An optical element surface processing method, device, equipment and storage medium

Abstract

This application discloses a method, apparatus, device, and storage medium for surface processing of optical components, relating to the field of optical surface processing. The method includes: establishing a target aperture mask based on the target processing area of ​​the optical surface to be processed to determine the target removal amount; determining the modal convolution kernel corresponding to each angular mode based on the target coordinate system and the tool removal function, establishing a target mapping relationship between the sampling points of the processing path and the grid nodes of the target active grid, embedding the modal convolution kernel into the target convolution grid to determine the target frequency domain kernel spectrum; determining the path dwelling variable to determine the path-side modal weights of each angular mode, thereby determining the predicted removal amount; determining the transpose feedback quantity corresponding to the path dwelling variable space using the target active grid based on the predicted removal amount and the target removal amount, iteratively updating the path dwelling variable, and determining the target dwell time upon convergence to process the optical surface to be processed. This application improves the efficiency of optical component surface processing.

Description

Technical Field

[0001] This invention relates to the field of optical surface processing, and in particular to a method, apparatus, equipment and storage medium for processing the surface of optical components. Background Technology

[0002] When the tool removal function is fixed and the resident variables are located on a regular grid, the removal process can be approximated as a two-dimensional convolution and efficiently calculated using the Fast Fourier Transform (FFT). However, in actual optical machining, the machining path is usually a spiral, grating, loop, locally refined path, or multi-segment combined path, and the resident variables are naturally defined on the actual sampling points of the machine tool path. Forcing the path resident variables to be resampled to a regular grid may introduce additional interpolation errors and is not conducive to directly expressing machine tool speed constraints and path execution characteristics. In addition, in deterministic machining scenarios such as small tool polishing, magnetorheological polishing, ion beam shaping, airbag polishing, strip polishing, and plasma shaping, the tool removal function may not be circularly symmetric. Especially in magnetorheological polishing, strip polishing, or machining methods with oblique incident or asymmetric flow fields, the tool removal function often exhibits significant anisotropy, and its major axis direction or effective removal direction may continuously change with the radial, tangential, scanning direction, tilting angle command, or machine tool attitude of the machining path.

[0003] When the tool removal function rotates with the path orientation, traditional fixed-kernel models struggle to accurately describe the actual removal process. While explicit removal matrix methods can express removal functions with arbitrary paths, aperture boundaries, and variable local orientations and directions, they incur significant matrix construction time and storage overhead when dealing with high-resolution surfaces, numerous path points, or large tool support areas. Especially when process parameters are repeatedly adjusted, rebuilding the matrix each time noticeably reduces simulation and optimization efficiency. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method, apparatus, device, and storage medium for surface processing of optical components, which can improve simulation and optimization efficiency, thereby improving the efficiency of surface processing of optical components. The specific solution is as follows: In a first aspect, this application discloses a method for surface processing of optical elements, including: The surface shape sampling data, processing path data, and target reference quantity corresponding to the tool removal function of the optical surface to be processed are determined, and a target aperture mask is established based on the target processing area corresponding to the optical surface to be processed to determine the target removal amount; the processing path data includes processing path sampling points, path increments between adjacent processing path sampling points, and local tool attitude angles corresponding to each processing path sampling point; the target reference quantity includes the target coordinate system, length unit, and sampling reference. Based on the target coordinate system, the tool removal function is subjected to angular mode expansion to determine the modal convolution kernel corresponding to each angular mode. The target active mesh and mesh filling size are determined according to the target aperture mask, the processing path data and the tool removal function, so as to establish the target mapping relationship between the processing path sampling points and the mesh nodes of the target active mesh. Based on the mesh filling size, the modal convolution kernel is embedded into the target convolution mesh to determine the target frequency domain kernel spectrum. The path dwelling variable corresponding to the optical surface to be processed is determined, and the path increment, the path dwelling variable and the phase weight of each angular mode corresponding to each local tool attitude angle are combined to determine the path side mode weight of each angular mode. The predicted removal amount in the target aperture mask is determined by using the target active mesh based on the target mapping relationship, the path side mode weight and the target frequency domain kernel spectrum. The target residual is determined based on the predicted removal amount and the target removal amount. The transpose feedback amount corresponding to the path dwell variable space is determined using the target active grid. The path dwell variable is iteratively updated based on the transpose feedback amount and the target residual. When the path dwell variable meets the preset convergence condition, the target dwell time is determined based on the path dwell variable. The optical surface to be processed is processed based on the target dwell time.

[0005] Optionally, the step of performing angular mode expansion on the tool removal function based on the target coordinate system to determine the mode convolution kernel corresponding to each angular mode includes: Based on the target coordinate system, the tool removal function is converted into polar coordinates, and the tool removal function in polar coordinates is expressed as the sum of finite-order angular modes, so as to determine the angular mode expansion form corresponding to the tool removal function; The modal convolution kernel corresponding to each angular mode is determined based on the angular mode expansion form; the angular mode includes any one or more combinations of complex exponential Fourier mode, real sine / cosine mode, circular harmonic function basis, orientable filter basis, low-rank direction dictionary, principal component mode or Zernike angular component.

[0006] Optionally, the target mapping relationship includes any one of bilinear scattering, bicubic interpolation, B-spline, radial basis function, kernel function, or conservative area weight mapping; the target active mesh includes any one of a single mesh covering the entire workpiece, a local sub-region mesh, a block mesh, a locally refined mesh, or a multi-resolution mesh; the boundary processing method corresponding to the mesh fill size includes any one or a combination of zero fill, mirror extension, overlap preservation, overlap addition, or boundary compensation.

[0007] Optionally, determining the predicted removal amount within the target aperture mask using the target active mesh based on the target mapping relationship, the path-side mode weights, and the target frequency domain kernel spectrum includes: The predicted removal amount within the target aperture mask is determined using the target active grid and the target positive operator based on the target mapping relationship, the path-side mode weights, and the target frequency domain kernel spectrum; Accordingly, determining the transpose feedback quantity corresponding to the path-resident variable space using the target activity grid includes: Using the target active grid and the target transpose operator, based on the target mapping relationship, the path-side modal weights, and the target frequency domain kernel spectrum, the transpose feedback quantity corresponding to the path-resident variable space is determined; wherein, the target forward operator and the target transpose operator satisfy an inner product consistency relationship in a discrete sense; Optionally, the iterative update of the path-resident variable based on the transposed feedback quantity and the target residual includes: Under the target constraints, the path dwelling variables are iteratively updated based on the transposed feedback and the target residual; wherein, the target constraints include upper and lower limit constraints on velocity, upper and lower limit constraints on dwelling density, non-negativity constraints, and smoothness constraints.

[0008] Optionally, the iterative update of the path-resident variable based on the transposed feedback and the target residual under the target constraint includes: The path-resident variables are iteratively updated based on the transpose feedback and the target residual under the objective constraint conditions using an objective constraint optimization method; the objective constraint optimization method includes bounded least squares optimization method, projective gradient optimization method and conjugate gradient optimization method.

[0009] Optionally, determining the target dwell time based on the path dwelling variable includes: If the path dwelling variable is the path dwelling density, then the path dwelling density is converted into a machine tool feed rate sequence, and a target dwelling speed program is constructed based on the machining path data and the machine tool feed rate sequence, so as to determine the target dwelling time based on the target dwelling speed program.

[0010] Secondly, this application discloses an optical element surface processing apparatus, comprising: The data processing module is used to determine the surface shape sampling data, processing path data, and target reference quantity corresponding to the tool removal function of the optical surface to be processed, and to establish a target aperture mask based on the target processing area corresponding to the optical surface to be processed to determine the target removal amount; the processing path data includes processing path sampling points, path increments between adjacent processing path sampling points, and local tool attitude angles corresponding to each processing path sampling point; the target reference quantity includes a target coordinate system, length unit, and sampling reference. The frequency domain kernel spectrum determination module is used to perform angular mode expansion on the tool removal function based on the target coordinate system to determine the mode convolution kernel corresponding to each angular mode, determine the target active grid and grid fill size according to the target aperture mask, the processing path data and the tool removal function, so as to establish the target mapping relationship between the processing path sampling points and the grid nodes of the target active grid, and embed the mode convolution kernel into the target convolution grid based on the grid fill size to determine the target frequency domain kernel spectrum; The removal amount prediction module is used to determine the path dwelling variable corresponding to the optical surface to be processed, and combine the path increment, the path dwelling variable and the phase weight of each angular mode corresponding to each local tool attitude angle to determine the path side mode weight of each angular mode, and use the target active mesh based on the target mapping relationship, the path side mode weight and the target frequency domain kernel spectrum to determine the predicted removal amount in the target aperture mask; An optical component processing module is used to determine a target residual based on the predicted removal amount and the target removal amount, determine the transpose feedback amount corresponding to the path dwell variable space using the target active grid, iteratively update the path dwell variable based on the transpose feedback amount and the target residual, and determine the target dwell time based on the path dwell variable when the path dwell variable meets a preset convergence condition, and process the optical surface to be processed based on the target dwell time.

[0011] Thirdly, this application discloses an electronic device, including: Memory, used to store computer programs; A processor is used to execute the computer program to implement the aforementioned optical element surface processing method.

[0012] Fourthly, this application discloses a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned optical element surface processing method.

[0013] In this application, when processing the surface of an optical element, the surface shape sampling data, processing path data, and target reference quantity corresponding to the tool removal function of the optical surface to be processed are determined. A target aperture mask is then established based on the target processing area corresponding to the optical surface to be processed to determine the target removal amount. The processing path data includes processing path sampling points, path increments between adjacent processing path sampling points, and local tool attitude angles corresponding to each processing path sampling point. The target reference quantity includes a target coordinate system, length unit, and sampling reference. The tool removal function is subjected to angular modal expansion based on the target coordinate system to determine the modal convolution kernels corresponding to each angular mode. The target active mesh and mesh fill size are determined according to the target aperture mask, the processing path data, and the tool removal function to establish a target mapping relationship between the processing path sampling points and the mesh nodes of the target active mesh. The target removal amount is then determined based on the mesh fill size. The modal convolution kernel is embedded into the target convolution mesh to determine the target frequency domain kernel spectrum; the path dwelling variable corresponding to the optical surface to be processed is determined, and the path increment, the path dwelling variable, and the phase weights of each angular mode corresponding to each local tool attitude angle are combined to determine the path-side mode weights of each angular mode. The predicted removal amount within the target aperture mask is determined using the target active mesh based on the target mapping relationship, the path-side mode weights, and the target frequency domain kernel spectrum; the target residual is determined based on the predicted removal amount and the target removal amount; the transpose feedback amount corresponding to the path dwelling variable space is determined using the target active mesh; the path dwelling variable is iteratively updated based on the transpose feedback amount and the target residual; and when the path dwelling variable meets the preset convergence condition, the target dwell time is determined based on the path dwelling variable; the optical surface to be processed is processed based on the target dwell time. As can be seen, this application uses angular modal phase weights to express tool attitude changes, avoiding point-by-point rotation and resampling of the two-dimensional tool removal function for each path sampling point. By establishing a mapping relationship between the processing path data and the target active mesh, and using active mesh and boundary filling, the computational scale is related to the effective processing area, path coverage, and tool support area, achieving matrix-independent forward computation rather than simply growing with the global large matrix size. This avoids explicitly constructing a large-scale path-surface sparse removal matrix. At the same time, modal convolution kernels are embedded into the active mesh, and the modal kernel spectrum can be reused in the same process task or multiple iterations, which is beneficial for scanning path spacing, velocity constraints, aperture masks, and resolution parameters. Thus, while obtaining dwell time calculation results that are approximately consistent with the numerical values ​​of explicit matrix reference methods, it significantly reduces operator construction and computation time, improving the efficiency and accuracy of optical component surface processing. In addition, this application does not limit specific tool types or specific software, and can cover processing scenarios related to magnetorheological polishing, ion beam shaping, small tool polishing, gasbag polishing, plasma shaping, and laser shaping. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0015] Figure 1 This is a flowchart of a surface processing method for an optical element disclosed in this application; Figure 2 This is a schematic diagram of the architecture of a specific angular modal Grid-FFT residence time calculation system disclosed in this application; Figure 3 This is a schematic diagram of a specific angular modal Grid-FFT dwell time calculation process disclosed in this application; Figure 4 This is a comparison chart of post-processing residuals disclosed in this application, wherein, Figure 4 (a) is a schematic diagram of the residual after machining at the back end of the explicit rotating template matrix. Figure 4 (b) is a schematic diagram of the post-processing residual at the back end of the angular modal Grid-FFT of this application. Figure 4 (c) is a comparison chart of the differences between the residuals obtained from solving the two back-ends respectively; Figure 5 This is a schematic diagram of the structure of an optical element surface processing device disclosed in this application; Figure 6 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] When the tool removal function rotates with the path orientation, traditional fixed convolution kernel models struggle to accurately describe the actual removal process. While explicit removal matrix methods can express removal functions with arbitrary paths, aperture boundaries, and variable local orientations and directions, they incur significant matrix construction time and storage overhead under high-resolution surface shapes, numerous path points, or large tool support ranges. Especially when process parameters are repeatedly adjusted, rebuilding the matrix each time significantly reduces simulation and optimization efficiency. To address these technical problems, this application discloses a surface processing method for optical components that improves simulation and optimization efficiency, thereby enhancing the overall efficiency of optical component surface processing.

[0018] See Figure 1 As shown in the figure, an embodiment of the present invention discloses a method for surface processing of optical components, including: Step S11: Determine the surface shape sampling data, processing path data, and target reference quantity corresponding to the tool removal function of the optical surface to be processed, and establish a target aperture mask based on the target processing area corresponding to the optical surface to be processed to determine the target removal amount; the processing path data includes processing path sampling points, path increments between adjacent processing path sampling points, and local tool attitude angles corresponding to each processing path sampling point; the target reference quantity includes the target coordinate system, length unit, and sampling reference.

[0019] To facilitate understanding, some terms used in this embodiment are explained first. The Tool Influence Function (TIF), also known as the tool effect function, describes the removal distribution of a local surface shape under unit dwell conditions. The Fast Fourier Transform (FFT) is used in this embodiment to accelerate modal convolution on the active grid. Grid-FFT, or FFT convolution based on a regular grid, refers to frequency domain convolution performed after mapping path-side variables to a regular grid. Angular mode refers to the basis function channels obtained by unfolding along an angular direction, used to transform the rotation problem of the tool removal function into a combination of a finite number of fixed convolution kernels and phase factors. The active grid refers to the local computational grid covering the aperture, path, and tool support regions, used to reduce unnecessary global grid FFT calculations. The matched transpose operator is the residual backpropagation operator conjugate-matched with the forward discrete operation, used for gradient, projection, or normal equation calculations in the optimizer.

[0020] In this embodiment, as Figure 2The diagram illustrates the architecture of a angular modal Grid-FFT dwell time calculation system for an optical element surface processing method. This system comprises an input data layer, an operator planning layer, a matrix-independent operator layer, and an optimization output layer. Data is transferred between these layers based on a unified coordinate reference, sampling unit, aperture mask, and path parameters to calculate dwell time under variable-direction tool removal function conditions. The input data layer provides the fundamental data required for dwell time calculation, including the surface shape error of the surface to be processed, the target removal amount, the effective aperture mask, processing path sampling points, the path increment between adjacent path points, the local tool attitude angle at each path point, the measured or fitted tool removal function, and upper and lower limits for speed, dwell density, smoothness, or other process constraints. This layer's function is to uniformly convert the actual processing object, machine tool execution path, and tool removal characteristics into calculable data input.

[0021] In this embodiment, as Figure 3 The diagram illustrates a specific flow chart for calculating dwell time in angular modal Grid-FFT. First, the surface shape, path, attitude, and removal function are acquired. Specifically, the surface shape sampling data of the optical surface to be processed, the processing path sampling points, the path increment between adjacent processing path sampling points, the local tool attitude angle corresponding to each processing path sampling point, and the measured or fitted tool removal function are obtained. Simultaneously, the coordinate system, length unit, and sampling reference are unified among the surface shape data, path data, and tool removal function, i.e., the target reference quantity that the above three types of data commonly follow is determined. It is understandable that the surface shape sampling data, processing path data, and tool removal function typically come from the surface shape detection equipment, path planning module, and tool calibration experiment, respectively. The coordinate origin, coordinate axis direction, length unit, sampling interval, and sampling start point of these three may not be consistent. Without unification, subsequent path-grid mapping and modal convolution cannot be performed within the same geometric framework. Therefore, this embodiment unifies the actual processed object, machine tool execution path, and tool removal characteristics into computable data inputs through the target coordinate system, length unit, and sampling reference. All subsequent calculations are performed under this target reference quantity.

[0022] The optical surface to be processed can be a plane, sphere, aspherical surface, freeform surface, large-aperture mirror, window, semiconductor wafer, mold, or other surface requiring dwell time planning. The surface shape sampling data can be surface shape error data obtained through an interferometer, profilometer, or other surface shape inspection equipment, or it can be surface shape error data after de-tilting, de-focusing, or other preprocessing. The processing path can be a spiral, grating, loop, locally refined path, or multi-segment combined path. In this embodiment, the path dwell variable is directly defined on the actual processing path sampling points executed by the machine tool, rather than resampled to dwell grid points on a regular grid, thus preserving the direct expressive ability of local path increments, endpoint dwell times, speed upper and lower limits, and the actual feed program. The path increment refers to the path length between two adjacent processing path sampling points, which can be calculated based on the coordinates of the processing path sampling points.

[0023] The local tool attitude angle describes the in-plane rotation angle of the tool removal function relative to the target coordinate system at each sampling point of the machining path. In one embodiment of this example, the local tool attitude angle can be given by the path tangent, path normal, path radial, machine tool tilt angle, tool major axis direction, external attitude planning module, or online sensing module; the local tool attitude angle can be given point by point, or it can be calculated by path parameters, time parameters, or machining area functions; the local tool attitude angle can also be the equivalent in-plane rotation angle in a multi-degree-of-freedom attitude, or it can be combined with tilt angle and yaw angle to form an equivalent direction weight. For example, for the helical path of magnetorheological polishing, the major axis direction of the tool removal function usually changes continuously with the radial direction of the path, and the local tool attitude angle can be calculated from the radial azimuth angle of each sampling point of the machining path relative to the center of the helix; for the grating path, the local tool attitude angle can be determined by the scanning direction and the machine tool tilt angle command.

[0024] The tool removal function can be derived from measured calibration, analytical fitting, finite element simulation, flow field model, machine learning prediction, or online calibration. The tool removal function can be unimodal, multimodal, non-circular symmetric, tailed, slanted, or a function that varies with process parameters. For cases where the tool removal function varies with process parameters such as pressure, gap, magnetic field, current, beam current, and dwell velocity, multiple sets of modal kernels or parameterized modal kernels can be established, and the appropriate modal kernel can be selected in subsequent steps based on the process parameters corresponding to the sampling points of each processing path. Therefore, this embodiment does not limit the specific tool type and can cover magnetorheological polishing, ion beam shaping, small tool polishing, gasbag polishing, strip polishing, plasma shaping, laser shaping, grinding shaping, and other sub-aperture deterministic processing scenarios.

[0025] In this embodiment, when establishing the effective aperture and target removal amount, a target aperture mask is created based on the effective processing area (i.e., the target processing area) of the optical surface to be processed. The target aperture mask is used to identify which surface sampling points are located within the effective processing area and participate in subsequent removal amount prediction and residual evaluation. Then, the target removal amount is generated based on the initial surface error and the target surface requirements. For processing methods that only allow non-negative removal, the surface shape to be corrected can be converted into a target removal amount distribution within the effective aperture through reference plane subtraction, overall translation, or process allowance settings, so as to ensure that the target removal amount is non-negative everywhere within the target aperture mask, thereby matching the non-negative path dwell variable. In addition, the target aperture mask can also be set in conjunction with process rules such as local no-processing areas and edge transition areas.

[0026] Step S12: Perform angular modal expansion on the tool removal function based on the target coordinate system to determine the modal convolution kernel corresponding to each angular mode. Determine the target active mesh and mesh fill size according to the target aperture mask, the processing path data and the tool removal function, so as to establish the target mapping relationship between the processing path sampling points and the mesh nodes of the target active mesh. Embed the modal convolution kernel into the target convolution mesh based on the mesh fill size to determine the target frequency domain kernel spectrum.

[0027] In this embodiment, the tool removal function is first subjected to angular modal expansion. Let the surface sampling point be... The processing path sampling points are The path increment is Path dwell density is The local tool attitude angle at the sampling point of the machining path is The unrotated tool removal function is The total number of sampling points along the processing path is For tool removal functions where direction varies with path, the surface sampling point... Cumulative removal at the location The overall model can be established using the following formula: (1); In the formula, Indicates tool removal function Rotate the local tool's attitude angle around the origin of the local tool coordinate system The resulting rotation tool removal function. As can be seen from equation (1), when the tool removal function rotates with the path orientation, the removal function directions corresponding to different processing path sampling points are different, which cannot be accurately represented by a single fixed convolution kernel. This is the fundamental reason why the traditional fixed convolution kernel FFT method is difficult to handle.

[0028] Therefore, this embodiment converts the tool removal function into polar coordinates based on the target coordinate system, and represents the tool removal function in polar coordinates as the sum of finite-order angular modes to determine the angular mode expansion form corresponding to the tool removal function. Specifically, firstly, polar coordinate sampling of the tool removal function is performed: the two-dimensional tool removal function in the local tool coordinate system is converted into polar coordinate sampling form to obtain the removal function values ​​at different radial and angular positions; for discrete measured tool removal functions, coordinate normalization, finite support truncation, interpolation resampling, or smoothing can be performed first to suppress measurement noise and ensure the stability of polar coordinate sampling. Then, the angular mode coefficients are calculated: the angular mode expansion of the tool removal function in polar coordinates is performed to calculate the finite-order angular mode coefficients. In one embodiment, the unrotated tool removal function is... Transform to local polar coordinates Then, it can be expressed as the sum of finite-order angular modes: (2); In the formula, K is the highest order of the angular mode, and m is the order of the angular mode. Let m be the m-th angular modal coefficient, and let its radial coordinate be... The function, where i is the imaginary unit. For radial sampling positions The m-th angular modal coefficient can be calculated using the following formula: (3); In the formula, The number of angular sampling points. Let q be the sampling position in the angular direction. Through the above steps, the tool removal function, which originally had directional dependence, is represented as several modal components, providing a foundation for subsequently converting tool attitude changes into modal phase weights.

[0029] When the tool is at the sampling point of the processing path Rotational local tool attitude angle At this time, the direction change is no longer achieved by regenerating the two-dimensional rotation kernel, but is represented by the attitude phase weights on each angular mode: (4); As can be seen from equation (4), the rotated tool removal function is equal to the product of each angular mode and the order m and the local tool attitude angle. Related phase factors The results are then summed, where the angular modes themselves do not change with the sampling points along the processing path. Based on this, this embodiment determines the modal convolution kernel corresponding to each angular mode based on the angular mode expansion form, i.e., generates the modal convolution kernel: spatial convolution kernels corresponding to each angular mode are generated based on the angular mode coefficients, and the m-th order modal convolution kernel... It can be represented as: (5); In the formula, These are the local spatial coordinates with the tool's center as the origin. for The corresponding polar coordinates. Each modal convolution kernel remains fixed during global computation and is used to represent the spatial distribution characteristics of the corresponding order in the tool removal function; the tool pose change is only reflected as the phase factor on the path side, and it is no longer necessary to rotate and resample the two-dimensional tool removal function point by point for each processing path sampling point.

[0030] It should be noted that the aforementioned angular modes are not limited to the complex exponential Fourier form, and can also be equivalently replaced by sine / cosine real modes, circular harmonic functions, orientable filter bases, low-rank direction dictionaries, or other angular basis functions that can express the changes in tool direction. That is, the angular modes in this embodiment can include any one or more combinations of complex exponential Fourier modes, real sine / cosine modes, circular harmonic function bases, orientable filter bases, low-rank direction dictionaries, principal component modes, or Zernike angular components. The number of angular modes (i.e., the highest order K) can be fixed, or it can be adaptively selected according to the degree of anisotropy of the tool removal function, the target accuracy, or the computational budget. For example, the stronger the anisotropy, the higher the order should be selected, or the order can be determined based on whether the reconstruction error after truncation is less than a preset threshold. In addition, only non-negative order modes can be used, positive and negative order modes can be symmetrically merged, or real-valued equivalent representations can be used to reduce the number of modes and the amount of computation.

[0031] Furthermore, the target active mesh and mesh fill size are determined based on the target aperture mask, machining path data, and tool removal function. Specifically, the active mesh region participating in the calculation, i.e., the target active mesh, is determined based on the effective aperture range corresponding to the target aperture mask, the outer envelope of the machining path sampling points, and the support radius of the tool removal function. Simultaneously, the mesh fill size is determined according to linear convolution requirements to avoid the impact of FFT cyclic convolution on the effective region results. It should be noted that the target active mesh in this embodiment does not necessarily have to be a complete global square mesh, but can be determined based on the effective aperture, machining path outer envelope, tool support range, and boundary extension requirements. The target active mesh can be a single mesh covering the entire workpiece, or any of the following: a local sub-region mesh, a block mesh, a locally refined mesh, or a multi-resolution mesh. For example, when the target machining area is only a local sub-region of the workpiece, the target active mesh can only cover that sub-region and the area within one tool support radius around it, thereby avoiding unnecessary FFT calculations on the entire workpiece mesh; when the accuracy requirements of different areas of the surface shape are different, a locally refined mesh or a multi-resolution mesh can be used.

[0032] To avoid the impact of FFT circular convolution on the results within the effective aperture, a filling region satisfying the linear convolution requirement can be set around the target active mesh. Alternatively, methods such as overlap saving, overlap addition, mirror extension, zero filling, and boundary compensation can be used. In other words, the boundary processing methods corresponding to the mesh filling size include any one or more combinations of zero filling, mirror extension, overlap saving, overlap addition, or boundary compensation. The specific filling size and boundary strategy can be determined based on the tool support radius, mesh sampling interval, and aperture boundary requirements. For example, in the zero-fill method, the filling size in each direction can be an integer not less than the ratio of the tool support radius to the mesh sampling interval to ensure that any mesh node within the target aperture mask is not affected by cyclic wrapping contributions from the other side of the mesh during convolution.

[0033] Furthermore, a path-mesh scattering table is constructed, establishing a target mapping relationship between the sampling points of the actual processing path and the grid nodes of the target active grid. This mapping can employ bilinear scattering, higher-order interpolation, or locally conservative mapping, allowing resident variables defined on the actual physical path to be injected into the regular target active grid for FFT convolution calculations. In other words, the target mapping relationship can include any one of bilinear scattering, bicubic interpolation, B-splines, radial basis functions, kernel functions, or conservative area weighting mapping. Taking bilinear scattering as an example, for each processing path sampling point, the four grid nodes of the grid cell it falls into are determined based on its position in the target active grid, and the weights assigned to the four grid nodes for that processing path sampling point are calculated according to the inverse distance relationship. These weights can be pre-calculated and stored in the form of a sparse table, forming a path-mesh scattering table. Subsequent forward and transpose calculations can be directly performed by looking up the table. It is understood that path-mesh mapping can be executed on CPUs, GPUs, FPGAs, or heterogeneous computing platforms. Since the path-mesh scattering table only depends on the coordinates of the sampling points along the processing path and the geometric parameters of the target active mesh, the path-mesh scattering table does not need to be rebuilt when the resident variables are repeatedly updated during the optimization iteration.

[0034] Furthermore, the modal FFT kernel spectrum is pre-calculated. Specifically, each modal convolution kernel is embedded into the target convolution mesh according to the target active mesh and mesh fill size, and its Fast Fourier Transform (FFT) frequency domain spectrum is calculated respectively, thus obtaining the target frequency domain kernel spectrum corresponding to each angular mode. The target convolution mesh refers to the mesh used to perform FFT convolution after the target active mesh is filled, and its size is equal to the sum of the target active mesh size and the mesh fill size. This modal FFT kernel spectrum is repeatedly used in subsequent optimization iterations, avoiding recalculation of the tool kernel in each iteration; at the same time, when adjusting parameters such as path spacing, velocity constraints, or aperture mask in the same process task, as long as the tool removal function, target active mesh, and mesh fill size remain unchanged, the target frequency domain kernel spectrum can be directly reused, which is beneficial for multi-parameter scanning and process optimization.

[0035] Understandable, Figure 2 The operator planning layer of the system is used to pre-build the operator structure required for subsequent calculations based on the input data. This layer includes functions such as angular mode decomposition, active mesh determination, path-mesh mapping, and modal kernel spectrum pre-calculation. Among them, angular mode decomposition is used to decompose the direction correlation removal function in the local tool coordinate system into a finite number of angular modes; active mesh determination is used to generate a computational mesh based on the effective aperture, processing path range, and tool support range, and reserve boundaries for linear convolution; path-mesh mapping is used to establish the local weight relationship between the real path sampling points and active mesh nodes; modal kernel spectrum pre-calculation is used to convert each angular mode kernel into an FFT frequency domain kernel spectrum for repeated use in subsequent iterations.

[0036] Step S13: Determine the path dwelling variable corresponding to the optical surface to be processed, and combine the path increment, the path dwelling variable and the phase weight of each angular mode corresponding to each local tool attitude angle to determine the path side mode weight of each angular mode. Then, using the target active mesh based on the target mapping relationship, the path side mode weight and the target frequency domain kernel spectrum, determine the predicted removal amount in the target aperture mask.

[0037] In this embodiment, the path dwelling variable is a dwelling variable defined at each sampling point of the processing path. It can be path dwelling density (i.e., dwelling time per unit path length), dwelling time, or an equivalent variable. In the first iteration of the optimization solution, the path dwelling variable can be taken as an initial value, such as a constant satisfying the upper and lower limits of the dwelling density constraints, an initial value estimated based on the target removal amount and the peak removal rate of the tool removal function, or the solution result of the previous processing round. Given the path dwelling density or dwelling time, the removal amount is predicted positively. Specifically, the path increment, path dwelling variable, and modal phase weights corresponding to the path attitude are combined to obtain the path-side modal weights for each angular mode. For a given path dwelling density... In this embodiment, the path increment, path dwell density, and attitude phase are first combined to form the path weights for each mode. The path-side mode weight of the m-th order angular mode at the j-th processing path sampling point is... It can be represented as: (6); In the formula, That is, the local tool attitude angle at the j-th machining path sampling point. The phase weights of the corresponding m-th angular mode are then determined. Next, the path-mesh scattering table is used to form the mesh source terms for each mode; that is, the mode weights are injected into the target active mesh via the path-mesh mapping module. (7); In the formula, S represents the path-grid scattering operator determined by the target mapping relationship. Let be the path-side mode weight vector of the m-th angular mode. This represents the grid source term corresponding to the m-th angular mode. Subsequently, the pre-computed modal FFT kernel spectrum is used for Grid-FFT convolution, i.e., the grid source term... Perform padding and fast Fourier transform, multiply element-wise with the target frequency domain kernel spectrum of the m-th angular mode in the frequency domain, and then perform inverse fast Fourier transform to return to the spatial domain; superimpose the convolution results of each mode and take the real part, clip back to the target active mesh and project it into the target aperture mask to obtain the predicted removal amount corresponding to the current path resident variable.

[0038] In a preferred discrete implementation, the forward Grid-FFT operator (i.e., the target forward operator) of this embodiment. It can be written as the following formula: (8); In the formula, This is the path dwell density vector; This is the path-side diagonal weighted operator corresponding to the m-th order angular mode, whose diagonal elements are derived from the path increment. With phase weight The product of , i.e. S is the path-grid scattering operator; A filling operator that embeds the target active mesh into the target convolutional mesh according to the mesh filling size; and These represent the two-dimensional fast Fourier transform and the two-dimensional inverse fast Fourier transform, respectively. The target frequency domain kernel spectrum of the m-th angular mode; Re denotes element-wise product; Re denotes taking the real part; A clipping operator to clip the target convolutional mesh back to the target active mesh or surface sampling region; An aperture projection operator is used to confine the results within the target aperture mask. Each projection, clipping, filling, path mapping, modal weighting, and convolution kernel spectrum in the equation can be discretized according to the specific mesh, aperture, and tool support range.

[0039] The above expression avoids explicitly writing out the contribution matrix of each processing path sampling point to each surface sampling point. That is, this embodiment utilizes the target active mesh and the target forward operator to determine the predicted removal amount within the target aperture mask based on the target mapping relationship, path-side modal weights, and the target frequency domain kernel spectrum. Throughout the process, it is not necessary to construct, store, or traverse the path-surface removal matrix. When the optimizer is called, the forward operator simply manifests as a matrix-independent interface that takes the residence density as input and outputs the predicted removal amount.

[0040] Step S14: Determine the target residual based on the predicted removal amount and the target removal amount, determine the transpose feedback amount corresponding to the path dwell variable space using the target active grid, iteratively update the path dwell variable based on the transpose feedback amount and the target residual, and when the path dwell variable meets the preset convergence condition, determine the target dwell time based on the path dwell variable, and process the optical surface to be processed based on the target dwell time.

[0041] In this embodiment, the target residual is first determined based on the predicted removal amount and the target removal amount. For example, the aperture residual e is obtained by subtracting the predicted removal amount from the target removal amount point by point within the target aperture mask. Then, a matching transpose calculation is performed: based on the residual between the predicted removal amount and the target removal amount, a transpose calculation matching the forward prediction process is performed. The aperture residual is fed back to the path resident variable space through operations such as modal frequency domain conjugate convolution, mesh-to-path aggregation, and modal phase conjugate weighting to obtain the transpose feedback amount used for optimization updates.

[0042] Specifically, to adapt to constrained optimizers such as bounded least squares, projected gradient, and conjugate gradient, this embodiment constructs a transpose operator (i.e., the target transpose operator) that matches the forward Grid-FFT discretization process. For the aperture residual e, the transpose process can be performed in the following order: First, inject the aperture residual into the surface sampling grid or the active clipping region, i.e., execute the aperture projection operator. The first step is to transpose the first step; the second step is to perform the transpose of the clipping, filling, or masking operation, i.e., to perform the clipping operator. and filling operator The first step involves transposing the residual and embedding it into the target convolutional mesh. The second step involves performing a Fast Fourier Transform on the embedded residual, multiplying it in the frequency domain by the conjugate of each mode's convolutional kernel spectrum, and transforming it back to the spatial domain. The third step involves using the transpose of the path-mesh mapping, i.e., the transpose of the scattering operator S (aggregation operation), to aggregate the mesh residual back to the processing path sampling points. The fifth step involves multiplying it by the conjugate weights of the path increment and attitude phase, i.e., performing a diagonal weighted operator. The conjugate transpose of the target is used, and the results of each angular mode are summed to obtain the path-side feedback quantity, which is also the transposed feedback quantity corresponding to the path-resident variable space. Through the above process, this embodiment uses the target active grid and the target transpose operator to determine the transposed feedback quantity corresponding to the path-resident variable space based on the target mapping relationship, path-side mode weights, and target frequency domain kernel spectrum. It reuses the path-grid scattering table and target frequency domain kernel spectrum used in the forward calculation, and also does not require explicit construction of the removal matrix. Through the above design, the forward operator and the transpose operator are matched in a discrete sense and satisfy the following inner product consistency relationship: (9); In the formula, Indicates the inner product. Let represent the target transpose operator. The above inner product consistency relation shows that for any path dwell density... And the residual e of arbitrary aperture, the target positive operator acts on The inner product of the second and e equals The inner product of the target transpose operator and e is, in a discrete sense, the target transpose operator is strictly the adjoint operator of the target forward operator. This reduces the convergence error introduced by operator inconsistency during optimization iterations, ensuring stable convergence of the constrained optimizer that relies on repeated forward / transpose products. In practical implementation, the satisfaction of equation (9) between the forward and transpose operators can be verified through a random vector dot product test, i.e., randomly generated... Calculate the inner product of e and e on both sides of the equation (9) and compare their relative errors.

[0043] Furthermore, the path dwelling variables are iteratively updated based on the transposed feedback quantity and the target residual. In this embodiment, this iterative update can be performed under target constraints, including speed upper and lower limit constraints, dwelling density upper and lower limit constraints, non-negativity constraints, smoothness constraints, and may also include other process rule constraints. In this embodiment, the path dwelling variables can be directly defined on the machine tool physical path sampling points. This represents the dwell density per unit path length at the j-th processing path sampling point. If we represent the corresponding feed rate, then the two can be converted using the following relationship: (10); When the machine tool speed is subject to upper and lower limits, the dwell density also has corresponding upper and lower limits: (11); In the formula, and These are the lower and upper limits of the machine tool feed rate, respectively. and These represent the lower and upper limits of the path dwell density, respectively. Therefore, the speed upper and lower limit constraints are equivalently transformed into dwell density upper and lower limit constraints, and since speed is a positive value, dwell density naturally satisfies the non-negative constraint condition. It is evident that this embodiment retains the path dwell variable at the actual physical path sampling points, allowing speed upper and lower limits, path increment, local no-processing zones, and machine tool execution constraints to be directly expressed at the path sampling point level without requiring a secondary transformation from dwell mesh to path.

[0044] In one implementation, the optimization objective can be written as follows: (12); In the formula, b is the target removal vector within the target aperture mask. For matrix-independent positive target operators, For process regularization terms, This represents the L2 norm. The target removal amount, matrix-independent positive operator, and process regularization term can all be determined based on the specific processing task; the process regularization term may include speed smoothing, acceleration limit, residence time upper limit, local removal amount limit, edge penalty or edge constraint, no-processing zone constraint, multi-objective weight, or other process rules, where speed smoothing and acceleration limit correspond to smoothness constraints.

[0045] Under objective constraints, the dwell density at the sampling points of the machining path is solved or updated based on the positive prediction results and the matched transpose feedback. This process can be implemented using objective constraint optimization methods, which may include bounded least squares optimization, projected gradient optimization, and conjugate gradient optimization. Other constraint optimization methods such as nonnegative least squares, LSQR, ADMM, primal-dual algorithms, or custom machine tool constraint solvers can also be used. The optimizer does not need to know the explicit matrix form of the above positive operators; it only needs to call the positive operators and the matched transpose operator, i.e., calculate them as needed in each iteration. (13); In the formula, y represents the current path dwell density. The corresponding predicted removal amount, z is the transposed feedback amount corresponding to the aperture residual e. Taking the projection gradient optimization method as an example, each iteration first uses the target positive operator to calculate the predicted removal amount corresponding to the current path resident variable and obtain the target residual, then uses the target transpose operator to backpropagate the target residual to obtain the transposed feedback amount, combines the transposed feedback amount with the gradient of the process regularization term to form the search direction, updates the path resident variable according to a certain step size, and then projects the updated path resident variable into the feasible region determined by the upper and lower limits of the resident density; taking the conjugate gradient optimization method as an example, the product of the positive operator and the transpose operator is used to construct the conjugate search direction in each iteration; taking the bounded least squares optimization method as an example, the least squares problem shown in equation (12) is directly solved under the upper and lower limits of the resident density.

[0046] In this embodiment, the three steps of forward prediction of removal amount, matching transpose calculation, and constraint solution of dwell density constitute an optimization solution loop, which can be iterated repeatedly according to the solver requirements until the path dwell variables meet the preset convergence conditions. The preset convergence conditions can be any one or more of the following: residual convergence conditions (e.g., the root mean square value of the target residual or its relative decrease is less than a preset threshold), reaching a preset number of iterations, or meeting the process error threshold (e.g., the predicted post-processing residual meets the surface accuracy requirements).

[0047] Furthermore, after the iterative process meets the preset convergence condition, the target dwell time is determined based on the path dwell variable, and the speed program and residual results are output. Specifically, if the path dwell variable is the path dwell density, the path dwell density is converted into a machine tool feed rate sequence. For example, the feed rate at each machining path sampling point is obtained by taking the reciprocal of each point according to equation (10), and the target dwell speed program is constructed based on the machining path data and the machine tool feed rate sequence. That is, the feed rate sequence is combined with the original machining path coordinates, local tool attitude angles and machine tool instruction format to form a speed program, so as to determine the target dwell time based on the target dwell speed program. It can be understood that the dwell time at each machining path sampling point is equal to the product of the path dwell density and the path increment, and the total machining time is equal to the sum of the dwell times at each machining path sampling point. If the path dwell variable itself is the dwell time, it can be directly converted into feed rate according to the path increment or the dwell time program can be directly output. Meanwhile, this embodiment can also output the predicted removal amount, the residual surface shape after processing, the root mean square value of the residual, the peak and valley values, the calculation time, and other process evaluation indicators. The output results can be used for subsequent CNC machining program generation, machining effect evaluation, and process parameter adjustment.

[0048] Finally, the optical surface to be processed is processed based on the target dwell time. For example, the target dwell speed program or dwell time program is sent to the CNC machine tool, which controls the tool to move on the optical surface to be processed according to the processing path and the corresponding feed speed or dwell time, thereby achieving deterministic shaping of the optical surface to be processed. After processing, the surface shape can be re-inspected, and the detected surface shape can be used as new surface shape sampling data to repeat the above steps, realizing closed-loop iterative processing.

[0049] It should be noted that, in one type of implementation, the main complexity of a single forward or transpose operator can be summarized as follows: (14); In the formula, The number of nodes in the target convolutional mesh. The number of sampling points for the processing path. The first term of Equation (14) corresponds to the FFT convolution calculation of 2K+1 angular modes, and the second term corresponds to the path-mesh scattering or aggregation calculation of 2K+1 angular modes. It can be seen that this embodiment uses active mesh and boundary filling, and the calculation scale is related to the effective processing area, path coverage and tool support area, rather than simply growing with the global large matrix size; and the complexity of a single forward or transpose calculation is linearly related to the number of angular modes, which has obvious advantages compared with the matrix construction and storage overhead that increases with the product of surface resolution, number of path points and tool support range in explicit matrix methods.

[0050] Understandable, Figure 2The matrix-independent operator layer is used to perform removal prediction and feedback calculation without explicitly constructing the path-surface removal matrix. This layer includes a forward Grid-FFT operator and a matched transpose operator. The forward Grid-FFT operator first maps the modal weights on the path to the active grid based on the current dwell density, path increment, and tool attitude phase weights, then performs FFT convolution through modal kernel spectra, and finally superimposes them to obtain the predicted removal amount; the matched transpose operator, based on the residual between the predicted removal amount and the target removal amount, feeds back the residual information to the path dwell variable space according to the correspondence of the forward calculation, which is used by the optimizer to update the dwell density. The function of this layer corresponds to the transpose feedback determination process in steps S13 and S14 mentioned above. The optimization output layer is used to complete the dwell time constraint solution and result generation. This layer calls the forward prediction and transpose feedback provided by the matrix-independent operator layer to solve the dwell variables at the path sampling points under the constraints of speed upper and lower limits, dwell density upper and lower limits, non-negativity constraints, smoothness constraints, or other process rules. After the solution is completed, the system outputs evaluation indicators such as dwell density, dwell time, machine tool feed rate program, predicted removal amount, post-machining residual surface shape, residual root mean square value, peak-valley value, and calculation time. The output results can be used for subsequent CNC machining program generation, machining effect evaluation, and process parameter adjustment. The function of this layer corresponds to the iterative update, target dwell time determination, and machining process in the aforementioned step S14.

[0051] To verify the feasibility and beneficial effects of this embodiment, numerical simulations were performed using measured optical surface shape data and measured non-circular symmetric magnetorheological tool removal functions. The effective aperture radius of the verification example was 100 mm, the surface shape sampling grid was 1601 × 1601, and the processing path was a spiral path containing 100,532 path sampling points. The local direction of the tool removal function continuously varied radially with the path, and the highest order K of the angular mode was set to 24. The reference explicit rotating template matrix backend and the angular mode Grid-FFT backend of this embodiment used the same target removal amount, processing path, tool attitude angle, velocity constraint, and dwell time optimization parameters.

[0052] See Figure 4 As shown, Figure 4 (a) is a schematic diagram of the residual after machining at the back end of the explicit rotating template matrix. Figure 4 (b) is a schematic diagram of the post-processing residual at the back end of the angular modal Grid-FFT of this application. Figure 4(c) is a comparison of the residuals obtained from the two back-end solutions. The peak-to-valley value of the residual obtained from the explicit rotation template matrix back-end is 112.4 nm, and the root mean square value is 6.569 nm. The peak-to-valley value of the residual obtained from the angular modal Grid-FFT back-end in this embodiment is 112.7 nm, and the root mean square value is 6.573 nm. After the two back-ends complete the dwell time calculation, the peak-to-valley value of the residual difference is 2.16 nm, and the root mean square value is 0.0782 nm. In this verification example, the total time of the explicit matrix back-end is 674.99 s, and the total time of the back-end in this embodiment is 3.01 s. The results show that this embodiment can obtain dwell time calculation results that are approximately consistent with the numerical values ​​of the explicit matrix reference method without explicitly constructing a large-scale path-surface rotation removal matrix, and significantly reduces the operator construction and calculation time, improving the computational efficiency by more than two orders of magnitude.

[0053] It should be noted that this embodiment can be applied to magnetorheological polishing, ion beam shaping, small tool polishing, airbag polishing, plasma shaping, laser shaping, grinding shaping, and other deterministic sub-aperture machining; it can be applied to planar, spherical, aspherical, freeform surfaces, large-aperture mirrors, windows, semiconductor wafers, molds, or other surfaces requiring dwell time planning; and it can be used for offline process planning, online correction, closed-loop iterative machining, parameter scanning, process window evaluation, and machine tool control program generation. In parameter scanning and process window evaluation, since pre-calculated results such as modal kernel spectra and path-grid scattering tables can be reused in the same process task, when only the upper and lower limits of velocity, dwell density, and regularization term weights are adjusted, step S12 does not need to be re-executed to directly re-optimize and solve the problem; when only the machining path (such as path spacing) is adjusted, only the path-grid scattering table needs to be reconstructed without recalculating the modal kernel spectra; when the surface resolution or aperture mask is adjusted, the modal convolution kernel can be re-embedded according to the new target active mesh, while the angular modal coefficients can still be reused. It should also be noted that, in addition to FFT, the convolution method in this embodiment can also be block FFT, overlapping storage, overlapping addition, non-uniform FFT, fast multipole, or other equivalent fast convolution methods; the calculation steps in this embodiment can be executed on CPU, GPU, field-programmable gate array, or heterogeneous computing platform; this embodiment does not limit the specific software implementation form.

[0054] As can be seen, this application uses angular modal phase weights to express tool attitude changes, avoiding point-by-point rotation and resampling of the two-dimensional tool removal function for each path sampling point; it achieves matrix-independent forward computation through path-mesh mapping and Grid-FFT convolution, avoiding explicit construction of large-scale path-surface sparse removal matrices; it retains resident variables on the real physical path sampling points, facilitating the direct expression of path increments, speed upper and lower limits, local no-machining zones, and machine tool execution constraints; it provides a transpose operator matching the forward operator, which can stably couple a constraint optimizer that depends on repeated forward / transpose multiplications; modal Nuclear spectra can be reused in the same process task or multiple iterations, which is beneficial for scanning path spacing, velocity constraints, aperture masks, and resolution parameters; the use of active meshes and boundary filling makes the computational scale related to the effective processing area, path coverage, and tool support area, rather than simply growing with the global large matrix size; it is not limited to specific tool types and can cover processing scenarios related to magnetorheological polishing, ion beam shaping, small tool polishing, gasbag polishing, plasma shaping, and laser shaping; it is not limited to specific software implementations and is suitable for forming multi-layer protection that links methods, devices, storage media, and processing equipment.

[0055] See Figure 5 As shown, this application discloses an optical element surface processing apparatus, comprising: Data processing module 11 is used to determine the surface shape sampling data, processing path data, and target reference quantity corresponding to the tool removal function of the optical surface to be processed, and to establish a target aperture mask based on the target processing area corresponding to the optical surface to be processed to determine the target removal amount; the processing path data includes processing path sampling points, path increments between adjacent processing path sampling points, and local tool attitude angles corresponding to each processing path sampling point; the target reference quantity includes a target coordinate system, length unit, and sampling reference. The frequency domain kernel spectrum determination module 12 is used to perform angular mode expansion on the tool removal function based on the target coordinate system to determine the mode convolution kernel corresponding to each angular mode, determine the target active grid and grid filling size according to the target aperture mask, the processing path data and the tool removal function, so as to establish the target mapping relationship between the processing path sampling points and the grid nodes of the target active grid, and embed the mode convolution kernel into the target convolution grid based on the grid filling size to determine the target frequency domain kernel spectrum; The removal amount prediction module 13 is used to determine the path dwelling variable corresponding to the optical surface to be processed, and combine the path increment, the path dwelling variable and the phase weight of each angular mode corresponding to each local tool attitude angle to determine the path side mode weight of each angular mode, and use the target active mesh based on the target mapping relationship, the path side mode weight and the target frequency domain kernel spectrum to determine the predicted removal amount in the target aperture mask; The optical element processing module 14 is used to determine the target residual based on the predicted removal amount and the target removal amount, determine the transpose feedback amount corresponding to the path dwell variable space using the target active grid, iteratively update the path dwell variable based on the transpose feedback amount and the target residual, and determine the target dwell time based on the path dwell variable when the path dwell variable meets the preset convergence condition, and process the optical surface to be processed based on the target dwell time.

[0056] As can be seen, this application uses angular modal phase weights to express tool attitude changes, avoiding point-by-point rotation and resampling of the two-dimensional tool removal function for each path sampling point. By establishing a mapping relationship between the processing path data and the target active mesh, and using active mesh and boundary filling, the computational scale is related to the effective processing area, path coverage, and tool support area, achieving matrix-independent forward computation rather than simply growing with the global large matrix size. This avoids explicitly constructing a large-scale path-surface sparse removal matrix. At the same time, modal convolution kernels are embedded into the active mesh, and the modal kernel spectrum can be reused in the same process task or multiple iterations, which is beneficial for scanning path spacing, velocity constraints, aperture masks, and resolution parameters. Thus, while obtaining dwell time calculation results that are approximately consistent with the numerical values ​​of explicit matrix reference methods, it significantly reduces operator construction and computation time, improving the efficiency and accuracy of optical component surface processing. In addition, this application does not limit specific tool types or specific software, and can cover processing scenarios related to magnetorheological polishing, ion beam shaping, small tool polishing, gasbag polishing, plasma shaping, and laser shaping.

[0057] In one specific implementation, the frequency domain nuclear spectrum determination module 12 may include: The function expansion submodule is used to convert the tool removal function into polar coordinates based on the target coordinate system, and to represent the tool removal function in polar coordinates as the sum of finite-order angular modes, so as to determine the angular mode expansion form corresponding to the tool removal function; The kernel determination submodule is used to determine the modal convolution kernel corresponding to each angular mode based on the angular mode expansion form; the angular mode includes any one or more combinations of complex exponential Fourier mode, real sine / cosine mode, circular harmonic function basis, orientable filter basis, low-rank direction dictionary, principal component mode or Zernike angular component.

[0058] In one specific implementation, the removal amount prediction module 13 may include: The removal amount prediction submodule is used to determine the predicted removal amount within the target aperture mask based on the target active grid and the target positive operator, the target mapping relationship, the path-side mode weights, and the target frequency domain kernel spectrum. Accordingly, the optical element processing module 14 may specifically include: The feedback quantity determination submodule is used to determine the transposed feedback quantity corresponding to the path-resident variable space based on the target active grid and the target transpose operator, according to the target mapping relationship, the path-side modal weights, and the target frequency domain kernel spectrum; wherein, the target forward operator and the target transpose operator satisfy the inner product consistency relationship in a discrete sense; In one specific embodiment, the optical element processing module 14 may include: The resident variable update submodule is used to iteratively update the path resident variables based on the transposed feedback and the target residual under target constraints; wherein, the target constraints include upper and lower limit constraints on speed, upper and lower limit constraints on resident density, non-negativity constraints, and smoothness constraints.

[0059] In one specific implementation, the resident variable update submodule may include: The resident variable update unit is used to iteratively update the path resident variables based on the transpose feedback and the target residual under the target constraint conditions using the target constraint optimization method; the target constraint optimization method includes the bounded least squares optimization method, the projected gradient optimization method, and the conjugate gradient optimization method.

[0060] In one specific embodiment, the optical element processing module 14 may include: The dwell time determination submodule is used to convert the path dwell density into a machine tool feed rate sequence if the path dwell variable is a path dwell density, and to construct a target dwell speed program based on the machining path data and the machine tool feed rate sequence, so as to determine the target dwell time based on the target dwell speed program.

[0061] Furthermore, embodiments of this application also disclose an electronic device, Figure 6 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application.

[0062] Figure 6This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the optical element surface processing method disclosed in any of the foregoing embodiments. Alternatively, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0063] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0064] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0065] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the optical element surface processing method executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include a computer program capable of performing other specific tasks.

[0066] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned disclosed method for processing the surface of optical elements. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0067] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0068] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0069] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0070] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0071] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for surface processing of an optical element, characterized in that, include: The surface shape sampling data, processing path data, and target reference quantity corresponding to the tool removal function of the optical surface to be processed are determined, and a target aperture mask is established based on the target processing area corresponding to the optical surface to be processed to determine the target removal amount; the processing path data includes processing path sampling points, path increments between adjacent processing path sampling points, and local tool attitude angles corresponding to each processing path sampling point; the target reference quantity includes the target coordinate system, length unit, and sampling reference. Based on the target coordinate system, the tool removal function is subjected to angular mode expansion to determine the modal convolution kernel corresponding to each angular mode. The target active mesh and mesh filling size are determined according to the target aperture mask, the processing path data and the tool removal function, so as to establish the target mapping relationship between the processing path sampling points and the mesh nodes of the target active mesh. Based on the mesh filling size, the modal convolution kernel is embedded into the target convolution mesh to determine the target frequency domain kernel spectrum. The path dwelling variable corresponding to the optical surface to be processed is determined, and the path increment, the path dwelling variable and the phase weight of each angular mode corresponding to each local tool attitude angle are combined to determine the path side mode weight of each angular mode. The predicted removal amount in the target aperture mask is determined by using the target active mesh based on the target mapping relationship, the path side mode weight and the target frequency domain kernel spectrum. The target residual is determined based on the predicted removal amount and the target removal amount. The transpose feedback amount corresponding to the path dwell variable space is determined using the target active grid. The path dwell variable is iteratively updated based on the transpose feedback amount and the target residual. When the path dwell variable meets the preset convergence condition, the target dwell time is determined based on the path dwell variable. The optical surface to be processed is processed based on the target dwell time.

2. The optical element surface processing method according to claim 1, characterized in that, The step of performing angular mode expansion on the tool removal function based on the target coordinate system to determine the mode convolution kernel corresponding to each angular mode includes: Based on the target coordinate system, the tool removal function is converted into polar coordinates, and the tool removal function in polar coordinates is expressed as the sum of finite-order angular modes, so as to determine the angular mode expansion form corresponding to the tool removal function; The modal convolution kernel corresponding to each angular mode is determined based on the angular mode expansion form; the angular mode includes any one or more combinations of complex exponential Fourier mode, real sine / cosine mode, circular harmonic function basis, orientable filter basis, low-rank direction dictionary, principal component mode or Zernike angular component.

3. The optical element surface processing method according to claim 1, characterized in that, The target mapping relationship includes any one of bilinear scattering, bicubic interpolation, B-spline, radial basis function, kernel function, or conservative area weighting mapping; the target active mesh includes any one of a single mesh covering the entire workpiece, a local sub-region mesh, a block mesh, a locally refined mesh, or a multi-resolution mesh; the boundary processing method corresponding to the mesh fill size includes any one or a combination of zero fill, mirror extension, overlap preservation, overlap addition, or boundary compensation.

4. The optical element surface processing method according to claim 1, characterized in that, The step of determining the predicted removal amount within the target aperture mask using the target active grid based on the target mapping relationship, the path-side mode weights, and the target frequency domain kernel spectrum includes: The predicted removal amount within the target aperture mask is determined using the target active grid and the target positive operator based on the target mapping relationship, the path-side mode weights, and the target frequency domain kernel spectrum; Accordingly, determining the transpose feedback quantity corresponding to the path-resident variable space using the target activity grid includes: Using the target active grid and the target transpose operator, based on the target mapping relationship, the path-side modal weights, and the target frequency domain kernel spectrum, the transpose feedback quantity corresponding to the path-resident variable space is determined; wherein, the target forward operator and the target transpose operator satisfy an inner product consistency relationship in a discrete sense.

5. The optical element surface processing method according to claim 1, characterized in that, The iterative update of the path-resident variables based on the transposed feedback quantity and the target residual includes: Under the target constraints, the path dwelling variables are iteratively updated based on the transposed feedback and the target residual; wherein, the target constraints include upper and lower limit constraints on velocity, upper and lower limit constraints on dwelling density, non-negativity constraints, and smoothness constraints.

6. The optical element surface processing method according to claim 5, characterized in that, The iterative update of the path-resident variables based on the transposed feedback and the target residual under the target constraint includes: The path-resident variables are iteratively updated based on the transpose feedback and the target residual under the objective constraint conditions using an objective constraint optimization method; the objective constraint optimization method includes bounded least squares optimization method, projective gradient optimization method and conjugate gradient optimization method.

7. The method for surface processing of optical elements according to any one of claims 1 to 6, characterized in that, Determining the target dwell time based on the path dwelling variable includes: If the path dwelling variable is the path dwelling density, then the path dwelling density is converted into a machine tool feed rate sequence, and a target dwelling speed program is constructed based on the machining path data and the machine tool feed rate sequence, so as to determine the target dwelling time based on the target dwelling speed program.

8. An apparatus for surface processing of optical elements, characterized in that, include: The data processing module is used to determine the surface shape sampling data, processing path data, and target reference quantity corresponding to the tool removal function of the optical surface to be processed, and to establish a target aperture mask based on the target processing area corresponding to the optical surface to be processed to determine the target removal amount; the processing path data includes processing path sampling points, path increments between adjacent processing path sampling points, and local tool attitude angles corresponding to each processing path sampling point; the target reference quantity includes a target coordinate system, length unit, and sampling reference. The frequency domain kernel spectrum determination module is used to perform angular mode expansion on the tool removal function based on the target coordinate system to determine the mode convolution kernel corresponding to each angular mode, determine the target active grid and grid fill size according to the target aperture mask, the processing path data and the tool removal function, so as to establish the target mapping relationship between the processing path sampling points and the grid nodes of the target active grid, and embed the mode convolution kernel into the target convolution grid based on the grid fill size to determine the target frequency domain kernel spectrum; The removal amount prediction module is used to determine the path dwelling variable corresponding to the optical surface to be processed, and combine the path increment, the path dwelling variable and the phase weight of each angular mode corresponding to each local tool attitude angle to determine the path side mode weight of each angular mode, and use the target active mesh based on the target mapping relationship, the path side mode weight and the target frequency domain kernel spectrum to determine the predicted removal amount in the target aperture mask; An optical component processing module is used to determine a target residual based on the predicted removal amount and the target removal amount, determine the transpose feedback amount corresponding to the path dwell variable space using the target active grid, iteratively update the path dwell variable based on the transpose feedback amount and the target residual, and determine the target dwell time based on the path dwell variable when the path dwell variable meets a preset convergence condition, and process the optical surface to be processed based on the target dwell time.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the optical element surface processing method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the optical element surface processing method as described in any one of claims 1 to 7.

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