Analysis Method for the Change Amount of the Curvature Radius of a Curvature-Adjustable Sub-Mirror and the Precision of Surface Actuation

Abstract

The present invention relates to the technical field of space camera mirror analysis, and specifically provides a method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of an adjustable curvature sub-mirror, including the steps of: creating a finite element analysis model, creating dr and two variables of RMS, and generating a finite element model calculation file; extracting n the numbers of i nodes and the corresponding node spatial coordinates ( x i , y i , z i ); constructing a first relationship function between dr and d z ; constructing a mirror surface curvature radius correction function; constructing a second relationship function between RMS and #imgabs0#; integrating the three functions into the finite element model calculation file of the adjustable curvature sub-mirror; submitting the finite element solver for calculation to obtain dr and RMS; effectively saving the conversion and reading / writing time of the sub-mirror surface node coordinates and displacement data formats, improving the iterative optimization efficiency of the mirror design, and having significant engineering significance for the optimized design of segmented and spliced mirrors.

Description

Technical Field

[0001] The present invention relates to the technical field of space camera mirror analysis, and specifically provides a method, device, and computer-readable medium for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of a curvature-adjustable sub-mirror. Background Technique

[0002] The segmented and spliced mirror is an important development trend of ultra-large-aperture optical remote sensors. The segmented and spliced mirror refers to designing the primary mirror into multiple sub-mirror components, which are actively adjusted by sub-mirror actuators and spliced into a complete mirror surface.

[0003] In actual engineering, it is very difficult to ensure the consistency of the curvature of each sub-mirror during the processing and manufacturing of the sub-mirrors, which is extremely likely to cause the optical system to be out of phase. Therefore, for the segmented and spliced mirror, it is very necessary to correct the curvature of each sub-mirror.

[0004] The curvature-adjustable sub-mirror is different from the traditional mirror. During the process of curvature correction, it is necessary to ensure that the sub-mirror has sufficient surface shape accuracy. Therefore, the ratio of the RMS value of the surface shape actuation accuracy of the sub-mirror to the change amount of the sub-mirror curvature radius is the most critical index reflecting the curvature correction performance of the sub-mirror, which is directly related to the imaging quality of the ultra-large-aperture optical remote sensor. In the process of sub-mirror design, simulation analysis is usually carried out by the finite element method. Existing commercial finite element analysis software does not yet have the function of analyzing the change amount of the sub-mirror curvature radius and the degradation amount of the curvature correction surface shape. The traditional analysis method exports the sub-mirror surface nodal coordinates and displacement data in the commercial finite element software to a calculation program for calculation to obtain the analysis results of the change amount of the sub-mirror curvature radius and the surface shape accuracy. Due to the non-uniform data interfaces between the commercial finite element software and the numerical calculation program, and the huge amount of sub-mirror surface nodal coordinates and displacement data, the conversion of data file formats and data reading and writing waste a lot of time, seriously restricting the iterative optimization efficiency of the design of the segmented and spliced mirror. Summary of the Invention

[0005] To solve the above problems, the present invention provides a method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of a curvature-adjustable sub-mirror, constructs a finite element analysis model of the curvature-adjustable sub-mirror, and generates a calculation file for the finite element model of the sub-mirror.

[0006] The present invention provides a method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of a curvature-adjustable sub-mirror, including the steps of:

[0007] S1. Create a finite element analysis model of the curvature-adjustable sub-mirror, create two variables of the change amount of the curvature radius dr and the RMS of the surface shape actuation accuracy in the finite element model of the curvature-adjustable sub-mirror, and generate a calculation file for the finite element model of the curvature-adjustable sub-mirror;

[0008] S2. Extract all n the numbers of the nodes i located on the surface of the curvature-adjustable secondary mirror, i extract the spatial coordinates of the nodes corresponding to the node numbers x i , y i , z i );

[0009] S3. Construct a first relationship function between the change in the radius of curvature x i , y i , z i and the displacement in the sagittal direction of all dr n n nodes; d z The first relationship function is as follows:

[0010] S4. Construct a mirror surface radius of curvature correction function according to the node numbers i , the spatial coordinates of the nodes x i , y i , z i );

[0011] S5. Construct a second relationship function between the surface shape actuation accuracy RMS and the displacement in the sagittal direction of the nodes on the secondary mirror surface after curvature correction according to the node numbers i ; The second relationship function is as follows:

[0012] S6. Integrate the first relationship function, the mirror surface radius of curvature correction function, and the second relationship function into the finite element model calculation file of the curvature-adjustable secondary mirror;

[0013] S7. Submit the integrated finite element analysis calculation file of the curvature-adjustable secondary mirror to the finite element solver for calculation to obtain the change in the radius of curvature dr and the surface shape actuation accuracy RMS.

[0014] Furthermore, the expression of the first relationship function between the change in the radius of curvature dr and the displacement in the sagittal direction of all n nodes d z is:

[0015] .

[0016] Furthermore, alln The displacement of the node in the sagittal direction d z The expression is:

[0017] ;

[0018] The expression of the free-form surface equation of the mirror surface of the curvature-adjustable sub-mirror along the Z-axis direction is:

[0019] ;

[0020] Among them, z i is the sag of the mirror surface at the point ( x i , y i ), represents the spherical sag part, R is the radius of curvature of the mirror surface; F ( x i , y i ) is the free-form surface sag correction part, indicating the deviation of the theoretical mirror surface from the sphere;

[0021] Taking the partial derivative of the above formula with respect to the radius of curvature R of the mirror surface, we can get:

[0022] ;

[0023] The expression of the displacement of the node i in the sagittal direction caused by the curvature change is:

[0024] ;

[0025] The square difference between the node sag displacement of the actual mirror surface and the node sag displacement caused by the curvature change is expressed as:

[0026] ;

[0027] Taking the partial derivative of the above formula E with respect to dr , and setting the partial derivative with respect to dr to 0, we obtain the expression of the first relationship function between the change in the radius of curvature dr and the displacements d z of the sagittal directions of all n nodes as:

[0028] .

[0029] Further, the expression of the mirror surface curvature radius correction function is:

[0030] ;

[0031] wherein, is the displacement in the sagittal direction after the curvature correction of the mirror node on the sub - mirror.

[0032] Further, the expression of the second relationship function between the surface shape actuation accuracy RMS and the displacement in the sagittal direction after the curvature correction of the mirror node on the sub - mirror is:

[0033] .

[0034] The present invention also provides an analysis device for the change amount of the curvature radius and the surface shape actuation accuracy of a curvature - adjustable sub - mirror, including:

[0035] An analysis model creation module, configured to create a finite - element analysis model of the curvature - adjustable sub - mirror;

[0036] A calculation file generation module, configured to create two variables, namely the change amount of the curvature radius dr and the surface shape actuation accuracy RMS, in the finite - element model of the curvature - adjustable sub - mirror, and generate a calculation file for the finite - element model of the curvature - adjustable sub - mirror;

[0037] A node extraction module, configured to extract the numbers of all n nodes located on the mirror surface of the curvature - adjustable sub - mirror i , and extract the spatial coordinates of the nodes corresponding to the node numbers i ([ x i , y i , z i ) ;

[0038] A first function construction module, configured to construct a first relationship function between the change amount of the curvature radius x i , y i , z i ) and the displacement in the sagittal direction dr of all n nodes; d z z

[0039] A second function construction module, configured to construct a second relationship function according to the node numbers i , the spatial coordinates of the nodes ([ x i , yi , z i )Construct a mirror surface curvature radius correction function;

[0040] A third function construction module, configured to construct a second relationship function between the RMS of the surface shape actuation accuracy and the displacement in the sagittal direction of the curvature correction of the sub - mirror surface nodes according to the node numbers i , ;

[0041] An integrated calculation module, configured to integrate the first relationship function, the mirror surface curvature radius correction function, and the second relationship function into the finite - element model calculation file of the curvature - adjustable sub - mirror; and submit the integrated finite - element analysis calculation file of the curvature - adjustable sub - mirror to a finite - element solver for calculation to obtain the change amount of the curvature radius dr and the RMS of the surface shape actuation accuracy.

[0042] The present invention further provides a computer device, including:

[0043] At least one processor; and

[0044] A memory communicatively connected to the at least one processor; wherein,

[0045] the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of the curvature - adjustable sub - mirror of the present invention.

[0046] The present invention further provides a non - transitory computer - readable storage medium storing computer instructions, and the computer instructions are used to make a computer execute the method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of the curvature - adjustable sub - mirror of the present invention.

[0047] The present invention provides a method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of a curvature - adjustable sub - mirror. By constructing a finite - element analysis model of the curvature - adjustable sub - mirror, a finite - element model calculation file of the sub - mirror is generated; a function for solving the change amount of the sub - mirror curvature radius, a mirror surface curvature correction function, and a function for solving the RMS value of the surface shape actuation accuracy are constructed and integrated into the finite - element model calculation file of the sub - mirror; and the finite - element solver is submitted for calculation. While solving the node displacement data of the sub - mirror finite - element model, the change amount of the sub - mirror curvature radius and the RMS value of the surface shape actuation accuracy are directly obtained. It effectively saves the time for converting and reading and writing the sub - mirror surface node coordinates and displacement data formats, improves the iterative optimization efficiency of the reflector design, and has significant engineering significance for the optimized design of segmented and spliced reflectors. Description of the Drawings

[0048] Figure 1 It is a schematic flowchart of the method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of the curvature-adjustable sub-mirror in a specific embodiment of the present invention;

[0049] Figure 2 It is a schematic diagram of an excerpt of the first relationship function in a specific embodiment of the present invention;

[0050] Figure 3 It is a schematic diagram of an excerpt of the mirror surface curvature radius correction function in a specific embodiment of the present invention;

[0051] Figure 4 It is a schematic diagram of an excerpt of the second relationship function in a specific embodiment of the present invention;

[0052] Figure 5 It is a schematic diagram of the analysis result in a specific embodiment of the present invention;

[0053] Figure 6 It is a structural block diagram of a computer device in a specific embodiment of the present invention. Specific Embodiments

[0054] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation to the present invention.

[0055] In specific embodiments, the present invention provides a method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of a curvature-adjustable sub-mirror, including the steps of:

[0056] S1. Create a finite element analysis model of the curvature-adjustable sub-mirror, create two variables of the change amount of the curvature radius dr and the surface shape actuation accuracy RMS in the finite element model of the curvature-adjustable sub-mirror, and generate a calculation file of the finite element model of the curvature-adjustable sub-mirror;

[0057] S2. Extract the numbers n of all i nodes located on the mirror surface of the curvature-adjustable sub-mirror i , and extract the corresponding node spatial coordinates ([[]] x i , y i , z i );

[0058] S3. According to the node spatial coordinates ([[]] x i , y i , z i)Construct the variation of the radius of curvature dr with the displacement in the sagittal direction of all n nodes to obtain a first relational function; d z

[0059] In a specific embodiment, the displacement in the sagittal direction of all n nodes is d z expressed as:

[0060] ;

[0061] wherein, represents the displacement in the sagittal direction of the nodes corresponding to all n mirror nodes.

[0062] The expression of the free-form surface equation of the mirror surface of the curvature-adjustable sub-mirror along the optical axis, i.e., the Z-axis direction, is:

[0063] ;

[0064] wherein, z i is the sag of the mirror surface at the point ([[]] x i , y i ), represents the spherical sag part, R is the radius of curvature of the mirror surface; F ( x i , y i ) is the free-form surface sag correction part, indicating the deviation of the theoretical mirror surface from the spherical surface;

[0065] Taking the partial derivative of the above formula with respect to the radius of curvature R of the mirror surface, we can obtain:

[0066] ;

[0067] The expression of the displacement in the sagittal direction of the node i caused by the curvature change is:

[0068] ;

[0069] The square difference between the node sag displacement of the actual mirror surface and the node sag displacement caused by the curvature change is expressed as:

[0070] ;

[0071] Solving the above formula E with respect to dr ​The partial derivative with respect to dr is set to 0, that is , and the change amount of the curvature radius dr and the displacement in the sagittal direction of all n nodes d z The expression of the first relationship function between them is:

[0072] .

[0073] S4. Construct a mirror surface curvature radius correction function according to the node number i , the node space coordinates ( x i , y i , z i );

[0074] In a specific implementation manner, the expression of the mirror surface curvature radius correction function is:

[0075] ;

[0076] wherein, is the displacement in the sagittal direction after the curvature correction of the sub - mirror surface node.

[0077] S5. Construct a second relationship function between the surface shape actuation accuracy RMS and the displacement in the sagittal direction after the curvature correction of the sub - mirror surface node according to the node number i ; In a specific implementation manner, the expression of the second relationship function between the surface shape actuation accuracy RMS and the displacement in the sagittal direction after the curvature correction of the sub - mirror surface node

[0078] is: The expression of the second relationship function is:

[0079] .

[0080] S6. Integrate the first relationship function, the mirror surface curvature radius correction function, and the second relationship function into the finite element model calculation file of the curvature - adjustable sub - mirror;

[0081] S7. Submit the integrated finite element analysis calculation file of the curvature - adjustable sub - mirror to the finite element solver for calculation. While solving the node displacements of the sub - mirror finite element model, automatically calculate the RMS value of the change amount of the sub - mirror curvature radius and the surface shape actuation error, that is, obtain the change amount of the curvature radius dr and the surface shape actuation accuracy RMS.

[0082] The traditional analysis method generally includes the following steps: 1) constructing a sub-mirror finite element model and generating a sub-mirror finite element model calculation file; 2) submitting the sub-mirror finite element model calculation file to a finite element solver for calculation; 3) extracting the sub-mirror mirror node coordinates and displacement data; 4) exporting the data to a calculation program for calculation to obtain the sub-mirror curvature radius change and surface shape accuracy analysis results; and the analysis method provided by the specific implementation method of the present invention: creatively creating three functions, and integrating the curvature-adjustable sub-mirror curvature radius change solution function, the mirror surface curvature correction function, and the surface shape actuation accuracy RMS value solution function into step 1) of the traditional method to generate a sub-mirror finite element model calculation file; submitting it to a finite element solver for calculation, and while obtaining the node displacement data, directly obtaining the sub-mirror curvature radius change and surface shape accuracy analysis results.

[0083] In a specific embodiment, the present invention further provides a device for analyzing the change in the curvature radius of a sub-mirror with adjustable curvature and the precision of actuating a surface shape, which is used to implement the method for analyzing the change in the curvature radius of a sub-mirror with adjustable curvature and the precision of actuating a surface shape provided by the present invention, and the device comprises:

[0084] An analysis model creation module, used to create a finite element analysis model of a sub-mirror with adjustable curvature;

[0085] A calculation file generation module for creating a curvature radius variation in the curvature adjustable sub-mirror finite element model dr and surface shape actuation accuracy RMS, generate a calculation file of the finite element model of the curvature-adjustable sub-mirror;

[0086] A node extraction module is used to extract all nodes located on the mirror surface of the curvature adjustable sub-mirror. n The number of nodes i , extract the node number i The corresponding node space coordinates ( x i , y i , z i ) ;

[0087] The first function building module is used to construct a function according to the node space coordinates ( x i , y i , z i ) construct the curvature radius variation dr With all n Displacement of the nodes in the direction of the sagittal height d z The first relationship function between

[0088] The second function construction module is used to construct a mirror surface curvature radius correction function according to the node number i and the node spatial coordinates ( x i , y i , z i );

[0089] The third function construction module is used to construct a second relationship function between the surface shape actuation accuracy RMS and the displacement in the sagittal direction after curvature correction of the sub - mirror surface nodes according to the node number i ;

[0090] The integrated calculation module is used to integrate the first relationship function, the mirror surface curvature radius correction function and the second relationship function into the finite element model calculation file of the curvature - adjustable sub - mirror; and submit the integrated finite element analysis calculation file of the curvature - adjustable sub - mirror to the finite element solver for calculation to obtain the change amount of the curvature radius dr and the surface shape actuation accuracy RMS.

[0091]

[0092]

[0093] In a specific embodiment of the present invention, a computer device is further provided, including:

[0094] at least one processor; and

[0095] a memory communicatively connected to the at least one processor; wherein,

[0096] the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of the curvature - adjustable sub - mirror of the present invention.

[0097]

[0098] Figure 1 Embodiment

[0098] As Figure 1As shown in the figure, it is a schematic flowchart of the method for analyzing the change amount of the curvature radius of the curvature-adjustable secondary mirror and the surface shape actuation accuracy in a specific embodiment of the present invention. It can be seen from the figure that the analysis method of the embodiment of the present invention includes: creating a finite element analysis model of the curvature-adjustable secondary mirror. Create two variables in the finite element model of the secondary mirror, which respectively represent the change amount of the curvature radius and the RMS value of the surface shape actuation accuracy, and generate a calculation file for the finite element model of the secondary mirror; extract the node numbers and node coordinates of the secondary mirror surface; construct a function representing the change amount of the curvature radius of the secondary mirror; construct a curvature correction function in the sagittal height direction of the secondary mirror surface; construct a function for solving the RMS value of the surface shape actuation error of the secondary mirror; integrate the function for solving the change amount of the curvature radius of the secondary mirror, the mirror surface curvature correction function, and the function for solving the RMS value of the surface shape actuation accuracy into the calculation file of the finite element model of the secondary mirror; submit the finite element solver for calculation, and directly obtain the RMS values of the change amount of the curvature radius of the secondary mirror and the surface shape actuation error while solving the node displacements of the finite element model of the secondary mirror.

[0099] Specifically, the method for analyzing the change amount of the curvature radius of the curvature-adjustable secondary mirror and the surface shape actuation accuracy in this embodiment includes the following steps:

[0100] Step 1: Create a finite element analysis model of the curvature-adjustable secondary mirror, and the working condition of the finite element model is the secondary mirror curvature correction working condition; create variables in the finite element model of the secondary mirror dr、 RMS, where dr represents the change amount of the curvature radius, and RMS represents the RMS value of the surface shape actuation accuracy, and generate a calculation file for the finite element model of the secondary mirror;

[0101] In this specific embodiment, a finite element analysis model of the curvature-adjustable secondary mirror is created through Patran software, and the working condition is the secondary mirror curvature correction working condition; by creating variables dr and RMS respectively in Step 1, where dr represents the change amount of the curvature radius, and RMS represents the RMS value of the surface shape actuation accuracy, and generate a bdf file (Nastran finite element solver calculation file) for the secondary mirror;

[0102] Step 2: Extract the numbers n of all i nodes located on the secondary mirror surface, and extract the node spatial coordinates ([[]] i corresponding to the node numbers x i , y i , z i );

[0103] In this specific embodiment, through Step 2, the range of the node numbers of 3182 nodes on the secondary mirror surface is extracted: 1 to 3182, and the node coordinates ( xi , y i , z i ).

[0104] Step 3: According to the sub-mirror surface node numbers described in Step 2 i , the node spatial coordinates ( x i , y i , z i ), construct a function about the variable dr that represents the change in the curvature radius dr of the sub-mirror surface and the displacement d z of all the nodes on the mirror surface in the sagittal direction, where

[0105] ;

[0106] In this specific embodiment, by constructing a function about the variable dr in Step 3 that represents the change in the curvature radius dr of the sub-mirror surface and the displacement d z of all 3182 nodes on the mirror surface in the sagittal direction, specifically as shown in Figure 2 .

[0107] Specifically, the general expression of the free-form surface equation of the sub-mirror surface along the optical axis, i.e., the Z-axis direction, can be represented as:

[0108] ;

[0109] where, z i is the sag of the mirror surface at the point ( x i , y i ), represents the spherical sag part, R is the curvature radius of the mirror surface; F ( x i , y i ) is the free-form surface sag correction part, representing the deviation of the theoretical mirror surface from the spherical surface.

[0110] Taking the partial derivative of the above equation with respect to the curvature radius R of the mirror surface, we can obtain:

[0111] ;

[0112] The node i displacement in the sagittal height direction caused by curvature change is expressed as:

[0113] ;

[0114] The square difference between the node sagittal height displacement of the actual mirror surface and the node sagittal height displacement caused by curvature change is expressed as:

[0115] ;

[0116] For the above formula E solve the partial derivative with respect to dr , and let the partial derivative with respect to dr be 0, that is , to obtain the change amount of the curvature radius dr and the sagittal height direction displacements d z of all n nodes, the expression of the first relationship function is:

[0117] .

[0118] The above formula is the least squares solution of the overdetermined equation of the sub - mirror curvature radius change, the sub - mirror mirror surface node sagittal height direction displacement, and the node coordinates, obtaining the function of the relationship between the sub - mirror mirror surface curvature radius change dr and the sagittal height direction displacements dz of all nodes on the mirror surface.

[0119] Step 4: Construct a sub - mirror mirror surface curvature radius change correction function according to the node number i , the node space coordinates ([[]] x i , y i , z i ):

[0120] ;

[0121] where is the sagittal height direction displacement after curvature correction of the sub - mirror mirror surface node i.

[0122] In this specific embodiment, through the sub - mirror mirror surface curvature radius change correction function constructed in Step 4, specifically as Figure 3 shown.

[0123] Step 5: According to the node number i , the relationship between the RMS value of the mirror surface shape actuation error and the sagittal height direction displacement of the sub - mirror mirror surface node after curvature correction is:

[0124] ;

[0125] In this specific embodiment, by constructing a function for solving the RMS value of the mirror surface shape actuation error in step 5, specifically as Figure 4 shown.

[0126] Specifically, the function for solving the RMS value of the surface shape error of the mirror optical surface:

[0127] ;

[0128] Step 6: Integrate the function for solving the change amount of the curvature radius of the curvature-adjustable sub-mirror, the mirror surface curvature correction function, and the function for solving the RMS value of the surface shape actuation accuracy into the calculation file of the sub-mirror finite element model;

[0129] Step 7: Submit the calculation to the finite element solver to obtain the RMS values of the change amount of the curvature radius of the sub-mirror and the surface shape actuation error.

[0130] In this specific embodiment, submit the calculation to the NASTRAN finite element solver. The calculation results are as Figure 5 shown. It can be seen from the figure that the change amount of the curvature radius of the sub-mirror mirror surface dr is 0.011937 mm, the RMS value of the surface shape actuation error is 231.29 nm / mm, and the analysis time is about 3 minutes.

[0131] Comparative example

[0132] By using the traditional analysis method, the calculation results such as the node coordinates and displacement data of the sub-mirror mirror surface in the finite element commercial software are exported to an external surface shape analysis program for calculation, and the analysis results of the change amount of the curvature radius of the sub-mirror and the surface shape accuracy are obtained.

[0133] The change amount of the curvature radius of the traditional analysis method dr is 0.01165 mm, the RMS value of the surface shape actuation error is 229.78 nm / mm, and the analysis time is about 5 minutes.

[0134] According to the above results, it can be seen that the results of the two analysis methods of the embodiment and the comparative example are consistent, which fully shows that the analysis method of the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy provided by the embodiment of the present invention is practical and effective, and the analysis speed of the method of the embodiment of the present invention is faster than that of the traditional method.

[0135] Due to the non-uniform data interfaces between finite element commercial software and numerical calculation programs in the traditional analysis method of the comparative example, the amount of data on the node coordinates and displacements of the sub-mirror mirror surface is huge, and a large amount of time is wasted on data file format conversion and data reading and writing. The present invention constructs a function for solving the change amount of the curvature radius of the sub-mirror with adjustable curvature through a finite element analysis software, integrates the function of analyzing the change amount of the curvature radius of the sub-mirror mirror surface and the surface shape accuracy into the calculation file of the sub-mirror finite element model, and directly obtains the change amount of the curvature radius of the sub-mirror mirror surface and the RMS value of the surface shape actuation accuracy while solving the node displacement data of the sub-mirror finite element model, effectively improving the optimization design efficiency of the segmented and spliced mirror.

[0136] Correspondingly, according to an embodiment of the present invention, the present invention also provides a computer device, a readable storage medium, and a computer program product.

[0137] Figure 6 It is a schematic structural diagram of a computer device 12 provided in an embodiment of the present invention. Figure 6 It shows a block diagram of an exemplary computer device 12 suitable for implementing the embodiments of the present invention. Figure 6 The shown computer device 12 is merely an example and should not impose any limitation on the functions and usage scope of the embodiments of the present invention.

[0138] As Figure 6 shown, the computer device 12 is presented in the form of a general-purpose computing device. The computer device 12 is intended to represent various forms of digital computers, such as, a laptop computer, a desktop computer, a workbench, a personal digital assistant, a server, a blade server, a mainframe computer, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as, a personal digital processor, a cellular phone, a smart phone, a wearable device, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described herein and / or claimed.

[0139] The components of the computer device 12 may include, but are not limited to: one or more processors or processing units 16, a system memory 28, and a bus 18 connecting different system components (including the system memory 28 and the processing unit 16).

[0140] The bus 18 represents one or more of several types of bus structures, including a memory bus or a memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the multiple bus structures. For example, these architectures include, but are not limited to, an Industry Standard Architecture (ISA) bus, a Micro Channel Architecture (MAC) bus, an Enhanced ISA bus, a Video Electronics Standards Association (VESA) local bus, and a Peripheral Component Interconnect (PCI) bus.

[0141] Computer device 12 typically includes a variety of computer system readable media. These media can be any available media accessible to computer device 12, including volatile and non-volatile media, removable and non-removable media.

[0142] System memory 28 can include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Computer device 12 can further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 can be used for reading and writing on non-removable, non-volatile magnetic media ( Figure 6 not shown, typically referred to as a "hard disk drive"). Although Figure 6 not shown in the figure, a disk drive for reading and writing on removable non-volatile disks (such as a "floppy disk"), and an optical disk drive for reading and writing on removable non-volatile optical disks (such as CD-ROM, DVD-ROM or other optical media) can be provided. In these cases, each drive can be connected to bus 18 through one or more data media interfaces. Memory 28 can include at least one program product having a set (such as at least one) of program modules configured to perform the functions of various embodiments of the present invention.

[0143] A program / utility 40 having a set (at least one) of program modules 42 can be stored, for example, in memory 28. Such program modules 42 include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 42 generally perform the functions and / or methods in the embodiments described in the present invention.

[0144] Computer device 12 can also communicate with one or more external devices 14 (such as a keyboard, a pointing device, a display 24, etc.), and can also communicate with one or more devices that enable a user to interact with the computer device 12, and / or communicate with any device that enables the computer device 12 to communicate with one or more other computing devices (such as a network card, a modem, etc.). Such communication can be carried out through an input / output (I / O) interface 22. And, computer device 12 can also communicate with one or more networks (such as a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) through a network adapter 20. As Figure 6As shown, network adapter 20 communicates with other modules of computer device 12 via bus 18. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with computer device 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0145] Processing unit 16 executes various functional applications and data processing by running programs stored in system memory 28, such as implementing the method for analyzing the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy provided by the embodiments of the present invention.

[0146] Embodiments of the present invention also provide a non-transitory computer-readable storage medium storing computer instructions, on which a computer program is stored, wherein when the program is executed by a processor, the method for analyzing the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy provided by all embodiments of the present application is implemented.

[0147] The computer storage medium of the embodiments of the present invention may adopt any combination of one or more computer-readable media. The computer-readable media may be a computer-readable signal medium or a computer-readable storage medium. More specific examples (non-exhaustive list) of the computer-readable storage medium include: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this document, the computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0148] The computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries the computer-readable program code. Such a propagated data signal may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The computer-readable signal medium may also be any computer-readable medium other than the computer-readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0149] The program code contained on a computer-readable medium can be transmitted using any appropriate medium, including but not limited to wireless, wire, optical fiber cable, RF, etc., or any suitable combination of the foregoing. The computer program code for performing the operations of the present invention can be written in one or more programming languages or combinations thereof, which include object-oriented programming languages such as Java, Smalltalk, C++, and also include conventional procedural programming languages - such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network including a local area network (LAN) or a wide area network (WAN), or, it can be connected to an external computer (for example, by using an Internet service provider to connect through the Internet).

[0150] An embodiment of the present invention also provides a computer program product, including a computer program, which when executed by a processor implements the method for analyzing the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy according to the above.

[0151] It should be understood that various forms of the flow shown above can be used, steps can be reordered, added, or deleted. For example, the steps described in the disclosure of the present invention can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and no limitation is made herein.

[0152] The above specific embodiments do not constitute a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of an adjustable curvature sub - mirror, characterized in that, The method for analyzing the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy includes the steps: S1. Create a finite element analysis model of the curvature-adjustable sub-mirror, and create two variables of the change amount of the radius of curvature and the RMS of the surface shape actuation accuracy in the finite element model of the curvature-adjustable sub-mirror to generate a calculation file for the finite element model of the curvature-adjustable sub-mirror; dr and the two variables of the surface shape actuation accuracy RMS, and generate a calculation file for the finite element model of the curvature-adjustable sub-mirror; S2. Extract all n the numbers of the nodes i located on the mirror surface of the curvature-adjustable secondary mirror, extract the node numbers i corresponding to the node space coordinates ( x i , y i , z i ); S3. Construct the variation x i , y i , z i of the radius of curvature dr and the first relationship function between the displacements n in the rise direction of all d z nodes; the first relationship function is: ； S4. According to the said node number i , the said node spatial coordinates ( x i , y i , z i ), construct a mirror curvature radius correction function; the mirror curvature radius correction function is: ； Among them, is the displacement in the sagittal height direction after the curvature correction of the mirror surface node of the sub-mirror; S5. According to the node numbers i , construct a second relationship function between the surface actuation accuracy RMS and the displacement in the sagittal height direction after curvature correction of the sub-mirror surface nodes ; the second relationship function is as follows: ； S6. Integrate the first relationship function, the mirror surface curvature radius correction function, and the second relationship function into the calculation file of the finite element model of the curvature-adjustable sub-mirror; S7. Submit the integrated finite element analysis calculation file of the curvature-adjustable sub-mirror to a finite element solver for calculation to obtain the change in the radius of curvature dr and the surface shape actuation accuracy RMS.

2. The method for analyzing the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy according to claim 1, wherein All of the n vertical displacement of the nodes d z is expressed as: ； The expression of the free-form surface equation of the mirror surface of the curvature-adjustable sub-mirror along the Z-axis direction is: ； Among them, z i is the sag of the mirror surface at the point ([[-]] x i , y i ), represents the spherical sag part, R is the radius of curvature of the mirror surface; F ( x i , y i ) is the free-form surface sag correction part, indicating the deviation of the theoretical mirror surface from the spherical surface; Take the partial derivative of the above formula with respect to the radius of curvature of the mirror surface R to obtain: ； Nodes caused by curvature change i The expression for the displacement of the rise direction is as follows: ； The square difference between the nodal elevation displacement of the actual mirror surface and the nodal elevation displacement caused by the curvature change is expressed as: ； Upward E Find out about dr The partial derivative of dr The partial derivative is 0, and the change in the radius of curvature is obtained. dr Displacement in the direction of the sagittal height of all n nodes d z The expression of the first relationship function between .

3. A device for analyzing the change amount of the curvature radius and the surface shape actuation accuracy of an adjustable curvature sub-mirror, characterized in that, The device for analyzing the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy includes: An analysis model creation module, configured to create a finite element analysis model of the curvature-adjustable sub-mirror; A calculation file generation module, configured to create two variables, namely, a change amount of the radius of curvature and an RMS of the surface shape actuation accuracy, in the finite element model of the curvature-adjustable secondary mirror, and generate a calculation file for the finite element model of the curvature-adjustable secondary mirror; dr and a surface shape actuation accuracy RMS, and generate a calculation file for the finite element model of the curvature-adjustable secondary mirror; Node extraction module, for extracting all n numbers of nodes i located on the mirror surface of the curvature-adjustable secondary mirror, i extracting the spatial coordinates of the nodes corresponding to the node numbers x i , y i , z i ) ; The first function construction module is used to construct the first relationship function between the change amount of the radius of curvature x i , y i , z i ) and the displacement in the sagitta direction of all dr nodes, and the first relationship function is: n The displacement in the sagitta direction of d z nodes, and the first relationship function is as follows: ； The second function construction module is used to build a mirror surface curvature radius correction function according to the node number i , the node space coordinates( x i , y i , z i ), and the mirror surface curvature radius correction function is as follows: ； Among them, is the displacement in the sagittal height direction after the curvature correction of the mirror surface node of the sub-mirror; The third function construction module is used to construct a second relationship function between the surface shape actuation accuracy RMS and the displacement in the sagittal direction after curvature correction of the sub-mirror surface nodes according to the node numbers i , where the second relationship function is : ； An integrated calculation module is used to integrate the first relationship function, the mirror surface curvature radius correction function, and the second relationship function into the finite element model calculation file of the curvature adjustable sub-mirror; and submit the integrated finite element analysis calculation file of the curvature adjustable sub-mirror to a finite element solver for calculation to obtain the change amount of the curvature radius dr and the surface shape actuation accuracy RMS.

4. A computer device, characterized in that, including: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method for analyzing the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy according to any one of claims 1 to 2.

5. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to execute the method for analyzing the change amount of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy according to any one of claims 1 to 2.

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