A residence time iterative solution method, system, medium, and apparatus

Abstract

This invention discloses a method, system, medium, and device for iteratively solving residence time. The method includes constructing a mathematical model of optical surface shape error and obtaining a discrete response matrix; setting initial sparse B-spline node vectors and convergence conditions; generating a B-spline basis function matrix based on the node vectors, performing matrix multiplication, and constructing an optimization coefficient matrix; solving a quadratic programming model to obtain the current control point vector and surface shape residual; calculating the projection of the full-aperture surface shape residual onto the parameter domain and constructing a sensitivity index function; identifying high-error hotspot intervals and adaptively inserting new nodes; dynamically updating the model topology until the convergence conditions are met; and finally determining the non-uniform node vectors adapted to local error characteristics and their corresponding residence time distributions. This invention effectively solves the contradiction between undercorrection and dimensional redundancy faced by traditional uniform models in complex surface shaping, and has significant advantages in local feature capture capability, computational efficiency, and process intelligence.

Description

Technical Field

[0001] This invention relates to a method, system, medium, and device for iteratively solving residence time, belonging to the field of optical precision manufacturing and data processing technology. Background Technology

[0002] In the field of modern high-end optical manufacturing, computer-controlled optical surface forming technology has become the mainstream method for processing large-diameter aspherical and complex freeform surface components. As the performance indicators of optical systems in aerospace, high-energy lasers, and extreme ultraviolet lithography continue to rise, optical components not only require extremely high surface accuracy but also face increasingly complex surface error characteristics. How to precisely correct these complex local features while simultaneously ensuring overall processing efficiency and process safety has become a pressing challenge in the field of ultra-precision optical manufacturing.

[0003] The dwell time calculation is a core element determining the accuracy of computer-controlled optical surface forming. With the development of parametric modeling techniques, B-spline basis function-based methods have alleviated, to some extent, the problems of high computational dimensionality and uneven motion in traditional discrete models. However, most current parametric methods construct models using pre-defined, fixed-interval uniform node vectors. This modeling approach has significant drawbacks when dealing with non-uniformly distributed surface errors: firstly, the error distribution of optical surfaces often exhibits strong locality; globally densifying nodes to correct a small, steep region leads to a large amount of redundant control points in flat areas, resulting in significant waste of computational resources and numerical instability; secondly, using sparse uniform nodes to maintain computational efficiency fails to effectively capture local high-frequency or steep error characteristics, making it difficult for the final processing residuals to converge. Furthermore, the traditional method of relying on repeated trial and error based on human experience to determine the optimal node density is inefficient and cannot guarantee the optimal solution.

[0004] Given the limitations of existing fixed-node parametric models in handling non-uniform and complex surfaces, such as poor flexibility and difficulty in balancing computational efficiency and local accuracy, traditional static modeling approaches are no longer sufficient to meet the high-precision manufacturing requirements of high-performance optical components.

[0005] Therefore, there is an urgent need for a dwell time solution method that can automatically adjust the model topology based on the surface residual characteristics and has the ability to "allocate" computing resources on demand, so as to solve the bottleneck of local convergence accuracy faced by the traditional uniform point distribution strategy and achieve efficient and high-precision convergence of complex optical surfaces. Summary of the Invention

[0006] The purpose of this invention is to provide a method, system, medium, and device for iteratively solving residence time. By establishing a dynamic topology update mechanism based on residual sensitivity analysis, the discrete response matrix is ​​preprocessed with dimensionality reduction, and a quadratic programming model is solved to obtain the current surface residual. High-error hotspot intervals are automatically identified using sensitivity indices, and new nodes are adaptively inserted to achieve dynamic evolution of the model topology and non-uniform optimization of residence time distribution. The method of this invention can effectively solve the contradiction between undercorrection and dimensional redundancy faced by traditional uniform models in complex surface trimming, and has significant advantages in terms of local feature capture capability, computational efficiency ratio, and process intelligence level.

[0007] To achieve the above objectives, the present invention is implemented using the following technical solution.

[0008] In a first aspect, the present invention provides an iterative solution method for dwell time, comprising:

[0009] A mathematical model of the optical surface shape error of an optical element is constructed, and a discrete response matrix characterizing the discrete mapping relationship between residence time and surface removal amount is obtained.

[0010] Define the initial sparse B-spline node vectors and convergence conditions;

[0011] Generate a B-spline basis function matrix based on the node vectors, perform matrix multiplication, and construct an optimized coefficient matrix;

[0012] Using the residence time control point vector as the optimization variable to be solved, a quadratic programming model containing non-negative inequality constraints is constructed based on the optimization coefficient matrix, and numerical solutions are obtained to obtain the surface residual distribution.

[0013] Calculate the projection of the full-caliber surface residual onto the parameter domain, and construct the sensitivity index function;

[0014] High-error hotspot intervals are identified based on sensitivity indicators, and new nodes are adaptively inserted.

[0015] Based on the control points and surface residual distribution obtained from the solution, the convergence of the iteration results is determined:

[0016] If the iteration result does not meet the convergence condition, update the node vector and return to rebuild the B-spline basis function matrix to continue iterative solution;

[0017] When the iteration results meet the convergence condition, the iteration stops, and the final optimized node vector and the corresponding control point vector are output to determine the optimal residence time distribution.

[0018] Furthermore, the construction of the mathematical model for optical surface shape error includes obtaining measured height data of the optical surface to be processed using interferometry or contour scanning equipment and combining it with optical design theory data. The measured data and theoretical data are unified to the same discrete coordinate grid through spatial coordinate alignment and grid interpolation. Based on the height difference between the measured surface shape and the target surface shape, a discrete surface shape error distribution characterizing the depth of material to be removed at each discrete point on the optical surface is constructed.

[0019] The process of obtaining the discrete response matrix is ​​as follows:

[0020] The motion trajectory of the machining tool along the scanning path is defined as a one-dimensional parameterized curve, and the continuous scanning path is discretized into multiple discrete dwell points distributed along the path.

[0021] A two-step search strategy combining spatial neighborhood coarse screening and geometric fine screening is adopted to construct a matrix. Specifically, the KD tree algorithm is used to establish a spatial index of surface monitoring points and the maximum envelope radius of the tool influence function is used as a threshold to quickly retrieve the set of candidate monitoring points that fall within the spatial neighborhood of each discrete dwell point.

[0022] Establish a local coordinate system that follows the machining tool and project the candidate monitoring points into this local coordinate system. Use the polygon inclusion test to determine whether the projected points are within the effective boundary contour of the tool's influence function in order to filter out the set of effective monitoring points.

[0023] Calculate the removal response value of each discrete residence point to the effective monitoring point based on the removal distribution characteristics of the tool's influence function, and fill the results into the discrete response matrix in sparse matrix format;

[0024] The discrete response matrix The expression is:

[0025] ;

[0026] in, The total number of discrete dwell points. This represents the total number of surface shape monitoring points. For the first The first station for the first Unit removal amount per surface monitoring point.

[0027] The method of this invention is to construct a discrete response matrix, and adopt a two-step search strategy that combines spatial neighborhood coarse screening and geometric fine screening. It only calculates the non-zero response values ​​within the effective scope of the tool influence function and stores them in a sparse matrix format, which significantly improves the computation and storage efficiency.

[0028] Furthermore, the principle for setting the initial sparse B-spline node vector is to uniformly set nodes in the parameter domain defined by the model, and the number of nodes set is less than the number of discrete dwell points. The sparse B-spline node vector restricts the degrees of freedom of the initial optimization problem to a low-dimensional space, which is used to ensure global smoothness in the early stage of iteration and effectively suppress high-frequency noise.

[0029] Furthermore, the dimensionality-reduced optimization coefficient matrix is ​​constructed. The calculation formula is the product of the discrete response matrix and the B-spline basis function matrix generated by the de Boer recursion formula based on the current node vector. Through matrix multiplication, the dimension of the optimization problem is compressed and mapped from the high-dimensional discrete dwell point space in the physical space to the low-dimensional control point space in the parameter space.

[0030] Furthermore, the objective function of the quadratic programming model is to minimize the surface residual vector. The sum of the norm squared and the regularization term, wherein the surface residual vector is the product of the optimization coefficient matrix and the control point vector to be solved for the dwell time minus the target surface error vector, and the regularization term is the sum of the squared norm and the regularization term of the control point vector. The product of the square of the norm and the Tikhonov regularization coefficient;

[0031] The inequality constraints include nonnegativity constraints that guarantee the physical realizability of the residence time and constraints that prevent over-throwing, ensuring that the theoretical removal amount at each point does not exceed the target error value.

[0032] Furthermore, the construction of the sensitivity index function includes calculating the current surface residual vector. In the optimization coefficient matrix The projection magnitude on the column space, the sensitivity index vector The expression is:

[0033] ;

[0034] in, To optimize the transpose of the coefficient matrix, For the current surface residual vector, Let this be the initial target surface shape error vector. The dwell time control point vector, To take the absolute value;

[0035] In the method of this invention, the sensitivity index vector Each element in the value represents the gradient contribution of the corresponding B-spline control point under the current residual distribution. The larger the value, the greater the potential contribution of increasing the degrees of freedom in the local area controlled by the control point to reducing the surface residual.

[0036] Furthermore, the process of identifying high-error hotspot regions and adaptively inserting new nodes includes:

[0037] Sensitivity index vector Sort the data in descending order and select the feature points with the largest amplitude. Calculate the distribution density of the feature points in each node interval and mark the interval with the highest density of feature points as the hotspot interval.

[0038] New nodes are adaptively inserted at the midpoint of the parameters in the hotspot interval to refine the local B-spline basis functions and improve the model's ability to correct and capture high-frequency local errors in the hotspot interval.

[0039] In the method of this invention, a dynamic topology update mechanism based on residual sensitivity analysis is established. The high-frequency hotspot areas in the full-aperture surface error distribution are automatically perceived by the sensitivity index and local node densification is performed, thereby realizing the on-demand precise allocation of computing resources and the adaptive evolution of the model structure.

[0040] Furthermore, based on the control points obtained from the solution and the distribution of surface residuals, the convergence judgment of the iteration results is performed: when the iteration results do not meet the convergence condition, it means that the root mean square value of the current surface residual is greater than the preset residual threshold, or the current iteration number has not reached the preset maximum value: the non-uniform node vector generated after inserting new nodes is used as the new input parameter, the node vector is updated, the B-spline basis function matrix is ​​regenerated based on the updated topology and the optimization coefficient matrix is ​​constructed, and then the quadratic programming model is solved again to form a closed-loop adaptive iterative optimization process;

[0041] When the iteration result meets the convergence condition, that is, the root mean square value of the current surface residual is less than the preset residual threshold, or the current iteration number reaches the preset maximum value: the iteration is terminated, the final non-uniform B-spline node vector and the corresponding residence time control point vector are output, and the residence time distribution function of the whole aperture is constructed by the linear combination of B-spline basis functions.

[0042] Secondly, the present invention provides a system for iteratively solving the residence time, comprising:

[0043] The response matrix acquisition module is used to construct a mathematical model of the optical surface shape error of optical elements and obtain a discrete response matrix that characterizes the discrete mapping relationship between residence time and surface removal amount.

[0044] The convergence condition setting module is used to set the initial sparse B-spline node vector and the convergence condition;

[0045] The coefficient matrix construction module is used to generate B-spline basis function matrices from node vectors, perform matrix multiplication operations, and construct optimized coefficient matrices.

[0046] The quadratic programming solution module is used to construct a quadratic programming model with non-negative inequality constraints based on the optimization coefficient matrix, using the dwell time control point vector as the optimization variable to be solved, and to perform numerical solution to obtain the surface residual distribution.

[0047] The sensitivity calculation module is used to calculate the projection of the full-aperture surface residual onto the parameter domain and construct the sensitivity index function.

[0048] The node insertion module is used to identify high-error hotspot regions based on sensitivity indicators and adaptively insert new nodes.

[0049] The iteration result output module is used to determine the convergence of the iteration results based on the control points and surface residual distribution obtained from the solution.

[0050] If the iteration result does not meet the convergence condition, update the node vector and return to rebuild the B-spline basis function matrix to continue iterative solution;

[0051] When the iteration results meet the convergence condition, the iteration stops, and the final optimized node vector and the corresponding control point vector are output to determine the optimal residence time distribution.

[0052] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the dwell time iterative solution method described in any of the first aspects.

[0053] Fourthly, the present invention provides a computer device, comprising:

[0054] Memory, used to store computer programs / instructions;

[0055] A processor for executing the computer program / instructions to implement the steps of the dwell time iterative solution method described in any one of the first aspects.

[0056] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0057] 1. The dwell time iterative solution method provided by this invention constructs a mathematical model of the surface shape error of an optical surface and obtains a discrete response matrix, sets an initial sparse B-spline node vector and convergence conditions; then, a B-spline basis function matrix is ​​generated based on the node vector, and an optimization coefficient matrix is ​​constructed through matrix operations; on this basis, the dwell time control point vector is used as the optimization variable to be solved, and a quadratic programming model with non-negative constraints is established based on the optimization coefficient matrix and numerically solved to obtain the surface shape residual distribution; further, by calculating the projection of the full-aperture residual on the parameter domain, a sensitivity index function is constructed, high-error hotspot intervals are automatically identified and new nodes are adaptively inserted, driving the dynamic evolution of the model topology and the non-uniform optimization of the dwell time distribution; the method of this invention, through a dynamic node update mechanism based on residual sensitivity analysis, effectively overcomes the core contradiction between "global encryption leading to the curse of dimensionality" and "sparse distribution leading to local underfitting" faced by traditional fixed uniform node parameterized models when dealing with non-uniform complex errors, significantly reducing the dimension of the optimization problem and the computational memory occupation, while significantly breaking through the bottleneck of the trimming accuracy of complex local features of optical surfaces;

[0058] 2. The dwell time iterative solution method provided by the present invention, by combining a quadratic programming model with strict anti-over-throw constraints, abandons the traditional mode of relying on manual experience to repeatedly try and fail to determine node parameters, realizes fully automatic closed-loop iteration and intelligent optimization in the dwell time solution process, and significantly improves the manufacturing efficiency and convergence determinism of optical components while ensuring process safety.

[0059] 3. The computer-readable storage medium and computer device provided by the present invention can execute the steps of the dwell time iterative solution method provided by the present invention. Attached Figure Description

[0060] Figure 1 This is an overall flowchart of the dwell time iterative solution method provided according to an embodiment of the present invention;

[0061] Figure 2 This is a flowchart illustrating the process of constructing a sparse discrete response matrix in the dwell time iterative solution method provided according to an embodiment of the present invention;

[0062] Figure 3 This is a schematic diagram of the two-dimensional spatial distribution of the initial target surface shape error of the optical element to be processed in the dwell time iterative solution method provided in the embodiment of the present invention;

[0063] Figure 4 This is a schematic diagram of the sparse distribution structure of the non-zero elements of the discrete response matrix in the dwell time iterative solution method provided according to an embodiment of the present invention;

[0064] Figure 5This is a schematic diagram of the two-dimensional distribution of the surface residual obtained in the initial sparse node state in the dwell time iterative solution method provided in the embodiment of the present invention;

[0065] Figure 6 This is a schematic diagram comparing the distribution of sensitivity index in the initial state with the distribution of uniform B-spline nodes in the dwell time iterative solution method provided according to an embodiment of the present invention.

[0066] Figure 7 This is a schematic diagram illustrating the mechanism of identifying hotspot intervals based on sensitivity in the dwell time iterative solution method provided according to an embodiment of the present invention and adaptively inserting new nodes.

[0067] Figure 8 This is a schematic diagram of the RMS decrease curve of the surface residual and the increase curve of the number of control points in the adaptive iteration process of the dwell time iterative solution method provided in the embodiment of the present invention;

[0068] Figure 9 This is a schematic diagram of the final optimized two-dimensional spatial distribution of the surface residual in the dwell time iterative solution method provided according to an embodiment of the present invention;

[0069] Figure 10 This is a schematic diagram comparing the distribution of the sensitivity index in the final state with the distribution of non-uniform B-spline nodes in the dwell time iterative solution method provided according to an embodiment of the present invention.

[0070] Figure 11 This is a schematic diagram of the final two-dimensional spatial distribution of dwell time generated in the dwell time iterative solution method provided according to an embodiment of the present invention;

[0071] Figure 12 This is a schematic diagram of the final one-dimensional distribution curve of the B-spline residence time generated in the residence time iterative solution method provided in the embodiment of the present invention. Detailed Implementation

[0072] It should be noted that:

[0073] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0074] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0075] Example 1

[0076] like Figure 1 As shown in the figure, this embodiment introduces an iterative solution method for residence time, including:

[0077] Construct a mathematical model of the target surface shape error and obtain the discrete response matrix;

[0078] Define the initial sparse B-spline node vectors and convergence conditions;

[0079] Generate a B-spline basis function matrix based on the node vectors, perform matrix multiplication, and construct an optimized coefficient matrix;

[0080] Using the control point vector as the optimization variable, a quadratic programming model with non-negative inequality constraints is constructed and numerically solved to obtain the surface residual distribution.

[0081] Calculate the projection of the full-caliber surface residual onto the parameter domain, and construct the sensitivity index function;

[0082] High-error hotspot intervals are identified based on sensitivity indicators, and new nodes are adaptively inserted.

[0083] Based on the control points and surface residual distribution obtained from the solution, the convergence of the iteration results is determined:

[0084] If the result does not meet the convergence condition, update the node vector and return to rebuild the B-spline basis function matrix to continue iteratively solving;

[0085] When the result meets the convergence condition, stop the iteration, output the final optimized node vector and the corresponding control point vector, and determine the optimal residence time distribution.

[0086] Furthermore, the construction of the target surface shape error mathematical model includes using interferometry or contour scanning equipment to obtain measured height data of the optical surface to be processed and combining it with optical design theory data. Through spatial coordinate alignment and grid interpolation processing, the measured data and theoretical data are unified to the same discrete coordinate grid. Based on the height difference between the measured surface shape and the target surface shape, a discrete surface shape error distribution characterizing the depth of material to be removed at each discrete point on the optical surface is constructed.

[0087] In this embodiment, a square optical element with an effective light transmission aperture of 96mm×96mm is selected as the simulation verification object to verify the efficiency and accuracy of the method of the present invention in dealing with large-aperture, non-uniform and complex surface shape errors.

[0088] To simulate the mid-frequency ripple characteristics commonly found in optical processing, this embodiment constructs a two-dimensional double sine wave function as the initial target surface shape error, expressed as:

[0089]

[0090] Among them, light wavelength The value is 632.8 nm; error amplitude Set as Spatial wavelength and All values ​​are set to 100 mm to ensure that the error exhibits a clear periodic gradient; constant term Set as This is used to ensure non-negativity;

[0091] like Figure 3 As shown, based on the mathematical model of the target surface shape error, the entire aperture is discretized with a sampling interval of 0.5 mm to obtain a grid with a resolution of 193×193, generating a total of There are 1 effective surface shape monitoring points; according to the simulation results, the root mean square (RMS) value of the initial surface shape is 354 nm.

[0092] Furthermore, the process of obtaining the discrete response matrix is ​​as follows:

[0093] The motion trajectory of the machining tool along the scanning path is defined as a one-dimensional parameterized curve, and the continuous scanning path is discretized into multiple discrete dwell points distributed along the path.

[0094] In this embodiment, the machining tool is set to run along the grating scanning path, with a total path length of 9410.2376 mm. To balance computational accuracy and scale, discrete sampling is performed along the scanning path at intervals of 0.5 mm, discretizing the continuous path into... Discrete dwell points.

[0095] A two-step search strategy combining spatial neighborhood coarse screening and geometric fine screening is adopted to construct a matrix. Specifically, the KD tree algorithm is used to establish a spatial index of surface monitoring points and the maximum envelope radius of the tool influence function is used as a threshold to quickly retrieve the set of candidate monitoring points that fall within the spatial neighborhood of each discrete dwell point.

[0096] The discrete response matrix The expression is:

[0097] ;

[0098] in, The total number of discrete dwell points. This represents the total number of surface shape monitoring points. For the first The first station for the first Unit removal amount per surface monitoring point;

[0099] like Figure 2 As shown, in this embodiment, the matrix establishes a structure from... Resident time and space to A linear mapping of the 3D surface error space, mathematically expressed as: 3D matrix, matrix elements For the first The number of stations within a unit of time for the first Removal depth at each monitoring point;

[0100] The theoretical dimension of the full matrix is ​​37249×18822. To address the resulting storage and computational bottlenecks, this embodiment employs a two-step search strategy based on KD Tree to construct the sparse matrix: a spatial index of all surface monitoring points is established using the KD Tree algorithm, and... Type-based tools affect the envelope radius of the function Using a threshold, quickly retrieve each discrete dwell point. A set of candidate monitoring points within the spatial neighborhood.

[0101] Establish a local coordinate system that follows the machining tool and project the candidate monitoring points to this local coordinate system. In this process, the polygon containment test is used to determine whether the projected points are within the effective boundary contour of the tool influence function (TIF) in order to filter out the set of effective monitoring points.

[0102] like Figure 4 As shown, the removal response value of each discrete residence point to the effective monitoring point is calculated based on the removal distribution characteristics of TIF. and the results Fill the discrete response matrix with sparse matrix triples; It exhibits a significant banded sparse structure, with the vast majority of elements being zero; statistically, the proportion of non-zero elements in the matrix is ​​only [percentage missing]. The actual memory usage is only 32.82MB.

[0103] The results show that the matrix construction method proposed in this invention greatly reduces the computational complexity while preserving the integrity of the physical model, laying the foundation for efficient subsequent solutions.

[0104] Furthermore, the principle for setting the initial sparse B-spline node vector is to uniformly set nodes in the parameter domain defined by the model and the number of nodes set is less than the number of discrete dwell points. The sparse B-spline node vector restricts the degrees of freedom of the initial optimization problem to a low-dimensional space, which is used to ensure global smoothness in the early stage of iteration and effectively suppress high-frequency noise.

[0105] To ensure good global smoothness and effectively suppress high-frequency noise interference in the early stages of the dwell time solution process, this embodiment does not directly adopt a high-density node distribution, but instead uses a coarse-to-fine adaptive strategy:

[0106] First, in the parameter domain of the residence time function definition The initial B-spline node vectors are uniformly set, and the initial number of B-spline control points is set to 100, taking into account the total number of generated discrete dwell points. With up to 18,822 degrees of freedom, the initial setting restricts the degree of freedom of the optimization problem to an extremely low dimension, thereby mathematically guaranteeing the low-frequency smoothness of the initial solution and avoiding the problem of fast but large jitter caused by the high degree of freedom in traditional methods.

[0107] Meanwhile, to control the progress of subsequent adaptive iterations, this embodiment sets a dual convergence condition, including a physical convergence criterion and a mathematical stagnation criterion. The physical convergence criterion is set when the RMS value of the surface residual decreases to 8% of the initial RMS value, i.e. The mathematical stagnation criterion is set to a maximum of no more than 20 iterations.

[0108] Furthermore, the optimization coefficient matrix after dimensionality reduction is constructed. The calculation formula is the product of the discrete response matrix and the B-spline basis function matrix generated by the de Boer recursion formula based on the current node vector. The dimension of the optimization problem is compressed and mapped from the high-dimensional discrete dwell point space in the physical space to the low-dimensional control point space in the parameter space through matrix multiplication.

[0109] By utilizing the local support property and the principle of linear superposition of B-spline basis functions, the high-dimensional solution problem in physical space is mapped to a low-dimensional solution problem in parameter space. The specific process is as follows:

[0110] Based on the currently defined sparse node vector, the B-spline basis function matrix is ​​generated using the De Boer recurrence formula. Perform sparse matrix multiplication:

[0111] ;

[0112] The matrix multiplication operation described above will yield a high-dimensional discrete response matrix with a dimension of 37249×18822. The compressed mapping is an optimized coefficient matrix with a dimension of only 37249×100. The dimensionality reduction process in this embodiment not only significantly reduces the number of decision variables in the subsequent quadratic programming model and greatly reduces the computational memory usage, but also fundamentally solves the common problems of dimensionality curse and ill-conditioned equations in solving the dwell time of large-scale optical processing, making it possible to quickly solve the processing instructions of large-diameter components on ordinary industrial control computers.

[0113] Furthermore, the objective function of the quadratic programming model is to minimize the surface residual vector. The sum of the norm squared and the regularization term, wherein the surface residual vector is the product of the optimization coefficient matrix and the control point vector to be solved for the dwell time minus the target surface error vector, and the regularization term is the sum of the squared norm and the regularization term of the control point vector. The product of the square of the norm and the Tikhonov regularization coefficient;

[0114] The inequality constraints include nonnegativity constraints that guarantee the physical realizability of the residence time and constraints that prevent over-throwing, ensuring that the theoretical removal amount at each point does not exceed the target error value.

[0115] like Figure 5 As shown and Figure 6 As shown, in this embodiment, the vector formed by the 100 B-spline control points determined above is... As the optimization variable to be solved, a quadratic programming mathematical model with strict constraints is constructed to obtain a physically realizable and process-safe residence time distribution. In order to minimize the surface residual while ensuring the smoothness and numerical stability of the solution, the model is numerically solved using the effective set method. The optimal control point vector and the corresponding surface residual distribution under the initial sparse node distribution are obtained. The obtained surface residual RMS is 89nm. Due to the insufficient degrees of freedom of the solution, it is in an undercorrected state.

[0116] The initial model, with only 100 degrees of freedom, yielded a solution with excellent global smoothness, but the surface residual RMS remained high, indicating that the model was undercorrected and could not accurately correct the peak and valley characteristics of the mid-frequency ripples of the double sine wave.

[0117] Furthermore, the construction of the sensitivity index function includes calculating the current surface residual vector. In the optimization coefficient matrix The projection magnitude on the column space, the sensitivity index vector The expression is:

[0118] ;

[0119] in, To optimize the transpose of the coefficient matrix, For the current surface residual vector, Let this be the initial target surface shape error vector. The dwell time control point vector, To take the absolute value;

[0120] In this embodiment, as Figure 7 As shown in the figure, the calculation results indicate that the sensitivity index The high-value region precisely corresponds to the location of the maximum error gradient of the double sine wave, indicating that the sensitivity index... It can effectively act as an "error detector," automatically locking onto the hotspot regions on the optical surface that most urgently need increased degrees of freedom, providing clear mathematical guidance for subsequent adaptive topology updates.

[0121] Furthermore, in Figure 7 In (a), the execution of identifying high-error hotspot regions and adaptively inserting new nodes includes:

[0122] Sensitivity index vector Sort the data in descending order and select the feature points with the largest amplitude. Calculate the distribution density of the feature points in each node interval and mark the interval with the highest density of feature points as the hotspot interval.

[0123] New nodes are adaptively inserted at the midpoint of the parameters in the hotspot interval to refine the local B-spline basis functions and improve the model's ability to correct and capture high-frequency local errors in the hotspot interval.

[0124] Based on the sensitivity distribution information obtained above, the algorithm initiates an adaptive topology update mechanism, specifically: updating the sensitivity index vector... The feature points are sorted in descending order to select the top 500 feature points with the largest amplitude. The distribution density of these feature points in each node interval of the current B-spline is then calculated.

[0125] Figure 7 (b) illustrates the principle of the adaptive node insertion mechanism. In regions with high error and sensitivity, the B-spline basis functions are automatically refined and densified; while in flat regions, the basis functions remain sparse, and the model topology is "allocated on demand".

[0126] Figure 7 In (c), this embodiment sets the upper limit of the number of nodes allowed to be added in a single iteration to 50. The spatial distribution of B-spline nodes undergoes a qualitative change, evolving from the initial global uniform sparseness to local on-demand density. That is, it maintains sparseness in flat areas to save computing power, while automatically densifying in high-frequency areas such as the peaks and valleys of the double sine wave to improve the fitting ability.

[0127] Furthermore, based on the distribution of the surface residuals obtained from the solution of the control points, the convergence of the iteration results is judged. The convergence conditions include the aforementioned physical convergence criterion and mathematical stagnation criterion. That is, the physical convergence criterion is set when the RMS value of the surface residual decreases to 8% of the initial RMS value. The mathematical stagnation criterion is set at a maximum of 20 iterations, and the judgment is as follows:

[0128] When the result does not meet the convergence condition, it means that the root mean square value of the current surface residual is greater than the preset residual threshold, or the current iteration number has not reached the preset maximum value: the non-uniform node vector generated after inserting the new node is used as the new input parameter, the node vector is updated, the B-spline basis function matrix is ​​regenerated based on the updated topology and the optimization coefficient matrix is ​​constructed, and then the quadratic programming model is solved again to form a closed-loop adaptive iterative optimization process.

[0129] like Figure 8 As shown, in this embodiment, the updated non-uniform node vectors are used to regenerate the basis function matrix and construct the optimized coefficient matrix based on the new topology. The quadratic programming model is solved again. As the iteration rounds progress, the number of control points gradually increases, the model's ability to capture local complex features is significantly enhanced, the surface residual RMS shows a significant downward trend, and the convergence condition is met after 8 adaptive closed-loop iterations.

[0130] When the result meets the convergence condition, it means that the root mean square value of the current surface residual is less than the preset residual threshold, or the current iteration number reaches the preset maximum value: terminate the iteration, output the final non-uniform B-spline node vector and the corresponding residence time control point vector, and construct the full-caliber residence time distribution function using the linear combination of B-spline basis functions.

[0131] Figure 9 As shown, in this embodiment, the final surface residual RMS converges to 27nm, which is less than the preset residual threshold of 28.32nm. Compared with the initial surface, the convergence ratio reaches 12.99 times. The final number of B-spline control points used is 344. Compared with the initially defined 18,822 discrete dwell points, the method of this invention compresses the dimension of the optimization variables to be solved by about 98.17%, and the computation time of the entire adaptive optimization process is 39.80 seconds. At the same time, compared with the global uniform encryption model usually required to achieve the same accuracy, the computational resource consumption is significantly reduced.

[0132] like Figure 10 As shown, the final non-uniform node distribution is in high agreement with the sensitivity index; as Figure 11 and Figure 12 As shown, the final generated two-dimensional dwell time distribution and one-dimensional dwell time curve both maintain extremely high smoothness and strictly satisfy the non-negativity and anti-over-jetting constraints, verifying the significant technical advantages of the method of the present invention in realizing efficient, precise and stable processing of large-aperture complex optical surfaces.

[0133] Example 2

[0134] Based on the dwell time iterative solution method described in Example 1, this example introduces a dwell time iterative solution system, including:

[0135] The response matrix acquisition module is used to construct a mathematical model of the optical surface shape error of optical elements and obtain a discrete response matrix that characterizes the discrete mapping relationship between residence time and surface removal amount.

[0136] The convergence condition setting module is used to set the initial sparse B-spline node vector and the convergence condition;

[0137] The coefficient matrix construction module is used to generate B-spline basis function matrices from node vectors, perform matrix multiplication operations, and construct optimized coefficient matrices.

[0138] The quadratic programming solution module is used to construct a quadratic programming model with non-negative inequality constraints based on the optimization coefficient matrix, using the dwell time control point vector as the optimization variable to be solved, and to perform numerical solution to obtain the surface residual distribution.

[0139] The sensitivity calculation module is used to calculate the projection of the full-aperture surface residual onto the parameter domain and construct the sensitivity index function.

[0140] The node insertion module is used to identify high-error hotspot regions based on sensitivity indicators and adaptively insert new nodes.

[0141] The iteration result output module is used to determine the convergence of the iteration results based on the control points and surface residual distribution obtained from the solution.

[0142] If the iteration result does not meet the convergence condition, update the node vector and return to rebuild the B-spline basis function matrix to continue iterative solution;

[0143] When the iteration results meet the convergence condition, the iteration stops, and the final optimized node vector and the corresponding control point vector are output to determine the optimal residence time distribution.

[0144] Example 3

[0145] Based on the dwell time iterative solution method described in Embodiment 1, this embodiment introduces a computer-readable storage medium storing a computer program / instruction thereon. When the computer program / instruction is executed by a processor, it implements the steps of the dwell time iterative solution method as described in any of Embodiment 1.

[0146] Example 4

[0147] Based on the dwell time iterative solution method described in Embodiment 1, this embodiment provides a computer device, including:

[0148] Memory, used to store computer programs / instructions;

[0149] A processor is configured to execute the computer program / instructions to implement the steps of the dwell time iterative solution method as described in any one of Embodiment 1.

[0150] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0151] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0152] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0153] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0154] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for iteratively solving the residence time, characterized in that, include: A mathematical model of the optical surface shape error of an optical element is constructed, and a discrete response matrix characterizing the discrete mapping relationship between residence time and surface removal amount is obtained. Define the initial sparse B-spline node vectors and convergence conditions; Generate a B-spline basis function matrix based on the node vectors, perform matrix multiplication, and construct an optimized coefficient matrix; Using the residence time control point vector as the optimization variable to be solved, a quadratic programming model containing non-negative inequality constraints is constructed based on the optimization coefficient matrix, and numerical solutions are obtained to obtain the surface residual distribution. Calculate the projection of the full-caliber surface residual onto the parameter domain, and construct the sensitivity index function; High-error hotspot intervals are identified based on sensitivity indicators, and new nodes are adaptively inserted. Based on the control points and surface residual distribution obtained from the solution, the convergence of the iteration results is determined: If the iteration result does not meet the convergence condition, update the node vector and return to rebuild the B-spline basis function matrix to continue iterative solution; When the iteration results meet the convergence condition, stop the iteration, output the final optimized node vector and the corresponding control point vector, and determine the optimal residence time distribution; The construction of the mathematical model for the optical surface shape error includes obtaining the measured height data of the optical surface to be processed using interferometry or contour scanning equipment and combining it with optical design theory data. The measured data and theoretical data are unified to the same discrete coordinate grid through spatial coordinate alignment and grid interpolation. Based on the height difference between the measured surface shape and the target surface shape, a discrete surface shape error distribution characterizing the depth of material to be removed at each discrete point on the optical surface is constructed. The process of obtaining the discrete response matrix is ​​as follows: The motion trajectory of the machining tool along the scanning path is defined as a one-dimensional parameterized curve, and the continuous scanning path is discretized into multiple discrete dwell points distributed along the path. A two-step search strategy combining spatial neighborhood coarse screening and geometric fine screening is used to construct the matrix; Establish a local coordinate system that follows the machining tool and project the candidate monitoring points into this local coordinate system. Use the polygon inclusion test to determine whether the projected points are within the effective boundary contour of the tool's influence function to filter out the set of effective monitoring points. Calculate the removal response value of each discrete residence point to the effective monitoring point based on the removal distribution characteristics of the tool's influence function, and fill the results into the discrete response matrix in sparse matrix format; The discrete response matrix The expression is: ； in, The total number of discrete dwell points. This represents the total number of surface shape monitoring points. For the first The first station for the first Unit removal amount per surface monitoring point.

2. The dwell time iterative solution method according to claim 1, characterized in that, The principle for setting the initial sparse B-spline node vector is to uniformly set nodes in the parameter domain defined by the model, and the number of nodes set is less than the number of discrete dwell points. The initial sparse B-spline node vector restricts the degrees of freedom of the initial optimization problem to a low-dimensional space, which is used to ensure global smoothness in the early stage of iteration and effectively suppress high-frequency noise.

3. The dwell time iterative solution method according to claim 1, characterized in that, The objective function of the quadratic programming model is to minimize the surface residual vector. The sum of the norm squared and the regularization term, wherein the surface residual vector is the product of the optimization coefficient matrix and the control point vector to be solved for the dwell time minus the target surface error vector, and the regularization term is the sum of the squared norm and the regularization term of the control point vector. The product of the square of the norm and the Tikhonov regularization coefficient; The inequality constraints include nonnegativity constraints that guarantee the physical realizability of the residence time and constraints that prevent over-throwing, ensuring that the theoretical removal amount at each point does not exceed the target error value.

4. The dwell time iterative solution method according to claim 1, characterized in that, The construction of the sensitivity index function includes calculating the current surface residual vector. In the optimization coefficient matrix The projection magnitude on the column space, the sensitivity index vector The expression is: ； in, To optimize the transpose of the coefficient matrix, For the current surface residual vector, Let this be the initial target surface shape error vector. The dwell time control point vector, To take the absolute value; the sensitivity index vector Each element in the value represents the gradient contribution of the corresponding B-spline control point under the current residual distribution.

5. The dwell time iterative solution method according to claim 4, characterized in that, The process of identifying high-error hotspot regions and adaptively inserting new nodes includes: Sensitivity index vector Sort the data in descending order and select the feature points with the largest amplitude. Calculate the distribution density of the feature points in each node interval and mark the interval with the highest density of feature points as the hotspot interval. New nodes are adaptively inserted at the midpoint of the parameters in the hotspot interval to refine the local B-spline basis functions and improve the model's ability to correct and capture high-frequency local errors in the hotspot interval.

6. The dwell time iterative solution method according to claim 1, characterized in that, The iteration result does not meet the convergence condition if the root mean square value of the current surface residual is greater than the preset residual threshold, or the current iteration number has not reached the preset maximum value: the non-uniform node vector generated after inserting the new node is used as the new input parameter, the node vector is updated, the B-spline basis function matrix is ​​regenerated based on the updated topology and the optimization coefficient matrix is ​​constructed, and then the quadratic programming model is solved again to form a closed-loop adaptive iterative optimization process. The convergence condition of the iteration result is that the root mean square value of the current surface residual is less than the preset residual threshold, or the current iteration number reaches the preset maximum value: the iteration is terminated, the final non-uniform B-spline node vector and the corresponding residence time control point vector are output, and the residence time distribution function of the whole aperture is constructed by the linear combination of B-spline basis functions.

7. A system for iteratively solving residence time, characterized in that, The dwell time iterative solution method according to any one of claims 1 to 6 includes: The response matrix acquisition module is used to construct a mathematical model of the optical surface shape error of optical elements and obtain a discrete response matrix that characterizes the discrete mapping relationship between residence time and surface removal amount. The convergence condition setting module is used to set the initial sparse B-spline node vector and the convergence condition; The coefficient matrix construction module is used to generate B-spline basis function matrices from node vectors, perform matrix multiplication operations, and construct optimized coefficient matrices. The quadratic programming solution module is used to construct a quadratic programming model with non-negative inequality constraints based on the optimization coefficient matrix, using the dwell time control point vector as the optimization variable to be solved, and to perform numerical solution to obtain the surface residual distribution. The sensitivity calculation module is used to calculate the projection of the full-aperture surface residual onto the parameter domain and construct the sensitivity index function. The node insertion module is used to identify high-error hotspot regions based on sensitivity indicators and adaptively insert new nodes. The iteration result output module is used to determine the convergence of the iteration results based on the control points and surface residual distribution obtained from the solution. If the iteration result does not meet the convergence condition, update the node vector and return to rebuild the B-spline basis function matrix to continue iterative solution; When the iteration results meet the convergence condition, the iteration stops, and the final optimized node vector and the corresponding control point vector are output to determine the optimal residence time distribution.

8. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the dwell time iterative solution method as described in any one of claims 1 to 6.

9. A computer device, characterized in that, include: Memory, used to store computer programs / instructions; A processor for executing the computer program / instructions to implement the steps of the dwell time iterative solution method according to any one of claims 1 to 6.

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