A free-form surface multi-objective optimization design method for laser shaping

Abstract

The present application relates to the field of free-form surface optical design, in particular to a free-form surface multi-objective optimization design method for laser shaping. The specific steps include: establishing the light mapping relationship between the light source surface and the target surface according to the light mapping method, obtaining the discrete sampling points of the light source surface, the discrete sampling points of the target surface, and obtaining the discrete sampling points of the free-form surface according to the refraction law; performing XY polynomial fitting on the discrete sampling points of the free-form surface to obtain a polynomial mathematical model of the free-form surface; constructing an objective function with the spot uniformity and the surface quality as the optimization targets, optimizing the coefficients in the polynomial mathematical model of the free-form surface using a multi-objective particle swarm algorithm, and outputting a Pareto optimal solution set; selecting a solution that meets the preset conditions from the Pareto optimal solution set to obtain the corresponding optimized polynomial mathematical model as the target free-form surface, and verifying the target free-form surface. The method of the present application can design a free-form surface that balances the optical indicators and the surface quality.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of freeform optical design, in particular to a freeform multi-objective optimization design method for laser shaping. BACKGROUND

[0002] In recent years, an important development direction in the field of optical design is the widespread application of freeform surfaces in laser shaping. Freeform surfaces refer to surfaces whose shape is not limited by a specific mathematical equation, and have complex and flexible surface shapes. This characteristic enables freeform optical elements to achieve more precise and multifunctional beam control and adjustment. In practical applications, these freeform surfaces are widely used in laser shaping of various shapes and energy distributions, such as laser processing, medical device manufacturing, and laser radar, etc.

[0003] However, in practical applications, due to the complex surface characteristics of freeform surfaces, various polynomials are needed to describe the designed freeform surfaces, which are usually obtained by fitting discrete point data. In addition, a single design of a freeform surface cannot directly obtain an optical performance optimized freeform surface structure. Therefore, in order to effectively fit the freeform surface and improve its initial structure, some optimization methods need to be introduced to improve the shaping effect. Currently, the freeform surface optimization process for laser shaping mainly focuses on optimizing optical indicators, while the quality evaluation of freeform surfaces has not been fully focused.

[0004] Therefore, how to balance the spot uniformity and surface quality during the freeform surface design optimization process, and perform multi-objective optimization between optical indicators and processing difficulty, is a problem that needs to be solved in the field at present. SUMMARY

[0005] To this end, the technical problem to be solved by the present application is to overcome the fact that the existing freeform surface design method does not take into account the spot uniformity and surface quality, thereby affecting the performance of the designed freeform surface.

[0006] To solve the above technical problems, the present application provides a freeform multi-objective optimization design method for laser shaping, comprising the following steps:

[0007] According to the ray mapping method, the light ray mapping relationship between the light source plane, the freeform surface and the target plane is established, and the discrete sampling points of the light source plane and the discrete sampling points of the target plane are calculated; the discrete sampling points of the freeform surface are calculated according to the discrete sampling points of the light source plane and the discrete sampling points of the target plane;

[0008] The XY polynomial fitting is performed on the discrete sampling points of the freeform surface to obtain a polynomial mathematical model of the freeform surface as the initial structure of the freeform surface;

[0009] The target function is constructed by taking the spot uniformity and the surface quality as the optimization targets of the free-form surface, a coefficient combination of a polynomial mathematical model of the free-form surface is represented by each particle, the coefficients in the polynomial mathematical model of the free-form surface are optimized by using a multi-objective particle swarm algorithm, and a Pareto optimal solution set is output;

[0010] An optimal solution meeting a preset condition is selected from the Pareto optimal solution set, a corresponding optimized polynomial mathematical model is obtained as the target free-form surface, and the target free-form surface is verified.

[0011] Preferably, the target function is constructed by taking the spot uniformity and the surface quality as the optimization targets of the free-form surface includes:

[0012] The first target function is established based on the average coordinate deviation of the discrete sampling points of the target surface and the average normal vector deviation of the discrete sampling points of the free-form surface, so as to represent the optical index of the free-form surface.

[0013] The second target function is established based on the standard deviation of the rate of change of the Gaussian curvature of the discrete sampling points of the free-form surface, so as to represent the surface quality of the free-form surface.

[0014] Preferably, the first target function is established based on the average coordinate deviation of the discrete sampling points of the target surface and the average normal vector deviation of the discrete sampling points of the free-form surface includes:

[0015] The average coordinate deviation of the discrete sampling points of the target surface is calculated according to the following formula:

[0016]

[0017] Wherein, And respectively represent the actual coordinates of the target surface discrete sampling point in the i-th row and the j-th column of the divided grid in the x-axis and y-axis directions; x i,j And y i,j represent the ideal design coordinates of the target surface discrete sampling point; wherein i and j respectively represent the i-th row and the j-th column in the M x N divided grid.

[0018] The average normal vector deviation of the discrete sampling points of the free-form surface is calculated according to the following formula:

[0019]

[0020] Wherein respectively represent the actual normal vectors of the free-form surface discrete sampling point on the free-form surface corresponding to the target surface discrete sampling point in the x-axis, y-axis and z-axis directions; Nx i,j , Ny i,j , Nz i,jThe ideal design normal vector of the free-form surface discrete sampling point in the x-axis, y-axis and z-axis direction is represented as

[0021] In summary, the first target function f1 is established, and the calculation formula is as follows:

[0022]

[0023] Wherein, w1, w2 respectively represent the weight of the average coordinate deviation of the target surface discrete sampling point and the average normal vector deviation of the free-form surface discrete sampling point.

[0024] Preferably, the second target function established based on the standard deviation of the rate of change of the Gaussian curvature of the free-form surface discrete sampling point comprises:

[0025] The Gaussian curvature K of the free-form surface discrete sampling point is calculated as follows:

[0026]

[0027] The gradient of the free-form surface discrete sampling point along the x-axis and y-axis direction is represented as The rate of change of the Gaussian curvature of the free-form surface discrete sampling point is represented as

[0028] The second target function f2 is established, and the calculation formula is as follows:

[0029]

[0030] In the formula The Gaussian curvature gradient of the free-form surface discrete sampling point is represented as The average value of the Gaussian curvature gradient of the free-form surface discrete sampling point is represented as And The Gaussian curvature gradient of the free-form surface discrete sampling point along the x-axis and y-axis direction is represented as N, which represents the number of free-form surface discrete sampling points.

[0031] Preferably, the combination of the polynomial mathematical model of the free-form surface represented by each particle uses a multi-objective particle swarm algorithm to optimize the coefficients in the polynomial mathematical model of the free-form surface, and outputs a Pareto optimal solution set, which comprises:

[0032] The position and speed of the particle swarm are initialized, and the target function value of each particle is calculated;

[0033] According to the target function value of each particle, the position and speed of each particle are iteratively updated, and the target function value of each particle after updating is calculated, and this step is cycled iteratively;

[0034] Through the updating of the position and speed of each particle within the iteration times, the coefficients of the polynomial mathematical model of the free-form surface are gradually optimized.

[0035] When the maximum iteration number is reached, the optimization process is ended and a Pareto optimal solution set is outputted;

[0036] wherein the updating formula of particle velocity and position is as follows:

[0037]

[0038] wherein X kl and V kl respectively represent the position and velocity of the kth particle in the lth dimension; T represents the maximum iteration number; t represents the current iteration number, ranging from 1 to T; w(t) represents the inertia coefficient in the current iteration number; w max and w min are respectively the maximum value and the minimum value of the inertia coefficient; c1 and c2 represent the learning factor for adjusting the search step; r1 and r2 represent two random values in the range of [0, 1]; P kl represents the historical optimal position of the kth particle in the lth dimension; g l represents the global optimal position of all particles in the lth dimension. Preferably, the light ray mapping relationship of the light source surface, the free-form surface and the target surface is established according to the light ray mapping method, and the discrete sampling points of the light source surface and the discrete sampling points of the target surface are calculated; the discrete sampling points of the free-form surface are calculated according to the discrete sampling points of the light source surface and the discrete sampling points of the target surface.

[0039] The light source surface and the target surface are equally energy grid divided, the light ray mapping relationship of the light source surface, the free-form surface and the target surface is established by the light ray mapping method, and the discrete sampling points of the light source surface and the discrete sampling points of the target surface are calculated according to the divided grid; the discrete sampling points of the free-form surface are calculated according to the discrete sampling points of the light source surface and the discrete sampling points of the target surface using the vector form of Snell's law of refraction according to the preset grid direction.

[0040] Preferably, the discrete sampling points of the free-form surface are subjected to XY polynomial fitting to obtain a polynomial mathematical model of the free-form surface as the initial structure of the free-form surface, which comprises:

[0041] According to the shape and complexity of the target spot, the polynomial form and order are determined;

[0042] Based on the determined polynomial form and order, the polynomial mathematical model of the free-form surface is obtained by preliminary fitting in combination with the discrete sampling points of the free-form surface, and is used as the initial structure of the free-form surface.

[0043] Preferably, the solution satisfying the preset condition is selected from the Pareto optimal solution set, and the corresponding optimized polynomial mathematical model is obtained as the target free-form surface, and the target free-form surface is verified, which comprises:

[0044] In the Pareto optimal solution set, a solution meeting preset conditions is selected, and a corresponding optimized polynomial mathematical model is obtained as the target free-form surface, wherein the preset conditions are meeting specific optical index requirements or processing index requirements, such as meeting spot uniformity and surface quality;

[0045] According to the Gaussian curvature of the free-form surface discrete sampling point, the surface quality of the target free-form surface is analyzed; and the simulation result obtained by ray tracing of the target free-form surface by using optical software is used to verify the spot uniformity of the target free-form surface.

[0046] The spot uniformity is described as the ratio of the average irradiance value to the maximum irradiance value, U RSD The relative standard deviation of the irradiance value of each pixel point of the simulation result output picture represents the uniformity of the spot area formed by the target surface, and the calculation formula is as follows:

[0047]

[0048]

[0049] The average value of the coherent irradiance is represented by I max The maximum value of the coherent irradiance is represented by I i The coherent irradiance value of each pixel point in the spot is represented by I, and N represents the number of pixel points of the simulation target plane, wherein the coherent irradiance values I of each pixel point in all spots have been normalized and the range is [0, 1]. i

[0050] Preferably, a free-form surface multi-objective optimization design device for laser shaping comprises:

[0051] A mapping relationship module is configured to establish a light mapping relationship among a light source plane, a free-form surface and a target plane according to a light mapping method, and to calculate discrete sampling points of the light source plane and the target plane; and to calculate discrete sampling points of the free-form surface according to the discrete sampling points of the light source plane and the target plane.

[0052] A polynomial construction module is configured to perform XY polynomial fitting on the discrete sampling points of the free-form surface, and to obtain a polynomial mathematical model of the free-form surface as an initial structure of the free-form surface.

[0053] An optimization coefficient module is configured to construct a target function by taking optical indexes and surface quality as optimization targets of the free-form surface, to represent one coefficient combination of the polynomial mathematical model of the free-form surface by each particle, to optimize the coefficients in the polynomial mathematical model of the free-form surface by using a multi-objective particle swarm algorithm, and to output a Pareto optimal solution set meeting the minimum target function value.​

[0054] a structure selection module, configured to select a solution meeting a preset condition from a Pareto optimal solution set, and obtain a corresponding optimized polynomial mathematical model as a target free-form surface, and verify the target free-form surface.

[0055] Preferably, a computer readable storage medium for free-form surface multi-objective optimization design for laser shaping comprises the following steps.

[0056] The computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement the steps of the free-form surface multi-objective optimization design method for laser shaping.

[0057] Compared with the prior art, the above technical scheme of the present application has the following beneficial effects:

[0058] The free-form surface multi-objective optimization design method for laser shaping firstly mathematically describes a free-form surface for laser shaping, designs two optimization targets of spot uniformity and surface quality, combines a multi-objective particle swarm optimization method, constructs an evaluation function to balance the spot uniformity and the surface quality, obtains a plurality of sets of solutions from each iteration in the Pareto frontier to construct a set of solutions with advantages and disadvantages, and selects an optimized polynomial mathematical model covering the entire Pareto frontier as much as possible as the target free-form surface through multiple iterations. BRIEF DESCRIPTION OF DRAWINGS

[0059] In order to make the content of the present application more easily understood, the present application will be further described in detail below according to specific embodiments of the present application and in conjunction with the accompanying drawings, in which:

[0060] Figure 1 is a flowchart of the method of the present application;

[0061] Figure 2 is a free-form surface geometric design layout for laser shaping according to embodiment 2 of the method of the present application;

[0062] Figure 3 is a multi-objective particle swarm optimization flowchart in the method of the present application;

[0063] Figure 4 is a Pareto frontier diagram in the method of the present application;

[0064] Figure 5is a case optimization before and after the shaping effect comparison chart of the light source and the solution in the method of the application;

[0065] Figure 6 is the optical simulation and Gaussian curvature comparison chart of different solutions in the Pareto front of the method of the application. DETAILED DESCRIPTION

[0066] The application will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the application and implement it, but the embodiments are not limiting to the application.

[0067] Embodiment 1

[0068] Reference Figure 1 , the overall flow of a free-form surface multi-objective optimization design method for laser shaping of the application is shown in the figure, and the specific steps are as follows:

[0069] S1: According to the ray mapping method, the light mapping relationship of the light source plane, the free-form surface and the target plane is established, and the discrete sampling points of the light source plane and the discrete sampling points of the target plane are calculated; the discrete sampling points of the free-form surface are calculated according to the discrete sampling points of the light source plane and the discrete sampling points of the target plane;

[0070] The light source plane and the target plane are equally divided into grids, the light mapping relationship of the light source and the target plane is established by the ray mapping method, and the discrete sampling points of the light source plane and the discrete sampling points of the target plane are calculated according to the divided grids; the discrete sampling points of the free-form surface are calculated according to the discrete sampling points of the light source plane and the discrete sampling points of the target plane using the vector form of Snell's law according to the preset grid direction i,j , i and j correspond to the first column in the i-th row of the M×N grids.

[0071] S2: The discrete sampling points of the free-form surface are fitted with XY polynomial to obtain a polynomial mathematical model of the free-form surface as the initial structure of the free-form surface;

[0072] According to the shape and complexity of the target spot, the polynomial form and order are determined;

[0073] Based on the discrete sampling points of the free-form surface, the polynomial form and order determined are preliminarily fitted to obtain a polynomial mathematical model z=f(x,y) of the free-form surface as the initial structure of the free-form surface, which is expressed as follows:

[0074] z=p 00 +p 20 x 2 +p 02 y 2 +p 40 x 4 +p 22x 2 y 2 +p 04 y 4 +p 60 x 6 +p 42 x 4 y 2 +p 24 x 2 y 4 +p 06 y 6

[0075] S3: constructing a target function with the spot uniformity and the curved surface quality as the optimization targets of the free-form surface, representing a coefficient combination of a polynomial mathematical model of the free-form surface by each particle, optimizing the coefficients in the polynomial mathematical model of the free-form surface by using a multi-objective particle swarm algorithm, and outputting a Pareto optimal solution set;

[0076] ①establishing a first target function based on an average coordinate deviation of discrete sampling points on the target surface and an average normal vector deviation of discrete sampling points on the free-form surface, so as to represent the spot uniformity of the free-form surface;

[0077] the average coordinate deviation of the discrete sampling points on the target surface, and the calculation formula is as follows:

[0078]

[0079] wherein, and respectively represent the actual coordinates of the target surface discrete sampling point in the i-th row and the j-th column of the divided grid on the x-axis and the y-axis; x i,j and y i,j represent the ideal design coordinates of the target surface discrete sampling point; wherein i and j respectively represent the i-th row and the j-th column in the M x N divided grid;

[0080] the average normal vector deviation of the discrete sampling points on the free-form surface, and the calculation formula is as follows:

[0081]

[0082] wherein respectively represent the actual normal vectors of the free-form surface discrete sampling point on the free-form surface corresponding to the target surface discrete sampling point on the x-axis, the y-axis and the z-axis; Nx i,j , Ny i,j , Nz i,j represent the ideal design normal vectors of the free-form surface discrete sampling point on the x-axis, the y-axis and the z-axis;

[0083] Accordingly, the first target function f1 is established, and the calculation formula is as follows:

[0084]

[0085] wherein w1, w2 represent the weight of the average coordinate deviation of the target surface discrete sampling points and the average normal vector deviation of the free-form surface discrete sampling points, respectively.

[0086] 2. establishing a second target function based on the standard deviation of the rate of change of the Gaussian curvature of the free-form surface discrete sampling points, so as to represent the surface quality of the free-form surface;

[0087] The Gaussian curvature K of the free-form surface discrete sampling points is calculated according to the following formula:

[0088]

[0089] The gradient of the free-form surface discrete sampling points along the x-axis and y-axis directions is represented as The rate of change of the Gaussian curvature of the free-form surface discrete sampling points is represented as

[0090] The second target function f2 is established, and the calculation formula is as follows:

[0091]

[0092]

[0093] In the formula, The Gaussian curvature gradient of the free-form surface discrete sampling points is represented as The average value of the Gaussian curvature gradient of the free-form surface discrete sampling points is represented as and The Gaussian curvature gradient of the free-form surface discrete sampling points along the x-axis and y-axis directions is represented as N represents the number of free-form surface discrete sampling points.

[0094] 3. Referring to the free-form surface polynomial mathematical model is established according to the following formula: Figure 3 The flow chart of the multi-objective particle swarm optimization method in the present application is shown in the figure.

[0095] The position and speed of the particle swarm are initialized, and the target function value of each particle is calculated;

[0096] According to the target function value of each particle, the position and speed of each particle are iteratively updated, and the target function value of each particle after updating is calculated, and this step is cycled and iterated;

[0097] Through the updating of the position and speed of each particle within the iteration times, the coefficients p of the polynomial mathematical model of the free-form surface are gradually optimized mn， Wherein m and n are the order of x and y corresponding to the coefficients in the polynomial mathematical model of the free-form surface;

[0098] When the maximum iteration number is reached, the optimization process is ended and the Pareto optimal solution set is outputted;

[0099] wherein the updating formula of particle velocity and position is as follows:

[0100]

[0101] wherein X kl and V kl respectively represent the position and velocity of the kth particle in the lth dimension; T represents the maximum iteration number; t represents the current iteration number, ranging from 1 to T; w(t) represents the inertia coefficient in the current iteration number; w max and w min are respectively the maximum and minimum values of the inertia coefficient; c1 and c2 represent the learning factor for adjusting the search step; r1 and r2 represent two random values in the range of [0, 1]; P kl represents the historical optimal position of the kth particle in the lth dimension; g l represents the global optimal position of all particles in the lth dimension.

[0102] S4: selecting a solution satisfying a preset condition in the Pareto optimal solution set, and obtaining a corresponding optimized polynomial mathematical model as the target free-form surface, and verifying the target free-form surface.

[0103] In the Pareto optimal solution set, a solution satisfying a preset condition is selected, and a corresponding optimized polynomial mathematical model is obtained as the target free-form surface, wherein the preset condition is to meet specific optical index requirements or processing index requirements, such as meeting the uniformity of the light spot and the surface quality.

[0104] According to the Gaussian curvature K of the discrete sampling points of the free-form surface, the surface quality of the target free-form surface is analyzed to observe whether there is a region with relatively steep Gaussian curvature change;

[0105] The simulation results obtained by ray tracing of the optical software on the target free-form surface are analyzed to determine whether the optimization result meets the requirements; the uniformity of the light spot is described as the ratio of the average irradiance value to the maximum irradiance value, U RSD represents the relative standard deviation of the irradiance value of each pixel point of the simulation result output picture, representing the uniformity of the light spot area formed by the target surface, and the calculation formula is as follows:

[0106]

[0107] represents the average value of the coherent irradiance, I max represents the maximum value of the coherent irradiance, I irepresents the coherent irradiance value of each pixel point in the light spot, N represents the number of pixel points of the simulation target plane, wherein the coherent irradiance value of each pixel point in all light spots I i have been normalized, and the range is [0, 1].

[0108] Embodiment 2

[0109] On the basis of embodiment 1, the target of this embodiment is to reshape the Gaussian irradiance with a circular boundary into a uniform irradiance distribution with a regular hexagon boundary. The free-form surface geometry design layout for laser reshaping is shown in FIG. 2. Figure 2

[0110] S1: According to the ray mapping method, the light mapping relationship of the light source plane, the free-form surface and the target plane is established, and the discrete sampling points of the light source plane, the discrete sampling points of the target plane are calculated. According to the discrete sampling points of the light source plane and the discrete sampling points of the target plane, the discrete sampling points of the free-form surface are calculated;

[0111] The light source plane and the target plane are equally divided into grids, the light mapping relationship of the light source plane, the free-form surface and the target plane is established by the ray mapping method, and the discrete sampling points of the light source plane and the discrete sampling points of the target plane are calculated according to the divided grids. According to the discrete sampling points of the light source plane and the discrete sampling points of the target plane, the discrete sampling points P i,j of the free-form surface are calculated in the preset grid direction using the vector form of Snell's law of refraction, i and j correspond to the i-th row and the j-th column in the divided grid.

[0112] Due to the rotational symmetry of the pattern, the region of 0-60° is taken as the sampling, the sampling number M=61 and N=501. The whole free-form surface can be obtained by rotation. The beam waist of the light source is 3mm. When the wavelength is 530nm, the refractive index of the lens is 1.495. The initial central thickness of the lens is 2mm, the distance from the lens to the target plane is 50mm, and the side length of the regular hexagon is 6mm.

[0113] S2: The XY polynomial fitting is performed on the discrete sampling points of the free-form surface, and the polynomial mathematical model of the free-form surface is obtained as the initial structure of the free-form surface;

[0114] According to the shape and complexity of the target light spot, the polynomial form and the order are determined;

[0115] Based on the discrete sampling points of the free-form surface, the polynomial form and the order determined are preliminarily fitted. Due to the symmetry, the polynomial mathematical model z=f(x,y) of the free-form surface is calculated and used as the initial structure of the free-form surface, which is expressed as follows:

[0116] z=p 00 +p 20 x 2 +p​02 y 2 +p 40 x 4 +p 22 x 2 y 2 +p 04 y 4 +p 60 x 6 +p 42 x 4 y 2 +p 24 x 2 y 4 +p 06 y 6

[0117] S3: constructing a target function with spot uniformity and surface quality as optimization targets of the free-form surface, representing a coefficient combination of a polynomial mathematical model of the free-form surface by each particle, optimizing coefficients in the polynomial mathematical model of the free-form surface by using a multi-objective particle swarm algorithm, and outputting a Pareto optimal solution set;

[0118] establishing a first target function based on average coordinate deviation of discrete sampling points of the target surface and average normal vector deviation of discrete sampling points of the free-form surface to represent optical indexes of the free-form surface;

[0119] establishing a second target function based on standard deviation of a change rate of Gaussian curvature of the discrete sampling points of the free-form surface to represent surface quality of the free-form surface;

[0120] initializing positions and speeds of the particle swarm and calculating a target function value of each particle;

[0121] updating positions and speeds of each particle according to the target function value of each particle, calculating a target function value of each particle after the update, and repeating the step;

[0122] optimizing coefficients p mn， in the polynomial mathematical model of the free-form surface by updating positions and speeds of each particle within a maximum number of iterations, wherein m and n are orders of x and y corresponding to the coefficients in the polynomial mathematical model of the free-form surface;

[0123] ending the optimization process and outputting a Pareto optimal solution set when the maximum number of iterations is reached.

[0124] In the embodiment, parameters of the decision space are shown in the following table:

[0125] Parameter Value ​ 2 [ca2] 2 w max ]]> 0.9 w min ]]> 0.4 Number of particles N 40 Maximum number of iterations T 200 Position range [-0.05,0.05] Velocity range [-0.01,0.01]

[0126] S4: Select a solution that satisfies the preset conditions from the Pareto optimal solution set, and obtain the corresponding optimized polynomial mathematical model as the target free surface, and verify the target free surface.

[0127] In the Pareto optimal solution set, the solution that satisfies the preset conditions is selected, and the corresponding optimized polynomial mathematical model is obtained as the target free surface. The preset conditions are to meet specific optical index requirements or processing index requirements, such as satisfying the uniformity of the light spot and the quality of the surface.

[0128] The surface quality of the target freeform surface is analyzed based on the Gaussian curvature K of the discrete sampling points of the freeform surface to observe whether there are regions with steep changes in Gaussian curvature.

[0129] The simulation results obtained by ray tracing the target freeform surface using optical software are used to analyze the uniformity U of the light spot on the target freeform surface and determine whether the optimization results meet the requirements.

[0130] The coefficients of the polynomial mathematical model corresponding to the solution (0.00387, 0.00176) in the Pareto optimal solution set and the coefficients of the polynomial mathematical model of the initial structure of the freeform surface are shown in the table below.

[0131] Serial number Coefficient Initial value Optimized value 1 p 00 (thickness) 2 2 2 p 20 ]]> 3.7 x 10 -2 ]]> 3.7 x 10 -2 ]]> 3 p 02 ]]> 3.7 × 10 -2 ]]> 3.7 × 10 -2 ]]> 4 p 40 ]]> -1.5 × 10 -3 ]]> -1.5 × 10 -3 ]]> 5 p 22 ]]> -3.1 × 10 -3 ]]> -3.0 × 10 -3 ]]> 6 p 04 ]]> -1.5 x 10 -3 ]]> -1.7 x 10 -3 ]] 7 p 60 ]]> 8.9 x 10 -5 ]] 4.3 x 10 -5 ]]> 8 p 42 ]]> -7.6 x 10 -4 ]]> -7.9 x 10 -5 ]] 9 p 24 ]]> 9.5 x 10 -4 ]]> 2.9 x 10 -4 ]]> 10 p 06 ]]> -2.5 x 10 -5 ]]> 4.6 x 10 -5 ]]>

[0132] To more intuitively compare the shaping performance, the irradiance distribution of the light spot before and after the shaping is as follows: Figure 5 As shown. After initial structural shaping of the freeform surface, the normalized irradiance uniformity of the target surface is U = 79.43%. RSD =82.20%. The irradiance uniformity along the x=0 and y=0 directions are U x =88.93% and U y =71.21%. For the optimized target freeform surface, the global uniformity is U = 92.03%, U RSD =87.85%. The irradiance uniformity along x=0 and y=0 are Ux=86.78% and U... y =87.24%. This demonstrates the advantages of the method of the present invention in improving the performance of the plastic surgery system, and provides excellent technical support for system research and development and application.

[0133] In this example, since the optimization analysis is performed on multiple objectives, the final result is not unique, but rather a set of solutions. The final optimization results are non-dominated, and the final solution can be selected from the Pareto optimal solution set according to the actual application requirements. When the surface quality requirements are increased, the uniformity of the light spot deteriorates; when focusing on improving the uniformity and shape of the light spot, the Gaussian curvature of the surface changes more significantly, resulting in poorer surface quality and increased processing difficulty. For example...Figure 6 As shown, the optical simulation of two solution cases of (0.00387, 0.00158) and (0.00433, 0.00124) is compared. Both can achieve good shaping effect, but the former has higher shaping uniformity, and the latter has more gentle Gaussian curvature change.

[0134] Embodiment 3

[0135] Based on embodiment 1, this embodiment introduces a free-form surface multi-objective optimization design device for laser shaping, comprising:

[0136] A mapping relationship module is configured to establish a light mapping relationship among a light source plane, a free-form surface and a target plane according to a light mapping method, and calculate discrete sampling points of the light source plane, discrete sampling points of the target plane and discrete sampling points of the free-form surface.

[0137] A polynomial construction module is configured to perform XY polynomial fitting on the discrete sampling points of the free-form surface to obtain a polynomial mathematical model of the free-form surface as an initial structure of the free-form surface.

[0138] An optimization coefficient module is configured to construct a target function with spot uniformity and surface quality as optimization objectives of the free-form surface, express a polynomial mathematical model of the free-form surface as a coefficient combination of each particle, optimize the coefficients in the polynomial mathematical model of the free-form surface using a multi-objective particle swarm algorithm, and output a Pareto optimal solution set.

[0139] A structure selection module is configured to select a solution meeting a preset condition from the Pareto optimal solution set, obtain a corresponding optimized polynomial mathematical model as a target free-form surface, and verify the target free-form surface.

[0140] Embodiment 4

[0141] Based on embodiment 1, this embodiment introduces a computer readable storage medium for free-form surface multi-objective optimization design of laser shaping, comprising:

[0142] The computer readable storage medium stores a computer program, and the computer program is executed by a processor to realize the steps of the free-form surface multi-objective optimization design method for laser shaping.

[0143] Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0144] The present application is described in reference to the flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0145] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0146] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0147] Obviously, the above-described embodiments are only examples and are not intended to limit the present application. Based on the above description, those skilled in the art can make other variations and modifications of the present application without departing from the present application. Thus, the present application is not limited to the embodiments described above, but rather only by the claims that follow.

Claims

1. A free-form surface multi-objective optimization design method for laser shaping, characterized in that, The method comprises the following steps: According to the light ray mapping method, the light ray mapping relationship of the light source surface, the free-form surface and the target surface is established, and the discrete sampling points of the light source surface and the discrete sampling points of the target surface are calculated; according to the discrete sampling points of the light source surface and the discrete sampling points of the target surface, the discrete sampling points of the free-form surface are calculated by using the vector form of Snell's law of refraction; According to the shape and complexity of the target spot, the polynomial form and order are determined, the XY polynomial fitting of the discrete sampling points of the free-form surface is performed, and the polynomial mathematical model of the free-form surface is obtained as the initial structure of the free-form surface; The spot uniformity and the surface quality of the free-form surface are taken as the optimization target to construct a target function, which comprises: a first target function is established based on the average coordinate deviation of the discrete sampling points of the target surface and the average normal vector deviation of the discrete sampling points of the free-form surface to represent the optical index of the free-form surface, the average coordinate deviation of the discrete sampling points of the target surface is calculated according to the following formula: wherein, with respectively represent the actual coordinates of the target surface discrete sampling point in the i-th row and j-th column of the divided grid on the target surface in the x-axis and y-axis directions; x i,j and y i,j respectively represent the ideal design coordinates of the target surface discrete sampling point; wherein i and j respectively represent the i-th row and j-th column in the divided M x N grid. The average normal vector deviation of the discrete sampling points of the free-form surface is calculated according to the following formula: wherein respectively represent the actual normal vectors of the free-form surface discrete sampling points on the free-form surface corresponding to the target surface discrete sampling points in the x-axis, y-axis, and z-axis directions; Nx i,j , Ny i,j , Nz i,j respectively represent the ideal design normal vectors of the free-form surface discrete sampling points in the x-axis, y-axis, and z-axis directions; Accordingly, the first target function f1 is established, and the calculation formula is as follows: Wherein, w1 and w2 respectively represent the weight of the average coordinate deviation of the discrete sampling points of the target surface and the average normal vector deviation of the discrete sampling points of the free-form surface; A second target function is established based on the standard deviation of the rate of change of the Gaussian curvature of the discrete sampling points of the free-form surface to represent the surface quality of the free-form surface, the Gaussian curvature K of the discrete sampling points of the free-form surface is calculated according to the following formula: a gradient of the discrete sampling points of the free-form surface along the x-axis and the y-axis a rate of change of the Gaussian curvature of the discrete sampling points of the free-form surface The second target function f2 is established, and the calculation formula is as follows: In the formula represents the Gaussian curvature gradient size of the discrete sampling point of the free-form surface; represents the average value of the Gaussian curvature gradient size of the discrete sampling point of the free-form surface; and represents the Gaussian curvature gradient of the discrete sampling point of the free-form surface along the x direction and the y direction; N represents the number of the discrete sampling points of the free-form surface; Each particle represents a coefficient combination of the polynomial mathematical model of the free-form surface, the multi-objective particle swarm optimization algorithm is used to optimize the coefficients in the polynomial mathematical model of the free-form surface, and a Pareto optimal solution set is output; In the Pareto optimal solution set, the solution meeting the preset condition is selected, and the corresponding optimized polynomial mathematical model is obtained as the target free-form surface, and the target free-form surface is verified, which comprises: in the Pareto optimal solution set, the solution meeting the preset condition is selected, and the corresponding optimized polynomial mathematical model is obtained as the target free-form surface, wherein the preset condition is to meet the spot uniformity and the surface quality; According to the Gaussian curvature of the discrete sampling points of the free-form surface, the surface quality of the target free-form surface is analyzed; the simulation results obtained by ray tracing of the target free-form surface are used to verify the spot uniformity of the target free-form surface; The spot uniformity is described as the ratio of the average irradiance value to the maximum irradiance value, U RSD The relative standard deviation of the irradiance value of each pixel point of the simulation result output picture represents the uniformity of the spot area formed by the target surface, and the calculation formula is as follows: denotes the average value of the coherent irradiance, I max denotes the maximum value of the coherent irradiance, I i denotes the coherent irradiance value of each pixel point in the facet, N denotes the number of pixel points of the simulation target plane, wherein the coherent irradiance value of each pixel point in all facets I i have been normalized to the range [0, 1].

2. The method of claim 1, wherein, The particle swarm is initialized, and the position and speed of each particle are calculated; according to the target function value of each particle, the position and speed of each particle are iteratively updated, and the target function value of each particle after updating is calculated, and this step is repeated in a loop; The coefficients of the polynomial mathematical model of the free-form surface are gradually optimized by updating the position and speed of each particle within the iteration times; When the maximum iteration times are reached, the optimization process is ended and the Pareto optimal solution set is output. ​ ​ Wherein, the particle velocity and position update formula is as follows: wherein X kl and V kl respectively represent the position and velocity of the kth particle in the lth dimension; T represents the maximum number of iterations; t represents the current iteration number, ranging from [1, T]; w(t) represents the inertia coefficient in the current iteration number; w max and w min are respectively the maximum and minimum values of the inertia coefficient; c1 and c2 represent the learning factors for adjusting the search step; r1 and r2 represent two random values in the range of [0, 1]; P kl represents the historical optimal position of the kth particle in the lth dimension; g l represents the global optimal position of all particles in the lth dimension.

3. The method of claim 1, wherein, The light ray mapping relationship of the light source surface, the free-form surface and the target surface is established according to the light ray mapping method, and the light source surface discrete sampling points and the target surface discrete sampling points are calculated; The free-form surface discrete sampling points are calculated according to the light source surface discrete sampling points and the target surface discrete sampling points by using the vector form of Snell's law of refraction. The light source surface and the target surface are equally divided into grids, the light ray mapping relationship of the light source surface, the free-form surface and the target surface is established by the light ray mapping method, and the light source surface discrete sampling points and the target surface discrete sampling points are calculated according to the divided grids; and the free-form surface discrete sampling points are calculated according to the light source surface discrete sampling points and the target surface discrete sampling points by using the vector form of Snell's law of refraction in a preset grid direction.

4. The method of claim 1, wherein, The polynomial form and order are determined according to the shape and complexity of the target light spot, the free-form surface discrete sampling points are fitted by an XY polynomial, and a polynomial mathematical model of the free-form surface is obtained as an initial structure of the free-form surface. The polynomial form and order are determined according to the shape and complexity of the target light spot; The polynomial mathematical model of the free-form surface is obtained by preliminary fitting based on the determined polynomial form and order and the free-form surface discrete sampling points, and is used as the initial structure of the free-form surface.

5. A free-form surface multi-objective optimization design apparatus for laser shaping, characterized by, It comprises: The mapping relationship module is configured to establish the light ray mapping relationship of the light source surface, the free-form surface and the target surface according to the light ray mapping method, and to calculate the light source surface discrete sampling points and the target surface discrete sampling points; and to calculate the free-form surface discrete sampling points according to the light source surface discrete sampling points and the target surface discrete sampling points by using the vector form of Snell's law of refraction; The polynomial construction module is configured to determine the polynomial form and order according to the shape and complexity of the target light spot, to fit the free-form surface discrete sampling points by an XY polynomial, and to obtain a polynomial mathematical model of the free-form surface as an initial structure of the free-form surface; The optimization coefficient module is configured to construct a target function by taking the optical index and the surface quality of the free-form surface as the optimization target of the free-form surface, and comprises: a first target function is established based on the average coordinate deviation of the target surface discrete sampling points and the average normal vector deviation of the free-form surface discrete sampling points, to represent the optical index of the free-form surface; the average coordinate deviation of the target surface discrete sampling points is calculated according to the following formula: wherein, with respectively represent the actual coordinates of the target surface discrete sampling point in the i-th row and j-th column of the divided grid on the target surface in the x-axis and y-axis directions; x i,j and y i,j respectively represent the ideal design coordinates of the target surface discrete sampling point; wherein i and j respectively represent the i-th row and j-th column in the divided M x N grid. The average normal vector deviation of the free-form surface discrete sampling points is calculated according to the following formula: wherein respectively represent actual normal vectors of the free-form surface discrete sampling points on the free-form surface corresponding to the target surface discrete sampling points in x-axis, y-axis, z-axis directions; Nx i,j , Ny i,j , Nz i,j respectively represent ideal design normal vectors of the free-form surface discrete sampling points in x-axis, y-axis, z-axis directions; In summary, the first target function f1 is established, and the calculation formula is as follows: Wherein, w1 and w2 represent the weights of the average coordinate deviation of the target surface discrete sampling points and the average normal vector deviation of the free-form surface discrete sampling points, respectively; A second target function is established based on the standard deviation of the rate of change of the Gaussian curvature of the free-form surface discrete sampling points, to represent the surface quality of the free-form surface; the Gaussian curvature K of the free-form surface discrete sampling points is calculated according to the following formula: a gradient of the discrete sampling points of the free-form surface along the x-axis and the y-axis a rate of change of a Gaussian curvature of the discrete sampling points of the free-form surface The second target function f2 is established, and the calculation formula is as follows: In the formula represents the Gaussian curvature gradient size of the discrete sampling point of the free-form surface; represents the average value of the Gaussian curvature gradient size of the discrete sampling point of the free-form surface; and represents the Gaussian curvature gradient of the discrete sampling point of the free-form surface along the x direction and the y direction; N represents the number of the discrete sampling points of the free-form surface; a set of combinations of a polynomial mathematical model representing the free-form surface by each particle is used to optimize the coefficients in the polynomial mathematical model of the free-form surface by using a multi-objective particle swarm algorithm, and a Pareto optimal solution set is output. The structure selection module is configured to select a solution satisfying a preset condition from the set of Pareto optimal solutions, obtain a corresponding optimized polynomial mathematical model as a target free-form surface, and verify the target free-form surface, including: selecting a solution satisfying a preset condition from the set of Pareto optimal solutions and obtaining a corresponding optimized polynomial mathematical model as a target free-form surface, wherein the preset condition is to satisfy spot uniformity and surface quality; The surface quality of the target free-form surface is analyzed according to the Gaussian curvature of the discrete sampling points of the free-form surface; and the spot uniformity of the target free-form surface is verified by simulation results obtained by ray tracing of the target free-form surface by using optical software. The spot uniformity is described as the ratio of the average irradiance value to the maximum irradiance value, U RSD The relative standard deviation of the irradiance value of each pixel point of the simulation result output picture represents the uniformity of the spot area formed by the target surface, and the calculation formula is as follows: denotes the average value of the coherent irradiance, I max denotes the maximum value of the coherent irradiance, I i denotes the coherent irradiance value of each pixel point in the facet, N denotes the number of pixel points of the simulation target plane, wherein the coherent irradiance value of each pixel point in all facets I i have all been normalized to the range [0, 1].

6. A computer readable storage medium for freeform surface multi-objective optimization design for laser shaping, comprising: The method comprises the following steps: The computer readable storage medium stores a computer program, and the computer program is executed by the processor to realize the steps of the free-form surface multi-objective optimization design method for laser shaping according to any one of claims 1 to 4.

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