Optical-mechanical heat integration analysis method

Abstract

The invention relates to an optical-mechanical heat integration analysis method. The method comprises the following steps: utilizing MATLAB to drive optical analysis software ZEMAX to establish a mirror surface optical model and a transmission model; using MATLAB to drive finite element analysis software ANSYS Workbench, establishing an analysis item, reading an optical model, carrying out thermodynamic and static analysis, and extracting a finite element calculation result; calculating a PV value, an RMS value and rigid body displacement of mirror surface deformation by utilizing an MATLAB self-compiled interface program, and performing mirror surface fitting by taking a Zernike Zernike polynomial as a fitting basis function; and finally, generating a ZPL macro file according to the Zernike polynomial coefficient obtained by the interface program, calling the ZEMAX to read the ZPL macro file, and adding the Zernike polynomial coefficient to the original optical model in a disturbance form to obtain an optical evaluation result of the mirror surfaces such as MTF and the like. In order to facilitate use, the whole process is packaged into software, the environment temperature and the acceleration are input, and the PV value, the RMS value, the simulation cloud picture, the mirror fitting cloud picture and the MTF evaluation result picture are output.

Description

Technical Field

[0001] The present invention relates to the technical field of opto-mechanical-thermal integration analysis, and relates to an opto-mechanical-thermal integration analysis method. Background Art

[0002] High-precision optical systems are vulnerable to the influence of the space environment. When the environmental temperature changes, in addition to rigid body displacement, the optical surfaces of the optical system will also change accordingly. These deformations will all lead to deterioration of image quality. Therefore, athermal compensation design is required. During the process of athermal compensation design, engineers usually need to conduct opto-mechanical-thermal integration analysis to obtain the thermal-induced surface shape changes, which are used as reference indicators for athermal compensation design. This is of great significance for improving the comprehensive performance of space optical equipment and the design efficiency of space optical equipment.

[0003] Traditional opto-mechanical-thermal integration analysis has been proposed and used for a long time. There is a complete set of analysis processes and methods, which have been proven to be able to effectively assist in athermal design to reduce the problem of image quality degradation caused by thermal-induced surface shape changes. However, the traditional opto-mechanical-thermal integration analysis process at least involves the interaction of thermal analysis, structural analysis, and optical analysis software. The whole process is cumbersome and complex, and requires engineers with different professional backgrounds in opto-mechanics and thermotics to complete through multiple rounds of iterative optimization. The software interaction and information exchange among multiple disciplines have also been restricting the efficiency of opto-mechanical-thermal integration analysis. Although there are already software such as SigFit that provides opto-mechanical-thermal integration analysis interfaces, or software such as isight that assists in integration, which can realize the integration of software in various disciplines of opto-mechanics and thermotics and parametric modeling. However, the commonly used commercial integration platforms on the market have problems such as high learning costs, complex version requirements for analysis software in various disciplines, and limited callable functions. This makes analysts need to add more workload such as learning the use of the integration platform, adjusting the interfaces of each software, and debugging the integration software.

[0004] Therefore, it is necessary to further optimize the process of opto-mechanical-thermal integration analysis, and then promote the research on athermal optical design methods considering thermal-induced surface shape changes, simplify the steps of athermal verification in the early design process of optical designers, improve the design efficiency, and shorten the development cycle. Summary of the Invention

[0005] The purpose of the present invention is to provide an opto-mechanical-thermal integration analysis method, which solves the problem that the existing opto-mechanical-thermal integration analysis process needs to be completed through multiple rounds of iterative optimization by engineers with different professional backgrounds in opto-mechanics and thermotics, and the process is cumbersome and complex.

[0006] To achieve the above purpose, the technical solution of the present invention is:

[0007] An opto-mechanical-thermal integration analysis method, based on the secondary development of MATLAB, ANSYS Workbench, and ZEMAX, includes the following steps,

[0008] Step S100: Drive the optical analysis software ZEMAX for modeling through secondary development and save it in STEP format.

[0009] Step S200: Drive ANSYS Workbench through secondary development to complete steady-state heat and static analysis, obtain the calculation results of the thermal stress deformation of the mirror surface, and export the mirror surface grid nodes, coordinates, displacements, and node connection relationships.

[0010] Step S300: Use a self-written MATLAB program to establish an opto-mechanical interface model and obtain finite element analysis result data; use MATLAB to read the data, remove rigid body displacements, calculate the PV value and RMS value after deformation, and perform surface fitting based on Zernike polynomials to obtain the mirror surface deformation fitting cloud map and Zernike polynomial coefficients.

[0011] Step S400: Use MATLAB to automatically generate a ZPL macro file, call ZEMAX to run the macro file, realize the image quality evaluation of the deformed mirror surface, and output the MTF as the evaluation result.

[0012] Step S100 refers to driving the ZEMAX software to complete relevant steps through MATLAB programming, including the following steps.

[0013] Step S101: Open the ZEMAX software and create a new file.

[0014] Step S102: Set the radius of curvature, distance, field of view, and coordinate system data and generate a model.

[0015] Step S103: Export the STEP / STP model and save it in the corresponding directory.

[0016] The secondary development in Step S200 refers to using MATLAB to open ANSYS Workbench and read the wbjn file in the same directory. The wbjn file contains ironpython code that can run in the ANSYS environment and can drive ANSYS Workbench for thermal and structural analysis. It mainly includes the following steps.

[0017] Step S201: Open ANSYS Workbench, establish a new engineering project, including material, model, steady-state heat, and static analysis modules, and communicate data.

[0018] Step S202: Establish a new material and set the material parameters.

[0019] Step S203: Read the STEP / STP model exported by the optical software and only perform necessary geometric model preprocessing such as grouping and naming.

[0020] In step S204, enter Mechanical to complete material assignment, mesh generation, boundary condition setting, and solution setting;

[0021] In step S205, confirm the running program and export the mirror mesh node numbers, coordinates, displacement data, and connection relationships, and save them as a txt file;

[0022] In step S206, exit Mechanical and close Workbench.

[0023] The method for removing rigid body displacements in step S300 is as follows:

[0024] According to the connection relationships between nodes, the area weighting coefficient for each node is solved, which is determined by the ratio of the area corresponding to the node to the total area. The formula is as follows:

[0025]

[0026] In the formula, W i is the weighting coefficient of the i-th node. A i is the area corresponding to the i-th node; A total is the total area of all nodes or elements;

[0027] The method for calculating the best-fit rigid body motion with reference to SigFit is by least squares fitting; assuming there are displacement data of n nodes (i = 1, 2,..., n), the weighted objective function is expressed as follows:

[0028]

[0029] In the formula, z′ i is the displacement of the node after deformation, z i is the original displacement of the node, T z is the translation along the Z-axis, R(θ i ) is the rotation function related to the node, and W i is the area weighting of the node;

[0030] Generally, the rotation R z (θ) can be represented by a rotation matrix. Assuming we are in three-dimensional space, the rotation can be decomposed into rotations about the X, Y, and Z axes; for rotation about the Z-axis, the rotation matrix R z (θ) can be expressed as:

[0031]

[0032] The output results of rigid body motion include translation and rotation parameters, which are usually expressed as:

[0033]

[0034] where \(T\) represents translation and \(\theta\) represents rotation;

[0035] To find the optimal rigid body motion parameters \(T\) z and \(\theta\), the partial derivatives of the objective function \(S\) are calculated and set to zero:

[0036]

[0037] Among them, the methods for calculating the RMS value and the mirror surface PV value are as follows:

[0038] Assume that the original point set is \(P\) original , and the point set after correction is \(P\) corrected , then the deformation \(D\) can be expressed as:

[0039] \(D = P\) corrected - \(P\) original

[0040] The calculation formula for the root mean square \(RMS\) is:

[0041]

[0042] The calculation formula for the peak - valley value \(PV\) is:

[0043] \(PV=\max(D)-\min(D)\)

[0044] The method of surface shape fitting based on Zernike polynomials in step \(S300\) is to convert the corrected deformation data into coordinates in the polar coordinate system, where \(r\) is the polar radius and \(\theta\) is the polar angle;

[0045] Calculate the Zernike polynomial of the given order \(n\) and degree \(m\), and the specific calculation method is as follows:

[0046] \(z(r,\theta)=\sum\) n \(\sum\) m \([A\) nm \(P\) nm \((\rho)\cos(m\theta)+B\) nm \(P\) nm \((\rho)\sin(m\theta)][\)

[0047] In the above equation,

[0048]

[0049] \(\rho\) is the normalized radius, and its value at the aperture edge is \(1.0\); the coefficients of the Zernike polynomial are solved using the least squares method;

[0050] Normalize the solved standard Zernike polynomial coefficients for importing into Zemax for fitting. The normalization rules are as follows:

[0051]

[0052] Save the solved Zernike polynomial coefficients as a.txt document for subsequent generation of macro files. Then, generate a fitting cloud map of the flexible deformation based on the solved and normalized Zernike polynomial coefficients. Compare the original data with the fitted data, calculate the residuals at each node, and obtain a residual map to visualize the error or deviation between the fitted Zernike polynomial result and the original data.

[0053] Step S400 includes

[0054] Step S401: Read the Zernike polynomial coefficients calculated in step S300, generate and save them as a ZPL macro file. The document content is used to modify specific parts of the optical system using commands.

[0055] Step S402: Open the optical model file generated in the first step in ZEMAX, run the ZPL macro file, and add the Zernike polynomial coefficients as perturbations to the original optical model.

[0056] Step S403: Obtain the deformed model of the mirror, perform image quality evaluation such as MTF analysis according to requirements, export and save it as a png / jpg format file, and exit the software.

[0057] Step S500: Use MATLAB's APP Designer to encapsulate all the above steps and simplify the human-computer interaction process.

[0058] Step S500 includes

[0059] Step S501: Design the interface of the fast analysis software, including area settings for input and output and range settings for input values. The inputs are environmental temperature and acceleration settings, and the outputs include simulation cloud maps, PV values and RMS values, mirror surface fitting cloud maps, and MTF evaluation result maps.

[0060] Step S502: Set the callback function for the input to ensure that the input values can be accurately passed to the main function to drive the analysis.

[0061] Step S503: Set the callback function for the output to ensure that the output results can be accurately fed back to the corresponding interface.

[0062] Step S504: Complete the encapsulation and save it as a fast analysis software for the mirror's temperature variation.

[0063] The advantages of the present invention are as follows: 1. The present invention does not rely on the specific operations of the three software of optics, mechanics and thermotics, that is, it is not necessary for an optical designer to be proficient in complex issues such as simulation analysis and data interface processing of each software of optics, mechanics and thermotics. Only by changing the environmental temperature and acceleration, the integrated analysis process of optics, mechanics and thermotics can be automatically carried out under the code drive and the analysis results can be fed back. The operation is simple and the calculation efficiency is high. 2. The parameterization of the whole process ensures that the method of the present invention can be migrated to the integrated analysis of optics, mechanics and thermotics of various types of mirror surfaces by modifying geometric parameters, and can also consider conditions such as vibration and acceleration by modifying the code part that calls ANSYS Workbench, which simplifies the solution work for optical designers to consider the surface deformation caused by heat. 3. Based on the secondary development of software, using matlab instead of integrated software improves the flexibility of the integrated analysis model. According to specific requirements, various parameters such as model geometry, material properties, boundary conditions, and solution requirements can be modified to quickly adapt to different models and analysis requirements, and it is more convenient to migrate compared with the operation of the integrated platform. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is the flow chart of the present invention;

[0065] Figure 2 is the schematic diagram of the software interface of the present invention;

[0066] Figure 3 is the feedback result diagram presented on the software interface after the application of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0067] The present invention will be further described below with reference to the accompanying drawings. The accompanying drawings are only for illustrative purposes and should not be construed as a limitation of this patent.

[0068] In order to describe this embodiment more concisely, some components that are well-known to those skilled in the art but not relevant to the main content of this creation will be omitted in the drawings or descriptions. In addition, for the sake of convenience of expression, some components in the drawings will be omitted, enlarged or reduced, but this does not represent the size or all structures of the actual product.

[0069] The present invention discloses an integrated analysis method of optics, mechanics and thermotics, as Figure 1 shown, it is an integrated analysis method of optics, mechanics and thermotics based on the secondary development of MATLAB, ANSYS Workbench and ZEMAX, including the following steps,

[0070] Step S100, drive the optical analysis software ZEMAX to perform modeling through secondary development and save it in the STEP / STP format;

[0071] Preferably, step S100 refers to driving the ZEMAX software to complete relevant steps through MATLAB programming, including the following steps,

[0072] Step S101: Open the ZEMAX software and create a new file.

[0073] Step S102: Set data such as radius of curvature, distance, field of view, and coordinate system, and generate a model.

[0074] Step S103: Export the STEP / STP model and save it in the corresponding directory.

[0075] Step S200: Through secondary development, drive ANSYS Workbench to complete steady-state thermal and static analysis, obtain the calculation results of the thermal stress deformation of the mirror surface, and export the mirror surface grid nodes, coordinates, displacements, and node connection relationships.

[0076] The secondary development in Step S200 refers to using MATLAB to open ANSYS Workbench and read the wbjn file in the same directory. The wbjn file contains ironpython code that can run in the ANSYS environment and can drive ANSYS Workbench for thermal and structural analysis. It mainly includes the following steps:

[0077] Step S201: Open ANSYS Workbench, create a new engineering project, including material, model, steady-state thermal, and static analysis modules, and communicate data.

[0078] Step S202: Create a new material and set material parameters.

[0079] Step S203: Read the STEP model exported by the optical software and only perform necessary geometric model preprocessing such as grouping and naming.

[0080] Step S204: Enter Mechanical, complete material assignment, mesh generation, boundary condition setting, and solution setting.

[0081] Step S205: Confirm the running program, and export the mirror surface grid node numbers, coordinates, displacement data, and connection relationships, and save them as a txt file.

[0082] Step S206: Exit Mechanical and close Workbench.

[0083] Step S300: Use a self-written MATLAB program to establish an optomechanical interface model and obtain finite element analysis result data; use MATLAB to read the data, remove rigid body displacements, calculate the PV value and RMS value after deformation, and perform surface fitting based on the Zernike polynomial to obtain the mirror surface deformation fitting cloud map and Zernike polynomial coefficients.

[0084] In step S300, a self-written program in MATLAB is used to establish an optical-mechanical interface model, and the fitting results of the mirror surface thermal stress deformation are obtained, including the removal of rigid body displacement according to the finite element model analysis results, the calculation of the RMS value and the mirror surface PV value, and the Zernike polynomial fitting and coefficient solution. Among them, the method for removing rigid body displacement is as follows:

[0085] According to the connection relationship between nodes, the area weighting coefficient of each node is solved, which is determined by the ratio of the area corresponding to the node to the total area. The formula is as follows:

[0086]

[0087] In the formula, W i is the weighting coefficient of the i-th node. A i is the area corresponding to the i-th node. A total is the total area of all nodes or elements;

[0088] The method for calculating the best-fitting rigid body motion with reference to SigFit is to perform fitting by the least squares method. Assuming there are displacement data of n nodes z( = 1, 2,.., n), the weighted objective function is expressed as follows:

[0089]

[0090] In the formula, z′ i is the displacement of the node after deformation, z i is the original displacement of the node, T z is the translation along the Z-axis, R(θ i ) is the rotation function related to the node, and W i is the area weighting of the node.

[0091] Generally, the rotation R z (θ) can be represented by a rotation matrix. Assuming we are in a three-dimensional space, the rotation can be decomposed into rotations around the X, Y, and Z axes. For the rotation around the Z-axis, the rotation matrix R z (θ) can be expressed as:

[0092]

[0093] The output results of rigid body motion include translation and rotation parameters, which are usually expressed as:

[0094]

[0095] In the formula, T represents translation and θ represents rotation.

[0096] To find the optimal rigid body motion parameters T zand θ, calculate the partial derivative of the objective function S and set it to zero:

[0097]

[0098] Among them, the calculation method of RMS value and mirror PV value is:

[0099] Assume that the original point set is P original , the corrected point set is P corrected , then the deformation D can be expressed as:

[0100] D=P corrected -P original

[0101] The calculation formula of root mean square error RMS is:

[0102]

[0103] The calculation formula for the peak-to-valley value PV is:

[0104] PV=max(D)-min(D)

[0105] The method for performing surface shape fitting based on Zernike polynomials in step S300 is:

[0106] The corrected deformation data is converted into coordinates in the polar coordinate system, where r is the polar diameter and θ is the polar angle.

[0107] Calculate the Zernike polynomial of given order n and degree m as follows:

[0108] z(r,θ)=∑ n ∑ m [A nm P nm (ρ)Cos(mθ)+B nm P nm (ρ)Sim(mθ)]

[0109] In the formula,

[0110]

[0111] In the above equation, ρ is the normalized radius, which has a value of 1.0 at the edge of the aperture;

[0112] Solve the coefficients of Zernike polynomials using the least squares method;

[0113] The solved standard Zernike polynomial coefficients are normalized to be imported into Zemax for fitting. The normalization rules are as follows:

[0114]

[0115] Perform flexible deformation cloud map fitting and residual map fitting based on the solved Zernike polynomial coefficients to verify the reliability of the calculation, and export and save the normalized Zernike polynomial coefficients.

[0116] Save the solved Zernike polynomial coefficients as a.txt document for subsequent generation of the ZPL macro file. Then, generate a fitting cloud map of flexible deformation based on the solved and normalized Zernike polynomial coefficients. Compare the original data with the fitted data, calculate the residual of each node, and obtain the residual map to visualize the error or deviation between the fitted Zernike polynomial result and the original data.

[0117] Step S400: Automatically generate a ZPL macro file using MATLAB, call the ZEMAX to run the macro file to perform image quality evaluation on the deformed mirror surface, and output the MTF as the evaluation result.

[0118] Step S400 includes:

[0119] Step S401: Read the Zernike polynomial coefficients calculated in Step S300, generate and save them as a ZPL macro file. The document content is used to modify specific parts of the optical system using commands.

[0120] This includes adjusting the position, rotation, thickness, and surface shape of the optical elements, etc. Taking SURP 002, EDVA, -6.505643008208717E-12, 8 as an example, SURP is an instruction in the ZPL macro file for modifying a specific optical element. 002 specifies the number of the target optical element. EDVA indicates that these coefficients are adjusted in electron microscope volts. The following number -6.505643008208717E-12 is the coefficient of the Zernike polynomial, and the last number 8 refers to the index or serial number of the Zernike polynomial coefficient.

[0121] Step S402: Open the optical model file generated in the first step in ZEMAX, run the ZPL macro file, and add the Zernike polynomial coefficients as perturbations to the original optical model.

[0122] Step S403: Obtain the model of the deformed mirror, perform image quality evaluation such as MTF analysis according to requirements, export and save it as a png / jpg format file, and exit the software.

[0123] Step S500: Package all the above steps using MATLAB's APP Designer to simplify the human-computer interaction process.

[0124] Step S500 includes:

[0125] Step S501, design the interface of the fast analysis software. As shown in Figure 2 , it includes the area settings for input and output and the range settings for input values. The input is the environmental temperature setting, and the output includes simulation cloud maps, PV values, RMS values, mirror fitting cloud maps, and MTF evaluation result graphs.

[0126] Step S502, set the callback function for the input to ensure that the input value can be accurately passed to the main function to drive the analysis.

[0127] Step S503, set the callback function for the output to ensure that the output result can be accurately feedback to the corresponding interface. As shown in Figure 3 .

[0128] Step S504, complete the encapsulation and save it as the fast analysis software for the mirror's temperature variation.

[0129] The relevant technical explanations in the present invention are as follows:

[0130] Secondary development: That is, customizing and modifying on the existing software and expanding functions to achieve the desired functions. Taking ANSYS Workbench as an example, the secondary development of this software includes horizontal development, namely the ACT technology, which can be used for process automation development, etc.; and vertical development of ANSYS Multiphysics technology, which can be used for batch processing, etc.

[0131] Finite element analysis: Finite element analysis divides the continuum into finite parts and uses the stresses and strains of finite cells to reflect the stresses and strains of the continuum. In the present invention, both steady-state heat and static analysis adopt finite element analysis.

[0132] Rigid body displacement: It is the displacement generated when the shape of the mirror does not change.

[0133] Mirror deformation analysis: The mirror deformation analysis in the present invention includes PV and RMS values and the use of Zernike polynomial-based surface fitting to obtain the flexible deformation analysis of the mirror after removing the rigid body displacement.

[0134] In summary, the above are only the preferred embodiments of the present invention and are not used to limit the scope of implementation of the present invention. That is, all equivalent changes and modifications made according to the content of the patent application scope of the present invention should fall within the technical scope of the present invention.

Claims

1. An optical-mechanical-thermal integration analysis method based on secondary development of MATLAB, ANSYS Workbench and ZEMAX, characterized by: The following steps are included: Step S100, modeling is performed by driving the optical analysis software ZEMAX through secondary development and saving in STEP format; Step S200, driving ANSYS Workbench through secondary development to complete steady-state thermal and static analysis, obtain the calculation results of thermally induced stress deformation of the mirror surface, and derive the mirror surface mesh nodes, coordinates, displacements and node connection relationships; Step S300, using MATLAB to create an optical-mechanical interface model; The finite element analysis result data was read using MATLAB, the rigid body displacement was removed, the PV value and RMS value after deformation were calculated, the surface shape was fitted based on the Zernike polynomial, and the mirror deformation fitting cloud map and Zernike polynomial coefficients were obtained; Step S400, using MATLAB to automatically generate a ZPL macro file, calling ZEMAX to run the macro file, implementing image quality evaluation for the deformed mirror surface, and outputting MTF as the evaluation result.

2. The optical-mechanical-thermal integration analysis method according to claim 1, characterized in that: Step S100 is to drive ZEMAX software to complete relevant steps through MATLAB programming. The following steps are included: Step S101, open ZEMAX software and create a new file; Step S102, setting the curvature radius, distance, field of view and coordinate system data and generating a model; Step S103, export the STEP / STP model and save it in a corresponding directory.

3. The optical-mechanical-thermal integration analysis method according to claim 1, characterized in that: The secondary development in step S200 refers to using MATLAB to open ANSYS Workbench and read the wbjn file in the same directory. The wbjn file contains ironpython code that can run in the ANSYS environment and can drive ANSYS Workbench to perform thermal and structural analysis. It mainly includes the following steps: Step S201, open ANSYS Workbench, create a new engineering project, including materials, models, steady-state thermal and static analysis modules, and communicate data; Step S202, creating a new material and setting material parameters; Step S203, reading the STEP / STP model exported by the optical software and performing necessary geometric model pre-processing such as grouping and naming; Step S204, enter Mechanical, complete material assignment, mesh division, boundary condition setting and solution setting; Step S205, confirm the running of the program, and export the analysis results, including the mirror mesh node number, coordinates, displacement data and connection relationship, and save them as a txt file; Step S206, exit Mechanical and close Workbench.

4. The optical-mechanical-thermal integration analysis method according to claim 1, characterized in that: The method for removing the rigid body displacement in step S300 is: According to the connection relationship between nodes, the area weighted coefficient of each node is solved, which is determined by the ratio of the area corresponding to the node to the total area. The formula is as follows: Where W i is the weight coefficient of the ith node, A i is the area corresponding to the i-th node; A total is the total area of ​​all nodes or elements; The method of calculating the best fitting rigid body motion with reference to SigFit is to fit it by the least square method. Assuming that there are n node displacement data 2 (=1, 2, ..:, n), the weighted objective function is expressed as follows: In the formula, z′ i is the displacement of the node after deformation, z i is the original displacement of the node, T z is the translation along the Z axis, R(θ i ) is the rotation function associated with the node, W i is the area weight of the node; Usually, the rotation R z (θ) can be represented by a rotation matrix. Assuming we are in three-dimensional space, the rotation can be decomposed into rotations around the X, Y, and Z axes. For rotation around the Z axis, the rotation matrix R z (θ) can be expressed as, The output of rigid body motion includes translation and rotation parameters, usually expressed as: Where T represents translation and θ represents rotation; In order to find the optimal rigid body motion parameter T z and θ, calculate the partial derivative of the objective function S and set it to zero: Among them, the calculation method of RMS value and mirror PV value is: Assume that the original point set is P original , the corrected point set is P corrected , then the deformation D can be expressed as: D=P corrected -P original The calculation formula of root mean square error RMS is: The calculation formula for the peak-to-valley value PV is: PV=max(D)-min(D) 5. The optical-mechanical-thermal integration analysis method according to claim 1, characterized in that: The method for performing surface fitting based on Zernike polynomials in step S300 is: The corrected deformation data is converted into coordinates in the polar coordinate system, where r is the polar diameter and θ is the polar angle; Calculate the Zernike polynomial of given order n and degree m as follows: z(r,θ)=∑ n ∑ m [A nm P nm (ρ)Cos(mθ)+E nm P nm (ρ)Sin(mθ)] In the formula, In the above equation, ρ is the normalized radius, which is 1.0 at the edge of the aperture; the coefficients of the Zernike polynomial are solved using the least squares method; The solved standard Zernike polynomial coefficients are normalized to be imported into Zemax for fitting. The normalization rules are as follows:

6. The optical-mechanical-thermal integration analysis method according to claim 5, characterized in that: The solved Zernike polynomial coefficients are saved as a .txt document for subsequent generation of macro files. Then, a fitting cloud map of flexible deformation is generated based on the solved and normalized Zernike polynomial coefficients. The original data is compared with the fitted data, and the residual of each node is calculated to obtain a residual map, which is used to visualize the error or deviation between the fitted Zernike polynomial result and the original data.

7. The optical-mechanical-thermal integration analysis method according to claim 6, characterized in that: Step S400 includes: Step S401, reading the Zernike polynomial coefficients calculated in step S300, generating and saving a ZPL macro file based on the coefficients, wherein the document content is used to modify a specific part of the optical system using commands; Step S402, opening the optical model file generated in the first step in ZEMAX, running the ZPL macro file, and adding the Zernike polynomial coefficients as disturbances to the original optical model; Step S403, obtain the model of the mirror after deformation, perform image quality evaluation such as MTF analysis according to requirements, export and save it as a file in png / jpg format, and exit the software.

8. The optical-mechanical-thermal integration analysis method according to claim 1, characterized in that: The method further includes step S500, in which all the above steps are encapsulated by using APP Designer of MATLAB to simplify the human-computer interaction process.

9. The optical-mechanical-thermal integration analysis method according to claim 8, characterized in that: Step S500 also includes, Step S501, designing the interface of the rapid analysis software, including the input and output area settings and the input value range settings, the input is the ambient temperature and acceleration settings, and the output includes the simulation cloud map, PV value and RMS value, mirror fitting cloud map, and MTF evaluation result map; Step S502, setting the input callback function to ensure that the input value can be accurately passed to the main function to drive the analysis; Step S503, setting the output callback function to ensure that the output result can be accurately fed back to the corresponding interface; Step S504, completing the packaging and saving it as software for rapid analysis of mirror surface changes with temperature.

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