A complex curved surface minimum machining amount optimization design method based on multi-parameter data

Abstract

The application discloses a kind of complex surface minimum machining quantity optimization design method based on multi-parameter data, solves technology cannot find optimal target surface in complete tolerance domain and other problems.The method comprises the following steps: obtaining the three-dimensional discrete topography data of measured surface and pre-processing;Determine the parameters to be adjusted and generate candidate parameter domain;Calculate the local surface error between the candidate target surface and the corresponding measured surface, and then obtain the expected material removal amount;Simulate the machining simulation to obtain the corresponding actual material removal amount;Integrate the actual material removal amount according to the sampling unit area to obtain the corresponding measured surface material processing amount, and then obtain the corresponding global surface error;Screen the candidate surface type parameters based on the global surface error, then perform multi-objective evolutionary search to output the Pareto optimal solution set, and then obtain the unique optimal solution that meets the preset requirements from the optimal solution set.The application greatly reduces the processing volume and polishing cycle by reducing the meaningless material removal amount from the root.

Description

Technical Field

[0001] This invention relates to a method for optimizing the design of precision and ultra-precision machining parameters for complex curved surfaces, specifically a method for optimizing the minimum machining amount of complex curved surfaces based on multi-parameter data. Background Technology

[0002] As optical systems evolve towards high performance and extreme simplification, the application of complex curved surface optical elements is becoming increasingly widespread. Their processing specifications typically involve the coupled requirements of multiple parameters, such as surface accuracy (PV / RMS), vertex radius of curvature R, quadratic surface constant K, higher-order aspherical coefficients, center thickness, and eccentricity. Currently, in the processing of complex curved surface optical elements, surface parameters such as the radius of curvature and quadratic surface constant are usually set to nominal values ​​(tolerances set to zero) before measuring the surface accuracy. The spatial domain deviation between the measured surface and the ideal nominal surface is then calculated, and this deviation is used as the amount of material to be processed. However, this method easily leads to large material removal, low accuracy convergence, long polishing cycles, and high processing costs.

[0003] Currently, various methods can be used to determine the machining quantity of complex optical surfaces, specifically:

[0004] (1) Determining the machining amount based on the ideal nominal surface: This method takes the ideal nominal surface as the sole machining target and treats all surface deviations between the measured surface and the ideal nominal surface as errors to be removed for shaping. The advantage of this method is that it can ensure that the surface parameters after machining are infinitely close to the design nominal value. However, it does not utilize the tolerance margin of the surface parameters given by the optical surface drawing, which will generate a large amount of unnecessary material removal, thereby significantly increasing the machining time and the number of iterations. This not only significantly reduces the machining efficiency and increases the optical material loss, but also easily causes dimensional deviations due to excessive material removal, resulting in poor machining economy and stability.

[0005] (2) Determining the machining amount by directly reusing the measured surface parameters: When the measured surface parameters (vertex radius of curvature / quadratic surface constant, etc.) have fallen within the tolerance range of the drawing, this method directly uses the ideal nominal surface corresponding to the measured surface parameters as the machining target surface, and then calculates the machining amount for surface accuracy correction. This method can reduce the machining amount to a certain extent, but it only passively adapts to the existing measured surface and lacks the core step of actively seeking optimization within the full parameter tolerance domain. It cannot traverse all feasible target surfaces within the tolerance interval, so the obtained machining target is usually not the optimal solution with the minimum material machining amount in theory.

[0006] (3) Determine the processing amount based on the least squares method: This method generates a fitted surface by performing least squares fitting on the measured surface, and then uses the fitted surface as the processing target surface, and defines the surface shape error to be removed and the processing amount. However, this method only uses the minimum of the square of the geometric error as the fitting criterion, and does not use the minimum of the material processing amount as the optimization objective. Therefore, the processing redundancy problem still exists.

[0007] Furthermore, the aforementioned methods all neglect the actual dynamic response performance constraints of precision machining equipment, making it difficult for the machining target surface to be accurately realized by the equipment. Simultaneously, for complex surfaces with multiple parameters and high dimensions, traditional enumeration search methods result in excessive computational costs and extremely poor real-time performance. Because multiple core indicators, such as minimum material processing volume, residual surface error, machining process feasibility, and computational efficiency, are mutually constraining and trade-offs, traditional single-dimensional optimization methods cannot achieve a synergistic balance among multiple objectives. Therefore, they struggle to simultaneously meet the precision machining requirements of low processing loss, high processing accuracy, strong process feasibility, and high computational efficiency.

[0008] In summary, there is an urgent need for a method that can efficiently obtain the minimum amount of material processing required to correct the surface accuracy of complex curved optical elements to the qualified threshold while meeting various constraints such as multi-parameter tolerances of surface shape and dynamic response performance of machine tools. Summary of the Invention

[0009] The purpose of this invention is to solve the technical problems of existing methods for determining the minimum machining amount of complex surfaces, such as the easy generation of redundant removal amounts, the inability to find the optimal target surface within the complete tolerance domain, the mismatch between geometric optimization results and actual machining processes, and the difficulty of co-optimizing multiple objectives. In response, this invention provides a method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data.

[0010] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0011] A method for optimizing the minimum machining requirements of complex surfaces based on multi-parameter data, characterized by the following steps:

[0012] S1, acquire three-dimensional discrete topographic data at different sampling positions of the measured surface, align the coordinate systems of the measured surface and the target surface, and preprocess the three-dimensional discrete topographic data; the measured surface is the actual surface of the component to be processed; the target surface is the ideal nominal surface with preset requirements;

[0013] S2, according to the preset requirements, obtain the mathematical expression, nominal value and tolerance of the target surface, and determine the parameters to be adjusted and their adjustment range, and generate a candidate parameter domain containing multiple sets of candidate surface parameters;

[0014] S3, take any set of candidate surface parameters, generate the corresponding candidate target surface at the same sampling position as the measured surface, and calculate the local surface error between the candidate target surface and the corresponding measured surface at each sampling position by combining the three-dimensional discrete topography data preprocessed in step S1.

[0015] S4. Based on the sign of the minimum value of the local surface error obtained in step S3, obtain the expected material removal amount at the sampling position corresponding to the measured curved surface.

[0016] S5. Combining the expected material removal amount obtained in step S4, the actual material removal amount at the corresponding sampling position of the measured curved surface is calculated by simulating the processing.

[0017] S6. Based on the actual material removal amount calculated in step S5, the actual material removal amount at all sampling positions within the effective diameter of the target surface is integrated according to the area of ​​the sampling unit to obtain the measured surface material processing amount corresponding to any set of candidate surface parameters mentioned in step S3.

[0018] S7. Following the methods of steps S3 to S6, obtain the measured surface material processing amount corresponding to the remaining candidate surface parameters.

[0019] S8. Based on the expected material removal amount obtained in step S4 and the actual material removal amount obtained in step S5, the residual error at each sampling position is calculated, and then the global surface shape error after the actual surface simulation processing corresponding to any set of candidate surface shape parameters in step S3 is obtained; the global surface shape error is characterized by the root mean square value and the peak-valley value.

[0020] S9. Following the methods of steps S3 to S5 and S8, obtain the global surface shape error after the actual surface simulation processing corresponding to the remaining candidate surface shape parameters.

[0021] S10: Judge the global surface shape error obtained in steps S8 and S9. If the corresponding root mean square value and / or peak-valley value exceed the preset constraint threshold, discard a set of candidate surface shape parameters corresponding to the corresponding global surface shape error; otherwise, retain the corresponding candidate surface shape parameters and execute step S11.

[0022] S11, with the minimum material processing amount obtained in steps S6 and S7 and the minimum global surface shape error obtained in steps S8 and S9 as the optimization objectives, perform multi-objective evolutionary iterative search on all candidate surface shape parameters retained in step S10, and output a Pareto optimal solution set containing multiple sets of candidate surface shape parameters;

[0023] S12, based on the preset requirements of the target surface, combines the Pareto front to obtain the unique optimal solution from the Pareto optimal solution set, which combines the minimum material processing amount with the optimal candidate surface parameters, thereby completing the minimum processing amount optimization design of complex surfaces based on multi-parameter data.

[0024] Further, in step S1, three-dimensional discrete topographic data at different sampling positions of the measured surface are acquired using a coordinate measuring machine, a laser interferometer, or a non-contact 3D optical surface shape measurement device. The three-dimensional discrete topographic data includes surface shape parameters characterizing the global geometric shape of the measured surface, and local surface shape error data characterizing the local contour deviation of the measured surface. The surface shape parameters include one or more of the following: vertex radius of curvature, quadratic surface constant, and higher-order aspherical coefficient. The local surface shape error data is the local irregular contour deviation value of the measured surface after removing the macroscopic surface shape parameter deviation.

[0025] The preprocessing includes invalid point removal, noise reduction, missing point processing, and effective aperture reduction.

[0026] The target surface is a rotationally symmetric quadratic aspheric surface or a higher-order aspheric surface.

[0027] Furthermore, in step S2, the parameter to be adjusted is the vertex radius of curvature and / or the quadratic surface constant, and the other surface parameters besides the parameter to be adjusted retain their corresponding nominal values; each group of candidate surface parameters is a combination of reasonable values ​​of all surface parameters.

[0028] Further, in step S3, the expression for the candidate target surface is:

[0029]

[0030] In the formula, For the first The group of candidate surface shape parameters corresponds to the aspherical sagitta of the candidate target surface. ; The radius of the sampling position corresponding to the candidate target surface; For the first Vertex curvature radius in the candidate surface type parameters; For the first The quadratic surface constant in the candidate surface type parameters; For higher-order aspherical coefficients, For higher-order terms, The value can be 2, ..., I, where I is the preset maximum order;

[0031] In step S3, the local surface shape error is expressed by the following formula:

[0032]

[0033] In the formula, Indicates the first The candidate target surfaces and their corresponding measured surfaces at the sampling positions Surface shape error at the location; For the measured surface at the sampling position The height of the arrow at the location; For the first The candidate target surface at the sampling location The height of the arrow at the location; It is the set of coordinates corresponding to all sampling positions within the effective light-transmitting aperture of the measured curved surface.

[0034] Further, step S4 specifically involves determining the sign of the minimum value among the local surface shape errors obtained in step S3. If the minimum value is positive or zero, the corresponding local surface shape error is used as the expected material removal amount at the corresponding sampling position of the measured surface. If the minimum value is negative, all local surface shape errors are non-negatively increased based on the minimum value, and the non-negatively increased local surface shape error is used as the expected material removal amount at the corresponding sampling position of the measured surface.

[0035] The desired amount of material to be removed is calculated using the following formula:

[0036]

[0037] In the formula, For the first The candidate target surface at the sampling location The corresponding expected material removal amount; For the first The candidate target surface at the sampling location The minimum value of the surface shape error corresponding to that location.

[0038] Furthermore, in step S5, the method for simulating the processing is specifically as follows:

[0039] First, a removal function model is constructed. Then, the ideal dwell time at each sampling position of the measured surface is calculated by combining the dwell time algorithm and the corresponding expected material removal amount. Then, under the constraints of the shape of the removal function and the dynamic response performance of the machine tool, the ideal dwell time is processed into the corresponding actual dwell time. Finally, the removal function and the actual dwell time are convolved to obtain the actual material removal amount at the corresponding sampling position of the measured surface.

[0040] The dwell time algorithm employs the pulse iteration method, Fourier transform method, linear equation system method, or non-negative least squares method.

[0041] Further, in step S6, the amount of material processed is calculated using the following formula:

[0042]

[0043] In the formula, For the first Material processing amount corresponding to the candidate surface shape parameters; Sampling location within the effective caliber The area of ​​the infinitesimal element corresponding to the location.

[0044] Further, in step S8, the residual error is calculated using the following formula:

[0045] ;

[0046] In the formula, For the first The candidate target surface at the sampling location The corresponding residual error at that location; For the first The candidate target surface at the sampling location The actual amount of material removed at that location;

[0047] The root mean square value is calculated using the following formula:

[0048]

[0049] In the formula, For the first The root mean square value of the global surface shape error after simulation processing of the measured surface corresponding to the candidate surface shape parameters; This represents the total number of discrete sampling points within the effective aperture of the optical element.

[0050] The peak and valley values ​​are calculated using the following formula:

[0051]

[0052] In the formula: For the first Peak and valley values ​​of global surface shape error after simulated processing of the measured curved surface corresponding to the candidate surface shape parameters; This represents the maximum residual error at all sampling locations after simulation processing; This represents the minimum residual error at all sampling locations after the simulation process.

[0053] Further, step S11 specifically involves using the minimum material processing amount obtained in steps S6 and S7 and the minimum global surface shape error obtained in steps S8 and S9 as optimization objectives. A multi-objective evolutionary iterative search is performed on all candidate surface shape parameters retained in step S10. After the search is complete, it is determined whether the preset number of iterations has been reached. If the preset number of iterations has not been reached, then based on the fitness evaluation results, all retained candidate surface shape parameters are non-dominated and individual selection is performed. Then, a candidate parameter set is generated through parameter crossover, parameter mutation, and elite retention, and the process returns to step S3. If the preset number of iterations has been reached, then based on the fitness evaluation results, a Pareto optimal solution set containing multiple sets of candidate surface shape parameters is output.

[0054] Furthermore, in step S11, the multi-objective evolutionary iterative search is implemented using a multi-objective genetic algorithm, a second-generation or third-generation genetic algorithm with elitist strategy and non-dominated sorting, a decomposition-based multi-objective evolutionary algorithm, a multi-objective particle swarm optimization algorithm, or a multi-objective differential evolutionary algorithm.

[0055] The fitness is used to measure how well each retained candidate face shape parameter satisfies the optimization objective, and its expression is:

[0056] In the formula, For the first The fitness evaluation function for candidate target surfaces. It represents the material processing amount corresponding to the ideal nominal surface. It is the root mean square value of the global surface shape error after the actual surface simulation processing corresponding to the ideal nominal surface.

[0057] The beneficial effects of this invention are as follows:

[0058] 1. This invention abandons the traditional approach of using only the ideal nominal surface as the sole processing target or directly adopting the measured surface shape parameters. Instead, it expands the ideal nominal surface into multiple complete candidate target surfaces within the parameter tolerance range. Under the premise of meeting the optical surface shape parameter tolerance requirements, it actively searches for the globally optimal target surface, thereby obtaining the corresponding optimal surface shape parameters. This fundamentally reduces the amount of meaningless material removal, significantly reducing the processing volume and polishing cycle.

[0059] 2. This invention differs from existing solutions that rely solely on geometric height differences to judge the amount of material removed. It incorporates the actual shape of the removal function, the non-negative constraint of the dwell time, the dynamic response performance of the machine tool, and the residual error of convolution processing into the evaluation system of the candidate target surface. By simulating the machining process, it predicts the surface shape error after machining and eliminates candidate surface shape parameters that exceed the machining index constraint threshold, thus avoiding the problem of geometrically optimal but with excessive surface shape error after machining.

[0060] 3. This invention constructs a normalized multi-objective fitness function with material processing amount and simulated processing surface error as the two cores, and uses a multi-objective evolutionary iterative search method to solve the Pareto optimal solution set, so that the optimal processing scheme can be flexibly selected according to the accuracy and cost requirements of different components to be processed, such as lithography objectives and large-aperture mirrors.

[0061] 4. The target surface model, optimization algorithm, evaluation index, etc. of this invention can be flexibly replaced, supporting the representation of various complex surfaces such as spheres, quadratic aspherical surfaces, higher-order aspherical surfaces, and partially freeform surfaces; it is compatible with various optimization algorithms such as non-dominated sorting second-generation genetic algorithm or third-generation genetic algorithm (NSGA-II / NSGA-III) with elitist strategy, decomposition-based multi-objective evolutionary algorithm (MOEA / D), multi-objective particle swarm optimization algorithm or multi-objective differential evolution algorithm; it can be extended with derivative functions such as robust optimization, multi-process joint optimization, and multi-dimensional surface quality evaluation, adapting to different optical manufacturing scenarios. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating an embodiment of the present invention.

[0063] Figure 2 This is a schematic diagram of the Pareto optimal solution set obtained in an embodiment of the present invention.

[0064] Figure 3 This is a schematic diagram illustrating the principle of adjusting candidate target surfaces within the tolerance range of surface parameters to reduce machining volume in an embodiment of the present invention.

[0065] Figure 4 This is a schematic diagram showing the addition of an irregular initial surface shape error of approximately 0.1 μm to each of the four mirror surfaces in an embodiment of the present invention.

[0066] Figure 5 The diagram shows a comparison of the material processing amount distribution obtained by the ideal nominal surface method and the method of the present invention for the sixth reflecting mirror. (a) is the material processing amount distribution obtained by the ideal nominal surface method, and (b) is the material processing amount distribution obtained in this embodiment. Detailed Implementation

[0067] To make the objectives, advantages, and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0068] like Figure 1 As shown in the figure, this embodiment provides a method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data, including the following steps:

[0069] S1, Data Acquisition and Preprocessing.

[0070] The three-dimensional discrete topography data at different sampling positions of the measured surface are obtained. After aligning the coordinate systems of the measured surface and the target surface, the three-dimensional discrete topography data are preprocessed. The measured surface is the actual surface of the component to be processed, and the target surface is the ideal nominal surface with preset requirements, and the surface shapes of the two are consistent.

[0071] This embodiment acquires three-dimensional discrete topographic data at different sampling positions of the measured surface using a coordinate measuring machine, a laser interferometer, or a non-contact 3D optical surface shape measurement device. This three-dimensional discrete topographic data is the multi-parameter data described in the subject matter of this invention, including surface shape parameters characterizing the global geometry of the measured surface, and local surface shape error data characterizing local contour deviations of the measured surface. The surface shape parameters include vertex radius of curvature R, quadratic surface constant K, and higher-order aspherical coefficients. One or more of the parameters can be included, depending on the surface type, including eccentricity, off-axis, tilt angle, etc. Each surface parameter has tolerance constraints; if no tolerance constraints exist, the nominal value is used. Specifically, the vertex radius of curvature R characterizes the basic curvature at the surface vertex; the quadratic surface constant K characterizes the quadratic surface type and degree of deviation of the surface relative to the sphere; and the higher-order aspherical coefficients characterize the aspherical correction amount of the surface at different orders. These parameters are organized according to a unified coordinate system, unified surface equation, and unified data format, collectively forming a multi-parameterized description of complex surfaces. The local surface error data is the local irregular contour deviation value of the measured surface after removing macroscopic surface parameter deviations, characterized by peak-to-valley values ​​(PV) and root mean square (RMS), with specific indices set according to design requirements.

[0072] The preprocessing described in this embodiment includes invalid point removal, noise reduction, missing point processing, and effective aperture trimming. Rigid body registration can be performed on the above data if necessary, but macroscopic shape errors must not be eliminated by changing the parameters of the surface to be controlled.

[0073] S2, construct the candidate parameter domain.

[0074] Based on preset requirements, obtain the mathematical expression, nominal values ​​and tolerances of the target surface, determine the parameters to be adjusted and their adjustment range, and generate a candidate parameter domain containing multiple sets of candidate surface parameters.

[0075] In this embodiment, the parameters to be adjusted are the vertex radius of curvature and / or the quadratic surface constant. All other surface parameters except the parameters to be adjusted retain their corresponding nominal values ​​or are constrained according to the measurement uncertainty. Therefore, each set of candidate surface parameters is a combination of reasonable values ​​of all surface parameters, which is the search space of the optimization algorithm.

[0076] The candidate parameter domain is a two-dimensional candidate parameter domain generated based on the nominal values ​​of the surface parameters and the adjustable tolerance range. ,in, For the first The vertex curvature radius of the candidate target surface corresponds to the group of candidate surface type parameters; For the first The candidate surface parameters correspond to the quadratic surface constants of the candidate target surface.

[0077] S3 generates candidate target surfaces and calculates local surface errors.

[0078] Take any set of candidate surface parameters, generate corresponding candidate target surfaces at the same sampling positions as the measured surface, and calculate the local surface error between the candidate target surfaces and the corresponding measured surfaces at each sampling position by combining the three-dimensional discrete topography data after preprocessing in step S1. This local surface error includes the local surface components that actually need to be corrected by the removal process under this set of candidate surface parameters.

[0079] The adjustable surface parameters (i.e., the parameters to be adjusted) of complex curved surfaces are uniformly represented as vectors. In this embodiment, the target surface is a rotationally symmetric quadratic aspheric surface or a rotationally symmetric higher-order aspheric surface. For a rotationally symmetric quadratic aspheric surface, we can let... For rotationally symmetric higher-order aspherical surfaces, we can let Then the expression for the corresponding candidate target surface is:

[0080]

[0081] In the formula, For the first The group of candidate surface shape parameters corresponds to the aspherical sagitta of the candidate target surface. ; Let be the radius of the sampling position corresponding to the candidate target surface, and ; For the first Vertex curvature radius in the candidate surface type parameters; For the first The quadratic surface constant in the candidate surface type parameters; For higher-order aspherical coefficients, For higher-order terms, The value can be 2, ..., I, where I is the preset maximum order, determined based on the actual parameters of the target surface; when the target surface is a quadratic aspherical surface... =0, when it is a higher-order aspherical surface 0.

[0082] For non-rotationally symmetric free surfaces It can be replaced by other computable shape models such as XY polynomials, Zernike basis (Zernike polynomials), Forbes Q (Q-type polynomial) freeform surfaces, etc. Optimization variables can be model parameters or constrained low-order basis function coefficients.

[0083] Within the effective aperture, the local surface shape error is expressed by the following formula:

[0084]

[0085] In the formula, Indicates the first The candidate target surfaces and their corresponding measured surfaces at the sampling positions Surface shape error at the location; For the measured surface at the sampling position The height of the arrow at the location; For the first The candidate target surface at the sampling location The height of the arrow at the location; It is the set of coordinates corresponding to all sampling positions within the effective light-transmitting aperture of the measured curved surface.

[0086] S4, calculate the expected material removal amount at each sampling location.

[0087] Determine the sign of the minimum value among the local surface shape errors at each sampling position obtained in step S3. If the minimum value is positive or zero, the corresponding local surface shape error is used as the expected material removal amount at the corresponding sampling position of the measured surface. If the minimum value is negative, all local surface shape errors are non-negatively raised based on the minimum value, that is, the negative margin is eliminated by uniformly raising the constant across the entire field, and the non-negatively raised local surface shape error is used as the expected material removal amount at the corresponding sampling position of the measured surface.

[0088] The desired material removal amount described in this embodiment is calculated using the following formula:

[0089]

[0090] In the formula, For the first The candidate target surface at the sampling location The corresponding expected material removal amount; For the first The candidate target surface at the sampling location The minimum value of the surface shape error corresponding to that location.

[0091] S5 simulates and calculates the actual amount of material removed at each sampling location.

[0092] Based on the expected material removal amount obtained in step S4, the actual material removal amount at the corresponding sampling location of the measured curved surface is calculated using a simulation method. The specific simulation method described in this embodiment is as follows:

[0093] First, a removal function model is constructed. Then, the ideal dwell time at each sampling position of the measured surface is calculated by combining the dwell time algorithm and the corresponding expected material removal amount. Then, under the constraints of the shape of the removal function and the dynamic response performance of the machine tool (path, speed, non-negativity of dwell time, and maximum / minimum dwell time constraints), the ideal dwell time is processed into the corresponding actual dwell time. Finally, the removal function and the actual dwell time are convolved to obtain the actual material removal amount at the corresponding sampling position of the measured surface.

[0094] The removal function is a removal function calibrated under the constraints of the machine tool and tool combination, and can be discretized into a convolution kernel or a convolution matrix. Solve for the actual dwell time under the conditions of non-negative dwell time and constrained speed and travel distance. ,make Approaching the desired material removal rate The actual material removal amount at the sampling location corresponding to the measured curved surface is obtained, that is:

[0095]

[0096] In the formula, For the first The candidate target surface at the sampling location The corresponding actual amount of material removed at that location. This is the removal function after discretization (convolution matrix / polishing kernel function). For the first The candidate target surface at the sampling location The corresponding actual length of stay.

[0097] The dwell time algorithm may employ the pulse iteration method, Fourier transform method, linear equation system method, non-negative least squares method, or other dwell time algorithms known in the art.

[0098] S6, calculate the measured surface material processing amount corresponding to the candidate surface parameters.

[0099] Based on the actual material removal amount calculated in step S5, the actual material removal amount at all sampling positions within the effective diameter of the target surface is integrated according to the sampling unit area to obtain the measured surface material processing amount corresponding to any set of candidate surface parameters mentioned in step S3.

[0100] The material processing quantity described in this embodiment is calculated using the following formula:

[0101]

[0102] In the formula, For the first Material processing amount corresponding to the candidate surface shape parameters; Sampling location within the effective caliber The area of ​​the infinitesimal element corresponding to the location.

[0103] S7, calculate the measured surface material processing amount corresponding to the remaining candidate surface parameters.

[0104] The measured surface material processing amount corresponding to the remaining candidate surface parameters is obtained by following steps S3 to S6.

[0105] S8 calculates the residual error and the global surface error.

[0106] Based on the expected material removal amount obtained in step S4 and the actual material removal amount obtained in step S5, the residual error at each sampling location is calculated, and then the global surface shape error after the simulated processing of the measured surface corresponding to any set of candidate surface shape parameters mentioned in step S3 is obtained. In this embodiment, the global surface shape error is characterized by the root mean square value and the peak-valley value; in some embodiments, the global surface shape error can also be characterized by edge residuals, spatial frequency band errors, or power spectral density.

[0107] The residual error described in this embodiment is calculated using the following formula:

[0108] ;

[0109] In the formula, For the first The candidate target surface at the sampling location The corresponding residual error at that location; For the first The candidate target surface at the sampling location The corresponding actual amount of material removed.

[0110] The root mean square value is calculated using the following formula:

[0111]

[0112] In the formula, For the first The root mean square value of the global surface shape error after simulation processing of the measured surface corresponding to the candidate surface shape parameters; This represents the total number of discrete sampling points within the effective aperture M of the optical element.

[0113] The peak and valley values ​​are calculated using the following formula:

[0114]

[0115] In the formula: For the first Peak and valley values ​​of global surface shape error after simulated processing of the measured curved surface corresponding to the candidate surface shape parameters; This represents the maximum residual error at all sampling locations after simulation processing; This represents the minimum residual error at all sampling locations after the simulation process.

[0116] When there are rigid requirements for accuracy, screening is required. and / or Solutions that exceed the processing index constraint threshold.

[0117] S9, calculate the global surface shape error corresponding to the remaining candidate surface shape parameters.

[0118] The global surface shape error after simulation processing of the measured surface corresponding to the remaining candidate surface shape parameters is obtained by following steps S3 to S5 and S8.

[0119] S10, filter candidate face shape parameters.

[0120] The global surface shape error obtained in steps S8 and S9 is judged. If the corresponding root mean square value and / or peak-valley value exceed the preset constraint threshold, a set of candidate surface shape parameters corresponding to the corresponding global surface shape error is discarded; otherwise, the corresponding candidate surface shape parameters are retained, and step S11 is executed.

[0121] S11, Multi-objective evolutionary iterative search and output of the optimal solution set.

[0122] Using the minimum material processing amount obtained in steps S6 and S7 and the minimum global surface shape error obtained in steps S8 and S9 as optimization objectives, a multi-objective evolutionary iterative search is performed on all candidate surface shape parameters retained in step S10. After the search is completed, it is determined whether the search has reached the preset number of iterations. If the preset number of iterations has not been reached, the non-dominated sorting and individual selection of all retained candidate surface shape parameters are performed according to the fitness evaluation results. Then, a candidate parameter set is generated through parameter crossover, parameter mutation, and elite retention (i.e., a new candidate parameter domain is formed, which includes all retained candidate surface shape parameters). Then, the process returns to step S3. If the preset number of iterations has been reached, the Pareto optimal solution set containing multiple sets of candidate surface shape parameters is output according to the fitness evaluation results.

[0123] The multi-objective evolutionary iterative search described in this embodiment is implemented using a multi-objective genetic algorithm, a second-generation or third-generation genetic algorithm with elitist strategy and non-dominated sorting (NSGA-II / NSGA-III), a decomposition-based multi-objective evolutionary algorithm (MOEA / D), a multi-objective particle swarm optimization algorithm, or a multi-objective differential evolution algorithm. Fitness is used to measure the degree to which each retained candidate face shape parameter satisfies the optimization objective and is the main basis for selection, crossover, and mutation in the genetic algorithm. Its expression is:

[0124]

[0125] In the formula, For the first The fitness evaluation function for candidate target surfaces. It represents the material processing amount corresponding to the ideal nominal surface. It is the root mean square value of the global surface shape error after the actual surface simulation processing corresponding to the ideal nominal surface.

[0126] S12, determine the optimal combination of surface parameters for minimum processing amount.

[0127] Based on the preset requirements of the target surface, the unique optimal solution with the minimum material processing amount and the optimal candidate surface parameter combination is obtained from the Pareto optimal solution set by combining the Pareto front, thereby completing the minimum processing amount optimization design of complex surfaces based on multi-parameter data.

[0128] like Figure 2 As shown, different global surface shape error values ​​correspond to different minimum material processing amounts. The Pareto front can determine a unique optimal solution that combines the minimum global surface shape error with the minimum material processing amount. However, in actual processing, subsequent coating, assembly, and other requirements may be considered, and the actual global surface shape error value may be required to be better than the global surface shape error processing index in the drawing. Based on the Pareto optimal solution set, the minimum material processing amount corresponding to the actual global surface shape error value and the corresponding optimal surface shape parameter combination can be determined. Based on this parameter combination, processing control data can be generated according to the machine tool interface format, and it can interface with computer-controlled shaping equipment such as ion beam, magnetorheological, and robotic CNC polishing and grinding equipment.

[0129] like Figure 3 As shown, when the ideal nominal surface is fixed as the target surface, all differences between the measured surface and the ideal nominal surface need to be removed. This embodiment allows the target surface to move or deform within the tolerance range of the surface shape parameters, making the optimal target surface closer to the measured surface, while still meeting the final shape index, thereby reducing material removal that does not generate system performance benefits. The final output includes the optimal target surface shape parameters, surface shape parameter error, global surface shape error after machining simulation, and minimum machining amount, which facilitates verification of whether the obtained complex surface meets the shape parameter requirements.

[0130] The following analysis takes the minimum processing amount optimization design of four high-order aspherical surfaces in a photolithography objective as an example. The No. 35 high-order aspherical mirror in the catadioptric deep ultraviolet photolithography objective system and the first, fourth and sixth high-order aspherical mirrors in the extreme ultraviolet projection objective system are selected as the analysis objects. Their aperture and surface parameters are shown in Table 1.

[0131] Table 1. Surface profile parameters of four high-order aspherical surfaces in the photolithography objective.

[0132]

[0133] Note: The input parameters in Table 1 are derived from data published in Chinese invention patents with publication numbers CN112859543A and CN102608737A.

[0134] An initial global surface shape error of approximately 0.1 μm was introduced into each of the four mirror surfaces, such as... Figure 4 As shown, the simulated three-dimensional discrete topographic data of the complex surface to be processed is generated as the input of the measured data. The vertex curvature radius and the quadratic aspherical constant after parameter decoupling are shown in Table 2. At the same time, the tolerances of vertex curvature radius and quadratic aspherical constant are set according to the requirements of the photolithography objective.

[0135] Table 2 Measured data of aspherical surface parameters, nominal values ​​of processing indicators and parameter tolerances

[0136]

[0137] Next, using the ideal nominal surface scheme as a control, candidate surface generation, non-negative removal amount calculation, dwell time solution, and convolution simulation were performed on each mirror surface according to the above method. Then, a multi-objective genetic algorithm was used to perform dual-objective optimization of minimum processing amount and global surface error PV. The specific operation process of this algorithm is as follows:

[0138] 1. Encoding and Population Initialization: The vertex curvature radius R and the quadratic surface constant K are used as optimization variables (i.e., parameters to be adjusted). The upper and lower boundaries of each variable are limited according to the tolerance range given in Table 2. Initial population candidate individuals (i.e., candidate parameter domain) are randomly generated within the parameter tolerance domain. Each candidate individual represents a combination of candidate surface parameters. The population size is set to 80.

[0139] 2. Candidate Individual Evaluation (Fitness Calculation and Constraint Handling): For each candidate individual in the population, a corresponding candidate target surface is constructed. Based on the measured initial surface shape, the local surface shape error at discrete sampling points, the expected material removal amount, the actual material removal amount at discrete sampling points after simulated processing, the material processing amount, residual error, and global surface shape error are calculated. The minimum processing amount and the global surface shape error peak-to-valley value PV ≤ 0.02λ (λ = 632 nm) are set as two optimization objectives. When a candidate individual violates any constraint, such as surface shape parameter exceeding the limit or global surface shape error exceeding the limit, it is directly eliminated.

[0140] 3. Non-dominated ranking and selection: All candidate individuals are ranked non-dominated according to Pareto dominance and crowding distance is calculated; a tournament selection strategy is adopted to prioritize individuals with high non-dominated levels and large crowding distances to enter the parent set (i.e., the new candidate parameter set) in order to preserve the diversity of the population.

[0141] 4. Crossover and Mutation: Perform real crossover on individuals in the parent set to generate offspring parameters; perform Gaussian mutation on optimization variables R and K, with variable asynchronous length constrained by parameter tolerance range, to ensure that the new individuals generated after crossover and mutation still fall within the allowable parameter tolerance range, avoiding the generation of invalid target surface parameters.

[0142] 5. Iteration Termination Determination: Repeat the iterative process of individual evaluation-selection-crossover-mutation, with the maximum number of generations (i.e., the preset number of iterations) set to 120 generations; stop evolution after reaching the maximum number of generations and output the final Pareto optimal solution set.

[0143] 6. Pareto solution selection: Select the set of surface parameters with the minimum material processing amount from the feasible solutions where the global surface error meets the processing index requirements, calculate the material processing amount of this method, and compare it with the material processing amount of the ideal nominal surface method (as shown in Table 3). This method can reduce the processing amount by 10.6%~42.0%.

[0144] Table 3. Optimization results of machining amount for four aspherical surfaces in this embodiment.

[0145]

[0146] Meanwhile, taking the sixth reflecting mirror as an example, a comparison is made between the material processing amount distribution obtained using the ideal nominal surface method and that obtained in this embodiment. Figure 5 As shown, (a) is a material processing amount distribution diagram obtained by the ideal nominal surface method, and (b) is a material processing amount distribution diagram obtained by the method described in this embodiment. As can be seen from the figure, compared with the ideal nominal surface method, the overall amplitude of the material processing amount distribution obtained in this embodiment is significantly reduced, thereby reducing the amount of material processing and reducing unnecessary material removal.

[0147] In summary, the minimum machining amount optimization design method for complex curved surfaces based on multi-parameter data of this invention can significantly reduce material machining amount and global surface shape error. For example, in this embodiment, the material machining amount optimization rate for the four complex aspherical surfaces is 10.6% to 42.0%, and the global surface shape error of the simulated machining decreases by 20.2% to 31.0% simultaneously. This method is even more effective for large-diameter mirror surfaces and fine polishing processes.

[0148] Furthermore, this invention employs a multi-objective evolutionary iterative search method, which can simultaneously reduce material processing volume and global surface shape error after simulated processing, thereby allowing different engineering solutions to be selected according to engineering decision-making logic (accuracy priority, cost weighting, inflection point screening).

[0149] Tables 4-1 to 4-4 define the parameters in this embodiment.

[0150] Table 4-1 Parameter Definitions (1)

[0151]

[0152] Table 4-2 Parameter Definitions (2)

[0153]

[0154] Table 4-3 Parameter Definitions (3)

[0155]

[0156] Table 4-4 Parameter Definitions (4)

[0157]

[0158] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein, and such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data, characterized in that, Includes the following steps: S1, acquire three-dimensional discrete topographic data at different sampling positions of the measured surface, align the coordinate systems of the measured surface and the target surface, and preprocess the three-dimensional discrete topographic data; the measured surface is the actual surface of the component to be processed; the target surface is the ideal nominal surface with preset requirements; S2, according to the preset requirements, obtain the mathematical expression, nominal value and tolerance of the target surface, and determine the parameters to be adjusted and their adjustment range, and generate a candidate parameter domain containing multiple sets of candidate surface parameters; S3, take any set of candidate surface parameters, generate the corresponding candidate target surface at the same sampling position as the measured surface, and calculate the local surface error between the candidate target surface and the corresponding measured surface at each sampling position by combining the three-dimensional discrete topography data preprocessed in step S1. S4. Based on the sign of the minimum value of the local surface error obtained in step S3, obtain the expected material removal amount at the sampling position corresponding to the measured curved surface. S5. Combining the expected material removal amount obtained in step S4, the actual material removal amount at the corresponding sampling position of the measured curved surface is calculated by simulating the processing. S6. Based on the actual material removal amount calculated in step S5, the actual material removal amount at all sampling positions within the effective diameter of the target surface is integrated according to the area of ​​the sampling unit to obtain the measured surface material processing amount corresponding to any set of candidate surface parameters mentioned in step S3. S7. Following the methods of steps S3 to S6, obtain the measured surface material processing amount corresponding to the remaining candidate surface parameters. S8. Based on the expected material removal amount obtained in step S4 and the actual material removal amount obtained in step S5, the residual error at each sampling position is calculated, and then the global surface shape error after the actual surface simulation processing corresponding to any set of candidate surface shape parameters in step S3 is obtained; the global surface shape error is characterized by the root mean square value and the peak-valley value. S9. Following the methods of steps S3 to S5 and S8, obtain the global surface shape error after the actual surface simulation processing corresponding to the remaining candidate surface shape parameters. S10: Judge the global surface shape error obtained in steps S8 and S9. If the corresponding root mean square value and / or peak-valley value exceed the preset constraint threshold, discard a set of candidate surface shape parameters corresponding to the corresponding global surface shape error; otherwise, retain the corresponding candidate surface shape parameters and execute step S11. S11, with the minimum material processing amount obtained in steps S6 and S7 and the minimum global surface shape error obtained in steps S8 and S9 as the optimization objectives, perform multi-objective evolutionary iterative search on all candidate surface shape parameters retained in step S10, and output a Pareto optimal solution set containing multiple sets of candidate surface shape parameters; S12, based on the preset requirements of the target surface, combines the Pareto front to obtain the unique optimal solution from the Pareto optimal solution set, which combines the minimum material processing amount with the optimal candidate surface parameters, thereby completing the minimum processing amount optimization design of complex surfaces based on multi-parameter data.

2. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 1, characterized in that: In step S1, three-dimensional discrete topographic data at different sampling positions of the measured surface are acquired using a coordinate measuring machine, a laser interferometer, or a non-contact 3D optical surface shape measurement device. The three-dimensional discrete topographic data includes surface shape parameters characterizing the global geometric shape of the measured surface, and local surface shape error data characterizing the local contour deviation of the measured surface. The surface shape parameters include one or more of the following: vertex radius of curvature, quadratic surface constant, and higher-order aspherical coefficient. The local surface shape error data is the local irregular contour deviation value of the measured surface after removing the macroscopic surface shape parameter deviation. The preprocessing includes invalid point removal, noise reduction, missing point processing, and effective aperture reduction. The target surface is a rotationally symmetric quadratic aspheric surface or a higher-order aspheric surface.

3. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 2, characterized in that: In step S2, the parameters to be adjusted are the vertex radius of curvature and / or the quadratic surface constant, and the other surface parameters except for the parameters to be adjusted retain their corresponding nominal values; each group of candidate surface parameters is a combination of reasonable values ​​of all surface parameters.

4. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 3, characterized in that: In step S3, the expression for the candidate target surface is: ； In the formula, For the first The group of candidate surface shape parameters corresponds to the aspherical sagitta of the candidate target surface. ; The radius of the sampling position corresponding to the candidate target surface; For the first Vertex curvature radius in the candidate surface type parameters; For the first The quadratic surface constant in the candidate surface type parameters; For higher-order aspherical coefficients, For higher-order terms, The value can be 2, ..., I, where I is the preset maximum order; In step S3, the local surface shape error is expressed by the following formula: ； In the formula, Indicates the first The candidate target surfaces and their corresponding measured surfaces at the sampling positions Surface shape error at the location; For the measured surface at the sampling position The height of the arrow at the location; For the first The candidate target surface at the sampling location The height of the arrow at the location; It is the set of coordinates corresponding to all sampling positions within the effective light-transmitting aperture of the measured curved surface.

5. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 4, characterized in that: Step S4 specifically involves determining the sign of the minimum value among the local surface shape errors obtained in step S3. If the minimum value is positive or zero, the corresponding local surface shape error is used as the expected material removal amount at the corresponding sampling position of the measured surface. If the minimum value is negative, all local surface shape errors are non-negatively increased based on the minimum value, and the non-negatively increased local surface shape error is used as the expected material removal amount at the corresponding sampling position of the measured surface. The desired amount of material to be removed is calculated using the following formula: ； In the formula, For the first The candidate target surface at the sampling location The expected amount of material to be removed at the corresponding location; For the first The candidate target surface at the sampling location The minimum value of the surface shape error corresponding to that location.

6. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 5, characterized in that: In step S5, the method for simulating the machining process is specifically as follows: First, a removal function model is constructed. Then, the ideal dwell time at each sampling position of the measured surface is calculated by combining the dwell time algorithm and the corresponding expected material removal amount. Then, under the constraints of the shape of the removal function and the dynamic response performance of the machine tool, the ideal dwell time is processed into the corresponding actual dwell time. Finally, the removal function and the actual dwell time are convolved to obtain the actual material removal amount at the corresponding sampling position of the measured surface. The dwell time algorithm employs the pulse iteration method, Fourier transform method, linear equation system method, or non-negative least squares method.

7. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 6, characterized in that: In step S6, the amount of material processed is calculated using the following formula: ； In the formula, For the first Material processing amount corresponding to the candidate surface shape parameters; Sampling location within the effective caliber The area of ​​the infinitesimal element corresponding to the location.

8. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 7, characterized in that: In step S8, the residual error is calculated using the following formula: ； In the formula, For the first The candidate target surface at the sampling location The corresponding residual error; For the first The candidate target surface at the sampling location The actual amount of material removed at that location; The root mean square value is calculated using the following formula: ； In the formula, For the first The root mean square value of the global surface shape error after simulation processing of the measured surface corresponding to the candidate surface shape parameters; This represents the total number of discrete sampling points within the effective aperture of the optical element. The peak and valley values ​​are calculated using the following formula: ； In the formula: For the first Peak and valley values ​​of global surface shape error after simulated processing of the measured curved surface corresponding to the candidate surface shape parameters; This represents the maximum residual error at all sampling locations after simulation processing; This represents the minimum residual error at all sampling locations after the simulation process.

9. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 8, characterized in that: Step S11 specifically involves using the minimum material processing amount obtained in steps S6 and S7 and the minimum global surface shape error obtained in steps S8 and S9 as optimization objectives. A multi-objective evolutionary iterative search is performed on all candidate surface shape parameters retained in step S10. After the search is complete, it is determined whether the preset number of iterations has been reached. If the preset number of iterations has not been reached, non-dominated sorting and individual selection are performed on all retained candidate surface shape parameters based on the fitness evaluation results. Then, a candidate parameter set is generated through parameter crossover, parameter mutation, and elite retention. The process then returns to step S3. If the preset number of iterations has been reached, a Pareto optimal solution set containing multiple sets of candidate surface shape parameters is output based on the fitness evaluation results.

10. The method for optimizing the minimum machining amount of complex surfaces based on multi-parameter data according to claim 9, characterized in that: In step S11, the multi-objective evolutionary iterative search is implemented using a multi-objective genetic algorithm, a second-generation or third-generation genetic algorithm with elitist strategy and non-dominated sorting, a decomposition-based multi-objective evolutionary algorithm, a multi-objective particle swarm optimization algorithm, or a multi-objective differential evolution algorithm. The fitness is used to measure how well each retained candidate face shape parameter satisfies the optimization objective, and its expression is: ; In the formula, For the first The fitness evaluation function for candidate target surfaces. It represents the material processing amount corresponding to the ideal nominal surface. It is the root mean square value of the global surface shape error after the actual surface simulation processing corresponding to the ideal nominal surface.

Images