Rectangular aperture curved surface shape error compensation method and system

Abstract

The invention provides a rectangular aperture curved surface shape error compensation method and system, and belongs to the field of free-form surface optical element ultra-precision machining.The method comprises the steps that the surface of a workpiece is machined based on an optimal moving path, coordinates and actual height values of all points on a curved surface shape are collected, and machining errors are obtained; performing unit square normalization on the processing error curved surface by using a Zernike polynomial, and then fitting a prediction error curved surface; and the predicted error curved surface is negated to correct the optimal moving path in the machining process, and the surface of the workpiece is remachined till the machining error meets the machining precision. The method strictly controls the precision and range of error compensation, and ensures that the compensated curved surface can meet the design requirements.

Description

Technical Field

[0001] The present application belongs to the field of ultra-precision processing of free-form surface optical elements, and more specifically, to a method and system for compensating surface shape errors of rectangular aperture surfaces. Background Art

[0002] Free-form surface optical elements play an important role in optical systems. Their high degree of freedom in surface design can effectively reduce the influence of optical aberration and chromatic aberration, improve imaging quality, and meet various complex optical requirements. They are widely used in lithography machines, laser nuclear fusion devices, space telescopes, and medical equipment. High-precision free-form surface optical elements play a key role in ensuring the performance of optical systems. However, the free-form surface processing process is affected by many factors, such as positioning and following errors of processing equipment, thermal deformation, tool wear, and material inhomogeneity, which leads to surface errors in the processed free-form surface, seriously affecting the performance of the optical system. Therefore, high-precision compensation methods are the key technologies for the convergence of free-form surface surface error processing. At the same time, in many current optical components, such as optical filters, laser resonators, and spectroscopes, rectangular apertures are mostly used. However, the current compensation algorithm is mainly designed for circular apertures. When applied to rectangular apertures, problems such as insufficient fitting accuracy and low convergence efficiency may occur, affecting the performance and production efficiency of optical components. Therefore, in order to meet the needs of rectangular aperture optical free-form surfaces, it is urgent to develop a more advanced and effective surface error compensation method to improve the fitting accuracy and convergence efficiency, achieve efficient and accurate error compensation, and thus improve the surface accuracy and optical performance of free-form optical elements. Summary of the invention

[0003] In view of the defects of the prior art, the purpose of this application is to provide a method and system for compensating the surface error of a rectangular aperture curved surface, aiming to solve the problem that the existing compensation algorithm for the free-form surface shape is mainly designed for circular apertures, and when applied to rectangular apertures, it will result in insufficient fitting accuracy and low convergence efficiency.

[0004] To achieve the above object, the present application provides a method for compensating a rectangular aperture curved surface shape error, comprising the following steps:

[0005] Step S1: constructing a machining program based on the parameters and features of the surface to be machined to obtain the optimal moving path during the machining process;

[0006] Step S2: Based on the optimal moving path obtained in step S1, the workpiece surface is processed, the coordinates and actual height values ​​of each point on the curved surface are collected, and the processing error is obtained;

[0007] Step S3: Determine whether the machining error meets the machining accuracy. If so, terminate the subsequent steps and take the workpiece processed in step S2 as the final workpiece. If not, go to step S4.

[0008] Step S4: using Zernike polynomials to normalize the machining error surface to a unit square and then fit the predicted error surface;

[0009] Step S5: invert the predicted error surface and add it to the processing program in step S1, correct the optimal moving path during the processing, and go to step S2 until the processing error meets the processing accuracy; wherein the surface shape of the workpiece is a rectangular aperture.

[0010] Further preferably, step S4 specifically includes the following steps:

[0011] Step S4.1: constructing a machining error surface coordinate system based on the machining error obtained in step S2, mapping the rectangular aperture surface area into a unit square for normalization processing;

[0012] Step S4.2: Taking the center of the unit square as the origin, calculate the relative distance and angle of each point to the center, and map the points of the rectangular aperture surface area to the polar coordinate system of the virtual unit circle;

[0013] Step S4.3: Determine the order of the Zernike polynomial based on the radius and angle parameters within the virtual unit circle, and initialize the coefficients of each term of the Zernike polynomial in the polar coordinate system;

[0014] Step S4.4: In the polar coordinate system, multiply each term of the Zernike polynomial by the corresponding coefficient of each term of the Zernike polynomial and add them up to obtain the predicted height value of each point on the surface;

[0015] Step S4.5: Use the least square method to fit the objective function, obtain the prediction error, adjust the coefficients of the Zernike polynomial, and go to step S4.4 until the minimum prediction error is obtained; wherein the error between the predicted height value and the actual height value is the prediction error, and the minimum prediction error is the objective function;

[0016] Step S4.6: Determine whether the minimum prediction error obtained in step S4.5 meets the preset conditions. If so, obtain the prediction error surface. If not, adjust the order of the Zernike polynomial and the step size of the least squares method, and go to step S4.4.

[0017] Further preferably, the method for constructing the machining error surface coordinate system is to keep the horizontal and vertical coordinates of the rectangular aperture surface unchanged, and use the machining error as the vertical coordinate axis.

[0018] Further preferably, when the prediction error does not satisfy a preset condition, the order of the Zernike polynomial is increased, or the step size of the least squares method is reduced.

[0019] Further preferably, when the predicted error surface is inverted and added to the machining program, the cutting depth, speed and direction of the tool at each point are adjusted.

[0020] Further preferably, the parameters and features of the surface to be machined include: machining process parameters, precision parameters of the machined surface and material properties of the workpiece.

[0021] In a second aspect, the present application provides a rectangular aperture curved surface shape error compensation system, comprising:

[0022] The machining path acquisition module is used to construct a machining program based on the parameters and features of the surface to be machined, so as to obtain the best moving path during the machining process;

[0023] A tool is used to process the workpiece surface according to an optimal movement path;

[0024] The profilometer measuring probe is used to collect the coordinates and actual height values ​​of each point on the curved surface;

[0025] A processing error calculation module is used to calculate the processing error of each point based on the actual height value of each point on the curved surface and the preset height value;

[0026] The first determination module is used to determine whether the machining error meets the machining accuracy. If so, the currently machined workpiece is used as the final workpiece. Otherwise, the predicted error surface fitting module is driven to run.

[0027] A prediction error surface fitting module is used to fit the prediction error surface after normalizing the machining error surface to a unit square using Zernike polynomials;

[0028] A moving path compensation module is used to invert the predicted error surface and add it to the processing program in the processing path acquisition module to correct the optimal moving path during the processing;

[0029] Among them, the curved surface shape of the workpiece is a rectangular aperture.

[0030] Further preferably, the prediction error surface fitting module includes:

[0031] A rectangular aperture surface normalization unit is used to construct a machining error surface coordinate system based on the machining error, and to map the rectangular aperture surface area into a unit square for normalization processing;

[0032] A coordinate conversion unit is used to calculate the relative distance and angle between each point and the center with the center of the unit square as the origin, and map the points of the rectangular aperture surface area to the polar coordinate system of the virtual unit circle;

[0033] A data initialization unit, used to determine the order of the Zernike polynomial based on the radius and angle parameters in the virtual unit circle, and initialize the coefficients of each Zernike polynomial in the polar coordinate system;

[0034] A height prediction unit is used to multiply each term of the Zernike polynomial by each coefficient of the corresponding Zernike polynomial in a polar coordinate system and then accumulate the results to obtain a predicted height value of each point on the surface;

[0035] A prediction error solving unit is used to fit the objective function using the least square method to obtain the prediction error;

[0036] A second determination unit, used to determine whether the minimum prediction error meets a preset condition;

[0037] A minimum prediction error search unit, used to adjust the coefficients of each Zernike polynomial based on the prediction error; or adjust the order of the Zernike polynomial and the step size of the least square method;

[0038] The error between the predicted height value and the actual height value is the prediction error, and the objective function is to minimize the prediction error.

[0039] Further preferably, the horizontal and vertical coordinates of the machining error surface coordinate system in the rectangular aperture surface normalization unit are the horizontal and vertical coordinates of the rectangular aperture surface, and the vertical coordinate is the machining error.

[0040] Further preferably, when the prediction error does not satisfy a preset condition in the minimum prediction error search unit, the order of the Zernike polynomial is increased, or the step size of the least squares method is reduced.

[0041] Further preferably, in the moving path compensation module, when the predicted error surface is inverted and added to the machining program, the cutting depth, speed and direction of the tool at each point are adjusted.

[0042] Further preferably, the parameters and features of the surface to be processed in the processing path acquisition module include: processing process parameters, precision parameters of the processed surface and material properties of the workpiece.

[0043] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art:

[0044] In view of the characteristics of rectangular aperture free-form surfaces, the present application provides a method for compensating surface shape errors of rectangular aperture surfaces to improve the accuracy and efficiency of compensation; the surface is normalized by unit square using Zernike polynomials. Since Zernike polynomials are orthogonal in a circular area, they no longer meet the orthogonal condition when directly converted and used in rectangular aperture surfaces. Therefore, they need to be orthogonalized; through calculation and adjustment, the Zernike polynomial fitting surface can better adapt to the shape characteristics of the rectangular aperture, thereby realizing the normalization of the unit square; after normalization, the amount to be compensated is calculated according to the normalized Zernike surface fitting result; then, the error of the surface is accurately compensated through corresponding processing or adjustment measures. During the compensation process, the accuracy and range of compensation are strictly controlled to ensure that the compensated surface can meet the design requirements.

[0045] For rectangular aperture free-form surfaces, this method uses Zernike polynomials to fit the overall three-dimensional surface error, which can comprehensively and effectively solve the problem of surface error compensation of rectangular aperture surfaces and significantly improve the machining accuracy and quality of rectangular aperture surfaces.

[0046] More specifically, for rectangular aperture surfaces, the Zernike surface is normalized to a unit square and then fitted and compensated, which significantly improves the fitting accuracy; through precise modeling and analysis of the surface shape, more subtle surface features can be captured, greatly reducing the deviation between the fitting result and actual needs; compared with traditional methods, it is more accurate in processing complex surfaces and small errors, thereby effectively improving the processing quality of rectangular aperture surfaces.

[0047] The rectangular aperture surface shape error compensation method provided by the present application greatly improves the iteration efficiency; compared with the prior art, the present application firstly targets the specific object of rectangular aperture surface, uses Zernike polynomials to fit the error surface and performs unit square normalization operation on the error surface, so that the originally complex rectangular aperture surface problem can be converted into a relatively standardized unit square problem for processing; in terms of calculation process, the rectangular area is mapped to a virtual unit circle polar coordinate system through area transformation, and the calculation steps and complexity are reduced by means of the characteristics of Zernike polynomials within the unit circle. In terms of algorithm, an optimization algorithm is used to adjust the Zernike polynomial coefficients during the fitting process so that the constructed surface is close to the actual processing error surface, and the error is calculated and the coefficient is adjusted according to the objective function to achieve rapid convergence. In terms of data processing and error evaluation, the parameters and error algorithm are adjusted by arranging the data to form an ordered matrix, evaluating the fitting results and comparing the original data, and improving the iteration efficiency. Through a series of means and optimized calculation processes and algorithms, unnecessary repeated calculations and parameter adjustments are reduced, so that more ideal compensation results can be obtained in a short time, the iterative efficiency of rectangular aperture surface processing is improved, the entire processing cycle is greatly shortened, and a strong guarantee is provided for mass production.

[0048] The high-precision surface shape error compensation method for rectangular aperture surfaces provided by the present application significantly reduces the surface shape error. First, the method innovatively adopts a strategy based on Zernike polynomial fitting for the specific object of rectangular aperture free-form surfaces. Compared with the prior art, the traditional compensation method often has the problem of insufficient fitting accuracy when facing rectangular aperture surfaces, while the method of the present application uses Zernike polynomials to normalize the surface to a unit square and then perform fitting compensation, which can more accurately describe the shape characteristics of the rectangular aperture surface. In the compensation process, the mathematical properties of Zernike polynomials are used to fit the error surface in the unit square coordinate system. In the fitting process, the coefficients of the polynomials are continuously adjusted so that the surface constructed by the polynomials is as close to the actual machining error surface as possible. Through repeated calculation and optimization, the Zernike polynomial expression that can most accurately describe the characteristics of the machining error surface is found, thereby realizing high-precision fitting of the machining error surface. In addition, the method also includes the steps of adding the original machining program after negating the machining error surface, and performing secondary machining after correcting the tool path. By repeating these steps, the machining process and parameters are continuously improved, and the machining error is gradually reduced. Compared with the existing technology, this iterative compensation method can more effectively eliminate surface errors and improve the machining accuracy of rectangular aperture surfaces.

[0049] In summary, the rectangular aperture curved surface shape error compensation method provided by the present application significantly reduces the shape error compared with the prior art through innovative fitting strategies and iterative compensation steps, providing a strong guarantee for reducing the subsequent processing and detection costs. Due to the improvement of compensation accuracy, the time for additional finishing and fine grinding processes is reduced, saving costs. At the same time, the improved production efficiency enables more processing tasks to be completed in the same time, increasing output and further improving economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a rectangular aperture curved surface shape error compensation method provided by the present application;

[0051] Figure 2 It is a schematic diagram of a rectangular aperture curved surface shape error compensation method provided in this application. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0053] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0054] The technical solutions provided in the embodiments of the present application are introduced.

[0055] In response to the demand for surface error compensation of rectangular aperture free-form surfaces, the present application provides a surface error compensation method for rectangular aperture free-form surfaces based on Zernike polynomial fitting, which aims to significantly improve the machining accuracy of rectangular aperture free-form surfaces, effectively solve the limitations of existing compensation methods in the application of rectangular aperture surfaces, greatly improve the accuracy and stability of compensation, reduce the adverse effects of machining errors on optical performance, and meet the strict requirements of high-precision optical systems for rectangular aperture free-form surfaces.

[0056] Example 1

[0057] like Figure 1 and Figure 2 As shown, the present application provides a method for compensating the surface error of a rectangular aperture free-form surface based on Zernike polynomial fitting, comprising the following steps:

[0058] Step S1: Design a machining program according to the ideal machining surface, plan the tool path, and perform the first machining;

[0059] More specifically, step S1 includes analyzing various parameters and features of the ideal machining surface, taking into full account the machining process requirements, precision standards, material properties and other factors, designing a suitable machining program according to the characteristics and performance of the machining equipment, and planning the best moving path of the tool during the machining process to ensure that the tool can efficiently and accurately cut the workpiece to achieve the ideal surface shape; starting the machining equipment for the first machining operation according to the designed machining program and tool path to preliminarily form a surface close to the ideal shape;

[0060] Step S2: using a profilometer to measure the actual machined surface shape and obtain the machining error;

[0061] More specifically, step S2 is: scanning the workpiece surface point by point and collecting data through the profilometer measuring probe, recording the coordinates and height of each point on the actual processing surface shape, and then comparing and analyzing the measured data with the design data of the ideal processing surface shape, so as to calculate the processing error generated in the actual processing process;

[0062] Step S3: Determine whether the machining error meets the machining accuracy. If so, terminate the execution of the following steps to obtain the final machined workpiece; if not, go to step S4;

[0063] Step S4: using Zernike polynomials to normalize the machining error surface to a unit square and then fit the predicted error surface;

[0064] More specifically, S4 includes the following steps:

[0065] Construct a machining error surface coordinate system, map the rectangular area to a relative unit square for normalization; take the center of the unit square as the origin, calculate the relative distance and angle of each point to the center, and map the points in the rectangular area to a polar coordinate system of a virtual unit circle;

[0066] Determine the order of the Zernike polynomial according to the "radius" and "angle" parameters in the transformed area, initialize the coefficients of the Zernike polynomials in the polar coordinate system, and calculate the predicted height value in each iteration by multiplying each Zernike polynomial by the corresponding Zernike polynomial coefficients on the virtual unit circle according to the current Zernike polynomial coefficients, and then accumulating and optimizing the objective function by least squares fitting, calculate the prediction error according to the objective function, and adjust the coefficients of the Zernike polynomials so that the error is gradually reduced; the objective function is to minimize the error between the predicted height value and the actual measured height value;

[0067] More specifically, the fitting result evaluation and correction method is as follows: if the minimum prediction error does not meet the requirements, the order of the Zernike polynomial can be increased, the step size of the least squares optimization algorithm can be adjusted, the processed data can be pre-processed by filtering, and step S4 can be repeated until the obtained prediction error is less than the preset error value, the prediction height value corresponding to the minimum prediction error is obtained, and the prediction error surface is constructed;

[0068] Step S5: invert the predicted error surface and add it to the original machining program, and perform secondary machining after correcting the tool path;

[0069] More specifically, S5 is as follows: performing an inversion operation on the prediction error surface obtained by analyzing in step S4, adding the inverted prediction error data to the originally designed processing program, correcting and supplementing the original processing program, replanning the tool path, adjusting the cutting depth, speed and direction of the tool at each position, and starting the processing equipment for secondary processing according to the corrected tool path;

[0070] Step S6: Repeat steps S1 to S5, iterate the processing technology and parameters, and gradually reduce the processing error until the processing accuracy meets the requirements.

[0071] Example 2

[0072] In a second aspect, the present application provides a rectangular aperture curved surface shape error compensation system, comprising:

[0073] The machining path acquisition module is used to construct a machining program based on the parameters and features of the surface to be machined, so as to obtain the best moving path during the machining process;

[0074] A tool is used to process the workpiece surface according to an optimal movement path;

[0075] The profilometer measuring probe is used to collect the coordinates and actual height values ​​of each point on the curved surface;

[0076] A processing error calculation module is used to calculate the processing error of each point based on the actual height value of each point on the curved surface and the preset height value;

[0077] The first determination module is used to determine whether the machining error meets the machining accuracy. If so, the currently machined workpiece is used as the final workpiece. Otherwise, the predicted error surface fitting module is driven to run.

[0078] A prediction error surface fitting module is used to fit the prediction error surface after normalizing the machining error surface to a unit square using Zernike polynomials;

[0079] A moving path compensation module is used to invert the predicted error surface and add it to the processing program in the processing path acquisition module to correct the optimal moving path during the processing;

[0080] Among them, the curved surface shape of the workpiece is a rectangular aperture.

[0081] Further preferably, the prediction error surface fitting module includes:

[0082] A rectangular aperture surface normalization unit is used to construct a machining error surface coordinate system based on the machining error, and to map the rectangular aperture surface area into a unit square for normalization processing;

[0083] A coordinate conversion unit is used to calculate the relative distance and angle between each point and the center with the center of the unit square as the origin, and map the points of the rectangular aperture surface area to the polar coordinate system of the virtual unit circle;

[0084] More specifically, Zernike polynomials are usually defined in polar coordinates, have good orthogonality, and perform well within the unit circle; for any point (r,θ) within the unit circle, the Zernike polynomial can be expressed as the product of a radial polynomial and an angular function; the basic form is as follows:

[0085]

[0086] Where: n is the order of the polynomial (a non-negative integer); m is the degree related to the angle, satisfying |m|≤n and n-|m| is an even number; ρ is the normalized radial distance; θ is the polar angle;

[0087] Radial Polynomial is defined as follows:

[0088]

[0089] For practical applications, especially in optics, it is common to use the real-valued form of the Zernike polynomials. The real-valued form can be expressed as:

[0090]

[0091] For rectangular areas, bilinear interpolation nonlinear mapping technology is used to convert points in the rectangular area into points in the unit circle. The side length of the rectangular area is set to L, and its center point is the origin. The coordinates (x, y) of the rectangular area can be converted to polar coordinates (r′, θ′), where:

[0092]

[0093] This transformation maps every point in the rectangular area to every point in the unit circle;

[0094] A data initialization unit, used to determine the order of the Zernike polynomial based on the radius and angle parameters in the virtual unit circle, and initialize the coefficients of each Zernike polynomial in the polar coordinate system;

[0095] A height prediction unit is used to multiply each term of the Zernike polynomial by each coefficient of the corresponding Zernike polynomial in a polar coordinate system and then accumulate the results to obtain a predicted height value of each point on the surface;

[0096] A prediction error solving unit is used to fit the objective function using the least square method to obtain the prediction error;

[0097] A second determination unit, used to determine whether the minimum prediction error meets a preset condition;

[0098] A minimum prediction error search unit, used to adjust the coefficients of each Zernike polynomial based on the prediction error; or adjust the order of the Zernike polynomial and the step size of the least square method;

[0099] The error between the predicted height value and the actual height value is the prediction error, and the objective function is to minimize the prediction error.

[0100] Further preferably, the horizontal and vertical coordinates of the machining error surface coordinate system in the rectangular aperture surface normalization unit are the horizontal and vertical coordinates of the rectangular aperture surface, and the vertical coordinate is the machining error.

[0101] Further preferably, when the prediction error does not satisfy a preset condition in the minimum prediction error search unit, the order of the Zernike polynomial is increased, or the step size of the least squares method is reduced.

[0102] Further preferably, in the moving path compensation module, when the predicted error surface is inverted and added to the machining program, the cutting depth, speed and direction of the tool at each point are adjusted.

[0103] Further preferably, the parameters and features of the surface to be processed in the processing path acquisition module include: processing process parameters, precision parameters of the processed surface and material properties of the workpiece.

[0104] In summary, compared with the prior art, the present application has the following advantages:

[0105] In view of the characteristics of rectangular aperture free-form surfaces, the present application provides a method for compensating surface shape errors of rectangular aperture surfaces to improve the accuracy and efficiency of compensation; the surface is normalized by unit square using Zernike polynomials. Since Zernike polynomials are orthogonal in a circular area, they no longer meet the orthogonal condition when directly converted and used in rectangular aperture surfaces. Therefore, they need to be orthogonalized; through calculation and adjustment, the Zernike polynomial fitting surface can better adapt to the shape characteristics of the rectangular aperture, thereby realizing the normalization of the unit square; after normalization, the amount to be compensated is calculated according to the normalized Zernike surface fitting result; then, the error of the surface is accurately compensated through corresponding processing or adjustment measures. During the compensation process, the accuracy and range of compensation are strictly controlled to ensure that the compensated surface can meet the design requirements.

[0106] For rectangular aperture free-form surfaces, this method uses Zernike polynomials to fit the overall three-dimensional surface error, which can comprehensively and effectively solve the problem of surface error compensation of rectangular aperture surfaces and significantly improve the machining accuracy and quality of rectangular aperture surfaces.

[0107] More specifically, the rectangular aperture surface is normalized to a unit square using the Zernike surface and then fitted and compensated, which significantly improves the fitting accuracy; through precise modeling and analysis of the surface shape, more subtle surface features can be captured, greatly reducing the deviation between the fitting result and actual requirements; compared with traditional methods, it is more accurate in processing complex surfaces and small errors, thereby effectively improving the processing quality of rectangular aperture surfaces.

[0108] The rectangular aperture curved surface error compensation method provided in this application greatly improves the iteration efficiency; during the compensation process, the calculation process and algorithm are optimized, and unnecessary repeated calculations and parameter adjustments are reduced; the fast convergence characteristics enable a relatively ideal compensation result to be obtained in a short time, greatly shortening the entire processing cycle and providing a strong guarantee for mass production.

[0109] The present application provides a method for compensating the surface error of a rectangular aperture curved surface, which significantly reduces the surface error, thereby reducing the cost of subsequent processing and testing; due to the improvement of compensation accuracy, the time for additional finishing and fine grinding processes is reduced, saving costs. At the same time, the improved production efficiency enables more processing tasks to be completed in the same time, increasing output and further improving economic benefits.

[0110] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0111] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A method for compensating a rectangular aperture curved surface shape error, characterized in that: The following steps are involved: Step S1: constructing a machining program based on the parameters and features of the surface to be machined to obtain the optimal moving path during the machining process; Step S2: Based on the optimal moving path obtained in step S1, the workpiece surface is processed, the coordinates and actual height values ​​of each point on the curved surface are collected, and the processing error is obtained; Step S3: Determine whether the machining error meets the machining accuracy. If so, terminate the subsequent steps and take the workpiece processed in step S2 as the final workpiece. If not, go to step S4. Step S4: using Zernike polynomials to normalize the machining error surface to a unit square and then fit the predicted error surface; Step S5: invert the predicted error surface and add it to the processing program in step S1, correct the optimal moving path during the processing, and go to step S2 until the processing error meets the processing accuracy; wherein the surface shape of the workpiece is a rectangular aperture.

2. The rectangular aperture curved surface shape error compensation method according to claim 1, characterized in that: Step S4 specifically includes the following steps: Step S4.1: constructing a machining error surface coordinate system based on the machining error obtained in step S2, mapping the rectangular aperture surface area into a unit square for normalization processing; Step S4.2: Taking the center of the unit square as the origin, calculate the relative distance and angle of each point to the center, and map the points of the rectangular aperture surface area to the polar coordinate system of the virtual unit circle; Step S4.3: Determine the order of the Zernike polynomial based on the radius and angle parameters within the virtual unit circle, and initialize the coefficients of each term of the Zernike polynomial in the polar coordinate system; Step S4.4: In the polar coordinate system, multiply each term of the Zernike polynomial by the corresponding coefficient of each term of the Zernike polynomial and add them up to obtain the predicted height value of each point on the surface; Step S4.5: Use the least square method to fit the objective function, obtain the prediction error, adjust the coefficients of the Zernike polynomial, and go to step S4.4 until the minimum prediction error is obtained; wherein the error between the predicted height value and the actual height value is the prediction error, and the minimum prediction error is the objective function; Step S4.6: Determine whether the minimum prediction error obtained in step S4.5 meets the preset conditions. If so, obtain the prediction error surface. If not, adjust the order of the Zernike polynomial and the step size of the least squares method, and go to step S4.

4.

3. The rectangular aperture curved surface shape error compensation method according to claim 2, characterized in that: The method for constructing the machining error surface coordinate system is to keep the horizontal and vertical coordinates of the rectangular aperture surface unchanged and use the machining error as the vertical coordinate axis.

4. The rectangular aperture curved surface shape error compensation method according to claim 2, characterized in that: When the prediction error does not meet the preset conditions, the order of the Zernike polynomial is increased, or the step size of the least squares method is reduced.

5. The method for compensating the surface error of a rectangular aperture curved surface according to any one of claims 2 to 4, characterized in that: When the predicted error surface is inverted and added to the machining program, the cutting depth, speed and direction of the tool at each point are adjusted.

6. The rectangular aperture curved surface shape error compensation method according to claim 1, characterized in that: The parameters and characteristics of the surface to be processed include: processing parameters, precision parameters of the processed surface and material properties of the workpiece.

7. A rectangular aperture curved surface shape error compensation system, characterized in that: include: The machining path acquisition module is used to construct a machining program based on the parameters and features of the surface to be machined, so as to obtain the best moving path during the machining process; A tool is used to process the workpiece surface according to an optimal movement path; The profilometer measuring probe is used to collect the coordinates and actual height values ​​of each point on the curved surface; A processing error calculation module is used to calculate the processing error of each point based on the actual height value of each point on the curved surface and the preset height value; The first determination module is used to determine whether the machining error meets the machining accuracy. If so, the currently machined workpiece is used as the final workpiece. Otherwise, the predicted error surface fitting module is driven to run. A prediction error surface fitting module is used to fit the prediction error surface after normalizing the machining error surface to a unit square using Zernike polynomials; A moving path compensation module is used to invert the predicted error surface and add it to the processing program in the processing path acquisition module to correct the optimal moving path during the processing; Among them, the curved surface shape of the workpiece is a rectangular aperture.

8. The rectangular aperture curved surface shape error compensation system according to claim 7, characterized in that: The prediction error surface fitting module includes: A rectangular aperture surface normalization unit is used to construct a machining error surface coordinate system based on the machining error, and to map the rectangular aperture surface area into a unit square for normalization processing; A coordinate conversion unit is used to calculate the relative distance and angle between each point and the center with the center of the unit square as the origin, and map the points of the rectangular aperture surface area to the polar coordinate system of the virtual unit circle; A data initialization unit, used to determine the order of the Zernike polynomial based on the radius and angle parameters in the virtual unit circle, and initialize the coefficients of each Zernike polynomial in the polar coordinate system; A height prediction unit is used to multiply each term of the Zernike polynomial by each coefficient of the corresponding Zernike polynomial in a polar coordinate system and then accumulate the results to obtain a predicted height value of each point on the surface; A prediction error solving unit is used to fit the objective function using the least square method to obtain the prediction error; A second determination unit, used to determine whether the minimum prediction error meets a preset condition; A minimum prediction error search unit, used to adjust the coefficients of each Zernike polynomial based on the prediction error; or adjust the order of the Zernike polynomial and the step size of the least square method; The error between the predicted height value and the actual height value is the prediction error, and the objective function is to minimize the prediction error.

9. The rectangular aperture curved surface shape error compensation system according to claim 8, characterized in that: When the prediction error in the minimum prediction error search unit does not meet the preset condition, the order of the Zernike polynomial is increased, or the step size of the least squares method is reduced.

10. The rectangular aperture curved surface shape error compensation system according to claim 8, characterized in that: In the moving path compensation module, when the predicted error surface is inverted and added to the machining program, the cutting depth, speed and direction of the tool at each point are adjusted.

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