Reflector surface shape active correction method and related equipment

Abstract

The invention discloses a reflector surface shape active correction method and related equipment, and the method comprises the steps: constructing a parameterized finite element model of a reflector, the model comprising a plurality of active correction points; acquiring the initial displacement of each node of the mirror surface when the correction force is not applied to the reflector; sequentially applying a unit correction force to each active correction point, obtaining the displacement of each node of the mirror surface after each application of the unit correction force, calculating the difference between the displacement and the initial displacement, and constructing a sensitivity matrix reflecting the mapping relation between the correction force and the node displacement based on the difference; based on the sensitivity matrix, calculating sensitive characteristics of each node, distributing weights for each node according to the sensitive characteristics, and constructing a weight matrix based on the weights of each node; on the basis of the weight matrix, a target correction force acting on each active correction point is obtained through calculation by adopting a weighted generalized inverse method; and applying the target correction force to the finite element model or entity of the mirror to correct the surface shape of the mirror surface. According to the invention, more accurate and efficient active correction of the surface shape of the reflector can be realized.

Description

Technical Field

[0001] This invention belongs to the field of optical mirror correction technology, specifically relating to an active correction method and related equipment for the shape of a reflecting mirror. Background Technology

[0002] With the ever-increasing demands on optical system performance in fields such as astronomical observation, space remote sensing, and high-energy lasers, optical mirrors, as key components of optical payloads such as space optical systems, high-precision lithography equipment, and astronomical telescopes, are showing a trend towards higher resolution, larger aperture, and lighter weight. However, during processing, assembly, and service, these mirrors are prone to surface distortion due to factors such as gravity, temperature, and support. Active correction technology is needed to compensate for deformation errors in real time to ensure the stability of the optical system performance.

[0003] The core of active correction technology lies in applying precise correction forces through an actuator array to correct the surface shape error of the mirror. The accuracy of the correction force calculation directly determines the final correction effect. When the least squares method is used as the core algorithm, it relies on fixed empirical node weights and is extremely sensitive to ill-conditioned matrices. This can easily lead to a mismatch between the correction force distribution and the actual deformation mode of the mirror, exceeding the actuator's bearing limit, and ultimately causing correction failure or even damage to the mirror structure. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides an active correction method and related equipment for the surface shape of a reflector. The purpose is to overcome the shortcomings of the traditional least squares method in solving for the correction force, which relies on fixed empirical node weights and is extremely sensitive to ill-conditioned matrices. This can easily lead to a mismatch between the correction force distribution and the actual deformation mode of the mirror surface, exceeding the actuator's bearing limit and ultimately causing correction failure or even damage to the reflector structure. This invention achieves more accurate and efficient active correction of the surface shape of the reflector.

[0005] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: According to a first aspect of the present invention, an active method for correcting the surface shape of a reflective mirror is provided, comprising: A parametric finite element model of the reflector is constructed, the model containing multiple active correction points; Obtain the initial displacement of each node on the mirror surface when no correction force is applied; A unit correction force is applied sequentially to each of the active correction points, and the displacement of each node on the mirror surface is obtained after each application of the unit correction force. The difference between the displacement and the initial displacement is calculated, and a sensitivity matrix reflecting the mapping relationship between the correction force and the node displacement is constructed based on the difference. Based on the sensitivity matrix, the sensitivity features of each node are calculated, and weights are assigned to each node according to the sensitivity features. A weight matrix is ​​then constructed based on the weights of each node. Based on the weight matrix, the target correction force acting on each active correction point is calculated using the weighted generalized inverse method. The target correction force is applied to the finite element model or solid of the reflector to correct the surface shape of the mirror.

[0006] In one possible implementation of the first aspect, the construction of a sensitivity matrix reflecting the mapping relationship between the correction force and the nodal displacement based on the difference specifically includes: The displacement difference generated by the unit correction force of all active correction points corresponding to each node is arranged in a row to form a sensitivity matrix.

[0007] In one possible implementation of the first aspect, the sensitive features include the total sensitivity of the node and the sensitivity dispersion; The total sensitivity is obtained by calculating the sum of the absolute values ​​of the row vector elements of the corresponding nodes in the sensitivity matrix; The sensitivity dispersion is obtained by calculating the standard deviation of the row vector elements of the corresponding node in the sensitivity matrix.

[0008] In one possible implementation of the first aspect, assigning weights to each node based on the sensitive features specifically includes: The total sensitivity and the sensitivity dispersion are respectively normalized. The normalized total sensitivity and the normalized sensitivity dispersion are weighted and fused to obtain the initial weight of each node. The initial weights are mapped to a preset engineering safety range to obtain the final weights of each node.

[0009] In one possible implementation of the first aspect, the formula for calculating the weighted fusion of the normalized total sensitivity and the normalized sensitivity dispersion is as follows:

[0010] in, For the first The initial weights of each node; For the first The overall sensitivity after normalization of each node; For the first Sensitivity dispersion after normalization of nodes These are the weighting coefficients.

[0011] In one possible implementation of the first aspect, the weight matrix is ​​a diagonal weight matrix, wherein the elements on the diagonal of the diagonal weight matrix are the final weights corresponding to each node.

[0012] In one possible implementation of the first aspect, the calculation of the target correction force acting on each active correction point using the weighted generalized inverse method specifically involves: The objective function is to minimize the residual surface error weighted by the weight matrix. The analytical solution of the target correction force is obtained by solving the objective function.

[0013] In one possible implementation of the first aspect, the analytical solution of the target correction force is calculated using the following formula:

[0014] in, For the target correction force, This is the sensitivity matrix. This is the weight matrix. This is the initial surface shape error vector determined based on the initial displacement.

[0015] According to a second aspect of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the aforementioned active correction method for the surface shape of a reflective mirror.

[0016] According to a third aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program, which, when executed by a processor, implements the aforementioned active correction method for the surface shape of a reflective mirror.

[0017] According to a fourth aspect of the present invention, a computer program product is provided that, when executed by a processor, implements the aforementioned active correction method for the surface shape of a reflective mirror.

[0018] Compared with the prior art, the present invention has at least the following beneficial effects: Traditional least squares methods rely on fixed engineering experience to set uniform node weights when solving for mirror correction forces. This fails to consider the varying sensitivity of different nodes to the correction force, leading to a mismatch between the correction force distribution and the actual deformation pattern of the mirror, ultimately resulting in insufficient accuracy in surface correction. Furthermore, the algorithm is highly sensitive to ill-conditioned characteristics such as singularity and column correlation in the sensitivity matrix, resulting in poor stability in the correction force solution. Exceeding the actuator's load-bearing limit can cause the correction process to fail or even damage the mirror structure.

[0019] This invention provides an active mirror shape correction method that employs a weighted generalized inverse method and introduces a node weighting theory based on sensitivity driving. By calculating the total sensitivity and sensitivity dispersion of each node in the sensitivity matrix, it obtains the comprehensive deformation impact of all correction forces on a single node and the sensitivity differences of a single node to different actuators, and constructs a weight matrix. Nodes with high total sensitivity (effective correction area) are assigned higher weights, allocating more correction force resources to the correction forces affecting that node, prioritizing the cancellation of deformation errors of that node; nodes with high sensitivity dispersion (high-difficulty correction area) are assigned compensatory weights, precisely directing correction force resources to the correction forces that play a dominant role in their deformation, efficiently and accurately canceling deformation errors of that node. Based on the weight matrix, the weighted generalized inverse method assigns small weights to the row vectors of nodes with low sensitivity and prone to noise, and large weights to the row vectors of nodes with high sensitivity and in the core area to maintain the stability of mirror shape correction accuracy. As can be seen, this invention fully considers the influence of node sensitivity characteristics on the solution analysis of mirror correction force. By using sensitivity weighting, the correction force distribution is accurately matched with the actual deformation mode of the mirror, avoiding the drastic fluctuations in the solution that exceed the actuator bearing limit, which could lead to uncontrolled mirror correction or even damage to the reflector structure. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the specific embodiments of the present invention, the drawings used in the description of the specific embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0021] Figure 1 This is a flowchart of an active correction method for the surface shape of a reflective mirror according to the present invention.

[0022] Figure 2 This is an example diagram of a reflector structure model. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions 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, 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.

[0024] like Figure 1 As shown, this invention provides an active method for correcting the surface shape of a reflective mirror, which specifically includes the following steps: S1. Construct a parametric finite element model of the reflector, which contains multiple active correction points.

[0025] For example, such as Figure 2 As shown, a specific reflector structure is used as an example for illustration. The reflector has an outer diameter of 450 mm, an inner diameter of 140 mm, and is made of microcrystalline glass. It has two support rings on its back, with three fixed support points on the inner ring and a total of 15 active calibration points on the inner and outer support rings for connecting actuators.

[0026] In the finite element method (FEM) software, a three-dimensional solid model of the reflector is established based on the aforementioned geometric dimensions and material properties. Fixed constraints are applied to the three support points on the inner support ring under gravity conditions. The positions of the 15 active correction points are parameterized and defined as application points where external forces can be applied, thus completing the construction of the parameterized finite element model.

[0027] S2. Obtain the initial displacement of each node on the mirror surface when no correction force is applied.

[0028] In detail, after completing the parametric modeling of the mirror in the finite element software, a mesh is generated and an array of mirror node numbers is defined. By indexing the node numbers, the displacement of the mirror nodes before the application of a unit correction force at the active correction point of the mirror is obtained, resulting in the displacement data of all nodes on the mirror surface, which is recorded as the initial displacement.

[0029] S3. Apply a unit correction force to each of the active correction points in sequence, obtain the displacement of each node of the mirror after each application of the unit correction force, calculate the difference between the displacement and the initial displacement, and construct a sensitivity matrix that reflects the mapping relationship between the correction force and the node displacement based on the difference.

[0030] Specifically, in the finite element method software, a unit force excitation is applied sequentially to each of the 15 active correction points, perpendicular to the mirror back, using a cyclic approach. After each force application, a static analysis is performed to obtain the displacement of all nodes on the mirror surface after that force application. The difference between this displacement and the initial displacement obtained in S2 is calculated; this difference represents the nodal displacement change caused by the unit correction force. The displacement differences generated by all 15 unit correction forces corresponding to each node are arranged sequentially as row vectors for that node, ultimately forming a matrix. The number of rows equals the number of mirror nodes, and the number of columns equals the number of active correction points. The matrix This is the sensitivity matrix, and its elements are... Indicates the first j The unit correction force at the first i Displacement changes caused at each node.

[0031] S4. Based on the sensitivity matrix, calculate the sensitivity features of each node, assign weights to each node according to the sensitivity features, and construct a weight matrix based on the weights of each node.

[0032] In other words, based on the sensitivity matrix The sensitive features of each node on the mirror are calculated, and weights are assigned to each node accordingly.

[0033] In one implementation, the sensitive features include the node's total sensitivity and sensitivity dispersion. The total sensitivity reflects the node's sensitivity to correction forces; a higher value indicates that the node is a highly effective area for the correction force, resulting in a rapid reduction in overall surface shape error after correction. Total sensitivity allows for precise identification of the nodes most sensitive to correction forces, providing a quantitative basis for weight skew. Sensitivity dispersion reflects the number of dominant correction forces affecting node deformation; a higher value indicates that node deformation is dominated by only a few correction forces, with other forces having minimal impact. This necessitates precise targeting during correction, increasing the difficulty of the correction process.

[0034] The total sensitivity is obtained by calculating the sum of the absolute values ​​of the row vector elements of the corresponding node in the sensitivity matrix, i.e., the total sensitivity of the node. By calculating the sensitivity matrix The Middle i The sum of the absolute values ​​of all elements in a row is obtained as follows:

[0035] In other words, by extracting the sensitivity matrix middle The unit correction force on the first The absolute values ​​of the displacements generated by each node are summed to quantify the sensitivity of each node to the correction force, thus obtaining the total sensitivity of each node. .

[0036] The sensitivity dispersion is obtained by calculating the standard deviation of the row vector elements of the corresponding node in the sensitivity matrix, i.e., the sensitivity dispersion of the node. By calculating the matrix The Middle i The standard deviation of all elements in the row is obtained as follows:

[0037] In other words, by extracting the sensitivity matrix middle The unit correction force on the first The displacement generated by the nth node is obtained. Each node for all Average sensitivity per unit correction force and sensitivity dispersion .

[0038] In one possible implementation, weights are assigned to each node based on the sensitive features, specifically including: First, the total sensitivity and the sensitivity dispersion are normalized to eliminate differences in feature dimensions and scales to ensure fusion fairness. The normalization process is as follows:

[0039] In the formula, For the first The total sensitivity normalized to each node, ranging from [0,1]. For the first The normalized sensitivity dispersion of each node, ranging from [0,1]. This is a minimum value, ranging from 10E-15. The numerical ranges of total sensitivity and dispersion can differ greatly. Normalization ensures that the features of both dimensions have equal influence, avoiding weight allocation bias caused by differences in numerical scales and improving the rationality of the weights.

[0040] Next, the normalized total sensitivity and the normalized sensitivity dispersion are weighted and fused to obtain the initial weights of each node.

[0041] Feature fusion prioritizes the correction contribution and difficulty by linearly fusing two normalized features using weighted coefficients to generate the first corrected feature. Initial weights of each node The specific calculation formula is as follows:

[0042] in, This is a weighting coefficient, with a value of 0.7. Even if a node with high overall sensitivity has low sensitivity dispersion, its initial weight will still be relatively high; even if a node with high sensitivity dispersion has moderate overall sensitivity, it can still receive a 30% weight bias. This ensures that the weight allocation both meets the core requirement of prioritizing correction in core regions and addresses the issue of avoiding failure in high-difficulty regions. Finally, the initial weights are mapped to a preset engineering safety range to obtain the final weights of each node.

[0043] Specifically, constraint optimization limits the weights to a safe range, and sets the initial weights... Scaling to the engineering safety range via linear mapping This generates the final weights that can be directly used to solve for the correction force. The weight of each node is calculated using the following formula:

[0044] This ultimately results in adaptive node weights that fit the mechanical properties of the mirror, preventing correction failure or damage to the mirror structure due to extreme weights. For example, the final weights of all nodes are... Build as Diagonal weight matrix of order 1.

[0045] Traditional methods for solving mirror correction forces rely on fixed engineering experience to set uniform node weights, failing to consider the varying sensitivity characteristics of different nodes to correction forces. This easily leads to a disconnect between the correction force distribution and actual needs, resulting in insufficient correction in core areas and over-correction in non-critical areas, thus limiting surface accuracy. This invention extracts and calculates the total sensitivity and sensitivity dispersion of each node from the sensitivity matrix, and then generates adaptive node weights that fit the actual mirror conditions through standardization, feature fusion, and constraint optimization. By quantifying two-dimensional sensitivity features, precise weight allocation at the individual node level is achieved. Nodes with high sensitivity and greater correction difficulty receive higher weights, providing a basis for targeted allocation of correction resources and improving the effectiveness of correction force calculation.

[0046] S5. Based on the weight matrix, the target correction force acting on each active correction point is calculated using the weighted generalized inverse method.

[0047] Specifically, the initial surface shape error vector of the reflector, determined by the initial displacement, is obtained. Based on the sensitivity matrix and the weight matrix The calculation is performed using the weighted generalized inverse method. Specifically, the goal is to minimize the residual surface shape error weighted by the weight matrix, i.e., to minimize... To find the target correction force vector acting on each active correction point, we need to determine the target correction force vector. The analytical solution to this problem is in the form of: .

[0048] In detail, the objective function of the traditional least squares method is to minimize the global surface shape error with uniform weights. However, when ill-conditioned features such as singularities in the sensitivity matrix and column correlation occur, it easily leads to poor stability and convergence in the correction force solution, exceeding the actuator's load-bearing limit, causing the correction process to fail or even damage the mirror structure. This invention optimizes the objective function by introducing a node weight matrix, constructing a weighted Gram matrix, and finally solving it using the weighted generalized inverse method. Different weights are assigned to the residual deformation of different nodes, allowing errors in the core optical region to be compensated first, while preventing over-correction of non-critical regions from consuming correction resources. This also improves the ill-conditioned nature of the solution matrix and ensures solution stability. The specific calculation formula is as follows:

[0049] To minimize the objective function, The derivative is then set to zero. The specific formula for calculation is as follows:

[0050] By using the weighted Gram matrix, the analytical solution of the weighted generalized inverse method is finally obtained, and its specific calculation formula is as follows:

[0051] S6. Apply the target correction force to the finite element model or solid of the reflector to correct the surface shape of the mirror.

[0052] The target correction force calculated in step S5 The load is applied to the corresponding active correction point of the finite element model of the reflector, and a static analysis is performed again. The resulting mirror surface shape is the corrected surface shape. By comparing the surface shape error data before and after correction, the correction effect of this method is verified. In practical engineering, the calculated target correction force can be used to drive the actual actuator array to actively correct the physical reflector.

[0053] For example, by writing batch processing automation and surface shape processing code, the solved mirror correction force is applied to the parameterized finite element model of the reflector, thereby realizing the application of correction force and the solution of surface shape error.

[0054] According to the method proposed in this invention, computer program instructions are written to solve the mirror correction force of the reflector in the above example in the software, and a comparative analysis is made with the traditional method as follows:

[0055] Comparative analysis revealed that the mirror correction force obtained using the method of this invention yielded superior surface shape error results compared to traditional methods. This invention effectively overcomes the inherent limitation of traditional least squares methods, which are sensitive to ill-conditioned sensitivity matrices, by introducing a sensitivity-based node weight matrix. The solution process is numerically stable, avoiding the divergence or abnormal increase in correction force values ​​that may occur with traditional methods, ensuring that the correction force remains within the actuator's safe bearing range. Simultaneously, by prioritizing the correction of critical optical regions through dynamic weighting, intelligent allocation of correction force resources is achieved, making active correction of the mirror surface shape highly efficient and reliable. Furthermore, existing least squares-based mirror surface shape correction methods typically involve manually extracting the response function of the unit correction force, inputting the obtained mirror correction force into the mirror finite element model to solve for surface shape data, and then importing it into specialized surface shape analysis software for surface shape error processing. This process involves large data transfer volumes and low correction efficiency. This embodiment, however, can automate the entire solution process from data reading to correction force verification by writing batch processing file code, effectively reducing labor and time costs.

[0056] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used in the operation of an active correction method for a reflective mirror surface.

[0057] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be Random Access Memory (RAM) or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the active correction method for a reflective mirror shape in the above embodiments.

[0058] 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, optical storage, etc.) containing computer-usable program code.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] This invention also provides a computer program product, which is used to execute any of the above-described active mirror shape correction methods. Since the computer program product provided by this invention belongs to the same inventive concept as the above-described active mirror shape correction method, it possesses all the advantages of the above-described active mirror shape correction method. Therefore, the beneficial effects of the computer program product provided by this invention will not be elaborated upon here.

[0063] In this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0064] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the scope of the technology disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention.

Claims

1. A method of active correction of a mirror surface figure, characterized in that, The application relates to a mirror surface active correction method. The application comprises the following steps: a parameterized finite element model of a mirror is constructed, and the model contains a plurality of active correction points; initial displacement amounts of nodes of the mirror surface when no correction force is applied are obtained; unit correction forces are sequentially applied to each active correction point, displacement amounts of the nodes of the mirror surface after each unit correction force is applied are obtained, differences between the displacement amounts and the initial displacement amounts are calculated, and a sensitivity matrix reflecting a mapping relationship between correction forces and node displacements is constructed based on the differences; sensitive features of the nodes are calculated based on the sensitivity matrix, weights of the nodes are assigned according to the sensitive features, and a weight matrix is constructed based on the weights of the nodes; target correction forces acting on the active correction points are calculated by using a weighted generalized inverse method based on the weight matrix; 2. The method of claim 1, wherein the target correction forces are applied to the finite element model or the entity of the mirror to correct the mirror surface shape. The sensitivity matrix reflecting the mapping relationship between the correction forces and the node displacements is constructed based on the differences, and specifically comprises the following steps:

3. The method of claim 1, wherein the mirror surface shape is actively corrected by a plurality of actuators. displacement difference values of each node corresponding to unit correction forces of all the active correction points are arranged into a row, thereby forming the sensitivity matrix. The sensitive features include total sensitivity and sensitivity dispersion degree of the nodes; the total sensitivity is obtained by calculating the sum of absolute values of row vector elements corresponding to the nodes in the sensitivity matrix; 4. The method of claim 3, wherein the mirror surface shape is determined by a computer program. the sensitivity dispersion degree is obtained by calculating the standard deviation of row vector elements corresponding to the nodes in the sensitivity matrix. The weights of the nodes are assigned according to the sensitive features, and specifically comprise the following steps: the total sensitivity and the sensitivity dispersion degree are normalized respectively; the normalized total sensitivity and the normalized sensitivity dispersion degree are weighted and fused to obtain initial weights of the nodes; 5. The active correction method for the surface shape of a reflective mirror according to claim 4, characterized in that, the initial weights are mapped to a preset engineering safety interval to obtain final weights of the nodes. wherein, is the initial weight of the first node; is the initial weight of the first node; is the total sensitivity of the first node; is the normalized total sensitivity of the first node; is the normalized sensitivity dispersion of the first node, is the normalized sensitivity dispersion of the first node, is the weighting coefficient.

6. The method of claim 1, wherein The calculation formula of the weighted fusion of the normalized total sensitivity and the normalized sensitivity dispersion degree is as follows:

7. The method of claim 1, wherein the mirror surface shape is actively corrected by a plurality of actuators. The weight matrix is a diagonal weight matrix, and elements on the diagonal line of the diagonal weight matrix are the final weights corresponding to the nodes. The target correction forces acting on the active correction points are calculated by using the weighted generalized inverse method, and specifically comprise the following steps:

8. The active surface shape correction method for a reflective mirror according to claim 7, characterized in that, an objective function of minimizing residual surface shape errors weighted by the weight matrix is taken as a target function, and an analytical solution of the target correction forces is obtained by solving the target function. wherein, is a target correction force, is a sensitivity matrix, is a weight matrix, is an initial surface error vector determined based on the initial displacement amount.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The analytical solution of the target correction forces is calculated by the following formula:

10. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 9. The processor executes the computer program to realize the mirror surface active correction method according to any one of claims 1 to 8. The computer program is executed by the processor to realize the mirror surface active correction method according to any one of claims 1 to 8.

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