Method for analyzing curvature radius variation and surface shape actuating precision of curvature-adjustable sub-mirror

Abstract

The invention relates to the technical field of space camera reflector analysis, and particularly provides a curvature-adjustable sub-mirror curvature radius variation and surface shape actuation precision analysis method, which comprises the following steps: creating a finite element analysis model, creating two variables of dr and RMS, and generating a finite element model calculation file; extracting serial numbers i of n nodes and corresponding node space coordinates (xi, yi, zi); constructing a first relation function between the dr and the dz; constructing a mirror curvature radius correction function; a second relation function between the RMS and # imgabs0 # is constructed; integrating the three functions into a curvature-adjustable sub-mirror finite element model calculation file; submitting to a finite element solver for calculation to obtain dr and RMS; according to the method, the sub-mirror surface node coordinate and displacement data format conversion and read-write time is effectively saved, the iterative optimization efficiency of the reflector design is improved, and the method has remarkable engineering significance for the optimization design of the block splicing type reflector.

Description

Technical Field

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

[0002] The block-jointed reflector is an important development trend of ultra-large aperture optical remote sensors. The block-jointed reflector refers to the design of the main reflector into multiple sub-mirror components, which are actively adjusted by the sub-mirror actuator and joined into a complete mirror surface.

[0003] In actual engineering, it is difficult to ensure the consistency of the curvature of each sub-mirror during the processing and manufacturing of the sub-mirrors, which can easily cause the optical system to be out of phase. Therefore, for the block-jointed reflector, it is very necessary to calibrate the curvature of each sub-mirror.

[0004] The curvature-adjustable sub-mirror is different from the traditional reflector. In the process of curvature correction, it is necessary to ensure that the sub-mirror has sufficient surface accuracy. Therefore, the ratio of the RMS value of the surface actuation accuracy of the sub-mirror to the change in the curvature radius of the sub-mirror is the most critical indicator 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 design process of the sub-mirror, simulation analysis is usually performed using the finite element method. The existing commercial finite element analysis software does not yet have the function of analyzing the change in the curvature radius of the sub-mirror and the curvature correction surface degradation. The traditional analysis method exports the sub-mirror mirror node coordinates and displacement data in the finite element commercial software to the calculation program for calculation, and obtains the sub-mirror curvature radius change and surface accuracy analysis results. Due to the inconsistency of the data interface between the finite element commercial software and the numerical calculation program, the amount of sub-mirror mirror node coordinates and displacement data is huge, and a lot of time is wasted on data file format conversion and data reading and writing, which seriously restricts the iterative optimization efficiency of the block splicing reflector design. Summary of the invention

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

[0006] The present invention provides a method for analyzing the variation of the curvature radius of a sub-mirror with adjustable curvature and the precision of surface shape actuation, comprising the steps of: S1. Create a finite element analysis model of a curvature-adjustable sub-mirror, and create 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; S2. Extract all the mirror surfaces located on the curvature adjustable sub-mirror nThe number of nodes i , extract the node number i The corresponding node space coordinates ( x i , y i , z i ); S3. 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 S4. According to the node number i , the node space coordinates ( x i , y i , z i ) construct a mirror curvature radius correction function; S5. According to the node number i , construct the surface shape actuation accuracy RMS and the displacement in the direction of the sag after the curvature correction of the sub-mirror surface node The second relationship function between S6. Integrating the first relationship function, the mirror curvature radius correction function and the second relationship function into the curvature adjustable sub-mirror finite element model calculation file; S7. Submit the integrated finite element analysis calculation file of the curvature-adjustable sub-mirror to the finite element solver for calculation to obtain the curvature radius change. dr Actuation accuracy RMS with the surface profile.

[0007] Furthermore, the curvature radius variation dr Displacement in the direction of the sagittal height of all n nodes d z The expression of the first relationship function between is: .

[0008] Furthermore, all of the n Displacement of the nodes in the direction of the sagittal height d z The expression is: ; The free-form surface equation of the curvature-adjustable sub-mirror along the Z-axis direction is expressed as: ; in, z i For the mirror surface ( x i , y i ) point, represents the spherical sagittal height, R is the curvature radius of the mirror; F ( x i , y i ) is the free-form surface sag correction part, which indicates the deviation of the theoretical mirror surface from the spherical surface; Calculate the radius of curvature of the mirror surface using the above formula R The partial derivative of , we can get: ; Nodes due to curvature changes i The expression of displacement in the direction of the sagittal height is: ; The square difference between the actual mirror's nodal sag displacement and the nodal sag 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 is: .

[0009] Furthermore, the expression of the mirror curvature radius correction function is: ; in, It is the displacement in the direction of the vector height after the curvature of the mirror node of the sub-mirror is corrected.

[0010] Furthermore, the surface shape actuation accuracy RMS is related to the displacement in the direction of the sag after the curvature correction of the sub-mirror surface node. The expression of the second relationship function between is: .

[0011] The present invention also provides a device for analyzing the variation of the curvature radius of a curvature-adjustable sub-mirror and the surface shape actuation accuracy, comprising: An analysis model creation module, used to create a finite element analysis model of a sub-mirror with adjustable curvature; 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; 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 ) ; 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 The second function constructs a module for determining the node number according to the node number. i , the node space coordinates ( x i , y i , z i ) construct a mirror curvature radius correction function; The third function builds a module for numbering the nodes according to the i , construct the surface shape actuation accuracy RMS and the displacement in the direction of the sag after the curvature correction of the sub-mirror surface node The second relationship function between An integrated calculation module is used to integrate the first relationship function, the mirror curvature radius correction function and the second relationship function into the curvature adjustable sub-mirror finite element model calculation file; and submit the integrated curvature adjustable sub-mirror finite element analysis calculation file to a finite element solver for calculation to obtain the curvature radius change amount. dr Actuation accuracy RMS with the surface profile.

[0012] The present invention also provides a computer device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed 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 in curvature radius and surface shape actuation accuracy of the curvature-adjustable sub-mirror of the present invention.

[0013] The present invention also provides a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable the computer to execute the method for analyzing the change in the curvature radius of a curvature-adjustable sub-mirror and the surface shape actuation accuracy of the present invention.

[0014] The present invention provides a method for analyzing the variation of the curvature radius and the precision of surface actuation of a sub-mirror with adjustable curvature. The method comprises the following steps: constructing a finite element analysis model of a sub-mirror with adjustable curvature to generate a sub-mirror finite element model calculation file; constructing a sub-mirror curvature radius variation solution function, a mirror surface curvature correction function, and a surface actuation precision RMS value solution function, and integrating them into the sub-mirror finite element model calculation file; submitting the sub-mirror curvature radius variation solution function, and directly obtaining the sub-mirror curvature radius variation and the RMS value of the surface actuation precision while solving the sub-mirror finite element model node displacement data; effectively saving the sub-mirror mirror surface node coordinate and displacement data format conversion and reading and writing time, improving the iterative optimization efficiency of the reflector design, and having significant engineering significance for the optimal design of the block-jointed reflector. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of a method for analyzing the variation of the curvature radius of a sub-mirror with adjustable curvature and the precision of surface shape actuation in a specific embodiment of the present invention; Figure 2 is a schematic diagram of a first relationship function selected in a specific embodiment of the present invention; Figure 3 is a schematic diagram of a selected mirror curvature radius correction function in a specific embodiment of the present invention; Figure 4 is a schematic diagram of a second relationship function selected in a specific embodiment of the present invention; Figure 5 is a schematic diagram of analysis results in a specific embodiment of the present invention; Figure 6 It is a structural block diagram of a computer device in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 of the present invention.

[0017] In a specific embodiment, the present invention provides a method for analyzing the change in the curvature radius of a curvature-adjustable sub-mirror and the surface shape actuation accuracy, comprising the steps of: S1. Create a finite element analysis model of a curvature-adjustable sub-mirror, and create 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; S2. Extract all the mirror surfaces located on 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 ); S3. 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 In a specific implementation manner, all of the n Displacement of the nodes in the direction of the sagittal height d z The expression is: ; in, Represents the displacement in the direction of the vector height of the nodes corresponding to all n mirror nodes.

[0018] The free-form surface equation of the curvature-adjustable sub-mirror along the optical axis, i.e., the Z-axis direction, is expressed as: ; in, z i For the mirror surface ( x i , y i ) point, represents the spherical sagittal height, R is the curvature radius of the mirror; F ( x i , y i ) is the free-form surface sag correction part, which indicates the deviation of the theoretical mirror surface from the spherical surface; Calculate the radius of curvature of the mirror surface using the above formula R The partial derivative of , we can get: ; Nodes due to curvature changes i The expression of displacement in the direction of the sagittal height is: ; The square difference between the actual mirror's nodal sag displacement and the nodal sag displacement caused by the curvature change is expressed as: ; Upward E Find out about dr The partial derivative of dr The partial derivative of is 0, that is , get the curvature radius change dr Displacement in the direction of the sagittal height of all n nodes d z The expression of the first relationship function between is: .

[0019] S4. According to the node number i , the node space coordinates ( x i , y i , z i ) construct a mirror curvature radius correction function; In a specific implementation, the expression of the mirror curvature radius correction function is: ; in, It is the displacement in the direction of the vector height after the curvature of the mirror node of the sub-mirror is corrected.

[0020] S5. According to the node number i , construct the surface shape actuation accuracy RMS and the displacement in the direction of the sag after the curvature correction of the sub-mirror surface node The second relationship function between In a specific implementation, the surface shape actuation accuracy RMS is related to the displacement in the direction of the sag after the curvature correction of the node of the sub-mirror surface. The expression of the second relationship function between is: .

[0021] S6. Integrating the first relationship function, the mirror curvature radius correction function and the second relationship function into the curvature adjustable sub-mirror finite element model calculation file; 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 displacement of the sub-mirror finite element model, the RMS value of the sub-mirror curvature radius change and the surface shape actuation error is automatically calculated, that is, the curvature radius change is obtained. dr Actuation accuracy RMS with the surface profile.

[0022] 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.

[0023] 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: An analysis model creation module, used to create a finite element analysis model of a sub-mirror with adjustable curvature; 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; 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 ) ; 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 The second function constructs a module for determining the node number according to the node number. i , the node space coordinates ( x i , y i , z i ) construct a mirror curvature radius correction function; The third function builds a module for numbering the nodes according to the i , construct the surface shape actuation accuracy RMS and the displacement in the direction of the sag after the curvature correction of the sub-mirror surface node The second relationship function between An integrated calculation module is used to integrate the first relationship function, the mirror curvature radius correction function and the second relationship function into the curvature adjustable sub-mirror finite element model calculation file; and submit the integrated curvature adjustable sub-mirror finite element analysis calculation file to a finite element solver for calculation to obtain the curvature radius change amount. dr Actuation accuracy RMS with the surface profile.

[0024] A specific embodiment of the present invention further provides a computer device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed 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 in curvature radius and surface shape actuation accuracy of the curvature-adjustable sub-mirror of the present invention.

[0025] A specific embodiment of the present invention also provides a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable the computer to execute the method for analyzing the change in the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy of the present invention.

[0026] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0027] Example like Figure 1 As shown in the figure, it is a flow chart of the method for analyzing the change in the curvature radius of a sub-mirror with adjustable curvature and the precision of surface shape actuation 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 a sub-mirror with adjustable curvature. Two variables are created in the sub-mirror finite element model, which respectively represent the change in the curvature radius and the RMS value of the surface shape actuation precision, and a sub-mirror finite element model calculation file is generated; the node number and node coordinates of the sub-mirror mirror surface are extracted; a function characterizing the change in the curvature radius of the sub-mirror is constructed; a curvature correction function in the direction of the vector height of the sub-mirror mirror surface is constructed; a function for solving the RMS value of the surface shape actuation error of the sub-mirror is constructed; the function for solving the change in the curvature radius of the sub-mirror, the mirror curvature correction function, and the RMS value for solving the surface shape actuation precision are integrated into the sub-mirror finite element model calculation file; the finite element solver is submitted for calculation, and while solving the node displacement of the sub-mirror finite element model, the RMS value of the change in the curvature radius of the sub-mirror and the surface shape actuation error is directly obtained.

[0028] Specifically, the method for analyzing the change in the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy in this embodiment includes the following steps: Step 1: Create a finite element analysis model of a sub-mirror with adjustable curvature. The finite element model condition is the sub-mirror curvature correction condition. Create variables in the sub-mirror finite element model. dr、 RMS, where dr Indicates the change in curvature radius, RMS indicates the RMS value of the surface actuation accuracy, and generates a sub-mirror finite element model calculation file; In this specific embodiment, a finite element analysis model of a sub-mirror with adjustable curvature is created by Patran software, and the working condition is a sub-mirror curvature correction working condition; by creating variables in step 1, dr , RMS, where dr It represents the change of curvature radius, RMS represents the RMS value of surface shape actuation accuracy, and generates bdf file (Nastran finite element solver calculation file) about the sub-mirror; Step 2: Extract all the sub-mirror surfaces n The number of nodes i , and extract the node number i The corresponding node space coordinates ( x i , y i , z i ); In this specific embodiment, the node number range of 3182 nodes on the sub-mirror surface is extracted in step 2: 1~3182, and the node coordinates ( x i , y i ,z i ).

[0029] Step 3: Number the mirror nodes of the sub-mirror according to step 2 i , the node space coordinates ( x i , y i , z i )Build about variables dr represents the change in the curvature radius of the sub-mirror surface dr Displacement in the direction of the sagittal height of all nodes of the mirror d z The function of the relationship between ; In this specific embodiment, by constructing the variable dr represents the change in the curvature radius of the sub-mirror surface dr Displacement in the direction of the sagittal height of all 3182 nodes of the mirror d z The function of the relationship between Figure 2 shown.

[0030] Specifically, the free-form surface equation of the sub-mirror surface along the optical axis, i.e., the Z-axis direction, can generally be expressed as: ; in, z i For the mirror surface ( x i , y i ) point, represents the spherical sagittal height, R is the curvature radius of the mirror; F ( x i , y i ) is the free-form surface vector height correction part, which represents the deviation of the theoretical mirror surface from the spherical surface.

[0031] Calculate the radius of curvature of the mirror surface using the above formula R The partial derivative of , we can get: ; Nodes due to curvature changes i The expression of displacement in the direction of the sagittal height is: ; The square difference between the actual mirror's nodal sag displacement and the nodal sag displacement caused by the curvature change is expressed as: ; Upward E Find out about dr The partial derivative of dr The partial derivative of is 0, that is , get the curvature radius change dr Displacement in the direction of the sagittal height of all n nodes d z The expression of the first relationship function between is: .

[0032] The above formula is the least square solution of the overdetermined equation of the change of the sub-mirror's curvature radius, the displacement of the sub-mirror's mirror node in the direction of the sag height, and the node coordinates, and the change of the sub-mirror's mirror curvature radius is obtained. dr Displacement in the direction of the sagittal height of all nodes of the mirror dz function of the relationship between them.

[0033] Step 4: According to the node number i , the node space coordinates ( x i , y i , z i ) Construct the correction function of the change of the curvature radius of the sub-mirror surface: ; in, It is the displacement in the direction of the sagittal height after the curvature correction of the node i of the sub-mirror.

[0034] In this specific implementation, the sub-mirror surface curvature radius change correction function constructed in step 4 is as follows: Figure 3 shown.

[0035] Step 5: According to the node number i , the relationship between the RMS value of the mirror surface actuation error and the displacement in the direction of the sag after the curvature correction of the sub-mirror mirror node is: ; In this specific implementation, the mirror surface shape actuation error RMS value solution function is constructed in step 5, as follows: Figure 4 shown.

[0036] Specifically, the function for calculating the RMS value of the optical surface shape error of the reflector is: ; Step 6: Integrate the curvature radius change solution function of the curvature-adjustable sub-mirror, the mirror curvature correction function, and the surface shape actuation accuracy RMS value solution function into the sub-mirror finite element model calculation file; Step 7: Submit the calculation to the finite element solver to obtain the RMS value of the change in the sub-mirror curvature radius and the surface shape actuation error.

[0037] In this specific embodiment, the solution is submitted to the NASTRAN finite element solver for calculation, and the calculation results are as follows: Figure 5 As shown in the figure, it can be seen that the curvature radius of the sub-mirror changes by two dr It is 0.011937mm, the RMS value of the surface actuation error is 231.29nm / mm, and the analysis time is about 3 minutes.

[0038] Comparative Example By adopting traditional analysis methods, the calculation results such as the sub-mirror surface node coordinates and displacement data in the finite element commercial software are exported to an external surface analysis program for calculation, and the sub-mirror curvature radius change and surface accuracy analysis results are obtained.

[0039] The change of curvature radius in traditional analysis method dr It is 0.01165mm, the RMS value of the surface actuation error is 229.78nm / mm, and the analysis time is about 5 minutes.

[0040] 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 demonstrates that the method for analyzing the change in 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.

[0041] In contrast, the traditional analysis method has a huge amount of sub-mirror surface node coordinates and displacement data due to the inconsistency of the data interface between the finite element commercial software and the numerical calculation program, and a lot of time is wasted on data file format conversion and data reading and writing. The present invention constructs a solution function for the change in the curvature radius of the curvature-adjustable sub-mirror through the finite element analysis software, and integrates the sub-mirror surface curvature radius change and surface shape accuracy analysis functions into the sub-mirror finite element model calculation file. While solving the sub-mirror finite element model node displacement data, the sub-mirror surface curvature radius change and the RMS value of the surface shape actuation accuracy are directly obtained, which effectively improves the optimization design efficiency of the block-jointed reflector.

[0042] Accordingly, 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.

[0043] Figure 6 FIG. 1 is a schematic diagram of the structure of a computer device 12 provided in an embodiment of the present invention. Figure 6 A block diagram of an exemplary computer device 12 suitable for use in implementing embodiments of the present invention is shown. Figure 6The computer device 12 shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present invention.

[0044] like Figure 6 As shown, computer device 12 is in the form of a general-purpose computing device. Computer device 12 is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, 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 and / or required herein.

[0045] Components of 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 that connects various system components including system memory 28 and processing unit 16 .

[0046] Bus 18 represents one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor or a local bus using any of a variety of bus architectures. By way of 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.

[0047] The computer device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by the computer device 12, including volatile and non-volatile media, removable and non-removable media.

[0048] The system memory 28 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. The computer device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the storage system 34 may be used to read and write non-removable, non-volatile magnetic media ( Figure 6 not shown, usually called a "hard drive"). Although Figure 6Not shown in the figure, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk"), and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, a DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to the bus 18 via one or more data medium interfaces. The memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to perform the functions of the embodiments of the present invention.

[0049] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in the memory 28, such program modules 42 including, but not limited to, an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment. The program modules 42 generally perform the functions and / or methods of the embodiments described herein.

[0050] The computer device 12 may also communicate with one or more external devices 14 (e.g., keyboards, pointing devices, displays 24, etc.), one or more devices that enable a user to interact with the computer device 12, and / or any device that enables the computer device 12 to communicate with one or more other computing devices (e.g., network cards, modems, etc.). Such communication may be performed through an input / output (I / O) interface 22. Furthermore, the computer device 12 may also communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) through a network adapter 20. Figure 6 As shown, the network adapter 20 communicates with other modules of the computer device 12 via the bus 18. It should be understood that, although not shown in the figure, other hardware and / or software modules can be used in conjunction with the 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.

[0051] The processing unit 16 executes various functional applications and data processing by running the programs stored in the system memory 28, such as implementing the method for analyzing the change in the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy provided in the embodiment of the present invention.

[0052] Also provided in an embodiment of the present invention is a non-transitory computer-readable storage medium storing computer instructions, on which a computer program is stored. When the program is executed by a processor, a method for analyzing the change in the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy provided in all the inventive embodiments of the present application is provided.

[0053] The computer storage medium of the embodiment of the present invention may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. More specific examples (non-exhaustive list) of computer-readable storage media include: an electrical connection with 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, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in combination with an instruction execution system, an apparatus, or a device.

[0054] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, which carry computer-readable program code. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Computer-readable signal media may also be any computer-readable medium other than a computer-readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0055] The program code included in the computer-readable medium can be transmitted with any appropriate medium, including but not limited to wireless, electric wire, optical cable, RF, etc., or any suitable combination of the above. The computer program code for performing the operation of the present invention can be written in one or more programming languages ​​or their combinations, and the programming language includes object-oriented programming languages ​​such as Java, Smalltalk, C++, and also includes conventional procedural programming languages-such as "C" language or similar programming languages. The program code can be executed completely on the user's computer, partially on the user's computer, executed as an independent software package, partially on the user's computer and partially on the remote computer, or completely on the remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer by any type of network including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, using an Internet service provider to connect to the Internet).

[0056] 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 in the curvature radius of an adjustable sub-mirror and the surface shape actuation accuracy according to the above-mentioned curvature.

[0057] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0058] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing the variation of curvature radius of a curvature-adjustable sub-mirror and the precision of surface shape actuation, characterized in that: The method for analyzing the variation of the curvature radius of the curvature-adjustable sub-mirror and the surface shape actuation accuracy comprises the following steps: S1. Create a finite element analysis model of a curvature-adjustable sub-mirror, and create 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; S2. Extract all the mirror surfaces located on 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 ); S3. 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 S4. According to the node number i , the node space coordinates ( x i , y i , z i ) construct a mirror curvature radius correction function; S5. According to the node number i , construct the surface shape actuation accuracy RMS and the displacement in the direction of the sag after the curvature correction of the sub-mirror surface node The second relationship function between S6. Integrating the first relationship function, the mirror curvature radius correction function and the second relationship function into the curvature adjustable sub-mirror finite element model calculation file; S7. Submit the integrated finite element analysis calculation file of the curvature-adjustable sub-mirror to the finite element solver for calculation to obtain the curvature radius change. dr Actuation accuracy RMS with the surface profile.

2. The method for analyzing the variation of curvature radius of curvature-adjustable sub-mirror and the precision of surface shape actuation according to claim 1, characterized in that: The change in the radius of curvature dr Displacement in the direction of the sagittal height of all n nodes d z The expression of the first relationship function between is: 。 3. The method for analyzing the variation of curvature radius of curvature-adjustable sub-mirror and the precision of surface shape actuation according to claim 2, characterized in that: All of the above n Displacement of the nodes in the direction of the sagittal height d z The expression is: ； The free-form surface equation of the curvature-adjustable sub-mirror along the Z-axis direction is expressed as: ； in, z i For the mirror surface ( x i , y i ) point, represents the spherical sagittal height, R is the curvature radius of the mirror; F ( x i , y i ) is the free-form surface sag correction part, which indicates the deviation of the theoretical mirror surface from the spherical surface; Calculate the radius of curvature of the mirror surface using the above formula R The partial derivative of , we can get: ； Nodes due to curvature changes i The expression of displacement in the direction of the sagittal height is: ； The square difference between the actual mirror's nodal sag displacement and the nodal sag 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 is: 。 4. The method for analyzing the variation of curvature radius of curvature-adjustable sub-mirror and the precision of surface shape actuation according to claim 1, characterized in that: The expression of the mirror curvature radius correction function is: ； in, It is the displacement in the direction of the vector height after the curvature of the mirror node of the sub-mirror is corrected.

5. The method for analyzing the variation of curvature radius of curvature-adjustable sub-mirror and the precision of surface shape actuation according to claim 1, characterized in that: The surface shape actuation accuracy RMS and the displacement in the direction of the sag after the curvature correction of the sub-mirror surface node The expression of the second relationship function between is: 。 6. A device for analyzing the change in curvature radius of a curvature-adjustable sub-mirror and the precision of surface shape actuation, characterized in that: The curvature-adjustable sub-mirror curvature radius variation and surface shape actuation accuracy analysis device comprises: An analysis model creation module, used to create a finite element analysis model of a sub-mirror with adjustable curvature; 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; 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 ) ; 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 The second function constructs a module for determining the node number according to the node number. i , the node space coordinates ( x i , y i , z i ) construct a mirror curvature radius correction function; The third function builds a module for numbering the nodes according to the i , construct the surface shape actuation accuracy RMS and the displacement in the direction of the sag after the curvature correction of the sub-mirror surface node The second relationship function between An integrated calculation module is used to integrate the first relationship function, the mirror curvature radius correction function and the second relationship function into the curvature adjustable sub-mirror finite element model calculation file; and submit the integrated curvature adjustable sub-mirror finite element analysis calculation file to a finite element solver for calculation to obtain the curvature radius change amount. dr Actuation accuracy RMS with the surface profile.

7. A computer device, characterized in that: include: at least one processor; as well as a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed 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 in curvature radius and surface shape actuation accuracy of the curvature-adjustable sub-mirror described in any one of claims 1 to 5.

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

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