Damping factor updating method in optical optimization

Abstract

The present invention provides a damping factor updating method in optical optimization, comprising the following steps: a preprocessing step S0, setting an initial value: setting an initial damping factor D0, a contraction factor s, an amplification factor a and a maximum scaling number t_max; S1, calculating an initial evaluation function #imgabs0 according to an initial structural parameter variable x0; S2, contracting the initial damping factor D0 s_t times by the contraction factor s to obtain a suboptimal damping factor D c and evaluation function #imgabs1#S3, if the evaluation function #imgabs2# is greater than or equal to the initial evaluation function #imgabs3#, the suboptimal damping factor D is adjusted by the amplification factor a. c Perform a_t times of amplification to obtain the optimal damping factor D y The present invention can improve the robustness of the damped least squares method by continuously updating the damping factor, and can improve the optimization efficiency while the evaluation function converges smoothly.

Description

Technical Field

[0001] The invention relates to the technical field of optical system optimization, and in particular to a damping factor updating method in optical optimization. Background Art

[0002] Optimization in optical system design is the process of obtaining the best result under given conditions, with the goal of minimizing the evaluation function under the constraints of boundary conditions. Since complex optical systems also have many structural parameters to be optimized, including both continuous variables and discrete variables, aberrations are nonlinear functions of variables and no analytical expressions can be found. There is generally no orthogonal relationship between aberrations. The evaluation function composed of aberration values ​​has numerous local minima in the multidimensional space of structural variables. Therefore, the optimization of optical systems has always been the core issue in the development of optical system design.

[0003] Damped least squares method is a common method for automatic optimization design of optical systems. It uses damping factor to control the length of solution vector. In each optimization cycle, by selecting appropriate damping factor, it solves the nonlinear problem of aberration function and makes the evaluation function converge quickly from the initial point to the local minimum. Therefore, the update method of damping factor in each optimization plays a crucial role in the speed and convergence effect of the algorithm.

[0004] The existing methods for updating the damping factor mainly include the nonlinear factor judgment method and the traversal search method. Among them, the nonlinear factor judgment method adjusts the damping factor according to the value of the nonlinear factor in the optimization cycle. For example, in the kth optimization cycle in the invention patent 202110421513.X, if the calculated nonlinear factor r is less than 0.25, the damping factor is updated in the following way: k+1 =10λ k ; If the calculated nonlinear factor r is greater than 0.75, the damping factor is updated as λ k+1 =0.1λ k ; In other cases, the damping factor is updated as λ k+1 =λ k . The traversal search method is also called the trial method. The damping factor is scaled in each optimization cycle until the next evaluation function is smaller than the previous evaluation function. As long as the damping factor is large enough, the damping factor that reduces the evaluation function can always be found. However, both of the above methods have certain limitations. The linear judgment threshold set by the nonlinear factor judgment method is a fixed value. For different optical systems, the use of the same fixed judgment threshold will cause the evaluation function to be unable to converge stably. Although the traversal search method can ensure that the evaluation function is constantly decreasing, it is easy to fall into a local minimum near the initial value and cannot jump out, and the convergence speed is slow. Summary of the invention

[0005] In view of the above problems, the purpose of the present invention is to propose a damping factor updating method in optical optimization, so as to solve the problem of unstable and slow descent of evaluation function in optical optimization.

[0006] To achieve the above object, the present invention adopts the following specific technical solutions:

[0007] The present invention discloses a damping factor updating method in optical optimization, comprising the following steps:

[0008] Preprocessing step S0, setting initial values: setting initial damping factor D0, contraction factor s, amplification factor a and maximum zoom times t_max;

[0009] S1. Calculate the initial evaluation function based on the initial structural parameter variable x0

[0010] S2, shrink the initial damping factor D0 s_t times by the shrinkage factor s to obtain a suboptimal damping factor D c and the evaluation function

[0011] S3. If the evaluation function Greater than or equal to the initial evaluation function Then the suboptimal damping factor D is adjusted by the amplification factor a. c Perform a_t times of amplification to obtain the optimal damping factor D y .

[0012] Preferably, the suboptimal damping factor D c =D0 / (s s_t ).

[0013] Preferably, step S2 includes the following sub-steps:

[0014] S21, performing a first contraction on the initial damping factor D0 by the contraction factor s to obtain a damping factor D s_t＝1 ;

[0015] The damping factor D s_t＝1 =D0 / s;

[0016] Calculate the structural parameter variable step length Δx0 according to the solution formula of the damped least squares method;

[0017] Calculate the structural parameter variable x1 according to the structural parameter variable formula;

[0018] The evaluation function is calculated based on the structural parameter variable x1

[0019] If the evaluation function Less than or equal to the initial evaluation function Then proceed to the next step;

[0020] If the evaluation function Greater than the initial evaluation function Then the suboptimal damping factor D is obtained c =D s_t＝1 ;

[0021] S22, the damping factor D is affected by the shrinkage factor s. s_t＝k-1 Perform the kth contraction to obtain the damping factor D s_t＝k ;

[0022] The damping factor D s_t＝k =D0 / (s k );

[0023] Calculate the structural parameter variable step length Δx according to the solution formula of the damped least squares method k-1 ;

[0024] According to the structural parameter variable formula, the structural parameter variable x is calculated. k ;

[0025] According to the structural parameter variable x k Calculate the evaluation function

[0026] If the evaluation function Less than or equal to the evaluation function Then the k+1th contraction process is carried out;

[0027] If the evaluation function Greater than the evaluation function Then the suboptimal damping factor D is obtained c =D s_t＝k ;

[0028] S23, repeat step S22 until the evaluation function Greater than the evaluation function Or the contraction times s_t is greater than or equal to the maximum scaling times t_max, and the suboptimal damping factor D is obtained. c and the evaluation function

[0029] Preferably, the solution formula of the damped least squares method is:

[0030] Δx k =-(A k T A k +DI) -1 A k Tf k-1 ;

[0031] in,

[0032] I is a diagonal matrix;

[0033] A is the difference quotient matrix of the aberration f to the structural parameter variable x;

[0034] D is the damping factor;

[0035] Δx k The step size of the structural parameter variables calculated for the kth optimization iteration.

[0036] Then Δx k Assigned to the kth structural parameter variable, get x k+1 The calculation formula is:

[0037] x k+1 =x k +Δx k ;

[0038] in,

[0039] x k is the k-th structural parameter variable, x k+1 is the k+1th structural parameter variable, Δx k is the step size of the structural parameters calculated at the kth iteration.

[0040] Preferably, step S3 includes the following sub-steps:

[0041] S31, the suboptimal damping factor D is amplified by the amplification factor a. c Perform the first amplification to obtain the damping factor D a_t＝1 ;

[0042] D a_t＝1 =D c ×a;

[0043] According to the damping factor D a_t＝1 Calculate the evaluation function

[0044] If the evaluation function Greater than or equal to the initial evaluation function Then proceed to the next amplification process;

[0045] If the evaluation function Less than the initial evaluation function The optimal damping factor D is obtained y .

[0046] S32, the suboptimal damping factor D is amplified by the amplification factor a. cPerform the jth amplification to obtain the damping factor D a_t＝j ;

[0047] D a_t＝j =D c ×a j ;

[0048] According to the damping factor D a_t＝j Calculate the evaluation function

[0049] If the evaluation function Greater than or equal to the evaluation function Then proceed to the next amplification process;

[0050] If the evaluation function Less than the evaluation function The optimal damping factor D is obtained y .

[0051] S33, repeat step S32 until the evaluation function Less than the evaluation function Or the amplification times a is greater than or equal to the maximum scaling times t_max, and the optimal damping factor D is obtained. y .

[0052] Preferably, the initial damping factor D0 is in the range of 0.1-2.

[0053] Preferably, the value of the shrinkage factor s is greater than or equal to the value of the magnification factor a.

[0054] Preferably, the maximum zooming times t_max ranges from 10 to 20. Compared with the prior art, the damping factor updating method in optical optimization of the present invention has the following advantages:

[0055] (1) High robustness

[0056] The method of the present invention can make the error function drop steadily by optimizing the damping factor a limited number of times. At the same time, due to the limitation of the maximum number of zooming times, the algorithm will not fall into the local minimum and be unable to jump out. Therefore, the algorithm of the present invention is used to update the damping factor, which can improve the robustness of the damped least squares method.

[0057] (2) High optimization efficiency

[0058] The present invention automatically shrinks the damping factor calculated in the previous step at each optimization iteration, avoiding the problem of slow convergence caused by the suppression of the variable step size in the early stage of optimization. At the same time, the algorithm sets the maximum number of zooms to avoid the damping factor being enlarged or reduced infinitely, and then performing optical tracing and evaluation function calculation to occupy a large amount of computing time. Therefore, the present invention can improve the optimization efficiency while the evaluation function converges smoothly. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 4 is a flow chart of a damping factor updating method in optical optimization provided according to an embodiment of the present invention.

[0060] Figure 2 It is a flowchart of a damping factor updating method in optical optimization provided according to an embodiment of the present invention.

[0061] Figure 3 It is a schematic diagram of setting structural parameter variables of a Cooke optical system according to a damping factor updating method in optical optimization provided by an embodiment of the present invention.

[0062] Figure 4 It is a schematic diagram comparing the optimization effects of the method of the present invention and other methods provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0064] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0065] Figure 1 A schematic flow chart of a damping factor updating method in optical optimization provided according to an embodiment of the present invention is shown.

[0066] Figure 2 A flowchart of a damping factor updating method in optical optimization provided according to an embodiment of the present invention is shown.

[0067] like Figure 1-2 As shown, the damping factor updating method in optical optimization provided by the embodiment of the present invention includes the following steps:

[0068] Preprocessing step S0, setting initial values: setting the initial damping factor D0, the contraction factor s, the amplification factor a and the maximum zooming times t_max.

[0069] The initial damping factor D0 should not be set too small or too large.

[0070] If the initial damping factor D0 is too small, the step size of the solved structural parameter variables will be too large, which may cause oscillation of the evaluation function. If the initial damping factor D0 is too large, the step size of the solved variables will be too small, and the convergence speed of the evaluation function will slow down. The preferred range of the initial value D0 of the damping factor D is: 0.1-2.

[0071] The shrinkage factor s refers to the ratio of the damping factor to be reduced each time during the damping factor optimization process.

[0072] The amplification factor a refers to the multiple by which the damping factor is amplified each time during the damping factor optimization process.

[0073] In order to make the evaluation function converge faster, the value of the shrinkage factor s needs to be greater than the value of the amplification factor a.

[0074] The maximum scaling times t_max refers to the maximum times of contraction or enlargement of the damping factor. If the maximum scaling times t_max is set too large, the convergence speed will be reduced, and if it is too small, the evaluation function will not descend smoothly. The preferred range of the maximum scaling times t_max is: 10 to 20.

[0075] Figure 3 A schematic diagram of setting structural parameter variables of a Cooke optical system according to a damping factor updating method in optical optimization provided by an embodiment of the present invention is shown.

[0076] like Figure 3 As shown, the Cooke optical system in this embodiment sets 6 curvature radius variables and 2 interval variables, and the structural parameter variables can be expressed as x0=[x 01, x 02, x 03, x 04, x 05, x 06, x 07, x 08 ], based on the initial parameters, the evaluation function of the initial optical system can be calculated

[0077] S1. Calculate the initial evaluation function based on the initial structural parameter variable x0

[0078] According to the initial structural parameter variable x0, the initial evaluation function can be calculated by the known ray tracing formula

[0079] The evaluation function is:

[0080]

[0081] in,

[0082] is the evaluation function;

[0083] f i is the generalized aberration including weights.

[0084] S2, shrink the initial damping factor D0 s_t times by shrinking the factor s to obtain the suboptimal damping factor D c ;

[0085] Suboptimal damping factor D c =D0 / (s s_t ).

[0086] Step S2 includes the following sub-steps:

[0087] S21, the initial damping factor D0 is first shrunk by the shrinkage factor s to obtain the damping factor D s_t＝1 ;

[0088] Damping factor D s_t＝1 =D0 / s;

[0089] Calculate the structural parameter variable step length Δx0 according to the solution formula of the damped least squares method;

[0090] The solution formula of the damped least squares method is:

[0091] Δx k =-(A k T A k +DI) -1 A k T f k-1 (2)

[0092] in,

[0093] I is a diagonal matrix;

[0094] A is the difference quotient matrix of aberration f to structural parameter x;

[0095] D is the damping factor;

[0096] Δx k The step size of the structural parameter variables calculated for the kth optimization iteration.

[0097] The damped least squares method can be used to solve the step size Δx of each iteration of the structural parameter variable x. k, the larger the damping factor, the smaller the variable step length Δx k The smaller the damping factor is, the higher the oscillation height is suppressed. The smaller the damping factor is, the smaller the variable step length Δx is. k The bigger it is.

[0098] In order to make the evaluation function For smooth and fast convergence, the damping factor needs to be updated in each optimization iteration.

[0099] The damped least squares solution formula (2) can be used to calculate the structural parameter variable step length Δx k , and then assign the step size to the k-th structural parameter variable to obtain x k+1 The calculation formula is:

[0100] x k+1 =x k +Δx k (3)

[0101] in,

[0102] x k is the k-th structural parameter variable, x k+1 is the k+1th structural parameter variable, Δx k is the step size of the structural parameters calculated at the kth iteration.

[0103] According to formula (3), the structural parameter variable x1 is calculated, and the evaluation function is calculated according to the structural parameter variable x1

[0104] Judging evaluation function Is it greater than the initial evaluation function?

[0105] If the evaluation function Less than the initial evaluation function Then proceed to the next step;

[0106] If the evaluation function Greater than or equal to the initial evaluation function Then the suboptimal damping factor D is obtained c =D s_t＝1 ;

[0107] S22, damping factor D through contraction factor s s_t＝k-1 Perform the kth contraction to obtain the damping factor D s_t＝k ;

[0108] Damping factor D s_t＝k =D0 / (s k );

[0109] The damping factor D s_t＝kSubstitute into formula (2) to calculate the structural parameter variable step length Δx k-1 ;

[0110] The structural parameter variable step length Δx k-1 Substitute into formula (3) to calculate the structural parameter variable x k ; Structural parameter variable x k Calculate the evaluation function

[0111] Judging evaluation function Is it greater than the evaluation function?

[0112] If the evaluation function Less than the evaluation function Then the k+1th contraction process is carried out;

[0113] If the evaluation function Greater than or equal to the evaluation function Then the suboptimal damping factor D is obtained c =D s_t＝k ;

[0114] S23, repeat step S22 until the evaluation function Greater than the evaluation function Or the contraction times s_t is greater than or equal to the maximum scaling times t_max, and the suboptimal damping factor D is obtained. c and the evaluation function

[0115] S3. If the evaluation function Greater than or equal to the initial evaluation function Then the suboptimal damping factor D is amplified by the factor a. c Perform a_t times of amplification to obtain the optimal damping factor D y .

[0116] D y =D c ×a a_t ;

[0117] Step S3 includes the following sub-steps:

[0118] S31, by amplifying the factor a to the suboptimal damping factor D c Perform the first amplification to obtain the damping factor D a_t＝1 ;

[0119] D a_t＝1 =D c ×a;

[0120] According to the damping factor D a_t＝1 Calculate the evaluation function

[0121] If the evaluation function Greater than or equal to the initial evaluation function Then proceed to the next amplification process;

[0122] If the evaluation function Less than the initial evaluation function The optimal damping factor D is obtained y .

[0123] S32, by amplifying the factor a to the suboptimal damping factor D c Perform the jth amplification to obtain the damping factor D a_t＝j ;

[0124] D a_t＝j =D c ×a j ;

[0125] According to the damping factor D a_t＝j Calculate the evaluation function

[0126] If the evaluation function Greater than or equal to the evaluation function Then proceed to the next amplification process;

[0127] If the evaluation function Less than the evaluation function The optimal damping factor D is obtained y .

[0128] S33, repeat step S32 until the evaluation function Less than the evaluation function Or the amplification times a is greater than or equal to the maximum scaling times t_max, and the optimal damping factor D is obtained. y .

[0129] In one embodiment of the present invention:

[0130] Initial damping factor D0 = 1;

[0131] The shrinkage factor s is taken as 2;

[0132] The amplification factor a is taken as 1.58;

[0133] The maximum number of zooms t_max is set to 10.

[0134] The present invention uses the MATLAB 2017a platform on a PC with Inter(R)CPU 2.7GHz, 4.00G, and uses the method provided by the present invention to Figure 3 The Cooke optical system shown has been optimized through simulation.

[0135] Figure 4 A schematic diagram comparing the optimization effects of the method of the present invention and other methods provided according to an embodiment of the present invention is shown.

[0136] like Figure 4 As shown, the method of the present invention and the nonlinearity judgment method and the traversal search method are used to Figure 3 The effect diagram of the optimized optical system is shown.

[0137] Among them, the parameter setting of the nonlinearity judgment method is consistent with the parameters described in Patent 202110421513.X, that is, in the kth optimization cycle, if the calculated nonlinear factor r is less than 0.25, the damping factor is updated in the manner of λ k+1 =10λ k ; If the calculated nonlinear factor r is greater than 0.75, the damping factor is updated as λ k+1 =0.1λ k The parameter damping factor scaling formula of the traversal search method adopts the formula in the reference book "Methods in Automatic Design of Optical Systems", that is, D = c α D0, where α = -1, 0, 1, 2…, c is taken as 1.5.

[0138] from Figure 4 It can be seen that the method of the present invention can reduce the error function relatively stably, and its optimization efficiency and robustness are better than the other two comparison methods.

[0139] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

[0140] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A damping factor updating method in optical optimization, characterized in that: The following steps are involved: Preprocessing step S0, setting initial values: setting initial damping factor D0, contraction factor s, amplification factor a and maximum zoom times t_max; S1. Calculate the initial evaluation function based on the initial structural parameter variable x0 S2, shrink the initial damping factor D0 s_t times by the shrinkage factor s to obtain a suboptimal damping factor D c and the evaluation function S3. If the evaluation function Greater than or equal to the initial evaluation function Then the suboptimal damping factor D is adjusted by the amplification factor a. c Perform a_t times of amplification to obtain the optimal damping factor D y ; The step S2 comprises the following sub-steps: S21, performing a first contraction on the initial damping factor D0 by the contraction factor s to obtain a damping factor D s_t＝1 ; The damping factor D s_t＝1 =D0 / s; Calculate the structural parameter variable step length Δx0 according to the solution formula of the damped least squares method; Calculate the structural parameter variable x1 according to the structural parameter variable formula; The evaluation function is calculated based on the structural parameter variable x1 If the evaluation function Less than or equal to the initial evaluation function Then proceed to the next step; If the evaluation function Greater than the initial evaluation function Then the suboptimal damping factor D is obtained c =D s_t＝1 ; S22, the damping factor D is affected by the shrinkage factor s. s_t＝k-1 Perform the kth contraction to obtain the damping factor D s_t＝k ; The damping factor D s_t＝k =D0 / (s k ); Calculate the structural parameter variable step length Δx according to the solution formula of the damped least squares method k-1 ; According to the structural parameter variable formula, the structural parameter variable x is calculated. k ; According to the structural parameter variable x k Calculate the evaluation function If the evaluation function Less than or equal to the evaluation function Then the k+1th contraction process is carried out; If the evaluation function Greater than the evaluation function Then the suboptimal damping factor D is obtained c =D s_t＝k ; S23, repeat step S22 until the evaluation function Greater than the evaluation function Or the contraction times s_t is greater than or equal to the maximum scaling times t_max, and the suboptimal damping factor D is obtained. c and the evaluation function The step S3 comprises the following sub-steps: S31, the suboptimal damping factor D is amplified by the amplification factor a. c Perform the first amplification to obtain the damping factor D a_t＝1 ; D a_t＝1 =D c ×a; According to the damping factor D a_t＝1 Calculate the evaluation function If the evaluation function Greater than or equal to the initial evaluation function Then proceed to the next amplification process; If the evaluation function Less than the initial evaluation function The optimal damping factor D is obtained y ; S32, the suboptimal damping factor D is amplified by the amplification factor a. c Perform the jth amplification to obtain the damping factor D a_t＝j ; D a_t＝j =D c ×a j ; According to the damping factor D a_t＝j Calculate the evaluation function If the evaluation function Greater than or equal to the evaluation function Then proceed to the next amplification process; If the evaluation function Less than the evaluation function The optimal damping factor D is obtained y ; S33, repeat step S32 until the evaluation function Less than the evaluation function Or the amplification factor a is greater than or equal to the maximum scaling times t_max, and the optimal damping factor D is obtained. y .

2. The damping factor updating method in optical optimization according to claim 1, characterized in that: The suboptimal damping factor D c =D0 / (s s_t ).

3. The damping factor updating method in optical optimization according to claim 1, characterized in that: The solution formula of the damped least squares method is: Δx k =-(A k T A k +DI) -1 A k T f k-1 ; in, I is a diagonal matrix; A is the difference quotient matrix of the aberration f to the structural parameter variable x, A k is the difference quotient matrix of the aberration f and the structural parameter variable x of the kth optimization iteration; f k-1 is the aberration of the kth optimization iteration; D is the damping factor; Δx k The step size of the structural parameter variables calculated for the kth optimization iteration; Then Δx k Assigned to the k-th structural parameter variable to get x k+1 The calculation formula is: x k+1 =x k +Δx k ; in, x k is the k-th structural parameter variable, x k+1 is the k+1th structural parameter variable, Δx k is the step size of the structural parameters calculated at the kth iteration.

4. The damping factor updating method in optical optimization according to claim 1, characterized in that: The range of the initial damping factor D0 is: 0.1-2.

5. The damping factor updating method in optical optimization according to claim 4, characterized in that: The value of the shrinkage factor s is greater than or equal to the value of the magnification factor a.

6. The damping factor updating method in optical optimization according to claim 5, characterized in that: The maximum zoom times t_max ranges from 10 to 20.

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