A mirror topology optimization method

Abstract

The application relates to the technical field of optical system design, in particular to a mirror topology optimization method, which comprises the following steps: establishing an initial structure of a mirror according to imaging requirements of an optical system; taking a first optimization object of the mirror as an optimization target, taking a second optimization object of the mirror as a constraint, determining an optimization method and a design variable, and establishing a topology optimization model; calculating the first optimization object and the second optimization object based on the topology optimization model; updating the design variable based on the first optimization object and the second optimization object; judging whether the updated design variable reaches an optimization convergence condition; if the optimization convergence condition is reached, setting a threshold value of the design variable, and obtaining an optimized structure of the mirror. The application directly establishes the relationship between the imaging quality and the structure, considers the imaging quality and the structure weight, and effectively improves the optical performance of the mirror and the structure design efficiency.

Description

Technical Field

[0001] This application belongs to the field of optical system design technology, specifically a method for optimizing the topology of a reflector. Background Technology

[0002] Optical telescope systems play a vital role in modern economic and military fields. With the rapid development of modern technology, optical telescope systems not only require large fields of view and high resolution, but also excellent maneuverability. In reflecting and catadioptric telescope systems, the mirror is a crucial component determining optical performance. Increasing the mirror aperture can improve optical performance, but it also significantly increases weight. Due to constraints such as carrying capacity and cost, optical telescopes need to strictly control their weight while ensuring image quality. However, to improve optical performance, the mirror aperture needs to be increased; therefore, image quality and weight are contradictory technical requirements.

[0003] The structure of a reflector significantly impacts its imaging quality and weight. Currently, reflector structural design typically relies on several approaches: first, design based on experience, employing lightweight aperture structures such as triangles, hexagons, and circles. This method heavily depends on the designer's experience, cannot achieve optimal structure, and has a long design cycle; second, optimization focuses on the reflector's flexibility, which can yield the stiffest structure but cannot guarantee imaging quality; third, optimization methods target wave aberration, which can control various wave aberration components during light propagation, but wave aberration is not a direct evaluation of the optical system's imaging quality. Therefore, establishing a direct relationship between imaging quality and structure, balancing imaging quality and structural weight, and effectively improving the optical performance and structural design efficiency of reflectors has become a pressing issue. Summary of the Invention

[0004] The purpose of the embodiments in this specification is to provide a mirror topology optimization method that can directly establish the relationship between imaging quality and structure, taking into account both imaging quality and structural weight, and effectively improving the optical performance and structural design efficiency of the mirror.

[0005] To solve the above-mentioned technical problems, the embodiments in this specification are implemented as follows:

[0006] In a first aspect, a method for topology optimization of a reflector is provided, comprising the following steps: establishing an initial structure of the reflector according to the imaging requirements of the optical system; determining the optimization method and design variables, and establishing a topology optimization model, with a first optimization object of the reflector as the optimization objective and a second optimization object of the reflector as the constraint; calculating the first optimization object and the second optimization object based on the topology optimization model; updating the design variables based on the first optimization object and the second optimization object; determining whether the updated design variables meet the optimization convergence condition; if the optimization convergence condition is met, setting a threshold for the design variables, and obtaining the optimized structure of the reflector; wherein, the first optimization object is one of the size index of the light spot and the structural index of the reflector, and the second optimization object is the other of the size index of the light spot and the structural index of the reflector.

[0007] As can be seen from the technical solutions provided in the embodiments of this specification above, the mirror topology optimization method provided in the embodiments of this invention is a mirror topology optimization method based on the size index of the light spot. By using the size index of the light spot to measure the imaging quality of the optical system on an object, the relationship between the mirror's structure and imaging quality can be directly established. This effectively balances the contradictory performance requirements of imaging quality and structural lightweighting, thus balancing imaging quality and structural weight, and effectively improving the optical performance and structural design efficiency of the mirror. For example, while meeting the structural weight requirements, the imaging quality of the system can be improved as much as possible. Therefore, this method can directly and effectively improve the imaging quality of the mirror and shorten the structural design cycle. Compared with traditional empirical methods, this method has complete theoretical support, achieving high mirror design efficiency and good optical performance. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments or prior art of this specification, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a flowchart illustrating a method for optimizing the topology of a reflector according to an embodiment of the present invention;

[0010] Figure 2(a) is a front view of the initial structure of the mirror in the mirror topology optimization method provided according to an embodiment of the present invention;

[0011] Figure 2(b) is a top view of the initial structure of the mirror shown in Figure 2(a);

[0012] Figure 3This is a schematic diagram of the optimization curves for the target and constraints using the mirror topology optimization method provided in the embodiment of the present invention;

[0013] Figure 4(a) is a schematic diagram of the optimized structure of the reflector after optimization by the reflector topology optimization method provided in the embodiment of the present invention. Figure 1 ;

[0014] Figure 4(b) is a schematic diagram of the mirror structure shown in Figure 4(a);

[0015] Figure 5 This is a schematic diagram of the light spot of the initial structure and the optimized mirror structure in the mirror topology optimization method provided according to an embodiment of the present invention.

[0016] 1-Mirror surface; 2-Design area; 3-Mounting hole. Detailed Implementation

[0017] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort should fall within the protection scope of this document.

[0018] This invention provides a mirror topology optimization method that can directly establish the relationship between imaging quality and structure, balancing imaging quality and structural weight, and effectively improving the optical performance and structural design efficiency of the mirror. The mirror topology optimization method and its various steps provided in this specification will be described in detail below.

[0019] Example 1

[0020] Reference Figure 1As shown in the embodiment of the present invention, a mirror topology optimization method is provided. The first optimization object is one of the light spot size index and the mirror's structural index, and the second optimization object is the other of the light spot size index and the mirror's structural index. The light spot size index of the optical system, i.e., the size of the light spot, can be used as a constraint, while the mirror's structural index, i.e., its volume, volume fraction, or weight and mass, can be used as the optimization objective. This approach can maximize the lightweighting of the structure while ensuring the mirror's imaging quality. Alternatively, the light spot size index can be used as the optimization objective, while the mirror's structural index is used as a constraint. This approach maximizes the imaging quality of the mirror while ensuring the mirror's weight meets requirements. The light spot size index can be parameters such as the sum of the root-mean-square radii of the imaging spot of a single or multiple object points by the optical system, the root-mean-square, the maximum radius of the light spot, or the average value of the light spot radius. The light spot size index can measure the imaging quality of the optical system on an object.

[0021] The mirror topology optimization method provided in this invention can directly establish the relationship between the mirror's structure and imaging quality, balancing both imaging quality and structural weight. This method can directly optimize the imaging quality of the optical system at the image plane, effectively improving the optical performance and structural design efficiency of the mirror. The main objective of this invention is to perform topology optimization design of the mirror structure using the spot size as the target. Based on the optomechanical integration design concept, using the spot size to measure the imaging quality of the optical system on the object can effectively balance the contradictory performance requirements of imaging quality and lightweight design. While meeting the structural weight requirements, it can maximize the system's imaging quality. Therefore, this method can directly and effectively improve the imaging quality of the mirror and shorten the structural design cycle. Using the root mean square size of the spot formed by each point on the object as the target is essentially using the image formed by the mirror on the object as the target, which can directly and effectively improve the imaging quality of the mirror on the object. The mirror topology optimization method provided in this invention is scalable and can be applied to the structural optimization design of multiple mirrors.

[0022] This invention can be described as a mirror topology optimization method with the root mean square radius of the light spot as the optimization target. The light spot is the image formed by the optical system on an object point, and its size directly reflects the imaging quality of the system. The point images formed by the optical system at each point of the object constitute the object's image. Optimizing the structure with the size of the light spot formed by each object point as the optimization target is an optimization that directly targets the imaging quality of the optical system, which can directly and effectively improve the imaging quality of the mirror structure.

[0023] An embodiment of the present invention provides a method for optimizing the topology of a reflector, which may include the following steps:

[0024] Step S10: Establish the initial structure of the reflector according to the imaging requirements of the optical system. The reflector topology optimization method provided in this embodiment of the invention first determines the mirror surface shape, aperture, and other parameters of the reflector according to the requirements of the optical system, and establishes the initial structure of the reflector.

[0025] Step S20: Taking the first optimization object of the reflector as the optimization objective and the second optimization object of the reflector as the constraint, determine the optimization method and design variables, and establish a topology optimization model. This model can use the root mean square radius of the light spot as the optimization objective and the volume, volume fraction, or mass of the reflector as constraints, employing a variable density method for optimization, and using node or element density as the structural optimization variable. Establish a finite element model of the reflector, add boundary conditions, set initial values ​​for the design variables, determine the incident point and direction of the light rays based on the optical system and the topology optimization model, and set the optimization convergence conditions.

[0026] Step S30: Calculate the first and second optimization objects based on the topology optimization model. The finite element method is used to analyze the mirror deformation. Orthogonal bases, such as Zernike bases or toroidal Zernike bases, are used to fit the mirror deformation. The fitted mirror deformation can be either sag displacement or normal displacement. Ray tracing is performed using the fitted deformed mirror to calculate the root mean square radius of the light spot on the image plane, which is the first optimization object. Then, the constraint values, i.e., the values ​​of the second optimization object, are calculated based on the structural optimization variables and the finite element mesh elements.

[0027] Step S40: Update the design variables based on the first and second optimization objects. The adjoint method can be used to analyze the sensitivity of the optimization objective and constraints to the structural optimization variables, and a gradient solver is used to update the design variables. Gradient solvers include, but are not limited to, MMA solvers, Snopt solvers, GCMMA solvers, and IPOPT solvers. Then, density filtering is performed to eliminate mesh dependencies, resulting in a smooth optimized mirror structure.

[0028] Step S50: Determine whether the updated design variables meet the optimization convergence conditions. If they do, set a design variable threshold and obtain the optimized structure of the reflector. Specifically, a design variable threshold can be set for the reflector; density variables with values ​​greater than the threshold after the current iteration constitute the optimized structure of the reflector. Optimize the reflector structure according to the topology optimization model to obtain the optimal structure that satisfies the optimization objective under the constraints. If the optimization convergence requirements are not met, repeat the above steps starting from step S30, performing multiple iterations until the optimization convergence conditions are met.

[0029] The mirror topology optimization method provided in this invention adopts an optomechanical integrated design concept. By utilizing deformed mirror surfaces for ray tracing, it achieves optical-mechanical coupling of the mirror, establishes a correlation between the size index of the light spot and structural optimization variables, and realizes topology optimization with the root mean square radius of the light spot as the optimization target. The light spot can measure imaging quality; using the imaging light spot at different positions of the object to be imaged as the optimization target can directly and effectively improve the imaging quality of the optical system.

[0030] Optionally, the topology optimization method for a reflector provided in this embodiment of the invention has the following components: a first optimization object is the size index of the light spot, and a second optimization object is the structural index of the reflector. The first optimization object of the reflector is used as the optimization objective, and the second optimization object of the reflector is used as a constraint. An optimization method and design variables are determined, and a topology optimization model is established. Specifically, this includes: using the size index of the light spot as the optimization objective and the mass index of the reflector as a constraint, determining structural optimization variables as design variables; and using a variable density method to optimize the size index of the light spot, using the density of finite element mesh nodes or finite element mesh elements as structural optimization variables. The variable density method establishes a functional relationship between the elastic modulus of the reflector material and the structural optimization variables.

[0031] Optionally, the mirror topology optimization method provided in this embodiment of the invention sets initial values ​​for design variables, optical analysis conditions, and optimization convergence conditions, specifically including: establishing a finite element analysis model of the mirror based on the topology optimization model, adding boundary conditions, and determining the initial values ​​of the density variables; determining the incident point and incident direction of the light rays, ensuring that the number of light rays balances the accuracy of optical analysis and the efficiency of optimization; and setting optimization convergence conditions, such as max|ρ k -ρ k-1 | <TOL,ρ k Let ρ be the density variable value in the k-th iteration. k-1 TOL represents the density variable value in the (k-1)th iteration, and TOL represents the upper limit of the difference between the density variables in two adjacent iterations.

[0032] Optionally, the mirror topology optimization method provided in this embodiment of the invention calculates a first optimization object and a second optimization object based on a topology optimization model, specifically including: analyzing the mirror surface deformation of the mirror using a finite element analysis model and calculating the mirror surface deformation parameters; fitting the mirror surface deformation parameters using an orthogonal basis to obtain a fitted deformed mirror surface; and performing ray tracing using the fitted deformed mirror surface to obtain the first optimization object and the second optimization object.

[0033] Optionally, the mirror topology optimization method provided in this embodiment of the invention updates the design variables based on the first optimization object and the second optimization object, specifically including: analyzing the sensitivity of the root mean square radius of the light spot and the volume fraction of the mirror to the density variable; updating the density variable using a gradient solver based on the sensitivity; and performing density filtering to eliminate the dependence on the finite element mesh.

[0034] Optionally, the mirror topology optimization method provided in this embodiment of the invention determines whether the updated density variable meets the optimization convergence condition, specifically including: the convergence condition is max|ρ k -ρ k-1 | <TOL,ρ k Let ρ be the density variable value in the k-th iteration. k-1 TOL represents the density variable value in the (k-1)th iteration, and TOL represents the upper limit of the difference between the density variables in two adjacent iterations.

[0035] Optionally, after determining whether the updated design variables meet the optimization convergence condition, if they do, a density variable threshold is set to obtain the optimized structure of the reflector. Specifically, this includes setting a structural density threshold for the reflector; density variables whose updated density variable values ​​in the current iteration step are greater than the density threshold constitute the optimized structure of the reflector. If the optimization convergence condition is not met, the calculation of the first and second optimization objects based on the topology optimization model is re-executed, and the design variables are updated based on the first and second optimization objects until the optimization convergence condition is met.

[0036] Optionally, the topology optimization method for a reflector provided in this embodiment of the invention uses the size of the light spot as the optimization objective and the structural parameters of the reflector as constraints to determine the optimization method and design variables, and establish a topology optimization model, specifically including:

[0037] The size index of the light spot is optimized using the variable density method, and the density variable of the finite element mesh node or finite element mesh cell is used as the structural optimization variable.

[0038] The topology optimization model is as follows:

[0039] Optimization goal:

[0040] KU = F

[0041] HC=P

[0042] Constraints:

[0043] J represents the optimization objective, is the root mean square radius of the light spot; m represents the number of rays used in the optical analysis; r iLet be the distance from the intersection point of the i-th ray and the image plane to the ideal image point; KU=F is the governing equation for the deformation of the mirror, K is the finite element stiffness matrix of the optimized structure, U is the displacement vector to be solved, and F is the load vector of the mirror structure; HC=P is the calculation equation for the fitting of the mirror deformation, C is the fitting coefficient to be solved, and H and P are the coefficient matrix and the right-hand side, respectively; S1 is the ideal mirror surface, and S2 is the image plane; The substrate for fitting the mirror deformation; r s1 k is the normalized radius for deformation fitting; 0i Let k be the position vector of the ray incident point. 1i Let k be the direction of light incidence. 2i The direction of light reflection; t 1i Let t be the optical path length from the point of incidence of the light to the reflecting mirror. 2i ρ is the optical path length from the point where the ray intersects the mirror surface to the image plane; e v represents the structural optimization variable of node e or element in a finite element; e γ represents the volume of node e or element in the finite element method; V is the volume of the design domain; γ represents the volume fraction; N is the number of structural optimization variables. The volume fraction is the ratio of the volume of the optimized structure in the design domain of the reflector to the volume of the design domain, and is used to constrain the weight of the reflector structure.

[0044] The topology optimization model is used to optimize the structure by using the variable density method. The density of finite element nodes or elements is used as the structural optimization variable, and the elastic modulus of the material is interpolated. SIMP or RAMP interpolation models can be used.

[0045] Configure the finite element analysis model of the reflector, add boundary conditions, and assign initial values ​​to the density variable. Determine the incident point and direction of the light rays based on the optical system and topology optimization model. The number of light rays should balance the accuracy of the optical analysis with the efficiency of the topology optimization. Set the optimization convergence condition, max|ρ k -ρ k-1 | <TOL,ρ k Let ρ be the density variable value in the k-th iteration. k-1 The value of the density variable is given for the (k-1)th iteration. The setting of TOL should take into account both computational efficiency and optimization effect.

[0046] Optionally, the mirror topology optimization method provided in this embodiment of the invention uses the finite element method to analyze the mirror surface deformation and calculate the mirror surface deformation parameters. Specifically, it includes: analyzing the mirror surface deformation using the finite element method, calculating the sag displacement or normal displacement of the mirror surface deformation, assuming the ideal mirror surface shape z = f(x,y), where the z-axis is the optical axis direction of the mirror, and the mirror node (x... i ,y i ,z i The nodal displacement of ) is (u i ,vi ,w i The elevation displacement is: δ i =z i +w i -f(x i +u i ,y i +v i ); the mirror node (x) of the reflecting mirror i ,y i ,z i The unit normal of ) is n i The normal displacement is: δ i =(u i ,v i ,w i )·n i .

[0047] Optionally, the mirror topology optimization method provided in this embodiment of the invention, based on fitting the mirror deformation parameters using the least squares method to obtain a fitted deformed mirror, specifically includes: fitting the mirror deformation parameters using an orthogonal basis to obtain a least squares objective function:

[0048] Among them, w i Let δ be the weight of node i. i Let c be the deformation to be fitted at node i of the finite element mesh. j Let j be the coefficient of the basis term. Let j be the value of the basis at node i;

[0049] Minimizing the least squares objective function yields the fitting equation for the deformable mirror: HC = P, where the elements in H are... Elements in P Based on the least squares method, orthogonal bases such as the Zernike basis and the cyclic Zernike basis are used to fit the mirror deformation. The fitted mirror deformation can be either the sag displacement or the normal displacement.

[0050] Optionally, the mirror topology optimization method provided in this embodiment of the invention uses the fitted deformable mirror surface to perform ray tracing to obtain a first optimization object and a second optimization object, specifically including:

[0051] Optical analysis was performed based on the fitting equation of the deformable mirror to calculate the root mean square radius of the light spot: in The point where the i-th ray intersects the image plane is P. 2i (x 2i ,y 2i ,z 2i The ideal image point is P3(x3,y3,z3);

[0052] The volume fraction of the mirror is calculated based on the finite element mesh and density variables.

[0053] Optionally, the mirror topology optimization method provided in this embodiment of the invention analyzes the sensitivity of the first optimization object and the second optimization object to design variables, specifically including: using the adjoint method to analyze the sensitivity of the root mean square radius of the light spot and the volume fraction of the mirror to density variables.

[0054] Sensitivity of the root mean square radius of the light spot to the density variable:

[0055]

[0056] Where, λ 1i , λ 2i Solve the equation:

[0057]

[0058] Sensitivity of the mirror's volume to density variables:

[0059] Then, a gradient solver is used to update the density variables. The gradient solver can include, but is not limited to, MMA solvers, Snopt solvers, GCMMA solvers, and IPOPT solvers. Next, density filtering is performed to eliminate dependence on the finite element mesh. It is then determined whether the updated density variables meet the optimization convergence criteria. If they do, the optimization stops, a threshold for the mirror's density variables is set, and the optimized structure of the mirror is extracted. Otherwise, the above steps are repeated starting from the finite element analysis.

[0060] Optionally, density filtering is performed to eliminate the dependence on the finite element mesh and to make the extracted optimized structure of the mirror smooth, specifically:

[0061]

[0062] Where ρ is the density variable; R represents the density variable after density filtering. min R is the filtering radius. To achieve a good filtering effect, R... min The size is typically taken as 1.5 to 3 times the finite element mesh size. Other filtering methods can also be used, such as projection filtering, or sensitivity filtering can be added.

[0063] Example

[0064] See Figures 2(a)-5 As shown, the topology optimization method for a circular mirror is used in this embodiment of the invention to perform topology optimization design. The results show that the topology optimization method is practical and effective.

[0065] The initial structure of the circular reflector is shown in Figure 2(a) and Figure 2(b). The mirror surface is parabolic, the focal length is 1m, the aperture is 0.2m, the mirror thickness is 5mm, and the thickness of the back structure of the reflector is 20mm. It adopts a passive support method with 3 points on the back.

[0066] The embodiment uses the root-mean-square radius of the light spot formed by the mirror on an object at infinity as the optimization objective, and performs topology optimization design of the mirror structure under the constraint of a volume fraction of 0.2 in the design domain. The topology optimization model is as follows:

[0067] Optimization goal:

[0068] KU = F

[0069] HC=P

[0070] Constraints:

[0071] J represents the optimization objective, which is the root mean square radius of the light spot; m represents the number of rays used in the optical analysis; r i Let S1 be the distance from the intersection point of the i-th ray and the image plane to the ideal image point; KU = F is the governing equation for mirror deformation; HC = P is the calculation equation for fitting mirror deformation; S1 is the ideal mirror plane, and S2 is the image plane; The substrate for fitting the mirror deformation; r s1 k is the normalized radius for deformation fitting; 0i Let k be the position vector of the ray incident point. 1i Let k be the direction of light incidence. 2i The direction of light reflection; t 1i Let t be the optical path length from the point of incidence of the light to the reflecting mirror. 2i ρ is the optical path length from the point where the ray intersects the mirror surface to the image plane; e Represents the density variable of node e; v e Let γ represent the volume of node e, where γ is 0.2; N is the number of density variables.

[0072] (1) A finite element analysis model was established based on the reflector structure, with gravity load and fixed constraints added. Nodal density variables were used and initial values ​​were assigned to the density variables. The material interpolation model was E = E0(ρ min +(1-ρ min )ρ P E0 is the elastic modulus of the material, ρ is the density variable, and P is the penalty factor. min A value of 0.001 can prevent the stiffness matrix from being singular;

[0073] (2) Take a plane perpendicular to the optical axis at a distance of 1m above the mirror surface, and take 1261 uniformly distributed light incident points on the plane, and set the incident direction of the light to be parallel to the optical axis.

[0074] (3) Set the optimization convergence condition, max|ρ k -ρ k-1 | <TOL,ρ k Let ρ be the density variable value in the k-th iteration. k-1 The value of the junction density variable is the (k-1)th iteration. The setting of TOL should take into account both computational efficiency and optimization effect, and is set to 1e-6.

[0075] (4) The mirror deformation of the reflector is calculated using the finite element method. The sag displacement of the mirror deformation is calculated based on the nodal coordinates of the mirror surface, and the mirror deformation is extracted:

[0076]

[0077] (5) Based on the least squares method, the sagittal displacement of the mirror is fitted using the Zernike orthogonal basis;

[0078] (6) Based on the fitted deformed mirror and the incident point and direction of the light rays, perform optical analysis and calculate the root mean square radius of the light spot on the Gaussian image plane, P. 2i (x 2i ,y 2i ,z 2i Let P(i) be the intersection point of the i-th ray and the image plane, and let P3(0,0,1) be the ideal image point. The root mean square radius of the light spot is

[0079] (7) Calculate the volume fraction of the mirror structure based on density variables and finite element mesh;

[0080] (8) Based on the sensitivity of the mirror's surface density variable, the target's sensitivity to the structural density variable:

[0081]

[0082] λ 1i , λ 2i Solve the equation:

[0083]

[0084] Sensitivity of volume constraints to density variables:

[0085] (9) Update the latest value of the density variable using the MMA solver based on the objective, constraint values ​​and their sensitivity;

[0086] (10) Perform density filtering to eliminate dependence on finite element mesh and improve the smoothness of the optimized mirror structure;

[0087] ρ is the density variable. R represents the density-filtered variables. min The filter radius is denoted as .

[0088] (11) Determine whether the updated density variable meets the optimization convergence condition. If yes, stop the optimization and set the density variable threshold to 0.6. Extract the optimized structure of the reflector. Figures 4(a) and 4(b) are schematic diagrams of the optimized structure of the reflector. If no, return to (4) to continue the finite element calculation and optimization.

[0089] From the optimization curve Figure 3 It can be seen that the topology optimization method can effectively optimize the size of the light spot under the condition of satisfying the volume constraint, and has good convergence. Figure 3 Curve 1 in the figure represents the normalized target curve, and curve 2 represents the volume fraction curve. The root mean square radius of the light spot in the initial structure of the reflector was 6.19e-7m, while the root mean square radius of the optimized structure of the reflector was 4.29e-8m, a reduction of 93.1%. (See [reference needed]). Figure 5 As shown.

[0090] The above analysis shows that the mirror topology optimization method provided in this invention is based on the size index of the light spot. By using the size index of the light spot to measure the imaging quality of the optical system, the relationship between the mirror's structure and imaging quality can be directly established. This effectively balances the contradictory performance requirements of imaging quality and structural lightweighting, thus balancing both imaging quality and structural weight, and effectively improving the optical performance and structural design efficiency of the mirror. For example, while meeting the structural weight requirements, the imaging quality of the system can be improved as much as possible. Therefore, this method can directly and effectively improve the imaging quality of the mirror and shorten the structural design cycle. Compared with traditional empirical methods, this method has complete theoretical support, achieving high mirror design efficiency and good optical performance.

[0091] In summary, the above description is merely a preferred embodiment of this specification and is not intended to limit the scope of protection of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

Claims

1. A method for optimizing the topology of a reflector, characterized in that, Includes the following steps: Establish the initial structure of the mirror according to the imaging requirements of the optical system; Taking the first optimization object of the reflector as the optimization objective and the second optimization object of the reflector as the constraint, the optimization method and design variables are determined, and a topology optimization model is established, including: The size index of the light spot is optimized by using the variable density method, and the density variable of the finite element mesh node or finite element mesh element is used as the structural optimization variable; The topology optimization model is as follows: Optimization goal: Constraints: J is the optimization target, and is the root mean square radius of the light spot; m represents the number of rays used in the optical analysis; Let be the distance from the intersection point of the i-th ray and the image plane to the ideal image point; KU=F is the governing equation for the deformation of the mirror, where K is the finite element stiffness matrix of the mirror structure, U is the displacement vector to be solved, and F is the load vector of the mirror structure; HC=P is the calculation equation for the fitting of the mirror deformation, where C is the fitting coefficient to be solved, and H and P are the coefficient matrix and the right-hand side, respectively; S1 is the ideal mirror surface, and S2 is the image plane; The substrate is used for fitting mirror deformation; k is the normalized radius for deformation fitting; 0i Let k be the position vector of the ray incident point. 1i Let k be the direction of light incidence. 2i The direction of light reflection; t 1i Let t be the optical path length from the point of incidence of the light to the reflecting mirror. 2i The optical path length from the point where the ray intersects the mirror surface to the image plane; This represents the structural optimization variable of node e or element in the finite element mesh; This represents the volume of node e or element in the finite element mesh; For the volume of the design domain, Represents volume fraction; N is the number of structural optimization variables; It also includes setting the initial values ​​of the design variables, optical analysis conditions, and optimization convergence conditions, specifically: Establish a finite element analysis model of the reflector, add boundary conditions, and determine the initial values ​​of the density variables; Determine the incident point and direction of the light rays, and the number of light rays should take into account both the accuracy of optical analysis and the efficiency of optimization. Set optimization convergence conditions. , ρ k Let ρ be the density variable value in the k-th iteration. k-1 Let TOL be the density variable value of the (k-1)th iteration, and TOL be the upper limit of the difference between the density variables of two adjacent iterations. The calculation of the first optimization object and the second optimization object based on the topology optimization model specifically includes: The finite element analysis model is used to analyze the mirror surface deformation and calculate the mirror surface deformation parameters, specifically including: The finite element method is used to analyze the mirror deformation, calculating the sag or normal displacement of the mirror deformation. Assuming an ideal mirror surface shape z = f(x,y), where the z-axis is the optical axis of the mirror, and the mirror node (x...)... i ,y i ,z i The nodal displacement of ) is (u i ,v i ,w i The elevation displacement is: The mirror node (x) of the reflecting mirror i ,y i ,z i The unit normal is The normal displacement is: ; The deformation parameters of the mirror are fitted using an orthogonal basis to obtain a fitted deformed mirror, specifically including: The mirror deformation parameters are fitted using an orthogonal basis to obtain the least-squares objective function: ,in, Let i be the weight of node i in the finite element mesh. Let be the deformation to be fitted at node i. Let j be the coefficient of the basis term. Let be the value of the j-th basis term at node i; minimize the least squares objective function to obtain the fitting equation for the deformable mirror: HC = P, where the elements in H are... Elements in P ; Ray tracing is performed using the fitted deformed mirror to obtain the first optimized object and the second optimized object, specifically including: Optical analysis was performed based on the fitting equation of the deformable mirror surface to calculate the root mean square radius of the light spot: ,in The intersection point of the i-th ray and the image plane is... Ideal image point is ; The volume fraction of the reflector is calculated based on the finite element mesh and the density variable; Update the design variables based on the first optimization object and the second optimization object; Determine whether the updated design variables meet the optimization convergence criteria; If the optimization convergence condition is met, then the threshold of the design variables is set to obtain the optimized structure of the reflector; The first optimization target is one of the size index of the light spot and the structural index of the reflector, and the second optimization target is the other of the size index of the light spot and the structural index of the reflector.

2. The mirror topology optimization method according to claim 1, characterized in that, The calculation of the first optimization object and the second optimization object based on the topology optimization model specifically includes: The finite element analysis model is used to analyze the mirror surface deformation and calculate the mirror surface deformation parameters. The deformation parameters of the mirror are fitted using an orthogonal basis to obtain the fitted deformed mirror. Ray tracing is performed using the fitted deformable mirror to obtain the first optimized object and the second optimized object.

3. The mirror topology optimization method according to claim 1, characterized in that, Updating the design variables based on the first optimization object and the second optimization object specifically includes: Analyze the sensitivity of the root mean square radius of the light spot and the volume fraction of the reflector to the density variable; The density variable is updated using a gradient solver based on the sensitivity. Density filtering is performed to eliminate the dependence on the finite element mesh.

4. The mirror topology optimization method according to claim 3, characterized in that, The sensitivity of the root mean square radius of the light spot and the volume fraction of the mirror to the density variable is analyzed, specifically including: The sensitivity of the root mean square radius of the light spot and the volume fraction of the mirror to the density variable was analyzed using the adjoint method: The sensitivity of the root mean square radius of the light spot to the density variable: ， in, , Solve the equation: The sensitivity of the volume of the mirror to density variables: .

5. The mirror topology optimization method according to claim 1, characterized in that, If the optimization convergence condition is met, the density variable threshold is set to obtain the optimized structure of the mirror, specifically including: Set the density threshold of the reflector. Density variables whose values ​​are greater than the density threshold in the current iteration step constitute the optimized structure of the reflector. Correspondingly, after determining whether the updated design variables meet the optimization convergence conditions, the method further includes: If the optimization convergence condition is not met, the calculation of the first optimization object and the second optimization object based on the topology optimization model is repeated, and the design variables are updated based on the first optimization object and the second optimization object until the optimization convergence condition is met.

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