Simulation system of double-free-form-surface collimating lens design based on differential manifold

Abstract

The invention relates to the field of optical design and optimization, and discloses a micro-manifold-based simulation system for double-free-form surface collimating lens design, which comprises a curved surface modeling module, an optical simulation module, an error analysis module, an optimization solution module and a result evaluation module, the curved surface modeling module is used for constructing a double-free-form-surface lens model; the optical simulation module simulates a propagation path of light on the curved surface of the lens, calculates a refracted light direction and analyzes light collimation performance; the error analysis module diagnoses local deviation and global continuity of the surface of the lens; the optimization solution module iteratively adjusts geometric parameters of the lens curved surface model to generate an optimized lens model; and the result evaluation module is used for comprehensively verifying the optical performance and the manufacturing adaptability of the optimized lens model. Through precise geometric modeling, optical simulation and optimization, the collimation performance and manufacturing adaptability of the lens are remarkably improved, and the method is suitable for optical design in the fields of laser collimation, high-precision imaging and optical communication.

Description

Technical Field

[0001] The invention relates to the technical field of optical design and optimization, and in particular to a simulation system for designing a double free-form surface collimating lens based on differential manifolds. Background Art

[0002] As an optical element with high flexibility and complex geometric characteristics, double free-form surface lenses have been widely used in laser collimation, high-precision imaging, optical communications and other fields. Its core design goal is to optimize the light propagation path through precise control of the curved surface shape, and ultimately achieve the purpose of collimating the light beam. However, the existing technology still has some difficult-to-overcome technical bottlenecks in the design and optimization of double free-form surface lenses.

[0003] At present, most traditional lens design methods rely on geometric modeling based on empirical formulas or simple numerical fitting. This method has limited ability to describe complex surfaces and it is difficult to accurately define the geometric parameters of the lens surface, such as the distribution of principal curvature and the change of normal vector. At the same time, traditional optimization methods usually only focus on improving local performance and fail to effectively achieve global optimization of the light propagation path. This method is not only prone to local accumulation of beam deviations, but may also cause gradient discontinuity, significantly affecting the overall collimation performance of the lens.

[0004] In addition, existing lens designs lack systematic consideration of manufacturing adaptability and usually fail to effectively evaluate the impact of processing errors on the optical performance of the lens. As a result, the optimization results are often overly dependent on high-precision manufacturing equipment, making it difficult to achieve the expected performance of the design in actual processing, increasing production costs and complexity.

[0005] In summary, the existing technology lacks a dual free-form surface lens design system that can simultaneously realize complex geometric modeling, global optical optimization and manufacturing adaptability analysis. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention provides a simulation system for the design of a double free-form surface collimating lens based on differential manifolds, which solves the problems of insufficient geometric modeling accuracy, incomplete optical performance optimization and poor manufacturing adaptability in the existing double free-form surface lens design.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solutions: A simulation system based on a double free-form surface collimating lens design of a differential manifold, comprising:

[0008] A surface modeling module, used to construct a double free-form surface lens model based on differential manifolds, wherein the double free-form surface lens model is represented by a parameterized method and defines principal curvature, normal vector distribution and optical refraction parameters;

[0009] Optical simulation module, used to simulate the propagation path of light on the lens surface and analyze the collimation performance of light after refraction;

[0010] Error analysis module, used to analyze the continuity and global changes of the deviation angle distribution in the light propagation path;

[0011] An optimization solution module is used to optimize and iterate the lens surface based on the goal of minimizing light deviation and adjust the geometric shape of the surface;

[0012] The result evaluation module is used to evaluate the performance of the optimized lens surface, including the light intensity distribution of the collimated beam, the deviation angle distribution and the adaptability of manufacturing errors.

[0013] Preferably, the surface modeling module defines the lens surface by a differential geometry method, and the surface is a two-dimensional differential manifold, and its local parameterized form is expressed as:

[0014] The coordinate value of each point on the surface is described by two independent variables, and the first basic quantity and the second basic quantity are constructed to characterize the intrinsic geometric characteristics of the surface;

[0015] The normal vector of the surface is used to determine the propagation direction and refraction angle of light on the lens surface.

[0016] Preferably, the normal vector distribution of the lens surface is based on the coupling constraint of the incident direction of the light source, and the propagation direction of the refracted light is determined by the surface normal vector, the light source direction and the refractive index of the material, thereby satisfying the directional consistency required for the collimated light beam.

[0017] Preferably, the optical simulation module simulates the path of light passing through the lens based on a ray tracing method, comprising the following steps:

[0018] Calculate the refraction angle of the light and output the propagation direction of the refracted light;

[0019] Analyze the collimation characteristics and intensity distribution of the refracted light beam.

[0020] Preferably, the refraction path of the light satisfies Snell's law, and the simulation module simulates the lens performance of different optical materials by adjusting the refraction parameters.

[0021] Preferably, the error analysis module diagnoses local deviations in the lens surface design by calculating the continuity of the light deviation angle distribution, specifically including:

[0022] Perform global analysis on the gradient distribution of light deviation angles;

[0023] Locate areas of large deviation angle gradients to aid in surface optimization.

[0024] Preferably, the optimization solution module establishes an optimization objective function based on the light deviation minimization objective, and the objective function includes:

[0025] The goal of minimizing the deviation angle;

[0026] The continuity constraint of the deviation angle distribution is used to avoid the phenomenon of uneven deviation.

[0027] Preferably, the optimization solution module discretizes the surface model by using a finite element method, and iteratively solves the lens surface shape using a variational method, so that the light deviation of the entire lens surface reaches a global optimum.

[0028] Preferably, the result evaluation module includes:

[0029] Output beam collimation performance indicators, including beam deviation angle distribution and light intensity distribution;

[0030] Output the manufacturing adaptability analysis of the optimized lens surface.

[0031] The present invention also provides a method for designing a double free-surface collimating lens based on differential manifolds, comprising the following steps:

[0032] A double free-form surface lens model based on differential manifolds is constructed, wherein the surface is defined by a parameterized method, including the distribution of principal curvatures, the distribution of normal vectors, and refractive index parameters;

[0033] Based on the lens model, simulate the propagation path of light on the curved surface, calculate the propagation direction of the light after refraction, and analyze the light collimation performance;

[0034] Analyze the optical simulation results, obtain the light deviation distribution, calculate the gradient change of the deviation distribution, and diagnose the local deviation and global continuity of the lens surface;

[0035] Based on the global minimization goal of light deviation, the geometric parameters of the lens surface model are iteratively adjusted through the optimization algorithm to generate an optimized lens model;

[0036] The performance of the optimized lens model is verified to evaluate the light collimation performance, deviation distribution and manufacturing adaptability, and the optimization results and design report are output.

[0037] The present invention provides a simulation system of a double free-form surface collimating lens design based on differential manifolds, which has the following beneficial effects:

[0038] 1. The present invention constructs a lens surface model based on differential manifolds, and accurately defines the principal curvature distribution and normal vector distribution through parameterization methods to ensure that the lens surface is highly matched with the light propagation path. The optimized lens has the characteristic of minimizing the global light deviation, which can significantly improve the beam collimation performance and meet the design requirements of high-precision optical systems.

[0039] 2. The present invention introduces the gradient continuity constraint of the deviation distribution through the optimization solution module to ensure that the optimization process not only pursues the minimization of the light deviation angle, but also controls the global continuity of the light propagation path. Compared with the traditional local optimization method, it can significantly reduce the beam divergence and unevenness, and improve the overall optical performance of the system.

[0040] 3. The present invention incorporates manufacturing error simulation and tolerance analysis into the optimization solution module, fully considering the impact of actual processing errors on lens performance. The optimized lens model has a strong ability to resist manufacturing errors, can effectively reduce the dependence on ultra-high precision processing, and improve the feasibility and economy of the design solution.

[0041] 4. The present invention provides multi-dimensional performance verification through the result evaluation module, including statistical analysis and visual display of core indicators such as light deviation distribution, beam intensity uniformity and manufacturing adaptability. The evaluation results are comprehensive and intuitive, providing a scientific basis and reference value for the optimization and final implementation of the design. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the system architecture of the present invention;

[0043] Figure 2 It is a schematic diagram of the flow of the surface modeling module of the present invention;

[0044] Figure 3 is a schematic diagram of the process of the optical simulation module of the present invention;

[0045] Figure 4 It is a schematic diagram of the method flow of the present invention. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the specification of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] Please refer to the attached Figure 1 -Attached Figure 3 The present invention provides a simulation system for designing a double free-form surface collimating lens based on differential manifolds, which can fully realize the design, optimization and verification of the double free-form surface collimating lens from theoretical modeling to performance evaluation.

[0048] like Figure 1As shown, the simulation system for the design of the double free-form surface collimating lens based on differential manifolds may include a surface modeling module, an optical simulation module, an error analysis module, an optimization solution module, and a result evaluation module. The following is a detailed description of each module of the simulation system.

[0049] For the surface modeling module, in this embodiment, the design of the double free-form surface collimating lens based on differential manifolds is realized through the surface modeling module, and its main function is to generate the initial geometric model of the lens and describe its optical properties. The surface modeling module is the basis of the entire simulation system, which is used to construct the geometric shape of the lens and provide input data for subsequent optical simulation, error analysis and optimization iteration.

[0050] In this embodiment, the lens surface is defined as a two-dimensional differential manifold, which is embedded in a three-dimensional Euclidean space and represented by parameterization. The local geometric properties of the surface, such as the distribution of principal curvature, the distribution of normal vectors, and the first and second basic quantities, are key data for describing the propagation path of light on the lens surface.

[0051] like Figure 2 As shown, the surface modeling module is implemented in the following way:

[0052] In this embodiment, the surface model is defined by a parameterization method in differential geometry. Assume that the surface M is a two-dimensional differential manifold, and the local parameterization is:

[0053]

[0054] in:

[0055] φ(u,v) represents the parameterized mapping function of the lens surface, which maps points in the two-dimensional parameter space U to the three-dimensional space The function describes the geometry of the lens surface.

[0056] u,v are the local coordinate system on the surface, i.e. the parameters of the lens surface in two-dimensional space. u,v represent two free variables on the surface.

[0057] It represents parameter space, which is a subset of the two-dimensional real space and represents the local area of ​​the surface. It is the area parameterized by u and v.

[0058] Represents the surface M in three-dimensional Euclidean space The shape of the surface is defined in three-dimensional space by the mapping φ(u,v).

[0059] This parameterized form allows flexible control over the lens surface shape and provides a basis for further optimization of optical performance.

[0060] In order to characterize the local intrinsic geometric characteristics of the surface, in this embodiment, the length measurement and normal vector change of the surface are defined by the first basic quantity and the second basic quantity.

[0061] The first basic quantity I of the surface is used to describe the distance and angle relationship within the surface. The expression is as follows:

[0062] I=EEdu 2 +2Fdudv+Gdv 2

[0063] in:

[0064]

[0065] In the above formula, <·,·> represents the inner product operation of vectors. and are the tangent vectors of the surface in the u and v directions respectively.

[0066] In this embodiment, the second basic quantity II is used to describe the change of the surface normal vector and is defined by the following expression:

[0067] II = edu 2 +2fdudv+gdv 2

[0068] in:

[0069]

[0070] In the above formula, n is the unit normal vector of the surface, which is calculated as:

[0071]

[0072] Among them, “×” represents the cross product of the vectors, and ∥·∥ represents the modulus of the vector.

[0073] The principal curvatures k1, k2 and the Gaussian curvature K of the surface can be calculated by using the first basic quantity and the second basic quantity. In this embodiment, the expressions of the Gaussian curvature K and the mean curvature H are:

[0074]

[0075] Among them, k1 and k2 are the two main eigenvalues ​​that describe the local curvature of the surface.

[0076] In this embodiment, the normal vector distribution of the surface is a key characteristic for simulating the light propagation path. In order to meet the design requirements of light collimation performance, the normal vector direction of each point on the lens surface needs to be consistent with the propagation direction of the refracted light.

[0077] The distribution of the normal vector n on the surface is related to the refractive index n of the material and needs to satisfy the refraction relationship of Snell's law. Specifically, the light deviation angle θ(p) on the surface is related to the normal vector distribution and the incident direction of the surface, and its mathematical model will be further described in subsequent modules.

[0078] In this embodiment, the surface modeling module not only defines the geometric properties of the lens surface, but also introduces the optical parameters of the material to describe the propagation behavior of light on the lens surface. The material parameters include the refractive index n, whose value can be adjusted according to the properties of the optical material (such as glass, plastic, etc.).

[0079] After modeling is completed, the geometric model and optical parameters of the lens surface will be passed to the optical simulation module to further simulate the light propagation path and refraction characteristics.

[0080] The surface modeling module in this embodiment can provide an accurate geometric basis for the optical system, and the shape of the lens surface can be flexibly adjusted to meet different optical requirements through the parameterization method of differential geometry.

[0081] like Figure 3 As shown, for the optical simulation module, in this embodiment, the optical simulation module is used to simulate the propagation path of light on the surface of the double free-form surface lens and evaluate the collimation performance of the lens. The module receives the parameterized lens geometry model and optical parameters such as the material refractive index output by the surface modeling module, and simulates and calculates the propagation direction, deviation angle distribution and optical performance of the light based on the ray tracing method and refraction theory.

[0082] The optical simulation module provides data support for the optimization solution module and error analysis module by calculating the incident and refraction paths and propagation characteristics of light, and provides a basis for performance evaluation of lens design.

[0083] In this embodiment, the propagation path of light is calculated based on Snell's law. Specifically, when light is incident from air to the lens surface, the propagation direction of the light is determined by the refractive index n of the lens material, the incident light direction d in and the surface normal vector n. The propagation direction of the refracted light d out It is expressed by the following formula:

[0084]

[0085] in:

[0086] θ i is the angle of incidence, which is related to the incident light direction and the surface normal vector as follows:

[0087] cosθ i =-n·d in

[0088] sin 2 θ i =1-cos 2 θ i , represents the sine square of the incident angle.

[0089] In this formula, n is the normal vector at the lens surface, which is provided by the surface modeling module, and the incident direction of the light d is in and the material refractive index n can be adjusted. Through this formula, the propagation direction of each ray after refraction can be calculated, thereby simulating the propagation path of the light on the entire lens surface.

[0090] In this embodiment, in order to evaluate the collimation performance of the lens, the optical simulation module analyzes the collimation of the light beam by calculating the deviation angle θ of the light beam. The light deviation angle θ represents the difference between the direction of the refracted light beam and the direction of the ideal collimated light beam d target The angle between them is expressed as:

[0091]

[0092] in:

[0093] d out is the propagation direction of the refracted light;

[0094] d target is the target direction of an ideal collimated beam.

[0095] Using the above formula, the deviation angle distribution of each refracted light can be calculated to evaluate the overall collimation performance of the lens.

[0096] In this embodiment, the optical simulation module can also simulate and analyze the intensity distribution of the light beam. The density distribution of light on the lens surface is directly related to the geometric characteristics of the surface. By integrating the incident light intensity and the refracted light intensity at each lens surface point, the intensity distribution of the light beam can be calculated. The intensity distribution function of the light beam is:

[0097] I(r)=I0·T·cosθ i

[0098] in:

[0099] I0 is the initial intensity of the light source;

[0100] T is the transmittance of the lens material;

[0101] cosθ i is the cosine of the angle between the incident light and the surface normal.

[0102] The above simulation results can intuitively describe the uniformity and intensity distribution of the lens collimated light beam and provide specific indicators of the lens performance.

[0103] In this embodiment, to ensure the accuracy of the simulation results, the optical simulation module uses the Monte Carlo ray tracing method to simulate the propagation paths and deviation angle distribution of a large number of light rays on the lens surface. By randomly generating light incident points on the lens surface and calculating the propagation path of each light ray, the optical performance distribution of the entire lens surface can be obtained.

[0104] The core steps of the Monte Carlo ray tracing method include:

[0105] Randomly generate the light incident point (x, y, z) and the incident direction d in ;

[0106] Calculate the refraction direction d of the light according to the surface normal vector n and the refractive index n out ;

[0107] Record the propagation direction and deviation angle θ of the refracted light;

[0108] Summarize the propagation path data of all rays and calculate the statistical distribution of the deviation angles.

[0109] Through the above method, a complete beam propagation path and performance analysis results can be generated, providing a reliable basis for subsequent error analysis and optimization solutions.

[0110] In this embodiment, the output data of the optical simulation module includes the propagation path of the light, the deviation angle distribution and the intensity distribution of the light beam. These data can not only be used to evaluate the collimation performance of the lens, but also provide support for the error analysis module to help diagnose the performance bottleneck in the lens design.

[0111] In addition, the optical simulation module also supports simulation analysis of lens performance of different materials. By adjusting the refractive index n and transmittance T, the lens performance of different optical materials can be simulated to provide a basis for material selection.

[0112] The optical simulation module in this embodiment can comprehensively and accurately evaluate the optical performance of the double free-form surface lens through high-precision ray tracing and refraction path calculation, and provide reliable data support for the optimization design of the entire simulation system.

[0113] As for the error analysis module, in this embodiment, the error analysis module is used to analyze the light propagation path and collimation performance data provided by the optical simulation module. Its main function is to diagnose the global and local continuity of the light deviation angle distribution, evaluate the error performance of the lens surface in light propagation, and provide targeted adjustment basis for the subsequent optimization solution module.

[0114] The key goal of the error analysis module is to quantify the distribution characteristics of the light deviation angle, locate the high deviation gradient areas that may exist on the lens surface, and determine the degree of impact of these areas on the optical performance. Through the calculation and analysis of this module, the performance bottleneck in the lens design can be accurately located.

[0115] In this embodiment, the error analysis module first receives the light deviation angle distribution data generated by the optical simulation module. The calculation formula of the light deviation angle θ(p) is:

[0116]

[0117] in:

[0118] d out is the propagation direction of the refracted light in the simulation calculation;

[0119] d target is the target direction of an ideal collimated beam.

[0120] The deviation angle describes the angle between the propagation direction of the refracted light and the ideal collimation direction, and is a core indicator for measuring the collimation performance of the lens. The optical simulation module outputs the distribution of the deviation angle on the lens surface as input data for the error analysis module.

[0121] In this embodiment, in order to further analyze the characteristics of the deviation angle distribution, the error analysis module calculates the gradient change of the deviation angle to quantify the continuity and uniformity of the optical performance of the lens surface. It represents the rate of change of the deviation angle in the surface parameter u, v coordinates. The calculation formula is:

[0122]

[0123] in:

[0124] and Represent the partial derivatives of the deviation angle in the u and v directions respectively.

[0125] The above gradient calculation process requires the use of parameterized surface information provided by the surface modeling module, including the local coordinate system of the lens surface and the distribution of surface normal vectors. It can be determined whether the deviation angle changes smoothly on the lens surface and whether there are areas with large gradients.

[0126] Areas with large gradients usually indicate significant geometric deviations on the lens surface, which can lead to a decrease in light collimation performance. By identifying these areas, the Error Analysis module provides a basis for the adjustment strategy of the Optimization Solver module.

[0127] In this embodiment, the error analysis module further performs statistical analysis on the deviation angle distribution. By quantifying the statistical characteristics of the deviation angle distribution, a global index of the lens collimation performance can be provided. The statistical characteristics include:

[0128] Average value of deviation angle It represents the average level of overall collimation performance and is calculated as:

[0129]

[0130] Where A is the area of ​​the lens surface.

[0131] Variance of the deviation angle It indicates the stability of the collimation performance, and its calculation formula is:

[0132]

[0133] Through the above indicators, the error analysis module can intuitively reflect the global distribution characteristics of lens surface deviations and provide reference data for subsequent result evaluation.

[0134] In this embodiment, the error analysis module displays the deviation angle distribution and gradient distribution in a visual manner. The deviation angle distribution can be displayed in the form of a two-dimensional or three-dimensional heat map, which intuitively reflects the size and position distribution of the deviation angle; the gradient distribution graphically displays the error change trend of the lens surface through a vector field or a gradient field.

[0135] For example, if the vector length shown in the gradient distribution diagram is long in a certain area on the lens surface, it means that the deviation angle in this area changes dramatically and needs to be adjusted in the optimization stage. For areas with smooth gradient distribution, it means that the collimation performance in this area is relatively stable, which can reduce the resource consumption of optimization calculation.

[0136] In this embodiment, the working process of the error analysis module is as follows:

[0137] 1. Receive the deviation angle distribution data output by the optical simulation module;

[0138] 2. Calculate the deviation angle gradient And generate a gradient distribution map;

[0139] 3. Global characteristics of the statistical deviation angle distribution, including mean and variance;

[0140] 4. Locate the area with larger gradient and provide the target area for the optimization solution module;

[0141] 5. Output the analysis results in the form of visualization and data.

[0142] In this embodiment, the output of the error analysis module includes the following:

[0143] Deviation angle distribution diagram;

[0144] Deviation angle gradient distribution map;

[0145] Deviation angle statistical indicators, including mean and variance;

[0146] Coordinate information of the area with larger gradient.

[0147] Through the above analysis process, the error analysis module can fully diagnose the performance bottleneck in the lens surface design and provide accurate optimization direction for the optimization solution module. In addition, the gradient analysis method used in the module can fully reflect the continuity of the deviation distribution, ensuring that the optical performance of the lens surface is significantly improved during the optimization process.

[0148] As for the optimization solution module, in this embodiment, the optimization solution module is used to optimize the lens surface based on the global light deviation minimization objective. Its main function is to receive the deviation distribution data and gradient information from the error analysis module, and to adjust the geometric parameters of the surface by establishing an optimization objective function, combining the variational method and the numerical optimization method, so as to generate an optimized lens model.

[0149] The optimization solution module is designed to ensure that the light deviation is globally minimized on the entire lens surface while satisfying the continuity constraint of the light propagation path, so that the optimized surface can achieve efficient collimation performance and adapt to actual manufacturing needs.

[0150] In this embodiment, the optimization objective function is based on the global minimization of the light deviation angle, and the gradient continuity constraint of the deviation distribution is added. The mathematical expression of the objective function J[M] is:

[0151]

[0152] in:

[0153] M represents the lens surface;

[0154] d out is the propagation direction of the refracted light, provided by the optical simulation module;

[0155] d target is the target direction of the ideal collimated beam;

[0156] ||d out -d target || 2 Represents the square error of the light deviation angle, which is the core goal of optimization;

[0157] It is the quadratic term of the deviation angle gradient, which is used to ensure the continuity of the light propagation path;

[0158] α is a weight factor used to adjust the importance of the two parts of the objective.

[0159] By constructing the above objective function, this embodiment can focus on both the collimation performance and the continuity of the gradient distribution, thereby avoiding the beam scattering problem caused by local optimization.

[0160] In this embodiment, the optimization solution module uses the variational method to derive the necessary conditions for optimizing the surface model. In order to minimize the objective function J[M], the Euler-Lagrange equation must be satisfied:

[0161]

[0162] in:

[0163] φ(u, v) is the parameterized expression of the lens surface;

[0164] K(p) is the curvature tensor on the surface;

[0165] is the light deviation angle gradient;

[0166] n(p) is the normal vector of the lens surface;

[0167] λ is the Lagrange multiplier, which is used to constrain the optimization results to meet material and geometric conditions.

[0168] By solving the above partial differential equation, the changing direction of the lens surface parameters u, v can be determined, thereby adjusting the geometric shape of the surface.

[0169] In this embodiment, in order to achieve numerical solution, the optimization solution module discretizes the surface model. Specifically, the continuous surface is divided into finite triangular units, and a parameterized function is defined on each unit. The discretized optimization objective function is expressed as:

[0170]

[0171] in:

[0172] N is the number of discrete units;

[0173] d out，i and d target，i are the refraction direction and target direction of the light on the i-th unit respectively;

[0174] is the gradient of the deviation angle on the i-th unit;

[0175] ΔA i is the area of ​​the ith unit.

[0176] By iteratively optimizing the discretized objective function, the module can gradually adjust the surface parameters and approach the optimal solution.

[0177] In this embodiment, the optimization solution module uses the gradient descent method as the core step of the optimization algorithm. The gradient descent method gradually adjusts the surface shape according to the gradient information of the objective function to the parameter, so that the objective function value gradually decreases. The specific implementation includes the following steps:

[0178] Initialize the parameterized model φ0(u, v) of the lens surface and calculate its initial deviation angle distribution and objective function value;

[0179] Calculate the gradient information of the objective function:

[0180]

[0181] Adjust surface parameters based on gradient direction:

[0182]

[0183] Among them, η is the step size factor, which is used to control the amplitude of parameter update;

[0184] Repeat the above iterative process until the objective function value converges or meets the design accuracy.

[0185] Through the above process, the optimization solution module can gradually optimize the geometric parameters of the lens surface and generate an optimized surface that meets the design objectives.

[0186] In this embodiment, the optimization solution module also verifies the optimization results through error tolerance analysis. To ensure that the optimized surface design is suitable for the actual manufacturing process, the module simulates the impact of lens processing errors and material deviations on alignment performance. Error tolerance analysis includes:

[0187] Simulate the shape deviation of lens surface during processing;

[0188] Calculate the effect of machining errors on the distribution of light deviation angles;

[0189] Adjust the constraints in the objective function to reduce the reliance on high-precision surface machining.

[0190] Through the above analysis, the surface generated by the optimization solution module can not only meet the optical performance requirements, but also adapt to the actual manufacturing conditions.

[0191] In this embodiment, the output of the optimization solution module includes the optimized lens surface model, the convergence curve of the objective function value, and the change record of the surface parameters during the optimization process. The output result will be passed to the result evaluation module for final performance verification and report generation.

[0192] The optimization solution module combines the variational method, numerical discretization and gradient descent method to achieve high-precision optimization design of double free-form surface lenses, providing a reliable geometric foundation and performance guarantee for the practical application of lenses.

[0193] As for the result evaluation module, in this embodiment, the result evaluation module is used to perform performance verification and comprehensive analysis on the lens model generated by the optimization solution module. The main function of this module is to verify whether the lens design meets the target requirements of collimation performance through calculation and visual analysis of the optimized optical performance indicators, and to evaluate the adaptability of the design under actual manufacturing conditions.

[0194] The design goal of the result evaluation module is to provide complete performance evaluation results, including the light deviation angle distribution, beam intensity distribution and the impact of manufacturing errors on lens performance, so as to provide a detailed quality evaluation and optimization direction reference for the final lens design solution.

[0195] In this embodiment, the result evaluation module first receives the lens surface model and optical performance data output by the optimization solution module, and evaluates the collimation performance of the lens in combination with the light propagation path of the optical simulation module. The core performance indicators include the statistical distribution of the light deviation angle and the beam intensity distribution.

[0196] The statistical distribution of the light deviation angle is calculated by the following formula:

[0197]

[0198] in:

[0199] is the average value of the deviation angle, indicating the overall level of light collimation performance;

[0200] θ(p) is the deviation angle of a point on the lens surface;

[0201] A is the total area of ​​the lens surface;

[0202] M is the lens surface.

[0203] Standard deviation of the deviation angle σ θ Calculated as:

[0204]

[0205] Among them, the standard deviation reflects the stability of the light collimation performance. The smaller the value, the more uniform the collimation performance.

[0206] Through the above formula, the result evaluation module can quantify the collimation effect of the light and provide a basis for judging whether the design scheme meets the performance requirements.

[0207] In this embodiment, the result evaluation module further calculates the intensity distribution of the optimized lens beam. The beam intensity distribution I(r) represents the energy distribution of the beam after passing through the lens, and its calculation formula is:

[0208] I(r)=I0·T·cosθ i

[0209] in:

[0210] I0 is the initial intensity of the incident light;

[0211] T is the transmittance of the lens material;

[0212] cosθ i is the cosine of the angle of incidence, related to the lens surface normal.

[0213] The uniformity of intensity distribution directly affects the quality of the light beam. By visually analyzing the intensity distribution of the light beam, it is possible to evaluate whether the optimized lens has uniform optical performance.

[0214] In this embodiment, the result evaluation module also analyzes the manufacturing adaptability of the optimized lens model. The manufacturing adaptability evaluation of the lens includes the following two aspects:

[0215] On the one hand, the module simulates the disturbance of manufacturing errors on lens surface parameters and analyzes the influence of errors on light deviation angle and beam intensity distribution. Assuming that the influence of manufacturing errors on lens surface φ(u, v) is a random disturbance δφ(u, v), the deviation angle distribution after disturbance is expressed as:

[0216]

[0217] Where d′ out is the propagation direction of the light after disturbance.

[0218] By analyzing the changes in the deviation angle distribution and the intensity distribution under perturbation conditions, the sensitivity of the lens to manufacturing errors can be quantified.

[0219] On the other hand, the module evaluates the processing feasibility of the lens based on the optimized lens geometry. The principal curvatures k1, k1 and Gaussian curvature K of the surface are key parameters for determining manufacturing feasibility. If the curvature value exceeds the capability of a specific material or processing equipment, the module will generate relevant warnings and output possible adjustment suggestions.

[0220] In this embodiment, in order to facilitate the user's understanding and use of the evaluation results, the result evaluation module supports multiple forms of result visualization. Specifically including:

[0221] 2D heat map and 3D surface map of deviation angle distribution, which intuitively show the distribution of deviation angle on the lens surface;

[0222] 2D contour plots of beam intensity distribution and beam cross-section plots for analyzing beam uniformity;

[0223] Overlay of simulation results for manufacturing errors to show how the errors affect optical performance.

[0224] Through these visualization methods, users can quickly understand the performance and potential problems of the optimization results, providing a reference for subsequent design adjustments.

[0225] In this embodiment, the workflow of the result evaluation module includes:

[0226] Receive optimized lens models and related performance data;

[0227] Calculate the statistical distribution of light deviation angles (including mean and standard deviation);

[0228] Calculate the beam intensity distribution and generate corresponding performance indicators;

[0229] Conduct manufacturing error simulation to evaluate the impact of errors on optical performance;

[0230] Outputs visualization charts and comprehensive performance reports of evaluation results.

[0231] In this embodiment, the final output of the result evaluation module includes:

[0232] Performance reports for optimized lens models, including deviation angle mean, standard deviation, and beam intensity distribution;

[0233] Manufacturing suitability analysis report, including the impact of manufacturing errors on performance and processing feasibility assessment;

[0234] Visualization chart files, including deviation angle distribution, beam intensity distribution and manufacturing error influence diagram.

[0235] Through the above design, the result evaluation module can comprehensively verify the optimized lens performance, ensure that the lens design meets the actual application requirements, and provide users with detailed evaluation results and design improvement suggestions.

[0236] Please refer to the attached Figure 4 Correspondingly, the present invention also provides a method for designing a double free-form surface collimating lens based on differential manifolds, including a complete workflow from lens model construction to performance verification. Specifically, the method includes the following steps:

[0237] 1. Construct a double free-form surface lens model based on differential manifolds;

[0238] In this embodiment, a double free-form surface lens model based on differential manifolds is firstly generated by a surface modeling module.

[0239] The lens surface is defined by parametric methods, including the distribution of principal curvatures, normal vectors, and refractive index parameters. The lens surface is expressed by local parameterization, describing the three-dimensional spatial coordinates and geometric properties of each point, ensuring that the surface model can accurately represent the light propagation path.

[0240] At the same time, in order to meet the design requirements of the collimating lens, the material refractive index n and the geometric shape of the lens were clarified during the modeling phase. The modeling results serve as the basic data for subsequent optical simulation and performance optimization.

[0241] 2. Simulate the propagation path of light on the surface based on the lens model;

[0242] In this embodiment, the optical simulation module receives the lens model generated by the surface modeling module and simulates the propagation path of light on the lens surface.

[0243] Specifically, the ray tracing algorithm is used to calculate the refraction path of each light ray according to Snell's law to obtain the propagation direction of the refracted light ray. The deviation angle θ is calculated by the angle between the propagation direction of the light ray and the ideal collimation direction, reflecting the degree of light deviation.

[0244] The simulation results include the light propagation path, refraction direction, and distribution of deviation angles, providing necessary data for subsequent error analysis and optimized design.

[0245] 3. Analyze the optical simulation results;

[0246] In this embodiment, the error analysis module receives the deviation angle distribution data output by the optical simulation module, and further analyzes the global and local continuity thereof.

[0247] Deviation angle gradient The calculation is used to diagnose local performance problems on the lens surface, identify areas where light deviation changes drastically, and locate the coordinates of these areas.

[0248] The module also performs statistical analysis on the mean and standard deviation of the deviation angle to provide global characteristic indicators of optical performance. The analysis results are used as input to the optimization solution module to provide direction for geometric optimization of the lens.

[0249] 4. Optimize the lens surface based on the global minimization goal of light deviation;

[0250] In this embodiment, the optimization solution module iteratively adjusts the geometric parameters of the lens surface through an optimization algorithm according to the global minimization goal of the light deviation.

[0251] The optimization objective function comprehensively considers the minimization of the deviation angle and the continuity constraint of the gradient. The optimization conditions are derived through the variational method and the numerical solution is achieved by combining the finite element discretization method.

[0252] The optimization process uses the gradient descent method to iterate parameters, gradually reduce the objective function value, and finally generate an optimized lens surface model. The optimized lens surface can significantly improve the collimation performance and adapt to the actual manufacturing process requirements.

[0253] 5. Verify the performance of the optimized lens model;

[0254] In this embodiment, the result evaluation module receives the lens model generated by the optimization solution module and comprehensively verifies its optical performance and manufacturing adaptability.

[0255] Performance verification includes statistical analysis of the light deviation angle distribution (such as mean and standard deviation) and uniformity evaluation of beam intensity distribution. At the same time, the module simulates the impact of manufacturing errors on lens performance and evaluates the adaptability of the design model in actual manufacturing.

[0256] The final evaluation results are output in a visual form, including deviation angle distribution diagram, beam intensity distribution diagram and manufacturing error influence diagram. At the same time, an optimization result report containing all performance indicators is generated to provide comprehensive support for design implementation and improvement.

[0257] Through the above steps, the system of the present invention can realize a complete design process from lens model construction to performance verification, ensuring that the optimized double free-form surface lens model has excellent optical performance and practical manufacturing feasibility.

[0258] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A simulation system for designing a double free-form surface collimating lens based on differential manifolds, characterized in that: include: A surface modeling module, used to construct a double free-form surface lens model based on differential manifolds, wherein the double free-form surface lens model is represented by a parameterized method and defines principal curvature, normal vector distribution and optical refraction parameters; Optical simulation module, used to simulate the propagation path of light on the lens surface and analyze the collimation performance of light after refraction; Error analysis module, used to analyze the continuity and global changes of the deviation angle distribution in the light propagation path; An optimization solution module is used to optimize and iterate the lens surface based on the goal of minimizing light deviation and adjust the geometric shape of the surface; The result evaluation module is used to evaluate the performance of the optimized lens surface, including the light intensity distribution of the collimated beam, the deviation angle distribution and the adaptability of manufacturing errors.

2. The simulation system of the double free-form surface collimating lens design based on differential manifold according to claim 1, characterized in that: The surface modeling module defines the lens surface by differential geometry method. The surface is a two-dimensional differential manifold, and its local parameterized form is expressed as: The coordinate value of each point on the surface is described by two independent variables, and the first basic quantity and the second basic quantity are constructed to characterize the intrinsic geometric characteristics of the surface; The normal vector of the surface is used to determine the propagation direction and refraction angle of light on the lens surface.

3. The simulation system of the double free-form surface collimating lens design based on differential manifold according to claim 1, characterized in that: The normal vector distribution of the lens surface is based on the coupling constraint of the incident direction of the light source. The propagation direction of the refracted light is determined by the surface normal vector, the light source direction and the material refractive index, which meets the directional consistency required for the collimated light beam.

4. The simulation system of the double free-form surface collimating lens design based on differential manifold according to claim 1, characterized in that: The optical simulation module simulates the path of light passing through the lens based on a ray tracing method, and includes the following steps: Calculate the refraction angle of the light and output the propagation direction of the refracted light; Analyze the collimation characteristics and intensity distribution of the refracted light beam.

5. The simulation system of the double free-form surface collimating lens design based on differential manifold according to claim 4, characterized in that: The refraction path of the light satisfies Snell's law, and the simulation module simulates the lens performance of different optical materials by adjusting the refraction parameters.

6. The simulation system of the double free-form surface collimating lens design based on differential manifold according to claim 1, characterized in that: The error analysis module diagnoses the local deviations in the lens surface design by calculating the continuity of the light deviation angle distribution, specifically including: Perform global analysis on the gradient distribution of light deviation angles; Locate areas of large deviation angle gradients to aid in surface optimization.

7. The simulation system of the double free-form surface collimating lens design based on differential manifold according to claim 1, characterized in that: The optimization solution module establishes an optimization objective function based on the light deviation minimization objective, and the objective function includes: The goal of minimizing the deviation angle; The continuity constraint of the deviation angle distribution is used to avoid the phenomenon of uneven deviation.

8. The simulation system of the double free-form surface collimating lens design based on differential manifold according to claim 7, characterized in that: The optimization solution module discretizes the surface model through the finite element method, and iteratively solves the lens surface shape using the variational method, so that the light deviation of the entire lens surface reaches the global optimum.

9. The simulation system of the double free-form surface collimating lens design based on differential manifold according to claim 1, characterized in that: The result evaluation module includes: Output beam collimation performance indicators, including beam deviation angle distribution and light intensity distribution; Output the manufacturing adaptability analysis of the optimized lens surface.

10. A method for designing a double free-form surface collimating lens based on differential manifolds, based on the system according to any one of claims 1 to 9, characterized in that: The following steps are involved: A double free-form surface lens model based on differential manifolds is constructed, wherein the surface is defined by a parameterized method, including the distribution of principal curvatures, the distribution of normal vectors, and refractive index parameters; Based on the lens model, simulate the propagation path of light on the curved surface, calculate the propagation direction of the light after refraction, and analyze the light collimation performance; Analyze the optical simulation results, obtain the light deviation distribution, calculate the gradient change of the deviation distribution, and diagnose the local deviation and global continuity of the lens surface; Based on the global minimization goal of light deviation, the geometric parameters of the lens surface model are iteratively adjusted through the optimization algorithm to generate an optimized lens model; The performance of the optimized lens model is verified to evaluate the light collimation performance, deviation distribution and manufacturing adaptability, and the optimization results and design report are output.

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