​used for subsequent data fitting. After preprocessing... Each element in the matrix represents the material removal depth at the corresponding pixel, which forms the basis for all subsequent analyses.

[0064] Then, the second-order partial derivatives of the pixels in the measurement area are obtained in the sliding window, and a Hessian matrix is ​​constructed based on the second-order partial derivatives. The eigenvalues ​​of the Hessian matrix in the pixels of the measurement area are calculated, the curvature sensitivity CSI is set using the eigenvalues, and the curvature sensitivity CSI is normalized by the known maximum possible curvature of the optical surface.

[0065] like Figure 2 As shown, for any 5×5 neighborhood window centered at a pixel in the matrix, firstly, the height data is calculated using the discrete difference method, and then the central difference formula is used to calculate the height within the neighborhood. and Second-order partial derivatives and mixed partial derivatives. Local Hessian matrix. Exported pixels The second partial derivative in the 5×5 neighborhood window is:

[0066] ,

[0067] ,

[0068] ,

[0069] in, The pixel physical size is expressed in micrometers and is converted into the pixel resolution in the interferometer metadata (1 pixel = k micrometers, where k is the device calibration coefficient).

[0070] As a spatial scale factor, pixels allow for the accurate calculation of derivatives. The three calculated second-order partial derivatives can be used to construct the Hessian matrix for that point. The Hessian matrix is ​​a 2×2 real symmetric matrix, where all second-order partial derivatives are derived from the first second-order partial derivatives. Then, the eigenvalues ​​of this Hessian matrix are solved. and The absolute value of the sum of two eigenvalues ​​reflects the degree of curvature of the surface at that point in the two principal directions. Curvature sensitivity is defined as the square root of the sum of the squares of the two eigenvalues, i.e. This index is a non-negative scalar; the larger the value, the more severe the local surface curvature near that point. For unified comparison and classification, the module normalizes the calculated CSI value to a theoretical value, and then multiplies it by the theoretical maximum value obtained based on the maximum design curvature of the optical element under test or statistically based on historical data. The CSI normalization process can be expressed as follows:

[0071]

[0072] The maximum possible curvature of the optical surface.

[0073] S103. Based on the curvature sensitivity CSI and classification threshold, the surface of the optical element is divided into a planar region, a gradually changing region, and a high curvature region. Fitting parameters are formulated for each region. The fitting parameters corresponding to each pixel in the measurement region are recorded using a parameter mapping matrix. The fitting parameters include the window size and the polynomial order.

[0074] Specifically, fitting parameters are formulated for each region, and can be designed to include:

[0075] For the planar region, the window size corresponding to each pixel in the measurement area is set as the first size, and the polynomial order is first order;

[0076] For the gradually varying region, the window size corresponding to each pixel in the measurement area is set to the second size, and the polynomial order is second order;

[0077] For high curvature regions, the window size corresponding to each pixel in the measurement area is set as the third size, the polynomial order is third, and the first size < the second size < the third size;

[0078] The parameter mapping matrix is ​​used to record the window size and polynomial order corresponding to each pixel in the measurement area.

[0079] When the normalized curvature sensitivity index of a pixel in an image is less than 0.05, it is classified as a planar region. At this point, the surface changes are relatively stable, the geometric features are simple, and the corresponding fitting parameters can be set to a 3×3 window and a first-order polynomial. When this value is greater than 0.05 and less than 0.2, it is classified as a gradually changing region. At this point, the surface exhibits a certain degree of curvature, but the change in curvature is slow and gentle. The corresponding fitting parameters can be set to a 5×5 window and a second-order polynomial. When the value is greater than or equal to 0.2, it will be classified as a high curvature region. The curvature at this time is generally found at the edge of an aspherical lens, a steep transition zone, or a local defect repair area. The curvature changes greatly, and the corresponding fitting parameters can be set to a 7×7 window and a third-order polynomial. Each region has its corresponding surface fitting parameters pre-defined in the system. Planar regions are fitted using a smaller 3×3 fitting window and a simple first-order polynomial model, suitable for quickly processing large advection areas without excessive computation. Gradually varying regions are fitted using a 5×5 fitting window and a second-order polynomial model. High-curvature regions use a larger 7×7 fitting window and a more complex third-order polynomial model to better fit local complex shapes. Parameter mapping matrix. Record each pixel The corresponding window and polynomial order.

[0080] S104. Based on the fitting parameters and using the least squares method, a weighted fitting is performed on each region to generate a continuous surface, so as to obtain the material removal volume by adaptive numerical integration on the continuous surface.

[0081] Specifically, based on the fitting parameters and using the least squares method to perform weighted fitting for each region, it can be designed to include:

[0082] The pixel fitting region and the pixel fitting region weight function are set according to the window radius and the Euclidean distance from the pixel point in each region to the window center.

[0083] Based on the pixel fitting region weight function, a diagonal weight matrix is ​​set, and a weighted least squares problem is constructed using the diagonal weight matrix, the polynomial coefficient matrix and the observation vector. The observation vector is composed of the measured values ​​of each pixel in the measurement region.

[0084] The continuous surface corresponding to the fitting region is obtained by solving the weighted least squares problem, and the weighted average is used to filter the overlapping parts of each fitting region to obtain the final continuous fitting surface.

[0085] Weighted least squares surface fitting is based on the parameter mapping matrix. Determine each pixel The fitting range, where the weighting function can be expressed as:

[0086]

[0087] in Let Euclidean distance be the distance from points within different regions to the center of the window. Set the window radius; set the weighted design matrix. With observation vector Solve the weighted least squares problem:

[0088]

[0089] For Let be the diagonal weight matrix of the elements. This is the vector of polynomial coefficients to be calculated. During the fitting process, points with weights greater than a set threshold are removed, i.e., points without data are excluded from the marked data, ensuring the robustness of the fitting process. A continuous surface is obtained in each fitting region. A weighted average method is used to transition at the overlapping points, ultimately yielding the fitted surface. .

[0090] like Figure 3 As shown, The parameter mapping of each pixel in the matrix determines the fitting region centered on that point. Within this region, weighted least squares is used to achieve local surface fitting. The design of the weight function is the most crucial step. The weight function is designed so that the contribution of the portion closer to the window center to the fitting result is greater than that of the portion farther from the window center, improving the local adaptability of the fitting and suppressing boundary effects. The weight function is a Gaussian function with the window center as the origin, where the Euclidean distance from any point to the window center is the window radius. Based on this weight function, the module assigns weight values ​​to valid data points within the fitting region, while points without data automatically have zero weight. According to the order of the fitted polynomial model, a weighted design matrix and observation vector are constructed, and the weighted least squares normal equation is solved to obtain the optimal polynomial coefficient vector, automatically eliminating low-weight and invalid points. After completing the local fitting of a point, the fitted surface function expression and fitting height value at that point are obtained. Overlapping sliding windows cause the same location to be covered by different windows. When handling overlapping regions, a distance-based weighted averaging method is used to fuse the fitting results of different windows together, obtaining a continuous, smooth, and complete fitted surface function for the entire measurement region.

[0091] Specifically, obtaining the material removal volume by adaptive numerical integration over a continuous surface may include:

[0092] For each fitting parameter, the fitting region is first divided into several sub-regions. The Simpson integral of each sub-region is calculated based on the continuous surface, and the relative error of the Simpson integral of each sub-region is obtained through evaluation.

[0093] If the relative error of the Simpson integral of a sub-region is greater than the threshold, the sub-region is divided again and the Simpson integral of each sub-region is re-acquired. The process of dividing and calculating the Simpson integral of the region is repeated until the relative error of the Simpson integral of all regions is less than the threshold or the maximum number of subdivisions is reached.

[0094] Data outside the fitted region is virtually generated based on the symmetrical points of the boundary of the fitted region. The information outside the region is used to simulate the complete region. The Simpson integral is linearly corrected based on the ratio of the effective region area to the complete region area. The corrected volumes of all local regions are summarized. The geometric relationship of the overlapping parts of the window is used to deduct the duplicated parts to obtain the total volume of material removed.

[0095] Initial region Divide the region into 4×4 sub-regions and calculate the Simpson value for each sub-region. For sub-regions with a relative error greater than 0.1%, the sub-regions with larger errors are further subdivided, and the results of the current subdivision level are compared with those of the previous subdivision level. This process is repeated until the relative error of the integration of all sub-regions is less than 0.1% or the maximum number of subdivisions is reached. Step S150 also requires boundary correction because the fitting region at the edge of the data matrix needs to detect incomplete boundaries. The mirror expansion method is mainly used, virtually expanding the data outside the region at the boundary symmetry point to obtain complete neighborhood information; the boundary region integral value is recalculated based on the expanded data, and the applied correction formula is:

[0096]

[0097] Volume correction is performed using the above formula, where The original integration result, For the area of ​​the complete theoretical region, The effective area is calculated by summing the volumes of all corrected local regions and removing duplicate calculations caused by overlapping sliding windows. .

[0098] An adaptive Simpson integral method is employed, dynamically adjusting the integration step size according to the degree of change in the integrand, thereby improving computational speed while maintaining accuracy. Integration is performed on a per-fit region basis. For each fitted region with defined parameter mappings, it is first initialized as 4×4 uniform regions, and the Simpson integral value of the fitted surface function in each region is calculated. Then, the integration result at this level is compared with the result of the previous level of subdivision. When the relative error of integration in a certain region is greater than 0.1%, the region is automatically subdivided, and this process is repeated until the relative error of integration in all regions is less than 0.1% or the maximum number of subdivisions is reached. This adaptive subdivision method uses a large step size for fast integration in flat surface regions and uses the maximum sampling point density in regions with drastic surface changes. When fitting to a fitted region located at the edge of the data matrix, direct integration may introduce errors due to the incomplete neighborhood. The module can modify the boundary to be incomplete, then use the mirror expansion method to virtually generate data outside the region based on the boundary's symmetrical points. It then uses this outside-region information to simulate the complete region, and linearly corrects the integration result based on the ratio of the effective region area to the complete theoretical region area. Finally, it summarizes the corrected volumes of all local regions. Since overlapping sliding windows cause some volumes to be calculated repeatedly, the geometric relationship of the overlapping window portions is used to deduct the double-counted parts, yielding the total volume removed from the material.

[0099] Specifically, a verification and evaluation process with optimized parameters can be set up. The relative error is obtained by comparing the material removal volume with the result calculated using the pixel summation method. The overall fitting stability of all current data points is verified using leave-one-out cross-validation. If the relative error exceeds a threshold or the current overall fitting stability is not met, an adaptive optimization process for surface fitting is triggered until the adaptive optimization termination condition is met. The adaptive optimization process for surface fitting involves adjusting the classification threshold and updating the surface region division of the optical element and the fitting parameters of each newly divided region using the adjusted classification threshold, so as to regenerate a continuous surface using the new fitting parameters. The adaptive optimization termination condition is that the maximum number of adaptive optimization iterations is met or the relative error is less than a threshold.

[0100] To verify the overall fit stability of all current data points using leave-one-out cross-validation, a single valid data point is masked, and the material removal volume is re-calculated using the remaining data. The impact of this single valid data point on the overall fit result is evaluated, and the sum of squares of the fitting residuals of all data points is calculated. In cross-validation, the overall fit stability of all current data points is evaluated based on the sum of squares of the fitting residuals.

[0101] To ensure accurate calculation results and achieve autonomous optimization, the relative error of the total volume calculated using the benchmark comparison method is first compared with that calculated using the pixel summation method. That is, the total volume... Pixel summation result In comparison, the relative error is expressed as Leave-one cross-validation: First, mask out a single valid data point, refit and calculate the volume using the remaining data, then evaluate the impact of that point on the overall result, and calculate the sum of squares of the fitting residuals for all data points to obtain the overall accuracy of the fitted model. The fitting residuals are represented as: N represents the number of effective pixels. If the relative error of the benchmark comparison exceeds 3% or the model shows instability during cross-validation, optimization is required. The optimization process automatically adjusts some parameters in the curvature sensitivity analysis module, such as fine-tuning the region classification threshold boundary. After adjustment, the system feeds the new parameters back to the start of the process and re-enters the curvature sensitivity analysis to volume calculation process. This iteration runs a maximum of 3 times or until the validation error is less than 3%. Finally, two outputs are generated: one is a differential data file in Zygo format, which can be used in existing detection workflows; the other is a comprehensive report including detailed volume calculation results, volume contribution of each region, calculated confidence intervals, error analysis, and optimization logs.

[0102] Furthermore, based on the above method, this embodiment of the invention also provides a curvature adaptive surface fitting system for optical element polishing, comprising: a data acquisition module, an index setting module, a parameter setting module, and a weighted fitting module, wherein,

[0103] The data acquisition module is used to acquire measurement values ​​of the optical element surface before and after polishing, and to obtain a height difference matrix of material removal based on the measurement values. The measurement values ​​include height data of the measurement area on the element surface.

[0104] The index setting module is used to traverse the height difference matrix through a sliding window and calculate the curvature sensitivity CSI using the eigenvalues ​​of the Hessian matrix.

[0105] The parameter setting module is used to divide the surface of the optical element into a planar region, a gradually changing region, and a high curvature region according to the curvature sensitivity CSI and the classification threshold, and to formulate fitting parameters for each region. The parameter mapping matrix is ​​used to record the fitting parameters corresponding to each pixel in the measurement area. The fitting parameters include the window size and the polynomial order.

[0106] The weighted fitting module is used to perform weighted fitting on each region based on the fitting parameters and using the least squares method to generate a continuous surface, so as to obtain the material removal volume by adaptive numerical integration on the continuous surface.

[0107] like Figure 4 As shown, the hardware consists of a Zygo interferometer connected to an industrial control computer, and the software includes a data preprocessing module, a curvature sensitivity module, an adaptive surface fitting module, a volume calculation module, and a result verification and optimization module.

[0108] The data preprocessing module preprocesses the data from the optical surface interferometry measurements before and after polishing to obtain the material removal height difference matrix.

[0109] The curvature sensitivity analysis module obtains the local Hessian matrix eigenvalues ​​and curvature sensitivity index (CSI) by traversing the height difference matrix through a sliding window, and divides the surface region into planar, gently changing, and high curvature regions according to the CSI.

[0110] The adaptive surface fitting module performs weighted least-squares surface fitting on each region according to the fitting parameter settings to obtain a continuous surface model.

[0111] The volume calculation module performs adaptive numerical integration on the continuous surface model to obtain the material removal volume.

[0112] The results verification and optimization module compares and optimizes the calculation results with traditional methods to obtain the fitting quality and calculation reliability. Based on the comparison results, it adjusts the curvature sensitivity analysis parameters to obtain the volume calculation results and error analysis report.

[0113] Quality supervision of batch polishing of small precision spherical optical components is crucial. When the overall curvature is similar, local high curvature can occur due to the rounded edges of the components, subsurface damage, and polishing tool marks. Traditional methods, being globally uniform, often suffer from low accuracy at abrupt changes or excessive calculations at flat areas. In this embodiment, higher global efficiency and the ability to capture local features are achieved through inter-module cooperation. The data preprocessing module loads the interferogram data of individual spherical components before polishing. The curvature sensitivity index is uniform in local areas, but significantly increases in the rounded edge region of the equipment. The curvature sensitivity analysis module can identify local high-index regions by traversing the elevation difference matrix. Based on a set dynamic classification threshold, the main body of the spherical component is divided into gradually changing regions, and small-scale rounded edge regions and small subsurface damage points are classified as high-curvature regions, resulting in a parameter mapping matrix.

[0114] The adaptive surface fitting module, based on this mapping matrix, uses a 5×5 window second-order polynomial to fit the gradually varying regions occupying a small area of ​​the main body, and a 7×7 window third-order polynomial to fit the high-curvature regions at the edges occupying a small area. This differentiated approach results in using more computational resources to describe local features that require a more complex model when reconstructing the spherical main body. The weight function in the weighted least squares fitting ensures that when the fitting window includes planar regions and steep edge transition zones, smooth transitions do not lead to discontinuous distortions at the boundaries. The volume calculation module is the main tool for performing adaptive Simpson integration. In large, gradually varying regions, the fitting function is smooth, and the integration speed is fast, requiring minimal subdivision. For high-curvature regions, the integration algorithm, due to the large rate of change of the function value, will subdivide, sampling and allocating integration to small areas such as rounded edges. The result verification and optimization module is the main tool for statistical analysis of batch calculation results. If a systematic deviation occurs in the edge volume calculation of a certain type of element (with a certain radius of curvature), it will automatically learn and suggest adjusting the curvature sensitivity classification threshold for that type of element, performing adaptive optimization of historical data parameters.

[0115] Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0116] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0117] The units and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations are not considered to be beyond the scope of this invention.

[0118] Those skilled in the art will understand that all or part of the steps in the above methods can be implemented by a program instructing related hardware, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk. Optionally, all or part of the steps in the above embodiments can also be implemented using one or more integrated circuits. Accordingly, each module / unit in the above embodiments can be implemented in hardware or as a software functional module. This invention is not limited to any particular combination of hardware and software.

[0119] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for adaptive curvature surface fitting in the polishing of optical elements, characterized in that, Include: Obtain measurement values ​​of the optical element surface before and after polishing, and obtain a height difference matrix of material removal based on the measurement values, wherein the measurement values ​​include height data of the measurement area on the element surface. The curvature sensitivity CSI is calculated by traversing the height difference matrix through a sliding window and using the eigenvalues ​​of the Hessian matrix. The surface of the optical element is divided into planar region, gradually changing region and high curvature region according to the curvature sensitivity CSI and classification threshold. Fitting parameters are formulated for each region. The fitting parameters corresponding to each pixel in the measurement area are recorded using a parameter mapping matrix. The fitting parameters include window size and polynomial order. Based on the fitting parameters and using the least squares method to perform weighted fitting for each region, a continuous surface is generated, and the material removal volume is obtained by adaptive numerical integration on the continuous surface.

2. The method for adaptive curvature surface fitting in optical element polishing according to claim 1, characterized in that, Obtain interferometric measurements of optical components before and after surface polishing, including: The optical element was measured twice, before and after polishing, using a Zygo interferometer to obtain the original data of the optical element surface before and after polishing. The original data before and after the measurement included the width (in pixels) of the measurement area, the height (in pixels) of the measurement area, the laser wavelength, and the physical size corresponding to each pixel.

3. The method for adaptive curvature surface fitting in optical element polishing according to claim 1, characterized in that, Before traversing the height difference matrix using a sliding window, the following is also included: Standardize the units for altitude data; A Gaussian filter is used to smooth the height difference matrix so that each element in the smoothed height difference matrix represents the material removal depth at the corresponding pixel.

4. The method for adaptive curvature surface fitting in optical element polishing according to claim 1, characterized in that, Curvature sensitivity (CSI) is calculated using the eigenvalues ​​of the Hessian matrix, including: Obtain the second-order partial derivatives of the pixels in the measurement region within the sliding window, and construct the Hessian matrix based on the second-order partial derivatives; Calculate the eigenvalues ​​of the Hessian matrix at the pixels in the measurement area, use the eigenvalues ​​to set the curvature sensitivity CSI, and normalize the curvature sensitivity CSI by using the known maximum possible curvature of the optical surface.

5. The method for adaptive curvature surface fitting in optical element polishing according to claim 1, characterized in that, Fitting parameters were defined for each region, including: For the planar region, the window size corresponding to each pixel in the corresponding measurement area is set as the first size, and the polynomial order is first order; For the gradually varying region, the window size corresponding to each pixel in the measurement area is set to the second size, and the polynomial order is second order; For high curvature regions, the window size corresponding to each pixel in the measurement area is set as the third size, the polynomial order is third, and the first size < the second size < the third size; The parameter mapping matrix is ​​used to record the window size and polynomial order corresponding to each pixel in the measurement area.

6. The method for adaptive curvature surface fitting in optical element polishing according to claim 1, characterized in that, Based on the fitted parameters, a weighted fit is performed on each region using the least squares method, including: The pixel fitting region and the pixel fitting region weight function are set according to the window radius and the Euclidean distance from the pixel point in each region to the window center. Based on the pixel fitting region weight function, a diagonal weight matrix is ​​set, and a weighted least squares problem is constructed using the diagonal weight matrix, the polynomial coefficient matrix and the observation vector. The observation vector is composed of the measured values ​​of each pixel in the measurement region. The continuous surface corresponding to the fitting region is obtained by solving the weighted least squares problem, and the weighted average is used to filter the overlapping parts of each fitting region to obtain the final continuous fitting surface.

7. The method for adaptive curvature surface fitting in optical element polishing according to claim 1, characterized in that, The material removal volume is obtained by adaptive numerical integration of a continuous surface, including: For each fitting parameter, the fitting region is first divided into several sub-regions. The Simpson integral of each sub-region is calculated based on the continuous surface, and the relative error of the Simpson integral of each sub-region is obtained through evaluation. If the relative error of the Simpson integral of a sub-region is greater than the threshold, the sub-region is divided again and the Simpson integral of each sub-region is re-acquired. The process of dividing and calculating the Simpson integral of the region is repeated until the relative error of the Simpson integral of all regions is less than the threshold or the maximum number of subdivisions is reached. Data outside the fitted region is virtually generated based on the symmetrical points of the boundary of the fitted region. The information outside the region is used to simulate the complete region. The Simpson integral is linearly corrected based on the ratio of the effective region area to the complete region area. The corrected volumes of all local regions are summarized. The geometric relationship of the overlapping parts of the window is used to deduct the duplicated parts to obtain the total volume of material removed.

8. The method for adaptive curvature surface fitting in optical element polishing according to claim 1 or 7, characterized in that, The material removal volume is obtained by adaptive numerical integration over a continuous surface, and also includes: The relative error is obtained by comparing the volume of material removed with the result of the volume removed using the pixel summation method. The overall fit stability of all current data points is verified using leave-one-out cross-validation. If the relative error exceeds the threshold or the current overall fitting stability is not met, the adaptive optimization process of surface fitting is triggered until the adaptive optimization termination condition is met. The adaptive optimization process of surface fitting is to adjust the classification threshold and use the adjusted classification threshold to update the surface region division of the optical element and the fitting parameters of each newly divided region, so as to regenerate the continuous surface using the new fitting parameters. The adaptive optimization termination condition is to meet the maximum number of adaptive optimization iterations or the relative error is less than the threshold.

9. The method for adaptive curvature surface fitting in optical element polishing according to claim 8, characterized in that, The overall fit stability of all current data points is verified using leave-one-out cross-validation, including: By masking a single valid data point and re-fitting the material removal volume using the remaining data, the impact of this single valid data point on the overall fitting result is evaluated. The sum of squares of the fitting residuals of all data points is then calculated to assess the overall fitting stability of all current data points in cross-validation based on the sum of squares of the fitting residuals.

10. A curvature adaptive surface fitting system for polishing optical elements, characterized in that, It includes: a data acquisition module, an indicator setting module, a parameter setting module, and a weighted fitting module. The data acquisition module is used to acquire measurement values ​​of the optical element surface before and after polishing, and to obtain a height difference matrix of material removal based on the measurement values. The measurement values ​​include height data of the measurement area on the element surface. The index setting module is used to traverse the height difference matrix through a sliding window and calculate the curvature sensitivity CSI using the eigenvalues ​​of the Hessian matrix. The parameter setting module is used to divide the surface of the optical element into a planar region, a gradually changing region, and a high curvature region according to the curvature sensitivity CSI and the classification threshold, and to formulate fitting parameters for each region. The parameter mapping matrix is ​​used to record the fitting parameters corresponding to each pixel in the measurement area. The fitting parameters include the window size and the polynomial order. The weighted fitting module is used to perform weighted fitting on each region based on the fitting parameters and using the least squares method to generate a continuous surface, so as to obtain the material removal volume by adaptive numerical integration on the continuous surface.

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