Optimization method of free-form surface lens for multi-parameter representation

Abstract

The invention relates to the technical field of lens design optimization, and discloses a free-form surface lens optimization method for multi-parameter characterization, which comprises the following steps: acquiring a plurality of parameters for characterizing the surface of a free-form surface lens, and carrying out overall optimization on all the parameters; calculating an optimization direction vector by combining the parameters before and after the overall optimization, and determining the parameters needing to be further optimized according to the positions and values of the elements in the optimization direction vector; performing local optimization on the parameters after overall optimization, and performing local optimization twice according to parameter transformation optimization variables required to be further optimized in the local optimization process; judging whether local optimization is ended or not according to the change of a local optimization function value during local optimization, and if the local optimization is not ended, returning to execute the step of performing overall optimization on all the parameters; otherwise, local optimization is ended, and a parameter optimization result of the free-form surface lens is obtained. According to the method, the optimization efficiency can be improved while the parameters of the free-form surface lens are effectively optimized, and the optimization process is simple.

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 lens characterized by multiple parameters. Background Art

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

[0003] In the prior art, when optimizing the parameters of a surface with a rotational symmetry plane, the method usually used is to add an additional correction polynomial (such as an xy polynomial) to represent the surface based on the equation of the original rotational symmetry plane (such as a spherical surface, an ellipsoidal surface, a hyperbolic surface, or a parabolic surface, etc.). However, a free-form lens usually has a free-form surface whose shape is not restricted by a specific mathematical equation, such as free-form surfaces like polynomials, non-uniform rational B-splines (NURBS), and Bézier curves. Therefore, the traditional method cannot effectively optimize the parameters of a free-form lens.

[0004] In order to optimize the parameters of a free-form lens and improve the parameter optimization effect, in the prior art, there is a method of using a differential equation to represent a free-form lens. However, this method needs to deal with complex differential equations during the optimization and solution process, and the optimization difficulty is high. There is also a method of iteratively solving the surface shape of each local surface through ray tracing means. However, this method needs to calculate each ray during the solution process and cannot improve the optimization efficiency. Summary of the Invention

[0005] Therefore, 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 a free-form lens characterized by multiple parameters, which can effectively optimize the parameters of the free-form lens while improving the optimization efficiency, the optimization process does not involve complex differential calculations, and the optimization process is simple.

[0006] To solve the above technical problem, the present invention provides an optimization method for a free-form lens characterized by multiple parameters, including: Obtain multiple parameters characterizing the surface of the freeform lens, perform overall optimization on all the parameters, and obtain the overall optimized parameters; Calculate the optimization direction vector by combining the parameters before and after overall optimization, and determine the parameters that need to be further optimized according to the positions and element values of the elements in the optimization direction vector; Perform local optimization on the overall optimized parameters. The local optimization includes: performing the first local optimization on the overall optimized parameters, and using the parameters that need to be further optimized as optimization variables and keeping the parameters that do not need to be further optimized unchanged during the first local optimization process; then performing the second local optimization, and keeping the optimized values of the parameters used as optimization variables during the first local optimization process unchanged, and using the parameters kept unchanged during the first local optimization process as optimization variables; Judge whether to end the local optimization according to the change of the local optimization function value during local optimization. If the local optimization is not ended, return to execute the step of performing overall optimization on all the parameters; otherwise, end the local optimization to obtain the parameter optimization result of the freeform lens.

[0007] Further, the calculation of the optimization direction vector by combining the parameters before and after overall optimization is specifically as follows: Denote any parameter on the surface of the freeform lens before overall optimization as , is the two-dimensional spatial coordinate of the parameter of the freeform lens surface, and denote the parameter vector before overall optimization as X , , is the number of parameters of the freeform lens surface; denote any parameter after overall optimization as , and denote the parameter vector after overall optimization as , ; Calculate the initial optimization direction vector as: , where is the initial optimization direction vector; Calculate the normalized optimization direction vector as: , where is the normalized optimization direction vector, represents divided by the corresponding element in X ; when the element value 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.

[0008] Further, determining the parameters that need to be further optimized according to the positions and element values of the elements in the optimization direction vector is specifically as follows: When the values of the N elements in the final optimized direction vector satisfy a preset condition, the elements at the positions in the overall optimized parameter vector corresponding to the original positions of these N elements in the final optimized direction vector are used as the parameters to be further optimized.

[0009] Further, when the values of the N elements in the final optimized direction vector satisfy a preset condition, the elements at the positions in the overall optimized parameter vector corresponding to the original positions of these N elements in the final optimized direction vector are used as the parameters to be further optimized. Specifically: Search for the element with the largest absolute value in , denoted as , and is the subscript of the element with the largest absolute value; Mark the subscript of the element of the parameter to be further optimized in as . When is satisfied, the element is used as the parameter to be further optimized; where is the threshold; The solution method for is: when the subscript of any element in is satisfied, the absolute value of the corresponding element in is ; if , are all satisfying and is the number of all

[0010] Further, when determining whether to end the local optimization based on the change of the local optimization function value during local optimization, the overall optimization function value after overall optimization is combined to determine whether to end the local optimization.

[0011] Further, the method of combining the overall optimization function value after overall optimization to determine whether to end the local optimization is specifically: Set the maximum number of iterations during local optimization, and the maximum number of iterations during local optimization is greater than the maximum number of iterations during overall optimization; Denote the overall optimization function value after overall optimization as , and denote the local optimization function value after local optimization when reaching the maximum number of iterations during local optimization as ; If is greater than or equal to a preset threshold, local optimization is not ended; if is less than the preset threshold, local optimization is ended.

[0012] Furthermore, when globally optimizing all parameters, the optimization methods used are gradient descent method, damped least squares method, genetic optimization algorithm, simulated annealing optimization algorithm, particle swarm optimization algorithm or ant colony optimization algorithm.

[0013] Furthermore, when obtaining multiple parameters characterizing the surface of the freeform lens, B-spline is used to fit the surface of the freeform lens to obtain the B-spline control vertices in two-dimensional space, and the B-spline control vertices are expanded into a one-dimensional vector to obtain the parameter vector corresponding to the parameters of the surface of the freeform lens.

[0014] The above technical solutions of the present invention have the following beneficial effects compared with the prior art: The present invention performs dimensionality reduction screening on the parameters of the surface of the freeform lens, and on this basis, globally optimizes and locally optimizes alternately. The parameter vectors before and after global optimization give the optimization direction of local optimization, so that the subsequent local optimization process can make the optimization direction proceed in the correct direction, realizing effective parameter optimization of the freeform 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 the optimization process is simple. Description of the Drawings

[0015] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to the specific embodiments of the present invention in conjunction with the drawings, wherein: Figure 1 is the flow chart of the method in the preferred embodiment of the present invention.

[0016] Figure 2 is the step diagram of the method in the preferred embodiment of the present invention.

[0017] Figure 3 is the comparison diagram of the time-consuming results of the comparative test and the optimization using the method of the present invention in the simulation experiment of the preferred embodiment of the present invention.

[0018] Figure 4 is the refractive power contour map of the freeform lens before and after parameter optimization in the simulation experiment of the preferred embodiment of the present invention.

[0019] Figure 5 is the astigmatism contour map of the freeform lens before and after parameter optimization in the simulation experiment of the preferred embodiment of the present invention. Detailed Embodiments

[0020] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments cited do not limit the present invention.

[0021] Referring to Figure 1 and Figure 2 as shown, the present invention discloses an optimization method for a free-form lens for multi-parameter characterization, including the following steps: S1: Obtain multiple parameters characterizing the surface of the free-form lens as the initial parameters before optimization. In this embodiment, B-spline is used to fit the surface of the free-form lens to obtain the B-spline control vertices in the two-dimensional space, and the B-spline control vertices are expanded into a one-dimensional vector to obtain the parameter vector corresponding to the parameters of the free-form lens surface. Denote any parameter on the surface of the free-form lens before overall optimization as , as the two-dimensional space coordinates of the parameters of the free-form lens surface, as the number of parameters of the free-form lens surface. Denote the parameter vector before overall optimization as X , , at this time, all elements in the vector X are used as optimization variables. In this embodiment, 80 < < 800.

[0022] S2: Overall optimize all parameters to obtain the parameters after overall optimization. Denote any parameter after overall optimization as , denote the parameter vector after overall optimization as , .

[0023] When overall optimizing all parameters, the optimization methods used are optimization methods such as gradient descent method, damped least squares method, genetic algorithm, simulated annealing algorithm, particle swarm optimization algorithm or ant colony algorithm, etc. Set the overall optimization function and the overall optimization end condition according to the optimization requirements of the free-form lens.

[0024] Set the overall optimization function and the end condition of the overall optimization. The overall optimization function can be adjusted according to the parameter characteristics of the actual free-form lens surface. The end condition of the overall optimization can be the preset maximum number of iterations, can be the convergence of the overall optimization function, or can be that the change amount of the overall optimization function is less than the preset threshold, etc. In this embodiment, the end condition of the overall optimization set is to set the maximum number of iterations m, and the maximum number of iterations is adjusted in combination with the parameters of the specific free-form lens. In the simulation experiment, m = 5 is set. The overall optimization function value obtained after the i th round of overall optimization is denoted as .

[0025] S3: Calculate the optimization direction vector by combining the parameters before and after the overall optimization.

[0026] S3-1: Calculate the initial optimization direction vector as: , where, is the initial optimization direction vector.

[0027] S3-2: Calculate the normalized optimization direction vector as: , where, is the normalized optimization direction vector, means divided by the corresponding element in X ; when the element value 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.

[0028] S4: Determine the parameters that need to be further optimized according to the positions and element values of the elements in the optimization direction vector. The present invention realizes the dimensionality reduction of the number of optimization variables by screening the parameters that need to be further optimized.

[0029] In this embodiment, 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 the parameters that need to be further optimized. Specifically: Find the element with the largest absolute value in , denoted as , is the subscript of the element with the largest absolute value; Mark the subscript of the element of the parameter that needs to be further optimized in as , when meets , take the element as the parameter that needs to be further optimized; where, is the threshold; The solution method of is: when the subscript of any element in meets , the absolute value of the corresponding element in is , are those that meet all of number, then the value is the value sought.

[0030] S5: Perform local optimization on the parameters after overall optimization. The local optimization includes: performing the first local optimization on the parameters after overall optimization, taking the parameters that need to be further optimized as optimization variables during the first local optimization and keeping the parameters that do not need to be further optimized unchanged; then performing the second local optimization, keeping the optimized values of the parameters that were used as optimization variables during the first local optimization unchanged during the second local optimization and taking the parameters that were kept unchanged during the first local optimization as optimization variables. Determine whether to end the local optimization based on the change in the local optimization function value during local optimization. If the local optimization is not ended, return to S2 to execute the step of performing overall optimization on all parameters; otherwise, end the local optimization. At this time, the overall optimization also ends simultaneously, and all optimizations end to obtain the parameter optimization result of the free-form lens.

[0031] 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 they are adjusted according to the actual optimization requirements of the free-form lens.

[0032] When determining whether to end the local optimization based on the change in the local optimization function value during local optimization, the determination condition can be whether the local optimization function converges, whether the change amount of the local optimization function value is less than a preset threshold, or other determination conditions designed according to the actual situation. In this embodiment, when determining whether to end the local optimization based on the change in the local optimization function value during local optimization, it is combined with the overall optimization function value after overall optimization to determine whether to end the local optimization. Specifically: Set the maximum number of iterations during local optimization, denoted as n. The maximum number of iterations during local optimization is greater than the maximum number of iterations during overall optimization, that is, n > m. In the simulation experiment, set n = 20, the first local optimization is performed 15 times, and the second local optimization is performed 5 times. The number of times of the first local optimization and the second local optimization can be adjusted according to the actual situation. Denote the overall optimization function value after overall optimization as , that is, the i overall optimization function value after the round of overall optimization is , denote the local optimization function set during local optimization as , that is, the i local optimization function value after the round of local optimization is Greater than or equal to a preset threshold α , then the local optimization is not ended; if less than the preset threshold α , then the local optimization is ended. In this embodiment, the optimization method used in local optimization is the same as that used in global optimization, that is . The threshold α is adjusted according to the actual situation, and is set to α = 0.0001 in the simulation experiment.

[0033] The present invention also discloses an optimization system for a free-form lens characterized by multiple parameters, including a data acquisition module, a global optimization module, and a local optimization module.

[0034] The data acquisition module acquires multiple parameters characterizing the surface of the free-form lens. The global optimization module globally optimizes all the parameters to obtain the globally optimized parameters. The local optimization module calculates an optimization direction vector by combining the parameters before and after global optimization, determines the parameters that need to be further optimized according to the positions and element values of the elements in the optimization direction vector; locally optimizes the globally optimized parameters, and the local optimization includes: performing a first local optimization on the globally optimized parameters, using the parameters that need to be further optimized as optimization variables during the first local optimization, and keeping the parameters that do not need to be further optimized unchanged; then performing a second local optimization, keeping the optimized values of the parameters used as optimization variables during the first local optimization unchanged during the second local optimization, and using the parameters kept unchanged during the first local optimization as optimization variables; determining whether to end the local optimization by combining the global optimization function value after global optimization, if the local optimization is not ended, then return to execute the step of globally optimizing all the parameters; otherwise, end the local optimization to obtain the optimization result of the free-form lens.

[0035] The present invention also discloses a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements an optimization method for a free-form lens characterized by multiple parameters.

[0036] The present invention also discloses a device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the computer program, it implements an optimization method for a free-form lens characterized by multiple parameters.

[0037] Through dimensionality reduction screening of the parameters on the surface of a freeform lens, and on this basis, alternately performing global optimization and local optimization, effective parameter optimization of the freeform lens can be achieved. Under global optimization, all parameters need to be optimized, and the number of iterations for full-variable optimization is less; after dimensionality reduction, the number of optimization variables to be optimized decreases, and the number of iterations is more. In the present invention, global optimization and local optimization are alternately performed, and the parameter vectors before and after global optimization give the optimization direction for local optimization. The reduction in the dimension of the optimization variables in local optimization improves the optimization efficiency. Although reducing the optimization variables will cause a deviation in the optimization direction, the optimization deviation is set under certain preset conditions, enabling the subsequent local optimization process to make the optimization direction move towards the correct direction. Therefore, the present invention can find the optimal optimization results of multiple parameters on the surface of the freeform lens and achieve effective parameter optimization of the freeform lens. At the same time, the local optimization process reduces the number of optimization variables and the total time required for optimization. Compared with traditional optimization methods, the calculation time is significantly reduced, improving the optimization efficiency. Compared with the existing calculus optimization method, the optimization process of the present invention does not involve complex differential calculations and the optimization process is simple.

[0038] To further illustrate the beneficial effects of the present invention, in this embodiment, 576 B-spline control vertices obtained are used for simulation experiments. First, perform the first round of optimization, and globally optimize all 576 B-spline control vertices as optimization variables. The initial global optimization function value is 8.4198. After 5 iterations, the global optimization function value decreases to 4.1927, and this process takes 13.11 minutes. After using the present invention to perform dimensionality reduction on the optimization variables, the B-spline control vertices at specific positions are retained as variables, while the remaining B-spline control vertices are regarded as fixed values and continue to be optimized. After the first local optimization with 15 iterations, the optimization variables and invariant variables are swapped for 5 times of the second local optimization, and the local optimization function value drops to 0.53946, and this process takes 8.53 minutes. The first round in total performs 25 iterations of optimization, taking 21.64 minutes. Then, perform the second round of optimization, and all B-spline control vertices are set as variables. After 5 iterations, the global optimization function value reaches 0.0438, taking 50.23 minutes. After using the present invention to perform dimensionality reduction on the optimization variables, 15 times of the first local optimization and 5 times of the second local optimization are performed, and the optimization function value drops to 0.0391, taking 16.24 minutes. The requirement for optimization to stop is reached. The second round in total performs 25 iterations, taking 66.47 minutes. Generally speaking, the parameter optimization process of the freeform lens is carried out for 2 rounds, the optimization function drops from 8.4198 to 0.0391, and the total time taken is 88.11 minutes.

[0039] In the simulation experiment, a comparative experiment was also carried out in which all B-spline control vertices were regarded as variables for optimization. This optimization loop also consisted of two rounds, with 25 iterations in each round, and the time consumed in each round was recorded. The time-consuming results of the comparative experiment and the optimization using the method of the present invention are compared as Figure 3 shown. The comparative experiment took 140.87 minutes for the first-round optimization and 205.16 minutes for the second-round optimization, with a total of 346.03 minutes, and 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 reduced the total calculation time by about 74.5%, effectively improving the optimization efficiency.

[0040] At the same time, in the simulation experiment, the surface height data of the initial and optimized lenses were also simulated. The refractive powers of the free-form lenses before and after parameter optimization are as Figure 4 shown, where the refractive power of the free-form lens before parameter optimization is as Figure 4 shown in (a), and the refractive power of the free-form lens after parameter optimization is as Figure 4 shown in (b); the astigmatism contour maps of the free-form lenses before and after parameter optimization are as Figure 5 shown, where Figure 5 (a) is the astigmatism contour map of the free-form lens before parameter optimization, Figure 5 (b) is the astigmatism contour map of the free-form lens after parameter optimization.

[0041] From Figure 4 it can be seen that the surface refractive powers of the lenses before and after optimization remained almost unchanged. Moreover, the optimized lens reduced the intensity of the refractive power change, thereby reducing astigmatism. The refractive power (in diopters, abbreviated as D) of the distance vision area of the lens before optimization was -3.54D, the refractive power of the near vision area was -5.54D, and the additional surface refractive power was 2.0D; after optimization, the refractive power of the distance vision area was -3.47D, the refractive power of the near vision area was -5.43D, and the additional surface refractive power was 1.96D, and the difference between the two was 0.04D. The difference between these two sets of data was less than 0.12D, meeting the requirements for refractive power error in ISO 8980-2:2017 standard.

[0042] From Figure 5It can be seen that for the upper half of the optimized freeform lens, the area with astigmatism less than 0.25D in the distance vision area changes very little; while in the near vision area (at x = 20 mm), the width of the area with astigmatism less than 0.5D changes from 13 mm to 16 mm, an increase of 3 mm. The maximum astigmatism of the original lens was 2.46D, which was effectively reduced to 2.18D after optimization. Compared with before optimization, the area on the left side of the lens with astigmatism greater than 2.0D is significantly reduced after optimization. Such optimization results can significantly reduce the maximum astigmatism of the progressive multifocal lens and significantly expand the clear range of the lens. Thus, it can be seen that the present invention realizes the effective optimization of the parameters of the freeform lens.

[0043] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0044] The present application is described with reference to the flowcharts and / or block diagrams of 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 can be implemented by computer program instructions, and the combination of processes and / or blocks in the flowchart and / or block diagram can also be implemented. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the specified functions in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0045] These computer program instructions can 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 generate a manufactured article including instruction means, and the instruction means implements the specified functions in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0046] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide means for implementing the specified functions in Figure 1 one process or multiple processes and / or blocksFigure 1 Steps of functions specified in one or more boxes.

[0047] Obviously, the above embodiments are merely examples given for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. An optimization method for a free-form lens for multi-parameter characterization, characterized in that, Including: Obtain multiple parameters characterizing the surface of the freeform lens, perform overall optimization on all the parameters, and obtain the overall optimized parameters; Calculate the optimization direction vector by combining the parameters before and after the overall optimization, and determine the parameters that need to be further optimized according to the positions and element values of the elements in the optimization direction vector; Perform local optimization on the overall optimized parameters. The local optimization includes: performing the first local optimization on the overall optimized parameters, using the parameters that need to be further optimized as optimization variables and keeping the parameters that do not need to be further optimized unchanged during the first local optimization process; then performing the second local optimization, keeping the optimized values of the parameters used as optimization variables during the first local optimization process unchanged during the second local optimization process, and using the parameters that were kept unchanged during the first local optimization process as optimization variables; Judge whether to end the local optimization according to the change of the local optimization function value during the local optimization. If the local optimization is not ended, return to execute the step of performing overall optimization on all the parameters; otherwise, end the local optimization and obtain the parameter optimization result of the freeform lens.

2. The optimization method for a free-form lens for multi-parameter characterization according to claim 1, wherein: The calculation of the optimization direction vector by combining the parameters before and after the overall optimization is specifically: Denote any parameter on the surface of the freeform lens before overall optimization as , as the two-dimensional spatial coordinates of the parameters on the surface of the freeform lens, and denote the parameter vector before overall optimization as X , , as the number of parameters on the surface of the freeform lens; Denote any parameter after overall optimization as , and denote the parameter vector after overall optimization as , ; The initial optimization direction vector is calculated as follows: , where is the initial optimization direction vector; The optimized direction vector after normalization is as follows: , where is the optimized direction vector after normalization, means is divided by the corresponding element in X ; when the element value at a certain position in X is 0, the element value at the corresponding position in is set to 0, and the optimized direction vector after normalization is used as the final optimized direction vector.

3. The optimization method for a free-form lens for multi-parameter characterization according to claim 2, characterized in that: Determining the parameters that need to be further optimized according to the positions and element values of the elements in the optimization direction vector is specifically: When the values of the N elements in the final optimized direction vector satisfy a preset condition, these N elements are used as the parameters to be further optimized at the positions corresponding to their original positions in the final optimized direction vector in the overall optimized parameter vector.

4. The optimization method for a freeform lens for multi-parameter characterization according to claim 3, characterized in that: When the values of the N elements in the final optimized direction vector satisfy a preset condition, the elements at the positions in the overall optimized parameter vector corresponding to the original positions of these N elements in the final optimized direction vector are used as the parameters to be further optimized. Specifically: Search for the element with the largest absolute value, denoted as , which is the subscript of the element with the largest absolute value; The subscript of the element of the parameter that needs to be further optimized in is marked as When is satisfied the element is used as the parameter that needs to be further optimized; where is the threshold value; The solution method is as follows: When the subscript of any element in satisfies , the absolute value of the corresponding element in is ; if , are all that satisfy the number of values is the value to be found.

5. The optimization method for a free-form lens for multi-parameter characterization according to claim 1, characterized in that: When judging whether to end the local optimization according to the change of the local optimization function value during the local optimization, judge whether to end the local optimization in combination with the overall optimization function value after the overall optimization.

6. The optimization method for a free-form lens for multi-parameter characterization according to claim 5, characterized in that: The judgment of whether to end the local optimization by combining the overall optimization function value after the overall optimization is specifically: Set the maximum number of iterations during the local optimization, and the maximum number of iterations during the local optimization is greater than the maximum number of iterations during the overall optimization; Denote the overall optimized overall optimization function value as , and denote the locally optimized locally optimized function value at the maximum number of iterations when local optimization is achieved as ; If is greater than or equal to a preset threshold, local optimization is not ended; if is less than the preset threshold, local optimization is ended.

7. The optimization method for a free-form lens for multi-parameter characterization according to any one of claims 1-6, characterized in that: When performing overall optimization on all the parameters, the optimization method used is the gradient descent method, the damped least squares method, the genetic optimization algorithm, the simulated annealing optimization algorithm, the particle swarm optimization algorithm or the ant colony optimization algorithm.

8. The optimization method for a free-form lens for multi-parameter characterization according to any one of claims 1-6, characterized in that: When obtaining multiple parameters characterizing the surface of the freeform lens, use B-spline to fit the surface of the freeform lens to obtain the B-spline control vertices in the two-dimensional space, and expand the B-spline control vertices into a one-dimensional vector to obtain the parameter vector corresponding to the parameters of the surface of the freeform lens.

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