Method and apparatus for optimizing the surface shape of a mirror

Abstract

The application provides a mirror surface shape optimization method and device. The mirror surface shape optimization method comprises the following steps: determining each heat flux vector according to a response matrix, a thermal deformation vector and each perturbation term; determining each residual surface shape error according to the response matrix, the thermal deformation vector and each heat flux vector meeting a constraint condition; and applying a heat flux vector corresponding to a minimum value of each residual surface shape error on a heating sheet of the mirror to optimize the surface shape of the mirror. The application can quickly determine an effective surface shape optimization scheme and meet the high-precision surface shape requirement.

Description

Technical Field

[0001] This invention relates to the field of optical system surface shape optimization technology, specifically to a method and apparatus for optimizing the surface shape of a mirror. Background Technology

[0002] Due to the requirements for coherent wavefront transmission, fourth-generation synchrotron radiation sources and high-repetition-rate free-electron laser devices have extremely high requirements for the surface shape of the mirrors, generally requiring a height error RMS of several nm and a slope error RMS of less than 100 nrad. When the mirror absorbs X-rays from upstream, it causes thermal deformation of the mirror surface, which ultimately has an adverse effect on the transmission efficiency and quality of the X-rays.

[0003] Traditional cooling solutions are no longer sufficient to meet the high-precision surface profile requirements. Current active surface profile control solutions include the water-cooled and multi-channel piezoelectric ceramic surface profile control scheme designed by Thelas SESO, which has been applied in light sources such as DLS (Diamond Light Source), ESRF (European Synchrotron Radiation Facility), and EU-XFEL (European X-ray Free Electron Laser); the REAL cooling scheme, which uses electric heating elements for temperature compensation, was proposed by the SLAC National Accelerator Laboratory in the United States.

[0004] The typical design uses more than ten electric heating elements to compensate for the surface shape of the reflector. To obtain the applied voltage (or current) on the heating elements, the traditional method is to set the range of voltage (or current) applied to each heating element in finite element analysis software, and then use multi-parameter optimization to obtain the voltage (or current) on each heating element when the surface shape is minimized. Optimizing with more than ten parameters is not only a very time-consuming task, but also limited by the optimization algorithm, and may not yield satisfactory results. Summary of the Invention

[0005] The main objective of this invention is to provide a method for optimizing the surface shape of a reflector, so as to quickly determine an effective surface shape optimization scheme and meet high-precision surface shape requirements.

[0006] To achieve the above objectives, embodiments of the present invention provide a method for optimizing the surface shape of a reflector, comprising:

[0007] Each heat flux vector is determined based on the response matrix, thermal deformation vector, and each disturbance term.

[0008] The residual surface shape error is determined based on the response matrix, thermal deformation vector, and heat flux vectors that satisfy the constraints.

[0009] The heat flux vector corresponding to the minimum value of each residual surface shape error is applied to the heating plate of the reflector to optimize the surface shape of the reflector.

[0010] In one embodiment, it further includes:

[0011] Heat flux vectors are applied sequentially to each heating element to obtain the corresponding heat flux deformation data of the reflector.

[0012] The response matrix is ​​determined based on the heat flux deformation data of the reflector.

[0013] In one embodiment, it further includes:

[0014] Thermal deformation data of the reflector is obtained by applying thermal power from the light source to the light spot on the reflector.

[0015] The thermal deformation vector is determined based on the thermal deformation data of the reflector.

[0016] In one embodiment, determining each heat flux vector based on the response matrix, the thermal deformation vector, and each perturbation term includes:

[0017] The total deformation disturbance vector is determined based on the thermal deformation vector, the initial deformation vector, and each disturbance term;

[0018] Each heat flux vector is determined based on the response matrix and each total deformation disturbance vector.

[0019] In one embodiment, determining each total deformation perturbation vector based on the thermal deformation vector, the initial deformation vector, and each perturbation term includes:

[0020] Each thermal deformation perturbation vector is determined based on the maximum value of the thermal deformation vector and each perturbation term;

[0021] The total deformation disturbance vector is determined based on the thermal deformation vector, the initial deformation vector, and each thermal deformation disturbance vector.

[0022] In one embodiment, determining each heat flux vector based on the response matrix and each total deformation perturbation vector includes:

[0023] Each heat flux vector is determined by the inverse of the product of the transpose and the response matrix, the transpose of the response matrix, and each total deformation perturbation vector.

[0024] In one embodiment, each heat flux vector is determined by the following formula:

[0025] H = (M T (x)M(x)) -1 M T(x)(-C(x)-K(x)+(max(K(x))+ε)I);

[0026] Where M(x) is the response matrix, H is the heat flux vector, C(x) is the initial deformation vector, K(x) is the thermal deformation vector, ε is the perturbation term, and -C(x)-K(x)+(max(K(x))+ε)I is the total deformation perturbation vector.

[0027] In one embodiment, determining each residual surface shape error based on the response matrix, the thermal deformation vector, and each heat flux vector satisfying the constraints includes:

[0028] Each thermal deformation perturbation vector is determined based on the maximum value of the thermal deformation vector and each perturbation term;

[0029] The residual surface errors are determined based on the response matrix, thermal deformation vector, initial deformation vector, each thermal deformation disturbance vector, and each heat flux vector that satisfies the constraints.

[0030] In one embodiment, each residual surface error is determined by the following formula:

[0031] e=M(x)H′+C(x)+K(x)-((max(K(x))+ε)I);

[0032] Where e is the residual surface shape error, M(x) is the response matrix, H′ is the heat flux vector that satisfies the constraints, C(x) is the initial deformation vector, K(x) is the thermal deformation vector, and (max(K(x))+ε)I is the thermal deformation disturbance vector.

[0033] This invention also provides a surface shape optimization device for a reflector, comprising:

[0034] The heat flux vector module is used to determine each heat flux vector based on the response matrix, thermal deformation vector, and each disturbance term.

[0035] The residual surface error module is used to determine each residual surface error based on the response matrix, thermal deformation vector, and heat flux vectors that satisfy the constraints.

[0036] The surface shape optimization module is used to apply the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector.

[0037] In one embodiment, it further includes:

[0038] The heat flux vector application module is used to sequentially apply heat flux vectors to each heating element to obtain the corresponding heat flux deformation data of the reflector.

[0039] The response matrix module is used to determine the response matrix based on the heat flux deformation data of the reflector.

[0040] In one embodiment, it further includes:

[0041] The thermal power application module is used to apply the thermal power of the light source to the light spot of the reflector to obtain thermal deformation data of the reflector.

[0042] The thermal deformation vector module is used to determine the thermal deformation vector based on the thermal deformation data of the reflector.

[0043] In one embodiment, the heat flux vector module includes:

[0044] The total deformation disturbance vector element is used to determine each total deformation disturbance vector based on the thermal deformation vector, the initial deformation vector, and each disturbance term;

[0045] Heat flux vector element, used to determine each heat flux vector based on the response matrix and each total deformation disturbance vector;

[0046] In one embodiment, the total deformation perturbation vector element includes:

[0047] The thermal deformation disturbance vector sub-unit is used to determine each thermal deformation disturbance vector based on the maximum value of the thermal deformation vector and each disturbance term;

[0048] The total deformation disturbance vector sub-element is used to determine each total deformation disturbance vector based on the thermal deformation vector, the initial deformation vector, and each thermal deformation disturbance vector.

[0049] In one embodiment, the heat flux vector unit is specifically used for:

[0050] Each heat flux vector is determined by the inverse of the product of the transpose and the response matrix, the transpose of the response matrix, and each total deformation perturbation vector.

[0051] In one embodiment, the heat flux vector module is specifically used for:

[0052] Each heat flux vector is determined using the following formula:

[0053] H = (M T (x)M(x)) -1 M T (x)(-C(x)-K(x)+(max(K(x))+ε)I);

[0054] Where M(x) is the response matrix, H is the heat flux vector, C(x) is the initial deformation vector, K(x) is the thermal deformation vector, ε is the perturbation term, and -C(x)-K(x)+(max(K(x))+ε)I is the total deformation perturbation vector.

[0055] In one embodiment, the residual surface error module includes:

[0056] The thermal deformation disturbance vector element is used to determine each thermal deformation disturbance vector based on the maximum value of the thermal deformation vector and each disturbance term.

[0057] The residual surface error element is used to determine each residual surface error based on the response matrix, thermal deformation vector, initial deformation vector, each thermal deformation disturbance vector, and each heat flux vector that satisfies the constraints.

[0058] In one embodiment, the residual surface error module is specifically used for:

[0059] Each residual surface shape error is determined using the following formula:

[0060] e=M(x)H′+C(x)+K(x)-((max(K(x))+ε)I);

[0061] Where e is the residual surface shape error, M(x) is the response matrix, H′ is the heat flux vector that satisfies the constraints, C(x) is the initial deformation vector, K(x) is the thermal deformation vector, ε is the perturbation term, and (max(K(x))+ε)I is the thermal deformation perturbation vector.

[0062] This invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of the surface shape optimization method for the aforementioned reflector.

[0063] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the surface shape optimization method for the aforementioned reflector.

[0064] This invention also provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of the surface optimization method for the reflector.

[0065] The surface shape optimization method and apparatus for a reflector according to embodiments of the present invention first determines each heat flux vector based on the response matrix, thermal deformation vector, and each disturbance term. Then, it determines each residual surface shape error based on the response matrix, thermal deformation vector, and each heat flux vector that satisfies the constraint conditions. Finally, it applies the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector. This method can quickly determine an effective surface shape optimization scheme and meet the high-precision surface shape requirements. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 This is a front view of the mirror surface shape control structure in an embodiment of the present invention;

[0068] Figure 2 This is a cross-sectional view of the mirror surface shape control structure in an embodiment of the present invention;

[0069] Figure 3 Based on the embodiments of the present invention Figure 1 and Figure 2 A flowchart of the surface shape optimization method;

[0070] Figure 4 In another embodiment of the present invention, based on Figure 1 and Figure 2 A flowchart of the surface shape optimization method;

[0071] Figure 5 This is a flowchart of S101 in an embodiment of the present invention;

[0072] Figure 6 This is the reflection curve without temperature compensation using an electric heating element;

[0073] Figure 7 This is the slope curve of the reflector without temperature compensation using an electric heating element;

[0074] Figure 8 It is the deformation curve of the reflector when a heat flux vector is applied to the heating element;

[0075] Figure 9 It is the slope curve of the reflector on which the heat flux vector is applied to the heating element;

[0076] Figure 10 This is a structural block diagram of the surface shape optimization device for the reflector in an embodiment of the present invention;

[0077] Figure 11 This is a structural block diagram of the electronic device in an embodiment of the present invention. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] Those skilled in the art will recognize that embodiments of the present invention can be implemented as a system, apparatus, device, method, or computer program product. Therefore, this disclosure can be specifically implemented in the following forms: entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software.

[0080] Given that current surface shape control schemes cannot meet the requirements for high-precision surface shape, this invention provides a method and apparatus for optimizing the surface shape of a reflector. Based on Singular Value Decomposition (SVD), surface shape optimization is performed to solve for the heat flux vector applied to the electric heating element. By searching for the perturbation term of the objective function, multiple constraints can be set on the heat flux vector applied to the electric heating element, and the numerical value of the heat flux vector on the electric heating element when the surface shape is minimized can be quickly obtained. This invention uses simple matrix calculations; optimizing only one perturbation term is sufficient to quickly calculate the heat flux vector applied to multiple electric heating elements when the surface shape is minimized, solving the problem of the time-consuming optimization algorithms in traditional finite element analysis software when performing multi-parameter optimization. For example, the deflector of FEL1 in S3FEL absorbs 5.4W of heat power. This invention can complete the optimization calculation of the heat flux vectors of 25 electric heating elements when the surface shape is minimized within seconds. The height error RMS is reduced from 40nm before compensation to 0.009nm, and the slope error is reduced from 192.7nrad to 0.4nrad. The present invention will now be described in detail with reference to the accompanying drawings.

[0081] This invention is applied to the surface shape control structure of a reflector. Figure 1 This is a front view of the mirror surface shape control structure in an embodiment of the present invention; Figure 2 This is a cross-sectional view of the mirror surface shape control structure in an embodiment of the present invention. For example... Figures 1-2 As shown, the reflector surface shape control structure includes an optical element body 100, a water-cooled copper plate 200, an indium gallium solution tank 105, a first stress relief tank 103, a second stress relief tank 104, and an electric heating element 202, etc.

[0082] The reflector body 100 is provided with a reflective surface 101, an upper surface 102, and an indium gallium solution tank 105. Both the reflective surface 101 and the indium gallium solution tank 105 extend along the length of the reflector body 100. The reflective surface 101 is used to reflect X-rays to obtain a light spot 106. The indium gallium solution tank 105 is formed on the upper surface 102 of the reflector and is filled with an indium gallium solution 300.

[0083] The optical element body 100 is made of single-crystal silicon, with dimensions of 850mm (length), 50mm (width), and 60mm (height). The lower end of the water-cooled copper plate 200 is immersed in an indium gallium (IGa) solution 300, 2mm away from the bottom surface of the IGa solution bath 105. The inner diameter of the pipe 201 within the water-cooled copper plate 200 is 8mm. The reflector surface absorbs 5.4W of power, and water at 25°C is passed through the pipe 201. Figure 1 As shown, there are 25 electric heating elements, each measuring 30mm × 10mm, with a spacing of 2mm between them.

[0084] Figure 3 This is a flowchart of the surface shape optimization method for the reflector in an embodiment of the present invention. Figure 4 This is a flowchart of a method for optimizing the surface shape of a reflector according to another embodiment of the present invention. For example... Figures 3-4 As shown, the surface shape optimization method for the reflector includes:

[0085] S101: Determine each heat flux vector based on the response matrix, thermal deformation vector, and each disturbance term.

[0086] Before executing S101, the process also includes: sequentially applying heat flux vectors to each heating element to obtain corresponding mirror heat flux deformation data, and determining the response matrix based on the mirror heat flux deformation data. Applying heat power from the light source to the light spot on the mirror to obtain mirror heat deformation data, and determining the heat deformation vector based on the mirror heat deformation data.

[0087] Figure 5 This is a flowchart of S101 in an embodiment of the present invention. Figure 5 As shown, S101 includes:

[0088] S201: Determine the total deformation disturbance vector based on the thermal deformation vector, the initial deformation vector, and each disturbance term.

[0089] In one embodiment, S201 includes: determining each thermal deformation disturbance vector based on the maximum value of the thermal deformation vector and each disturbance term, and determining each total deformation disturbance vector based on the thermal deformation vector, the initial deformation vector, and each thermal deformation disturbance vector.

[0090] In specific implementation, the thermal deformation perturbation vector is (max(K(x))+ε)I, and the total deformation perturbation vector is -C(x)-K(x)+(max(K(x))+ε)I, where K(x) is the thermal deformation vector, ε is the perturbation term, C(x) is the initial deformation vector, and I is the identity matrix.

[0091] S202: Determine each heat flux vector based on the response matrix and each total deformation disturbance vector.

[0092] In one embodiment, S202 includes: determining each heat flux vector based on 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 perturbation vector.

[0093] In practical implementation, the inverse matrix of the product of the transpose of the response matrix and the response matrix is ​​(M T (x)M(x)) -1 M(x) is the response matrix. The heat flux vector can be determined using the following formula:

[0094] H = (M T (x)M(x)) -1 M T (x)(-C(x)-K(x)+(max(K(x))+ε)I);

[0095] Where H is the heat flux vector applied to the electric heating element, and ε is the heat flux vector corresponding to all perturbation terms within the range of perturbation terms; M(x) is the response matrix, K(x) is the thermal deformation vector, C(x) is the initial deformation vector, and ε is the perturbation term.

[0096] In this invention, heat flux vectors are used instead of voltage (or current) in finite element analysis, and their temperature compensation effects are consistent. The purpose of surface shape compensation is to apply heat flux vectors to multiple electric heating elements, thereby minimizing the surface shape by reducing the meridional square temperature gradient. Thus, an MHCKF model for reflector surface shape compensation is established, as shown in (1):

[0097] M(x)H+C(x)+K(x)=F(x); (1)

[0098] Where x is the coordinate of the light spot in the meridional direction; M(x) is the response function (response matrix) of the electric heating element, M(x)∈R m×n Let m be the number of rows in M(x) and n be the number of columns in M(x); H is the heat flux vector (column vector) applied to the electric heating element, H∈R. n C(x) is the initial deformation vector, which is affected by various factors such as mirror processing, clamping, and gravity. C(X)∈R m K(x) is the deformed column vector produced by the X-ray power absorbed by the mirror, K(x)∈Rm F(x) represents the deformation distribution resulting from the combined effects of electric heating surface shape compensation, initial deformation of the mirror, and thermal deformation. It is typically very complex, with F(x) ∈ R. m .

[0099] Research revealed that the ideal case for F(x) is a straight line, while the simplest case is:

[0100] F(x)=(max(K(x))+ε)I; (2)

[0101] Where max(K(x)) is the maximum deformed value of K(x), ε is the perturbation term, which is a scalar, and I is a column vector (identity matrix) with all 1s.

[0102] From (1) and (2), we can obtain (3)-(6) as follows:

[0103] M(x)H+C(x)+K(x)=(max(K(x))+ε)I; (3)

[0104] M(x)H=-C(x)-K(x)+(max(K(x))+ε)I; (4)

[0105] M T (x)M(x)H=M T (x)(-C(x)-K(x)+(max(K(x))+ε)I); (5)

[0106] H = (M T (x)M(x)) -1 M T (x)(-C(x)-K(x)+(max(K(x))+ε)I); (6)

[0107] Where T is the transpose and -1 represents the inverse matrix.

[0108] Gravity has a very small effect on the surface shape of the mirror when it is placed on its side. In addition, a stress-free mirror clamping scheme is used in the engineering, and surface shape errors caused by manufacturing are generally not considered in finite element analysis. Therefore, the initial deformation vector C(x) is usually measured with an interferometer after the mirror is installed and can be temporarily ignored in the finite element simulation.

[0109] S102: Determine each residual surface shape error based on the response matrix, thermal deformation vector, and heat flux vectors that satisfy the constraints.

[0110] In one embodiment, S102 includes: determining each thermal deformation perturbation vector based on the maximum value of the thermal deformation vector and each perturbation term, and determining each residual surface error based on the response matrix, the thermal deformation vector, the initial deformation vector, each thermal deformation perturbation vector and each heat flux vector that satisfies the constraint conditions.

[0111] In practice, the residual surface errors can be determined using the following formula:

[0112] e=M(x)H'+C(x)+K(x)-((max(K(x))+ε)I).

[0113] Where e is the residual surface shape error, M(x) is the response matrix, H′ is the heat flux vector satisfying the constraints, C(x) is the initial deformation vector, K(x) is the thermal deformation vector, and (max(K(x))+ε)I is the thermal deformation perturbation vector. The residual surface shape error can be used to obtain the PV (Peak-to-Valley, the difference between the highest and lowest points of the surface) and RMS (root mean square) values ​​of the height error or slope error.

[0114] S103: Apply the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector.

[0115] Figure 3 The surface shape optimization method for the mirror shown can be implemented by a computer. Figure 3 and Figure 4 As shown in the flowchart, the surface shape optimization method for the reflector in this embodiment of the invention first establishes a finite element model of the optical system, then calculates the response data of the electric heating element, that is, applying a certain amount of heat flux vector to the finite element model one by one and calculating the deformation of the reflector to obtain the response matrix M(x). Next, X-ray thermal power is applied separately to the light spot to obtain the thermal deformation vector K(x). Then, the perturbation term is searched within the range of perturbation term values, based on the SVD algorithm and H = (M... T (x)M(x)) -1 M T The heat flux vector on the heating element is obtained by using (x)(-C(x)-K(x)+(max(K(x))+ε)I). If the heat flux vector satisfies the constraint conditions, the residual surface shape error is calculated. At the end of the loop, the heat flux vector corresponding to the minimum residual surface shape error is found. By applying this heat flux vector to the heating element, the surface shape of the reflector can be optimized, achieving high efficiency while meeting high-precision surface shape requirements.

[0116] Figure 6 This is the reflection curve without temperature compensation using an electric heating element. Figure 7 This is the slope curve of the reflector without temperature compensation using an electric heating element. For example... Figure 6 and Figure 7As shown, Figure 6 and Figure 7 The horizontal axis represents the distance from the mirror to the center of the light spot. Figure 6 The vertical axis represents the deformation data of the reflector. Figure 7 The vertical axis represents the slope data of the reflecting mirror. (Through...) Figure 6 and Figure 7 The RMS value of the height error is 40 nm, and the RMS value of the slope error is 192.7 nrad.

[0117] Figure 8 It is the deformation curve of the reflector when a heat flux vector is applied to the heating element. Figure 9 It is the slope curve of the mirror to which the heat flux vector is applied on the heating element. For example... Figures 8-9 As shown, 0.001 W / mm is applied to the heating element. 2 After adjusting the heat flux vector at / ℃, the RMS value of the height error is 0.009nm, and the RMS value of the slope error is 0.4nrad, which is several orders of magnitude lower than before optimization. Therefore, the surface shape optimization scheme proposed in this invention is feasible and can meet the stringent surface shape requirements of fourth-generation synchrotron radiation sources and high-repetition-rate free-electron laser devices.

[0118] In summary, the surface shape optimization method for the reflector in this embodiment of the invention first determines each heat flux vector based on the response matrix, thermal deformation vector, and each perturbation term. Then, it determines each residual surface shape error based on the response matrix, thermal deformation vector, and each heat flux vector that satisfies the constraint conditions. Finally, it applies the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector. This method can quickly determine an effective surface shape optimization scheme and meet the high-precision surface shape requirements.

[0119] Based on the same inventive concept, this embodiment of the invention also provides a surface shape optimization device for a reflector. Since the principle of this device in solving the problem is similar to that of the surface shape optimization method for a reflector, the implementation of this device can refer to the implementation of the method, and the repeated parts will not be described again.

[0120] Figure 10 This is a structural block diagram of the surface shape optimization device for the reflector in an embodiment of the present invention. Figure 10 As shown, the surface shape optimization device for the reflector includes:

[0121] The heat flux vector module is used to determine each heat flux vector based on the response matrix, thermal deformation vector, and each disturbance term.

[0122] The residual surface error module is used to determine each residual surface error based on the response matrix, thermal deformation vector, and heat flux vectors that satisfy the constraints.

[0123] The surface shape optimization module is used to apply the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector.

[0124] In one embodiment, it further includes:

[0125] The heat flux vector application module is used to sequentially apply heat flux vectors to each heating element to obtain the corresponding heat flux deformation data of the reflector.

[0126] The response matrix module is used to determine the response matrix based on the heat flux deformation data of the reflector.

[0127] In one embodiment, it further includes:

[0128] The thermal power application module is used to apply the thermal power of the light source to the light spot of the reflector to obtain thermal deformation data of the reflector.

[0129] The thermal deformation vector module is used to determine the thermal deformation vector based on the thermal deformation data of the reflector.

[0130] In one embodiment, the heat flux vector module includes:

[0131] The total deformation disturbance vector element is used to determine each total deformation disturbance vector based on the thermal deformation vector, the initial deformation vector, and each disturbance term;

[0132] Heat flux vector element, used to determine each heat flux vector based on the response matrix and each total deformation disturbance vector;

[0133] In one embodiment, the total deformation perturbation vector element includes:

[0134] The thermal deformation disturbance vector sub-unit is used to determine each thermal deformation disturbance vector based on the maximum value of the thermal deformation vector and each disturbance term;

[0135] The total deformation disturbance vector sub-element is used to determine each total deformation disturbance vector based on the thermal deformation vector, the initial deformation vector, and each thermal deformation disturbance vector.

[0136] In one embodiment, the heat flux vector unit is specifically used for:

[0137] Each heat flux vector is determined by the inverse of the product of the transpose and the response matrix, the transpose of the response matrix, and each total deformation perturbation vector.

[0138] In one embodiment, the heat flux vector module is specifically used for:

[0139] Each heat flux vector is determined using the following formula:

[0140] H = (M T (x)M(x)) -1M T (x)(-C(x)-K(x)+(max(K(x))+ε)I);

[0141] Where M(x) is the response matrix, H is the heat flux vector, C(x) is the initial deformation vector, K(x) is the thermal deformation vector, ε is the perturbation term, and -C(x)-K(x)+(max(K(x))+ε)I is the total deformation perturbation vector.

[0142] In one embodiment, the residual surface error module includes:

[0143] The thermal deformation disturbance vector element is used to determine each thermal deformation disturbance vector based on the maximum value of the thermal deformation vector and each disturbance term.

[0144] The residual surface error element is used to determine each residual surface error based on the response matrix, thermal deformation vector, initial deformation vector, each thermal deformation disturbance vector, and each heat flux vector that satisfies the constraints.

[0145] In one embodiment, the residual surface error module is specifically used for:

[0146] Each residual surface shape error is determined using the following formula:

[0147] e=M(x)H′+C(x)+K(x)-((max(K(x))+ε)I);

[0148] Where e is the residual surface shape error, M(x) is the response matrix, H′ is the heat flux vector that satisfies the constraints, C(x) is the initial deformation vector, K(x) is the thermal deformation vector, ε is the perturbation term, and (max(K(x))+ε)I is the thermal deformation perturbation vector.

[0149] In summary, the surface shape optimization device for the reflector in this embodiment of the invention first determines each heat flux vector based on the response matrix, the thermal deformation vector, and each disturbance term. Then, it determines each residual surface shape error based on the response matrix, the thermal deformation vector, and each heat flux vector that satisfies the constraint conditions. Finally, it applies the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector. This method can quickly determine an effective surface shape optimization scheme and meet high-precision surface shape requirements.

[0150] Figure 11 This is a schematic block diagram illustrating the system configuration of the electronic device 9600 according to an embodiment of this application. Figure 11 As shown, the electronic device 9600 may include a central processing unit 9100 and a memory 9140; the memory 9140 is coupled to the central processing unit 9100. It is worth noting that... Figure 11 This is an example; other types of structures can also be used to supplement or replace this structure to achieve telecommunications functions or other functions.

[0151] In one embodiment, the surface shape optimization method for the reflector can be integrated into the central processing unit 9100. The central processing unit 9100 can be configured to perform the following control:

[0152] Each heat flux vector is determined based on the response matrix, thermal deformation vector, and each disturbance term.

[0153] The residual surface shape error is determined based on the response matrix, thermal deformation vector, and heat flux vectors that satisfy the constraints.

[0154] The heat flux vector corresponding to the minimum value of each residual surface shape error is applied to the heating plate of the reflector to optimize the surface shape of the reflector.

[0155] As can be seen from the above description, the surface shape optimization method of the reflector provided in this application first determines each heat flux vector based on the response matrix, thermal deformation vector, and each disturbance term, then determines each residual surface shape error based on the response matrix, thermal deformation vector, and each heat flux vector that satisfies the constraint conditions, and finally applies the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector. This method can quickly determine an effective surface shape optimization scheme and meet the high-precision surface shape requirements.

[0156] In another embodiment, the surface shape optimization device of the reflector can be configured separately from the central processing unit 9100. For example, the surface shape optimization device of the reflector can be configured as a chip connected to the central processing unit 9100, and the function of the surface shape optimization method of the reflector can be realized through the control of the central processing unit.

[0157] like Figure 11 As shown, the electronic device 9600 may further include: a communication module 9110, an input unit 9120, an audio processor 9130, a display 9160, and a power supply 9170. It is worth noting that the electronic device 9600 does not necessarily need to include these components. Figure 11 All components shown; in addition, the electronic device 9600 may also include Figure 11 For components not shown, please refer to existing technologies.

[0158] like Figure 11 As shown, the central processing unit 9100, sometimes also referred to as a controller or operating control, may include a microprocessor or other processor device and / or logic device, which receives inputs and controls the operation of various components of the electronic device 9600.

[0159] The memory 9140 may be, for example, one or more of a cache, flash memory, hard drive, removable media, volatile memory, non-volatile memory, or other suitable devices. It may store the aforementioned failure-related information, and also store a program for executing that information. The central processing unit 9100 may execute the program stored in the memory 9140 to perform information storage or processing, etc.

[0160] Input unit 9120 provides input to central processing unit 9100. Input unit 9120 may be, for example, a keypad or touch input device. Power supply 9170 provides power to electronic device 9600. Display 9160 displays images and text. Display may be, for example, an LCD display, but is not limited thereto.

[0161] The memory 9140 can be a solid-state memory, such as a read-only memory (ROM), random access memory (RAM), a SIM card, etc. It can also be a memory that retains information even when power is off, can be selectively erased, and contains more data; examples of this type of memory are sometimes referred to as EPROMs. The memory 9140 can also be some other type of device. The memory 9140 includes a buffer memory 9141 (sometimes referred to as a buffer). The memory 9140 may include an application / function storage unit 9142 for storing application programs and function programs or processes for executing the operation of the electronic device 9600 via the central processing unit 9100.

[0162] The memory 9140 may also include a data storage unit 9143 for storing data, such as contacts, digital data, pictures, sounds, and / or any other data used by the electronic device. The driver storage unit 9144 of the memory 9140 may include various drivers for the electronic device's communication functions and / or for performing other functions of the electronic device (such as messaging applications, address book applications, etc.).

[0163] The communication module 9110 is a transmitter / receiver 9110 that transmits and receives signals via the antenna 9111. The communication module (transmitter / receiver) 9110 is coupled to the central processing unit 9100 to provide input signals and receive output signals, which can be the same as in a conventional mobile communication terminal.

[0164] Based on different communication technologies, multiple communication modules 9110 can be configured in the same electronic device, such as cellular network modules, Bluetooth modules, and / or wireless LAN modules. The communication module (transmitter / receiver) 9110 is also coupled to a speaker 9131 and a microphone 9132 via an audio processor 9130 to provide audio output via the speaker 9131 and receive audio input from the microphone 9132, thereby realizing typical telecommunications functions. The audio processor 9130 may include any suitable buffer, decoder, amplifier, etc. Additionally, the audio processor 9130 is coupled to a central processing unit 9100, enabling on-device recording via the microphone 9132 and on-device playback of stored sound via the speaker 9131.

[0165] This invention also provides a computer-readable storage medium capable of implementing all steps of the surface optimization method for a reflector in the above embodiments, where the execution subject is a server or client. The computer-readable storage medium stores a computer program that, when executed by a processor, implements all steps of the surface optimization method for a reflector in the above embodiments. For example, when the processor executes the computer program, it implements the following steps:

[0166] Each heat flux vector is determined based on the response matrix, thermal deformation vector, and each disturbance term.

[0167] The residual surface shape error is determined based on the response matrix, thermal deformation vector, and heat flux vectors that satisfy the constraints.

[0168] The heat flux vector corresponding to the minimum value of each residual surface shape error is applied to the heating plate of the reflector to optimize the surface shape of the reflector.

[0169] In summary, the computer-readable storage medium of this invention first determines each heat flux vector based on the response matrix, the thermal deformation vector, and each perturbation term. Then, it determines each residual surface shape error based on the response matrix, the thermal deformation vector, and each heat flux vector that satisfies the constraint conditions. Finally, it applies the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector. This can quickly determine an effective surface shape optimization scheme and meet the high-precision surface shape requirements.

[0170] This invention also provides a computer program product capable of implementing all steps of the surface optimization method for a reflector in the above embodiments, where the execution subject is a server or client. The computer program product includes a computer program / instructions, which, when executed by a processor, implements all steps of the surface optimization method for a reflector in the above embodiments. For example, when the processor executes the computer program, it implements the following steps:

[0171] Each heat flux vector is determined based on the response matrix, thermal deformation vector, and each disturbance term.

[0172] The residual surface shape error is determined based on the response matrix, thermal deformation vector, and heat flux vectors that satisfy the constraints.

[0173] The heat flux vector corresponding to the minimum value of each residual surface shape error is applied to the heating plate of the reflector to optimize the surface shape of the reflector.

[0174] In summary, the computer program product of this invention first determines each heat flux vector based on the response matrix, thermal deformation vector, and each disturbance term. Then, it determines each residual surface shape error based on the response matrix, thermal deformation vector, and each heat flux vector that satisfies the constraint conditions. Finally, it applies the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector. This can quickly determine an effective surface shape optimization scheme and meet the high-precision surface shape requirements.

[0175] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0176] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, hardware + program embodiments are relatively simple in description because they are fundamentally similar to method embodiments; relevant parts can be referred to the descriptions in the method embodiments.

[0177] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0178] While this specification provides method operation steps as described in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive means. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only execution order. In actual device or end product execution, the methods shown in the embodiments or drawings may be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment, or even a distributed data processing environment). The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, product, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, product, or apparatus. Without further limitations, the presence of other identical or equivalent elements in the process, method, product, or apparatus that includes said elements is not excluded.

[0179] Those skilled in the art will also understand that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention can be implemented by electronic hardware, computer software, or a combination of both. To clearly demonstrate the interchangeability of hardware and software, the functions of the various illustrative components, units, and steps described above have been generally described. Whether such functionality is implemented through hardware or software depends on the specific application and the overall system design requirements. Those skilled in the art can implement the described functions using various methods for each specific application, but such implementation should not be construed as exceeding the scope of protection of the embodiments of the present invention.

[0180] The various illustrative logic blocks, units, or devices described in the embodiments of this invention can be implemented or operate the described functions using a general-purpose processor, digital signal processor, application-specific integrated circuit (ASIC), field-programmable gate array or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof. The general-purpose processor can be a microprocessor; alternatively, it can be any conventional processor, controller, microcontroller, or state machine. The processor can also be implemented using a combination of computing devices, such as a digital signal processor and a microprocessor, multiple microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

[0181] The steps of the methods or algorithms described in the embodiments of this invention can be directly embedded in hardware, a software module executed by a processor, or a combination of both. The software module can be stored in RAM, flash memory, ROM, EPROM, EEPROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium in the art. Exemplarily, the storage medium can be connected to the processor so that the processor can read information from and write information to the storage medium. Optionally, the storage medium can also be integrated into the processor. The processor and storage medium can be housed in an ASIC, which can be housed in a user terminal. Optionally, the processor and storage medium can also be housed in different components of the user terminal.

[0182] In one or more exemplary designs, the functions described in the embodiments of the present invention can be implemented in hardware, software, firmware, or any combination of these three. If implemented in software, these functions can be stored on a computer-readable medium or transmitted on a computer-readable medium in the form of one or more instructions or code. Computer-readable media include computer storage media and communication media that facilitate the transfer of computer programs from one place to another. Storage media can be any available media that can be accessed by a general-purpose or special-purpose computer. For example, such computer-readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program code in the form of instructions or data structures and other forms that can be read by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Furthermore, any connection can be suitably defined as a computer-readable medium, for example, if the software is transmitted from a website, server or other remote resource via a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL) or wirelessly, such as infrared, wireless and microwave, it is also included in the defined computer-readable medium. The disks and discs mentioned include compressed disks, laser discs, optical discs, DVDs, floppy disks, and Blu-ray discs. Disks typically copy data magnetically, while disks typically copy data optically using lasers. Combinations of the above can also be contained in computer-readable media.

[0183] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0184] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0185] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0186] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0187] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for optimizing the surface shape of a reflector, characterized in that, include: Each heat flux vector is determined based on the response matrix, thermal deformation vector, and each disturbance term. Each residual surface shape error is determined based on the response matrix, the thermal deformation vector, and the heat flux vectors that satisfy the constraints. Apply the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector; The process of determining each heat flux vector based on the response matrix, thermal deformation vector, and each disturbance term includes: The total deformation disturbance vector is determined based on the thermal deformation vector, the initial deformation vector, and each disturbance term; Each heat flux vector is determined based on the response matrix and each total deformation disturbance vector; The heat flux vectors are determined based on the response matrix and each total deformation perturbation vector, including: Each heat flux vector is determined based on the inverse matrix of the product of the transpose and the response matrix, the transpose of the response matrix, and each total deformation perturbation vector.

2. The surface shape optimization method for a reflector according to claim 1, characterized in that, Also includes: Heat flux vectors are applied sequentially to each heating element to obtain the corresponding heat flux deformation data of the reflector. The response matrix is ​​determined based on the heat flux deformation data of the reflector.

3. The method for optimizing the surface shape of a reflector according to claim 1, characterized in that, Also includes: Thermal deformation data of the reflector is obtained by applying thermal power from the light source to the light spot on the reflector. The thermal deformation vector is determined based on the thermal deformation data of the reflector.

4. The method for optimizing the surface shape of a reflector according to claim 1, characterized in that, The determination of each total deformation perturbation vector based on the thermal deformation vector, the initial deformation vector, and each perturbation term includes: Each thermal deformation perturbation vector is determined based on the maximum value of the thermal deformation vector and each perturbation term; Each total deformation disturbance vector is determined based on the thermal deformation vector, the initial deformation vector, and each thermal deformation disturbance vector.

5. The method for optimizing the surface shape of a reflector according to claim 1, characterized in that, Each heat flux vector is determined using the following formula: ； in, The response matrix, Let be the heat flux vector. The initial deformation vector; Let be the thermal deformation vector. For the disturbance term, Let be the total deformation disturbance vector.

6. The method for optimizing the surface shape of a reflector according to claim 1, characterized in that, The residual surface shape errors are determined based on the response matrix, the thermal deformation vector, and the heat flux vectors that satisfy the constraints, including: Each thermal deformation perturbation vector is determined based on the maximum value of the thermal deformation vector and each perturbation term; Each residual surface error is determined based on the response matrix, the thermal deformation vector, the initial deformation vector, each thermal deformation disturbance vector, and each heat flux vector that satisfies the constraints.

7. The method for optimizing the surface shape of a reflector according to claim 6, characterized in that, Each residual surface shape error is determined using the following formula: ； in, The residual surface shape error, The response matrix, Let be the heat flux vector that satisfies the constraints. The initial deformation vector; Let be the thermal deformation vector. Let be the thermal deformation disturbance vector.

8. A surface shape optimization device for a reflector, characterized in that, include: The heat flux vector module is used to determine each heat flux vector based on the response matrix, thermal deformation vector, and each disturbance term. The residual surface shape error module is used to determine each residual surface shape error based on the response matrix, the thermal deformation vector, and the heat flux vectors that satisfy the constraints. The surface shape optimization module is used to apply the heat flux vector corresponding to the minimum value of each residual surface shape error to the heating plate of the reflector to optimize the surface shape of the reflector. The heat flux vector module includes: The total deformation disturbance vector unit is used to determine each total deformation disturbance vector based on the thermal deformation vector, the initial deformation vector, and each disturbance term; A heat flux vector unit is used to determine each heat flux vector based on the response matrix and each total deformation disturbance vector. The heat flux vector unit is specifically used for: Each heat flux vector is determined based on the inverse matrix of the product of the transpose and the response matrix, the transpose of the response matrix, and each total deformation perturbation vector.

9. The surface shape optimization device for a reflector according to claim 8, characterized in that, Also includes: The heat flux vector application module is used to sequentially apply heat flux vectors to each heating element to obtain the corresponding heat flux deformation data of the reflector. The response matrix module is used to determine the response matrix based on the heat flux deformation data of the reflector.

10. The reflector surface shape optimization device according to claim 8, characterized in that, Also includes: The thermal power application module is used to apply the thermal power of the light source to the light spot of the reflector to obtain thermal deformation data of the reflector. A thermal deformation vector module is used to determine the thermal deformation vector based on the thermal deformation data of the reflector.

11. The reflector surface shape optimization device according to claim 8, characterized in that, The total deformation disturbance vector unit includes: A thermal deformation disturbance vector sub-unit is used to determine each thermal deformation disturbance vector based on the maximum value of the thermal deformation vector and each disturbance term; The total deformation disturbance vector sub-unit is used to determine each total deformation disturbance vector based on the thermal deformation vector, the initial deformation vector, and each thermal deformation disturbance vector.

12. The reflector surface shape optimization device according to claim 8, characterized in that, The heat flux vector module is specifically used for: Each heat flux vector is determined using the following formula: ； in, The response matrix, Let be the heat flux vector. The initial deformation vector; Let be the thermal deformation vector. For the disturbance term, Let be the total deformation disturbance vector.

13. The reflector surface shape optimization device according to claim 8, characterized in that, The residual surface error module includes: A thermal deformation disturbance vector unit is used to determine each thermal deformation disturbance vector based on the maximum value of the thermal deformation vector and each disturbance term; The residual surface error unit is used to determine each residual surface error based on the response matrix, the thermal deformation vector, the initial deformation vector, each thermal deformation disturbance vector, and each heat flux vector that satisfies the constraint conditions.

14. The reflector surface shape optimization device according to claim 13, characterized in that, The residual surface error module is specifically used for: Each residual surface shape error is determined using the following formula: ； in, The residual surface shape error, The response matrix, Let be the heat flux vector that satisfies the constraints. The initial deformation vector; Let be the thermal deformation vector. For the disturbance term, Let be the thermal deformation disturbance vector.

15. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the surface shape optimization method for the mirror according to any one of claims 1 to 7.

16. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the surface shape optimization method for the reflector according to any one of claims 1 to 7.

17. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the surface shape optimization method for the reflector according to any one of claims 1 to 7.

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