Optimization method for free-form lens with multi-parameter characterization

Abstract

The present invention relates to the technical field of lens design optimization, and discloses an optimization method for a free-form surface lens characterized by multiple parameters, comprising: obtaining multiple parameters characterizing the surface of the free-form surface lens, and performing overall optimization on all parameters; calculating an optimization direction vector based on the parameters before and after overall optimization, and determining parameters that need further optimization based on the positions and values of each element in the optimization direction vector; performing local optimization on the overall optimized parameters, and performing two local optimizations according to the parameters that need further optimization during the local optimization process by transforming the optimization variables; judging whether to terminate the local optimization based on the change in the value of the local optimization function during the local optimization, and if not, returning to the step of performing overall optimization on all parameters; otherwise, terminating the local optimization to obtain parameter optimization results for the free-form surface lens. The present invention can effectively optimize the parameters of the free-form surface lens while improving optimization efficiency and simplifying the optimization process.

Description

Technical Field

[0001] The present invention relates to the technical field of lens design optimization, and in particular to an optimization method for a free-form surface lens characterized by multiple parameters. Background Art

[0002] A lens is an optical element used to converge or disperse light, and a free-form surface is a complex surface with non-rotational symmetry. In the field of optical design, the characteristics of free-form surfaces enable optical elements to achieve more precise and versatile light beam control and adjustment. Therefore, free-form surface lenses have been increasingly used. When designing free-form surface lenses, it is usually necessary to optimize the parameterized free-form surface lens to facilitate subsequent design and control of the light path. Given that free-form surface lenses have complex and flexible surface shapes, characterizing complex surfaces often requires dozens or even hundreds of parameters. Such a large number of parameters makes the parameter optimization process very time-consuming.

[0003] Conventional methods for optimizing parameters of surfaces with rotational symmetry typically involve adding additional correction polynomials (such as xy polynomials) to the equations of the original rotational symmetry (such as spheres, ellipsoids, hyperbolas, or paraboloids) to represent them. However, free-form lenses often have free-form surfaces whose shapes are not constrained by specific mathematical equations, such as polynomials, non-uniform rational B-splines (NURBS), and Bezier curves. Therefore, traditional methods are ineffective for optimizing parameters of free-form lenses.

[0004] To optimize the parameters of free-form lenses and improve their effectiveness, existing techniques employ differential equations to represent them. However, this approach requires dealing with complex differential equations during the optimization process, making optimization difficult. Another approach employs ray tracing to iteratively determine the shape of each local surface, but this requires calculating each ray individually, which hinders optimization efficiency. Summary of the Invention

[0005] To this end, the technical problem to be solved by the present invention is to overcome the deficiencies in the prior art and provide an optimization method for free-form surface lenses characterized by multiple parameters, which can improve the optimization efficiency while achieving effective optimization of the free-form surface lens parameters, and the optimization process does not involve complex differential calculations and is simple.

[0006] To solve the above technical problems, the present invention provides an optimization method for a free-form surface lens characterized by multiple parameters, comprising:

[0007] Acquire multiple parameters characterizing the surface of the free-form lens, optimize all the parameters as a whole, and obtain the parameters after overall optimization;

[0008] Calculating an optimization direction vector based on the parameters before and after the overall optimization, and determining parameters that need to be further optimized based on the position and value of each element in the optimization direction vector;

[0009] Performing local optimization on the parameters after overall optimization, the local optimization comprising: performing a first local optimization on the parameters after overall optimization, wherein in the first local optimization process, the parameters that need to be further optimized are used as optimization variables, and the parameters that do not need to be further optimized remain unchanged; then performing a second local optimization, wherein in the second local optimization process, the optimized values of the parameters used as optimization variables in the first local optimization process remain unchanged, and the parameters that remain unchanged in the first local optimization process are used as optimization variables;

[0010] Whether to terminate the local optimization is determined based on the change in the local optimization function value during the local optimization. If the local optimization is not terminated, the process returns to the step of performing overall optimization on all parameters. Otherwise, the local optimization is terminated to obtain the parameter optimization result of the free-form surface lens.

[0011] Furthermore, the optimization direction vector is calculated by combining the parameters before and after the overall optimization, specifically:

[0012] Any parameter of the free-form lens surface before overall optimization is , is the two-dimensional space coordinate of the parameters of the free-form lens surface, and the parameter vector before overall optimization is X , , is the number of parameters on the free-form lens surface; any parameter after overall optimization is , the parameter vector after overall optimization is , ;

[0013] Calculate the initial optimization direction vector as: ,in, is the initial optimization direction vector;

[0014] The normalized optimized direction vector is calculated as: ,in, is the normalized optimization direction vector, express and X Divide the corresponding elements in ; when X When the value of an element at a certain position in is 0, The element value at the corresponding position in is set to 0, and the normalized optimization direction vector is used as the final optimization direction vector.

[0015] Furthermore, the parameters that need to be further optimized are determined according to the position and element value of each element in the optimization direction vector, specifically:

[0016] When the final optimized direction vector N When the value of an element meets the preset conditions, N The elements at positions in the parameter vector after overall optimization corresponding to the original positions of the elements in the final optimization direction vector are taken as parameters that need to be further optimized.

[0017] Furthermore, when the final optimized direction vector N When the value of an element meets the preset conditions, N The elements at the positions in the parameter vector after overall optimization corresponding to the original positions of the elements in the final optimization direction vector are taken as parameters that need to be further optimized, specifically:

[0018] Find The element with the largest absolute value is denoted as , is the subscript of the element with the largest absolute value;

[0019] Will The elements whose parameters need to be further optimized are marked as ,when satisfy When the element As parameters that need to be further optimized; among them, is the threshold;

[0020] The solution is: when The subscript of any element in satisfy When The absolute value of the elements in ;like 、 To satisfy All The number of The value is the desired value.

[0021] Furthermore, when determining whether to terminate the local optimization based on the change of the local optimization function value during the local optimization, the overall optimization function value after the overall optimization is combined to determine whether to terminate the local optimization.

[0022] Furthermore, the overall optimization function value after the overall optimization is combined to determine whether to end the local optimization, specifically:

[0023] Set the maximum number of iterations for local optimization. The maximum number of iterations for local optimization is greater than the maximum number of iterations for overall optimization.

[0024] The overall optimization function value after overall optimization is , the local optimization function value after local optimization when the maximum number of iterations is reached is ;

[0025] like If it is greater than or equal to the preset threshold, the local optimization will not be terminated; if If the value is less than the preset threshold, the local optimization is terminated.

[0026] Furthermore, when all parameters are optimized as a whole, the optimization method used is a gradient descent method, a damped least squares method, a genetic optimization algorithm, a simulated annealing optimization algorithm, a particle swarm optimization algorithm or an ant colony optimization algorithm.

[0027] Furthermore, when obtaining multiple parameters characterizing the free-form lens surface, the free-form lens surface is fitted using B-spline to obtain B-spline control vertices in two-dimensional space, and the B-spline control vertices are expanded into one-dimensional vectors to obtain parameter vectors corresponding to the parameters of the free-form lens surface.

[0028] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0029] The present invention performs dimensionality reduction screening on the parameters of the free-form surface lens, and then alternately performs overall optimization and local optimization on this basis. The parameter vectors before and after the overall optimization provide the optimization direction of the local optimization, so that the subsequent local optimization process can make the optimization direction go in the right direction, thereby achieving effective parameter optimization of the free-form surface lens; the local optimization process reduces the number of optimization variables, reduces the total time required for optimization, and improves the optimization efficiency; the optimization process does not involve complex differential calculations and is simple. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0031] Figure 1 Flowchart of the method in the preferred embodiment of the present invention.

[0032] Figure 2 1 is a step diagram of a method in a preferred embodiment of the present invention.

[0033] Figure 3 This is a comparison chart of the time-consuming results of the comparative test in the simulation experiment and the optimization using the method of the present invention in the preferred embodiment of the present invention.

[0034] Figure 4 This is a contour diagram of the refractive power of the free-form surface lens before and after parameter optimization in the simulation experiment in the preferred embodiment of the present invention.

[0035] Figure 5 1 is an astigmatism contour map of the free-form surface lens before and after parameter optimization in a simulation experiment in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0037] Reference Figure 1 、 Figure 2 As shown, the present invention discloses an optimization method for a free-form surface lens characterized by multiple parameters, comprising the following steps:

[0038] S1: Obtain multiple parameters that characterize the free-form lens surface as initial parameters before optimization. In this embodiment, the free-form lens surface is fitted using B-spline to obtain B-spline control vertices in two-dimensional space, and the B-spline control vertices are expanded into one-dimensional vectors to obtain parameter vectors corresponding to the parameters of the free-form lens surface. Any parameter of the free-form lens surface before overall optimization is denoted as , is the two-dimensional space coordinate of the parameters of the free-form lens surface, is the number of parameters of the free-form lens surface. The parameter vector before overall optimization is X , , then the vector X All elements in are used as optimization variables. <800.

[0039] S2: Optimize all parameters as a whole to obtain the parameters after overall optimization. Any parameter after overall optimization is recorded as , the parameter vector after overall optimization is , .

[0040] When optimizing all parameters as a whole, the optimization methods used are gradient descent, damped least squares, genetic algorithm, simulated annealing, particle swarm optimization, or ant colony algorithm. The overall optimization function is set according to the optimization requirements of the free-form surface lens. and the overall optimization end condition.

[0041] The overall optimization function and the end condition of the overall optimization are set. The overall optimization function can be adjusted according to the actual parameter characteristics of the free-form surface lens surface. The end condition of the overall optimization can be a preset maximum number of iterations, the convergence of the overall optimization function, or the change of the overall optimization function is less than a preset threshold. The end condition of the overall optimization set in this embodiment is to set the maximum number of iterations m. The maximum number of iterations is adjusted according to the specific parameters of the free-form surface lens. In the simulation experiment, m=5. i The overall optimization function value obtained after the overall optimization is recorded as .

[0042] S3: Calculate the optimization direction vector by combining the parameters before and after the overall optimization.

[0043] S3-1: Calculate the initial optimization direction vector as:

[0044] ,

[0045] in, is the initial optimization direction vector.

[0046] S3-2: Calculate the normalized optimized direction vector as:

[0047] ,

[0048] in, is the normalized optimization direction vector, express and X Divide the corresponding elements in ; when X When the value of an element at a certain position in is 0, The element value at the corresponding position in is set to 0, and the normalized optimization direction vector is used as the final optimization direction vector.

[0049] S4: Determine the parameters that need to be further optimized according to the position and element value of each element in the optimization direction vector. The present invention achieves dimensionality reduction of the number of optimization variables by screening the parameters that need to be further optimized.

[0050] In this embodiment, when the final optimization direction vector N When the value of an element meets the preset conditions, N The element at the position in the parameter vector after overall optimization corresponding to the original position of the element in the final optimization direction vector is used as the parameter that needs to be further optimized. Specifically:

[0051] Find The element with the largest absolute value is denoted as , is the subscript of the element with the largest absolute value;

[0052] Will The elements whose parameters need to be further optimized are marked as ,when satisfy When the element As parameters that need to be further optimized; among them, is the threshold;

[0053] The solution is: when The subscript of any element in satisfy When The absolute value of the elements in ;like 、 To satisfy All The number of The value is the desired value.

[0054] S5: Locally optimize the parameters after overall optimization. The local optimization includes: performing a first local optimization on the parameters after overall optimization, wherein the parameters that need to be further optimized are used as optimization variables during the first local optimization process, while the parameters that do not need to be further optimized remain unchanged; then performing a second local optimization, wherein the optimized values of the parameters used as optimization variables during the first local optimization process remain unchanged during the second local optimization process, and the parameters that remain unchanged during the first local optimization process are used as optimization variables. Determine whether to terminate the local optimization based on the change in the value of the local optimization function during the local optimization. If the local optimization is not terminated, return to S2 to execute the step of performing overall optimization on all parameters; otherwise, terminate the local optimization, which also terminates the overall optimization. All optimizations are terminated to obtain the parameter optimization results of the free-form surface lens.

[0055] In this embodiment, the local optimization function set during local optimization is the same as the overall optimization function set during overall optimization. The overall optimization function set during overall optimization and the local optimization function set during local optimization can also be different, and are adjusted according to the actual optimization requirements of the free-form surface lens.

[0056] When determining whether to terminate the local optimization based on the change in the local optimization function value during the local optimization, the judgment condition may be whether the local optimization function has converged, whether the change in the local optimization function value is less than a preset threshold, or other judgment conditions designed according to actual conditions. In this embodiment, when determining whether to terminate the local optimization based on the change in the local optimization function value during the local optimization, the determination of whether to terminate the local optimization is made in conjunction with the overall optimization function value after the overall optimization, specifically:

[0057] Set the maximum number of iterations for local optimization, denoted as n. The maximum number of iterations for local optimization is greater than the maximum number of iterations for overall optimization, that is, n>m. In the simulation experiment, n=20 is set, the first local optimization is performed 15 times, and the second local optimization is performed 5 times. The number of the first and second local optimizations can be adjusted according to actual conditions. The overall optimization function value after overall optimization is recorded as , that is, i The overall optimization function value after the round of overall optimization is , the local optimization function set during local optimization is , the local optimization function value after local optimization when the maximum number of iterations is reached is , that is, i The local optimization function value after the round of local optimization is .like Greater than or equal to the preset threshold α , then the local optimization is not terminated; if Less than the preset threshold α , then the local optimization is ended. In this embodiment, the optimization method used in the local optimization is the same as the method used in the overall optimization, that is, Threshold α Adjust according to actual situation, set in simulation experiment α =0.0001.

[0058] The present invention also discloses an optimization system for a free-form surface lens characterized by multiple parameters, comprising a data acquisition module, an overall optimization module, and a local optimization module.

[0059] The data acquisition module obtains multiple parameters that characterize the surface of the free-form lens. The overall optimization module performs overall optimization on all parameters to obtain the overall optimized parameters. The local optimization module calculates the optimization direction vector based on the parameters before and after the overall optimization, and determines the parameters that need to be further optimized based on the position and element value of each element in the optimization direction vector; the overall optimized parameters are locally optimized, and the local optimization includes: performing a first local optimization on the overall optimized parameters, in which the parameters that need to be further optimized are used as optimization variables and the parameters that do not need to be further optimized remain unchanged; then performing a second local optimization, in which the optimized values of the parameters used as optimization variables in the first local optimization process are kept unchanged, and the parameters that remain unchanged in the first local optimization process are used as optimization variables; judging whether to terminate the local optimization based on the overall optimization function value after the overall optimization, if not, returning to the step of performing the overall optimization of all parameters; otherwise, terminating the local optimization to obtain the optimization result of the free-form lens.

[0060] The present invention also discloses a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, an optimization method for a free-form surface lens characterized by multiple parameters is implemented.

[0061] The present invention also discloses a device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, an optimization method for a free-form surface lens characterized by multiple parameters is implemented.

[0062] The present invention achieves effective parameter optimization of free-form lens surfaces by performing dimensionality reduction screening on the parameters of the free-form lens surface and then performing global optimization and local optimization alternately on this basis. Under global optimization, all parameters must be optimized, resulting in fewer iterations for full-variable optimization. After dimensionality reduction, the number of optimization variables to be optimized is reduced, resulting in more iterations. In the present invention, global optimization and local optimization are performed alternately, and the parameter vectors before and after global optimization provide the optimization direction for local optimization. Reducing the dimensionality of optimization variables in local optimization improves optimization efficiency. Although reducing the optimization variables can lead to deviations in the optimization direction, setting the optimization deviation under certain preset conditions allows subsequent local optimization processes to steer the optimization direction in the correct direction. Therefore, the present invention can find the optimal optimization results for multiple parameters of the free-form lens surface, achieving effective parameter optimization of the free-form lens. Furthermore, the local optimization process reduces the number of optimization variables and the total time required for optimization. Compared with traditional optimization methods, the computational time is significantly reduced, thereby improving optimization efficiency. Compared with existing calculus optimization methods, the optimization process of the present invention does not involve complex differential calculations and is simple.

[0063] In order to further illustrate the beneficial effects of the present invention, a simulation experiment was conducted using 576 B-spline control vertices obtained in this embodiment. First, the first round of optimization was performed, and all 576 B-spline control vertices were used as optimization variables for overall optimization. The initial overall optimization function value was 8.4198. After 5 iterations, the overall optimization function value was 1. After the optimization variables are reduced in dimension using the present invention, the B-spline control vertices at specific locations are retained as variables, while the remaining B-spline control vertices are considered as fixed values for continued optimization. After performing the first local optimization for 15 iterations, the optimization variables and invariants are swapped for 5 second local optimizations. The local optimization function value is The value of the optimization function is reduced to 0.53946, which takes 8.53 minutes. The first round of optimization is performed 25 times in total, which takes 21.64 minutes. Then, the second round of optimization is performed, and all B-spline control vertices are set as variables. After 5 iterations, the overall optimization function value is After using the present invention to reduce the dimension of the optimization variables, 15 first local optimizations and 5 second local optimizations were performed to optimize the function value. It dropped to 0.0391, taking 16.24 minutes. The optimization stop requirement was met. Round 2 performed a total of 25 iterations, taking 66.47 minutes. Overall, the parameter optimization process for the freeform lens was completed in two rounds, and the optimization function was reduced from 8.4198 to 0.0391, taking a total of 88.11 minutes.

[0064] In the simulation experiment, a comparative experiment was also performed in which all B-spline control vertices were treated as variables for optimization. This optimization cycle also included two rounds, each with 25 iterations, and the time consumed for each round was recorded. The time consumption results of the comparative experiment and the optimization method of the present invention are compared. Figure 3 As shown in the figure, the comparison experiment took 140.87 minutes in the first round of optimization and 205.16 minutes in the second round of optimization, for a total of 346.03 minutes. The optimization function decreased from 8.4198 to 0.0380. When the decrease in the optimization function value was almost the same, Figure 3 It can be seen that the method of the present invention reduces the total calculation time by about 74.5%, effectively improving the optimization efficiency.

[0065] At the same time, the surface height data of the initial and optimized lenses are simulated in the simulation experiment. The refractive power of the free-form surface lens before and after parameter optimization is as follows: Figure 4 As shown in the figure, the refractive power of the free-form surface lens before parameter optimization is as follows: Figure 4 As shown in (a), the refractive power of the free-form surface lens after parameter optimization is as follows Figure 4 As shown in (b); the astigmatism contour map of the free-form surface lens before and after parameter optimization is shown in Figure 5 As shown, Figure 5 (a) is the astigmatism contour map of the free-form surface lens before parameter optimization. Figure 5 (b) is the astigmatism contour map of the free-form surface lens after parameter optimization.

[0066] from Figure 4 As can be seen, the surface refractive power of the lens remains virtually unchanged before and after optimization. Furthermore, the optimized lens reduces the intensity of the refractive power change, thereby reducing astigmatism. Before optimization, the refractive power (measured in diopters, or D) of the lens in the distance zone was -3.54D, the refractive power in the near zone was -5.54D, and the additional surface refractive power was 2.0D. After optimization, the refractive power in the distance zone was -3.47D, the refractive power in the near zone was -5.43D, and the additional surface refractive power was 1.96D, a difference of 0.04D. The difference between these two sets of data is less than 0.12D, which meets the requirements for refractive power error in the ISO 8980-2:2017 standard.

[0067] from Figure 5 As can be seen, the area of astigmatism less than 0.25D in the upper half of the free-form lens's distance zone after optimization has changed very little. In the near zone (at x = 20 mm), the width of the area with astigmatism less than 0.5D has increased by 3 mm, from 13 mm to 16 mm. The original lens's maximum astigmatism was 2.46D, which was effectively reduced to 2.18D after optimization. Compared to before optimization, the area of astigmatism greater than 2.0D on the left side of the lens has been significantly reduced after optimization. This optimization result significantly reduces the maximum astigmatism of progressive addition lenses and significantly expands the lens's range of focus. This demonstrates that the present invention effectively optimizes the parameters of free-form lens.

[0068] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0069] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0070] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0071] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0072] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. An optimization method for a free-form surface lens characterized by multiple parameters, characterized in that: include: Acquire multiple parameters characterizing the surface of the free-form lens, optimize all the parameters as a whole, and obtain the parameters after overall optimization; Calculating an optimization direction vector based on the parameters before and after the overall optimization, and determining parameters that need to be further optimized based on the position and value of each element in the optimization direction vector; Performing local optimization on the parameters after overall optimization, the local optimization comprising: performing a first local optimization on the parameters after overall optimization, wherein in the first local optimization process, the parameters that need to be further optimized are used as optimization variables, and the parameters that do not need to be further optimized remain unchanged; then performing a second local optimization, wherein in the second local optimization process, the optimized values of the parameters used as optimization variables in the first local optimization process remain unchanged, and the parameters that remain unchanged in the first local optimization process are used as optimization variables; Determining whether to terminate the local optimization according to the change in the local optimization function value during the local optimization; if the local optimization is not terminated, returning to the step of performing overall optimization on all parameters; otherwise, terminating the local optimization to obtain the parameter optimization result of the free-form surface lens; The optimization direction vector is calculated by combining the parameters before and after the overall optimization, specifically: Any parameter of the free-form lens surface before overall optimization is x i，j , (i, j) is the two-dimensional space coordinate of the parameters of the free-form lens surface, and the parameter vector before overall optimization is X, X = {x i，j |i, j = 1, 2, ..., l}, l 2 is the number of parameters on the free-form lens surface; any parameter after overall optimization is The parameter vector after overall optimization is Calculate the initial optimization direction vector as: in, is the initial optimization direction vector; The normalized optimized direction vector is calculated as: in, is the normalized optimization direction vector, . / represents Divide by the corresponding element in X; when the value of an element at a certain position in X is 0, The element value at the corresponding position in is set to 0, and the normalized optimization direction vector is used as the final optimization direction vector; The parameters that need to be further optimized are determined according to the position and element value of each element in the optimization direction vector, specifically: When the values of the N elements in the final optimization direction vector meet the preset conditions, the elements at the positions in the overall optimized parameter vector corresponding to the original positions of these N elements in the final optimization direction vector are used as parameters that need to be further optimized; specifically: Find The element with the largest absolute value is denoted as (i m ,j m ) is the subscript of the element with the largest absolute value; Will The elements of the parameters that need to be further optimized are marked as (i r ,j r ), when (i r ,j r )satisfy When the element As a parameter that needs to be further optimized; among them, N r is the threshold; N r The solution is: when The subscript of any element in (i n ,j n )satisfy When The absolute value of the elements in like To satisfy All The number of N r The value is the desired value.

2. The optimization method for a free-form surface lens characterized by multiple parameters according to claim 1, characterized in that: When determining whether to terminate the local optimization based on the change in the local optimization function value during the local optimization, the overall optimization function value after the overall optimization is combined to determine whether to terminate the local optimization.

3. The optimization method for a free-form surface lens characterized by multiple parameters according to claim 2, characterized in that: The determination of whether to end the local optimization by combining the overall optimization function value after the overall optimization is specifically as follows: Set the maximum number of iterations for local optimization. The maximum number of iterations for local optimization is greater than the maximum number of iterations for overall optimization. The overall optimization function value after overall optimization is The local optimization function value after local optimization when the maximum number of iterations is reached is like If it is greater than or equal to the preset threshold, the local optimization will not be terminated; if If the value is less than the preset threshold, the local optimization is terminated.

4. The method for optimizing a free-form surface lens characterized by multiple parameters according to any one of claims 1 to 3, characterized in that: When all parameters are optimized as a whole, the optimization method used is a gradient descent method, a damped least squares method, a genetic optimization algorithm, a simulated annealing optimization algorithm, a particle swarm optimization algorithm, or an ant colony optimization algorithm.

5. The optimization method for a free-form surface lens characterized by multiple parameters according to any one of claims 1 to 3, characterized in that: When obtaining multiple parameters characterizing the free-form lens surface, the free-form lens surface is fitted using B-spline to obtain B-spline control vertices in two-dimensional space, and the B-spline control vertices are expanded into one-dimensional vectors to obtain parameter vectors corresponding to the parameters of the free-form lens surface.

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