CN-116203722-B - Surface shape optimization method and device for reflecting mirror

CN116203722BCN 116203722 BCN116203722 BCN 116203722BCN-116203722-B

Abstract

The invention provides a surface shape optimization method and device of a reflector. The surface shape optimization method of the reflector comprises the steps of determining each heat flux vector according to a response matrix, a thermal deformation vector and each disturbance item, determining each residual surface shape error according to the response matrix, the thermal deformation vector and each heat flux vector meeting constraint conditions, and applying the heat flux vector corresponding to the minimum value of each residual surface shape error on a heating plate of the reflector to optimize the surface shape of the reflector. The invention can rapidly determine an effective surface optimization scheme and meet the surface shape requirement of high precision.

Inventors

XU ZHONGMIN

Assignees

深圳综合粒子设施研究院

Dates

Publication Date: 20260508
Application Date: 20230104

Claims (17)

1. A method for optimizing the shape of a mirror, comprising: Determining each heat flux vector according to the response matrix, the thermal deformation vector and each disturbance term; determining each residual surface shape error according to the response matrix, the thermal deformation vector and each heat flux vector meeting constraint conditions; applying a heat flux vector corresponding to the minimum value of each residual surface shape error on the heating plate of the reflector to optimize the surface shape of the reflector; The determining each heat flux vector from the response matrix, the heat distortion vector, and each disturbance term comprises: determining each total deformation disturbance vector according to the thermal deformation vector, the initial deformation vector and each disturbance term; Determining each heat flux vector according to the response matrix and each total deformation disturbance vector; determining each heat flux vector from the response matrix and each total deformation disturbance vector comprises: and determining each heat flux vector according to the inverse matrix of the product of the transpose of the response matrix and the response matrix, the transpose of the response matrix and each total deformation disturbance vector.
2. The method of optimizing the surface shape of a mirror according to claim 1, further comprising: Sequentially applying heat flux vectors on each heating plate to obtain corresponding reflector heat flux deformation data; and determining the response matrix according to the reflector heat flux deformation data.
3. The method of optimizing the surface shape of a mirror according to claim 1, further comprising: Applying the thermal power of the light source to the light spot of the reflector to obtain the thermal deformation data of the reflector; and determining the thermal deformation vector according to the thermal deformation data of the reflector.
4. The method of claim 1, wherein determining each total deformation disturbance vector from the thermal deformation vector, the initial deformation vector, and each disturbance term comprises: determining each thermal deformation disturbance vector according to the maximum value of the thermal deformation vector and each disturbance term; and determining each total deformation disturbance vector according to the thermal deformation vector, the initial deformation vector and each thermal deformation disturbance vector.
5. The method of optimizing the surface shape of a mirror according to claim 1, wherein each heat flux vector is determined by the following formula: ; Wherein, the For the response matrix to be a function of the response matrix, For the heat flux vector to be used, Is the initial deformation vector; As the thermal deformation vector of the above-mentioned material, For the term of the disturbance in question, Is the total deformation disturbance vector.
6. The method of claim 1, wherein determining each residual shape error from the response matrix, the heat distortion vector, and each heat flux vector satisfying a constraint condition comprises: determining each thermal deformation disturbance vector according to the maximum value of the thermal deformation vector and each disturbance term; And determining each residual surface shape error according to the response matrix, the thermal deformation vector, the initial deformation vector, each thermal deformation disturbance vector and each heat flux vector meeting constraint conditions.
7. The method of claim 6, wherein each residual surface shape error is determined by the following formula: ; Wherein, the For the residual shape of the face error, For the response matrix to be a function of the response matrix, For the heat flux vector satisfying the constraint, Is the initial deformation vector; As the thermal deformation vector of the above-mentioned material, Is the thermal deformation disturbance vector.
8. A mirror surface shape optimizing apparatus, comprising: the heat flux vector module is used for determining each heat flux vector according to the response matrix, the thermal deformation vector and each disturbance term; the residual surface shape error module is used for determining each residual surface shape error according to the response matrix, the thermal deformation vector and each heat flux vector meeting constraint conditions; The surface shape optimization module is used for applying a heat flux vector corresponding to the minimum value of each residual surface shape error on the heating plate of the reflector so as to optimize the surface shape of the reflector; The heat flux vector module includes: The total deformation disturbance vector unit is used for determining each total deformation disturbance vector according to the thermal deformation vector, the initial deformation vector and each disturbance item; The heat flux vector unit is used for determining each heat flux vector according to the response matrix and each total deformation disturbance vector; The heat flux vector unit is specifically configured to: and determining each heat flux vector according to the inverse matrix of the product of the transpose of the response matrix and the response matrix, the transpose of the response matrix and each total deformation disturbance vector.
9. The mirror surface shape optimizing device according to claim 8, further comprising: The heat flux vector application module is used for sequentially applying heat flux vectors on each heating plate to obtain corresponding reflector heat flux deformation data; And the response matrix module is used for determining the response matrix according to the reflector heat flux deformation data.
10. The mirror surface shape optimizing device according to claim 8, further comprising: the thermal power application module is used for applying the thermal power of the light source to the light spots of the reflector to obtain the thermal deformation data of the reflector; And the thermal deformation vector module is used for determining the thermal deformation vector according to the thermal deformation data of the reflector.
11. The mirror surface shape optimizing apparatus according to claim 8, wherein the total deformation disturbance vector unit includes: A thermal deformation disturbance vector subunit, configured to determine each thermal deformation disturbance vector according to a maximum value of the thermal deformation vector and each disturbance term; and the total deformation disturbance vector subunit is used for determining each total deformation disturbance vector according to the thermal deformation vector, the initial deformation vector and each thermal deformation disturbance vector.
12. The mirror surface shape optimizing device according to claim 8, wherein the heat flux vector module is specifically configured to: Each heat flux vector is determined by the following formula: ; Wherein, the For the response matrix to be a function of the response matrix, For the heat flux vector to be used, Is the initial deformation vector; As the thermal deformation vector of the above-mentioned material, For the term of the disturbance in question, Is the total deformation disturbance vector.
13. The mirror surface shape optimizing device according to claim 8, wherein the residual surface shape error module includes: The thermal deformation disturbance vector unit is used for determining each thermal deformation disturbance vector according to the maximum value of the thermal deformation vector and each disturbance term; And the residual surface shape error unit is used for determining each residual surface shape error according to the response matrix, the thermal deformation vector, the initial deformation vector, each thermal deformation disturbance vector and each heat flux vector meeting constraint conditions.
14. The mirror surface shape optimizing device according to claim 13, wherein the residual surface shape error module is specifically configured to: each residual surface shape error is determined by the following formula: ; Wherein, the For the residual shape of the face error, For the response matrix to be a function of the response matrix, For the heat flux vector satisfying the constraint, Is the initial deformation vector; As the thermal deformation vector of the above-mentioned material, For the term of the disturbance in question, Is the thermal deformation disturbance vector.
15. An electronic device comprising a memory, a processor and a computer program stored on the memory and running on the processor, characterized in that the processor implements the steps of the method for optimizing the surface shape of a mirror according to any one of claims 1 to 7 when the computer program is executed by the processor.
16. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, carries out the steps of the method for optimizing the shape of a mirror according to any one of claims 1 to 7.
17. A computer program product comprising computer programs/instructions which, when executed by a processor, implement the steps of the method for shape optimization of a mirror according to any one of claims 1 to 7.

Description

Surface shape optimization method and device for reflecting mirror Technical Field The invention relates to the technical field of surface shape optimization of optical systems, in particular to a surface shape optimization method and device of a reflecting mirror. Background Due to the need for wavefront coherent transmission, the fourth generation synchrotron radiation light source and the high-repetition frequency free electron laser device have very high requirements on the surface shape of the mirror, generally require a height error RMS of several nm, and a slope error RMS value of less than 100nrad orders of magnitude. When the mirror absorbs the X-rays from upstream, the mirror surface is thermally deformed, and the transmission efficiency and the transmission quality of the X-rays are adversely affected. Conventional cooling schemes have failed to meet such high precision surface shape requirements. The active surface shape control schemes at present comprise a water cooling surface shape control scheme of Thelas SESO designed and a surface shape control scheme of multi-channel piezoelectric ceramics, and are applied to DLS (Diamond Light Source, "diamond" synchrotron radiation light source), ESRF (European Synchrotron Radiation Facility, european synchrotron radiation light source), EU-XFEL (European free electron laser) and other light sources, and a REAL cooling scheme using an electric heating plate for temperature compensation is proposed by the American SL AC national accelerator laboratory (SLAC National Accelerator Laboratory). The solution of electric heating plates is generally to use more than ten electric heating plates to compensate the surface shape of the reflector. In order to obtain the voltage (or current) applied to the electric heating plates, the conventional method is to set the range of the voltage (or current) applied to each electric heating plate in finite element analysis software, and then obtain the voltage (or current) on each electric heating plate when the surface shape is minimum by using a multi-parameter optimization method. Optimization of more than ten parameters is not only a very time-consuming task, but is also limited by the optimization algorithm, and does not necessarily result in satisfactory results. Disclosure of Invention The invention mainly aims to provide a surface shape optimization method of a reflector, so that an effective surface shape optimization scheme can be rapidly determined, and the surface shape requirement of high precision can be met. In order to achieve the above object, an embodiment of the present invention provides a method for optimizing a surface shape of a reflecting mirror, including: Determining each heat flux vector according to the response matrix, the thermal deformation vector and each disturbance term; determining each residual surface shape error according to the response matrix, the thermal deformation vector and each heat flux vector meeting constraint conditions; and applying a heat flux vector corresponding to the minimum value of each residual surface shape error on the heating plate of the reflector to optimize the surface shape of the reflector. In one embodiment, the method further comprises: Sequentially applying heat flux vectors on each heating plate to obtain corresponding reflector heat flux deformation data; A response matrix is determined from the reflector heat flux deformation data. In one embodiment, the method further comprises: Applying the thermal power of the light source to the light spot of the reflector to obtain the thermal deformation data of the reflector; and determining a thermal deformation vector according to the thermal deformation data of the reflector. In one embodiment, determining each heat flux vector from the response matrix, the heat distortion vector, and each disturbance term comprises: Determining each total deformation disturbance vector according to the thermal deformation vector, the initial deformation vector and each disturbance term; And determining each heat flux vector according to the response matrix and each total deformation disturbance vector. In one embodiment, determining each total deformation disturbance vector from the thermal deformation vector, the initial deformation vector, and each disturbance term comprises: Determining each thermal deformation disturbance vector according to the maximum value of the thermal deformation vector and each disturbance term; And determining each total deformation disturbance vector according to the thermal deformation vector, the initial deformation vector and each thermal deformation disturbance vector. In one embodiment, determining each heat flux vector from the response matrix and each total deformation disturbance vector comprises: each heat flux vector is determined based on the inverse of the product of the transpose of the response matrix and the response matrix, the transpose of the response matrix, and each total def