Virtual system for design of double free-form collimator based on differential manifold

Abstract

The application relates to the field of optical design and optimization, and discloses a pseudo-real system based on differential manifold double free-form surface collimating lens design, which comprises a curved surface modeling module, an optical simulation module, an error analysis module, an optimization solving 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 the propagation path of light on the lens curved surface, calculates the direction of refracted light and analyzes the light collimating performance; the error analysis module diagnoses the local deviation and global continuity of the lens surface; the optimization solving module iteratively adjusts the geometric parameters of the lens curved surface model to generate an optimized lens model; and the result evaluation module comprehensively verifies the optical performance and manufacturing adaptability of the optimized lens model. Through accurate geometric modeling, optical simulation and optimization, the application significantly improves the collimating performance and manufacturing adaptability of the lens, and is suitable for optical design in the fields of laser collimation, high-precision imaging and optical communication.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical design and optimization, specifically to a quasi-real system for designing a double free-form surface collimating lens based on differential manifold. BACKGROUND

[0002] Double free-form surface lenses, as a kind of optical elements with high flexibility and complex geometric characteristics, have been widely used in laser collimation, high-precision imaging, and optical communication. The core design goal is to optimize the light propagation path through precise control of the surface shape, ultimately achieving the purpose of collimating the beam. However, there are still some technical bottlenecks in the design and optimization of double free-form surface lenses in the existing technology.

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

[0004] In addition, existing lens design lacks systematic consideration of manufacturing adaptability, and usually cannot effectively evaluate the impact of processing errors on the optical performance of the lens. Therefore, the optimization result is often too dependent on high-precision manufacturing equipment, making it difficult to achieve the expected performance in actual processing, increasing production cost and complexity.

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

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

[0007] To achieve the above purpose, the present application realizes the following technical scheme: a quasi-real system for designing a double free-form surface collimating lens based on differential manifold, comprising:

[0008] a surface modeling module for constructing a double free-form surface lens model based on differential manifold, the double free-form surface lens model being represented by a parameterization method and defining principal curvatures, normal vector distribution, and optical refraction parameters;

[0009] The optical simulation module is used to simulate the propagation path of light on the curved surface of a lens and analyze the collimation performance after light refraction.

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

[0011] The optimization solution module is used to perform iterative optimization on the lens surface based on the goal of minimizing light deviation, and adjust the geometry of the surface.

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

[0013] Preferably, the surface modeling module defines the lens surface using differential geometry methods. The surface is a two-dimensional differential manifold, and its local parameterized form is expressed as follows:

[0014] By describing the coordinate values ​​of each point on the surface using two independent variables, the first and second fundamental quantities are constructed to characterize the intrinsic geometric properties of the surface.

[0015] The normal vector of the curved surface is used to determine the direction of light propagation and the angle of refraction 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, so as to meet the directional consistency required for collimating the beam.

[0017] Preferably, the optical simulation module is based on a ray tracing method to simulate the path of light rays passing through a lens, including the following steps:

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

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

[0020] Preferably, the refraction path of the light rays 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 angular distribution, specifically including:

[0022] A global analysis of the gradient distribution of the light deviation angle is performed.

[0023] Regions with large angular gradients in the positioning deviation are used to assist in surface optimization.

[0024] Preferably, the optimization solving module establishes an optimization objective function based on a ray deviation minimization objective, and the objective function comprises:

[0025] a minimization objective of the deviation angle;

[0026] a continuity constraint of the deviation angle distribution for avoiding uneven deviation.

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

[0028] Preferably, the result evaluation module comprises:

[0029] outputting a light beam collimation performance index, including a ray deviation angle distribution and a light intensity distribution;

[0030] outputting a manufacturing adaptability analysis of the optimized lens curved surface.

[0031] The application also provides a method for designing a double free curved surface collimation lens based on a differential manifold, comprising the following steps:

[0032] constructing a double free curved surface lens model based on a differential manifold, wherein the curved surface is defined by a parameterization method, including a principal curvature distribution, a normal vector distribution and a refractive index parameter;

[0033] based on the lens model, simulating a ray propagation path on the curved surface, calculating a propagation direction of the refracted ray, and analyzing a ray collimation performance;

[0034] analyzing the optical simulation result, obtaining a ray deviation distribution, and calculating a gradient change of the deviation distribution to diagnose a local deviation and a global continuity of the lens surface;

[0035] based on a global minimization objective of the ray deviation, iteratively adjusting geometric parameters of the lens curved surface model by an optimization algorithm to generate an optimized lens model;

[0036] verifying the performance of the optimized lens model, evaluating a ray collimation performance, a deviation distribution and a manufacturing adaptability, and outputting an optimization result and a design report.

[0037] The application provides a pseudo-real system for designing a double free curved surface collimation lens based on a differential manifold, which has the following beneficial effects:

[0038] 1. The application constructs a lens curved surface model based on a differential manifold, accurately defines a principal curvature distribution and a normal vector distribution by a parameterization method, and ensures a high matching between the lens curved surface and a ray propagation path. The optimized lens has a global ray deviation minimization characteristic, can significantly improve a light beam collimation performance, and meets the design requirements of a high-precision optical system.

[0039] 2、The application introduces gradient continuity constraints of bias distribution in the optimization solving module, ensuring that the optimization process not only pursues the minimization of light deviation angle, but also controls the global continuity of light propagation path. Compared with traditional local optimization methods, it can significantly reduce beam divergence and unevenness, and improve the overall optical performance of the system.

[0040] 3、The application integrates manufacturing error simulation and tolerance analysis in the optimization solving module, fully considering the influence of actual machining errors on lens performance. The optimized lens model has strong anti-manufacturing error ability, which can effectively reduce the dependence on ultra-high precision machining, and improve the implementability and economy of the design scheme.

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

[0042] Figure 1 is a schematic diagram of the system architecture of the application;

[0043] Figure 2 is a flowchart of the surface modeling module of the application;

[0044] Figure 3 is a flowchart of the optical simulation module of the application;

[0045] Figure 4 is a flowchart of the method of the application. DETAILED DESCRIPTION

[0046] The technical solutions in the embodiments of the application will be described below with reference to the drawings in the specification of the application. Obviously, the described embodiments are only part of the embodiments of the application, not all embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the application.

[0047] Please refer to the drawings in the specification of the application Figure 1 - the drawings in the specification of the application Figure 3 The application provides a pseudo-real system for designing double free-form surface collimating lens based on differential manifold, which can comprehensively realize the design, optimization and verification of double free-form surface collimating lens from theoretical modeling to performance evaluation.

[0048] As Figure 1As shown, the quasi-real system based on the differential manifold-based double free-form surface collimating lens design can include a curved surface modeling module, an optical simulation module, an error analysis module, an optimization solving module, and a result evaluation module. The various modules of the quasi-real system are described in detail below.

[0049] For the curved surface modeling module, in this embodiment, the design of the differential manifold-based double free-form surface collimating lens is implemented through the curved surface modeling module, and the main function is to generate an initial geometric model of the lens and describe its optical properties. The curved surface modeling module is the basis of the entire quasi-real system, and 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 principal curvature distribution, the normal vector distribution, and the first and second fundamental quantities, are key data for describing the propagation path of light on the lens surface.

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

[0052] In this embodiment, the curved surface model is defined through the parameterization method in differential geometry. Let the surface M be a two-dimensional differential manifold, which is locally parameterized as:

[0053]

[0054] where:

[0055] φ(u,v) represents the parameterization mapping function of the lens surface, which maps a point in the two-dimensional parameter space U to a surface point in the three-dimensional space through this function. This function describes the geometric shape 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] represents the parameter space, which is a subset of the two-dimensional real number space, representing a local region of the surface. It is parameterized by u,v.

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

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

[0060] In order to characterize the intrinsic geometric properties of the curved surface in the local, the length measure and the normal vector variation of the curved surface are defined by the first fundamental quantity and the second fundamental quantity in the embodiment.

[0061] The first fundamental quantity I of the curved surface is used to describe the distance and angle relationship in the curved surface, and the expression is as follows:

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

[0063] Wherein:

[0064]

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

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

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

[0068] Wherein:

[0069]

[0070] In the above formula, n is the unit normal vector of the curved surface, and the calculation method is as follows:

[0071]

[0072] Wherein, "×" represents the cross product of the vector, and ||·|| represents the modulus of the vector.

[0073] By the first fundamental quantity and the second fundamental quantity, the principal curvatures k1, k2 and the Gaussian curvature K of the curved surface can be calculated. In the embodiment, the expressions of the Gaussian curvature K and the mean curvature H are as follows:

[0074]

[0075] Wherein, k1, k2 are two main eigenvalues describing the local bending degree of the curved surface.

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

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

[0078] In this embodiment, the curved surface modeling module not only defines the geometric characteristics of the lens surface, but also introduces the optical parameters of the material for describing the propagation behavior of light on the lens surface. The material parameters include the refractive index n, which can be adjusted according to the characteristics of optical materials such as glass, plastic, etc.

[0079] The geometric model and optical parameters of the lens curved surface will be passed to the optical simulation module after modeling, for further simulating the light propagation path and refraction characteristics.

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

[0081] As shown in Figure 3 , 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 curved lens, and to evaluate the collimation performance of the lens. This module receives the parameterized lens geometric model and material refractive index and other optical parameters output by the curved surface modeling module, and simulates 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 solving module and error analysis module by calculating the incidence, refraction path and propagation characteristics of the light, and provides a basis for performance evaluation of the lens design.

[0083] In this embodiment, the propagation path of the light is calculated based on Snell's law. Specifically, when the light is incident from the 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 normal vector n of the curved surface. The propagation direction d out of the refracted light is represented by the following formula:

[0084]

[0085] Where:

[0086] θ i is the incident angle, and the relationship between the incident light direction and the normal vector of the curved surface is:

[0087] cosθ i = -n·d in

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

[0089] In the formula, n is the normal vector at the lens surface, which is provided by the curved surface modeling module, and the incident direction d in of the light ray and the material refractive index n can be adjusted. Through this formula, the propagation direction of each refracted light ray can be calculated, thereby simulating the propagation path of the light ray on the entire lens curved 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 ray. The light ray deviation angle θ represents the included angle between the refracted light ray direction and the ideal collimated light beam direction d target , and its expression is:

[0091]

[0092] Wherein:

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

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

[0095] Through the above formula, the deviation angle distribution of each refracted light ray can be calculated, thereby evaluating 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 the light rays on the lens surface is directly related to the geometric characteristics of the curved surface. By integrating the incident light intensity and the refracted light intensity of each lens surface point, the light intensity distribution of the light beam can be calculated, and the intensity distribution function of the light beam is:

[0097] I(r) = I0·T·cosθ i

[0098] Wherein:

[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 value of the included angle between the incident light ray and the surface normal vector.

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

[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 path 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 light incident points (x, y, z) and incident direction d in ;

[0106] Calculate the refracted 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 all the propagation path data of the light and calculate the statistical distribution of the deviation angle.

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

[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 not only can be used to evaluate the collimation performance of the lens, but also can provide support for the error analysis module, helping to diagnose the performance bottleneck in the lens design.

[0111] In addition, the optical simulation module also supports simulation analysis of the performance of lenses made of different materials. By adjusting the refractive index n and the transmittance T, the performance of lenses made of different optical materials can be simulated, providing 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 refractive path calculation, and provide reliable data support for the optimization design of the entire simulation system.

[0113] 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 the light propagation, and provide targeted adjustment basis for the subsequent optimization solution module.

[0114] The key objective of the error analysis module is to quantify the distribution characteristics of the ray deviation angle, locate the regions of high deviation gradient on the lens surface, and judge the degree of influence of these regions on the optical performance. Through the calculation and analysis of this module, the precise positioning of the performance bottleneck in the lens design can be realized.

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

[0116]

[0117] Wherein:

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

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

[0120] This deviation angle describes the size of the angle between the refracted ray propagation direction and the ideal collimated direction, and is the core index for measuring the collimation performance of the lens. The optical simulation module will output the distribution of this deviation angle on the lens surface as the input data of the error analysis module.

[0121] In this embodiment, 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. The deviation angle gradient represents the rate of change of the deviation angle in the u, v coordinates of the curved surface, and its calculation formula is:

[0122]

[0123] Wherein:

[0124] and respectively represent the partial derivative of the deviation angle in the u and v directions.

[0125] The above gradient calculation process needs to use the parameterized curved surface information provided by the curved surface modeling module, including the local coordinate system of the lens surface and the distribution of the curved surface normal vector. By calculating whether the change of the deviation angle on the lens surface is smooth and whether there are regions with large gradient.

[0126] Regions with large gradient usually indicate that there is a significant geometric deviation on the lens surface, which may lead to a decline in the light collimation performance. By identifying these regions, the error analysis module provides a basis for the adjustment strategy of the optimization solving 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 The average level of overall collimation performance is represented by the following formula:

[0129]

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

[0131] variance of the deviation angle The stability of collimation performance is represented by the following formula:

[0132]

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

[0134] In this embodiment, the error analysis module visualizes the deviation angle distribution and gradient distribution. The deviation angle distribution can be displayed in the form of a two-dimensional or three-dimensional heatmap, intuitively reflecting the magnitude and position distribution of the deviation angle; the gradient distribution is graphically displayed through a vector field or gradient field to show the error change trend of the lens surface.

[0135] For example, if the vector length shown in the gradient distribution diagram is relatively long within a certain region of the lens surface, it indicates that the deviation angle changes drastically in that region, requiring focused adjustment during the optimization phase. Conversely, a region with a smooth gradient distribution indicates that the collimation performance in that region is relatively stable, reducing the resource consumption for optimization computation.

[0136] In this embodiment, the workflow 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 bias angular distribution, including mean and variance;

[0140] 4. Locate regions with large gradients to provide target regions for the optimization solution module;

[0141] 5. Output the analysis results in visual and data format.

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

[0143] Deviation angle distribution diagram;

[0144] Deviation angle gradient distribution diagram;

[0145] Statistical indicators of deviation angle, including mean and variance;

[0146] Coordinate information of regions with large gradients.

[0147] Through the above analysis process, the error analysis module can fully diagnose performance bottlenecks in the lens surface design and provide precise optimization directions for the optimization solution module. Furthermore, the gradient analysis method used in the module comprehensively reflects the continuity of the deviation distribution, ensuring that the optical performance of the lens surface is significantly improved during the optimization process.

[0148] In this embodiment, the optimization solution module is used to perform iterative optimization of the lens surface based on minimizing global ray deviation. Its main function is to receive deviation distribution data and gradient information from the error analysis module, establish an optimization objective function, and adjust the geometric parameters of the surface using variational and numerical optimization methods to generate an optimized lens model.

[0149] The optimization solution module is designed to ensure that the light deviation is minimized globally across the entire lens surface, while satisfying the continuity constraint of the light propagation path. This allows the optimized surface to achieve both high-efficiency collimation performance and adaptability to actual manufacturing requirements.

[0150] In this embodiment, the objective function is optimized 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 The direction of propagation of refracted light is provided by the optical simulation module;

[0155] d target The target direction of an ideal collimated beam;

[0156] ||d out -d target || 2 The squared error representing the light deviation angle is the core objective of optimization;

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

[0158] α is a weighting factor used to adjust the importance of the two objectives.

[0159] By constructing the objective function described above, this embodiment can simultaneously focus on collimation performance and the continuity of gradient distribution, thereby avoiding beam scattering problems 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. To minimize the objective function J[M], the Euler-Lagrange equations must be satisfied:

[0161]

[0162] in:

[0163] φ(u, v) is the parametric representation of the lens surface;

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

[0165] The gradient of the light deviation angle;

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

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

[0168] By solving the above partial differential equations, the direction of change of the lens surface parameters u and v can be determined, thereby adjusting the geometry of the surface.

[0169] In this embodiment, to achieve numerical solution, the optimization module discretizes the surface model. Specifically, the continuous surface is divided into a finite number of triangular elements, and a parameterized function is defined on each element. 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 These represent the refraction direction and target direction of the light ray in the i-th unit, respectively;

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

[0175] ΔA i Let be the area of ​​the i-th 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 gradient descent as the core step of the optimization algorithm. Gradient descent adjusts the surface shape gradually based on the gradient information of the objective function with respect to the parameters, thereby gradually reducing the value of the objective function. The specific implementation includes the following steps:

[0178] Initialize the parametric 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 according to gradient direction:

[0182]

[0183] Where η is the step size factor, used to control the magnitude of parameter updates;

[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 compatible with actual manufacturing processes, the module simulates the impact of lens processing errors and material deviations on alignment performance. The error tolerance analysis includes:

[0187] Simulate the shape deviation of a lens surface during the manufacturing process;

[0188] Calculate the effect of processing errors on the angular distribution of light deviation;

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

[0190] Based on the above analysis, the surface generated by the optimized solution module can not only meet the optical performance requirements, but also adapt to 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 a record of the changes in surface parameters during the optimization process. This output will be passed to the result evaluation module for final performance verification and report generation.

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

[0193] 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 collimation performance target requirements through calculation and visualization analysis of the optimized optical performance indicators, and to evaluate the design's adaptability under actual manufacturing conditions.

[0194] The design goal of the results evaluation module is to provide complete performance evaluation results, including the influence of light deviation angular distribution, beam intensity distribution, and manufacturing errors on lens performance, thereby providing detailed quality assessment and optimization direction references for the final lens design scheme.

[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 then evaluates the collimation performance of the lens by combining the light propagation path from the optical simulation module. Key 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 using the following formula:

[0197]

[0198] in:

[0199] The average value of the deviation angle represents the overall level of light collimation performance;

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

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

[0202] M represents the lens surface.

[0203] The standard deviation σ of the deviation angle θ The calculation is as follows:

[0204]

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

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

[0207] In this embodiment, the result evaluation module further calculates and optimizes the intensity distribution of the 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 It is the cosine of the incident angle, which is related to the normal vector of the lens surface.

[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 assess whether the 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 one hand, the module simulates the perturbation of lens surface parameters by manufacturing errors, analyzing the impact of these errors on the light deviation angle and beam intensity distribution. Assuming the influence of manufacturing errors on the lens surface φ(u, v) is a random perturbation δφ(u, v), the perturbed deviation angle distribution is expressed as:

[0216]

[0217] Where, d′ out This represents the direction of light propagation after the disturbance.

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

[0219] On the other hand, the module assesses the manufacturing 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 values ​​exceed the capabilities of a specific material or processing equipment, the module will generate relevant warnings and output possible adjustment suggestions.

[0220] In this embodiment, to facilitate user understanding and use of the evaluation results, the results evaluation module supports various forms of result visualization. Specifically, these include:

[0221] Two-dimensional thermal images and three-dimensional surface maps of the deviation angle distribution visually demonstrate the distribution of the deviation angle on the lens surface;

[0222] Two-dimensional contour plots and cross-sectional plots of beam intensity distribution are used to analyze the uniformity of the beam.

[0223] The superimposed display of manufacturing error simulation results is used to illustrate the impact of errors on optical performance.

[0224] These visualization tools allow users to 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 (including mean and standard deviation) of the light deviation angle;

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

[0229] Simulate manufacturing errors to evaluate their impact on optical performance;

[0230] Output visualizations of the evaluation results and comprehensive performance reports.

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

[0232] Optimize the lens model's performance report, including the mean deviation angle, standard deviation, and beam intensity distribution;

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

[0234] Visual charts and graphs, including deviation angle distribution diagrams, beam intensity distribution diagrams, and manufacturing error effect diagrams.

[0235] Through the above design, the results evaluation module can comprehensively verify the performance of the optimized lens, ensure that the lens design meets the needs of practical applications, and provide users with detailed evaluation results and design improvement suggestions.

[0236] Please see the appendix Figure 4 Correspondingly, this invention also provides a method for designing a collimating lens based on a differential manifold and two freeform surfaces, including a complete workflow from lens model construction to performance verification. Specifically, it includes the following steps:

[0237] 1. Construct a double freeform lens model based on a differential manifold;

[0238] In this embodiment, a double freeform lens model based on a differential manifold is first generated using the surface modeling module.

[0239] The lens surface is defined using a parametric method, including principal curvature distribution, normal vector distribution, and refractive index parameter. The lens surface is expressed through local parametric representation, describing the three-dimensional spatial coordinates and geometric properties of each point, ensuring that the surface model accurately represents the light propagation path.

[0240] Meanwhile, to meet the design requirements of the collimating lens, the refractive index n of the material and the geometry of the lens were defined during the modeling stage. The modeling results serve as the basis for subsequent optical simulations and performance optimization.

[0241] 2. Simulate the propagation path of light on a curved surface based on a 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 refraction path of each ray is calculated using a ray tracing algorithm based on Snell's law, thus obtaining the propagation direction of the refracted ray. The deviation angle θ is calculated as the angle between the ray propagation direction and the ideal collimation direction, reflecting the degree of ray deviation.

[0244] The simulation results include the propagation path of light, the direction of refraction, and the distribution of the deviation angle, providing necessary data for subsequent error analysis and optimization 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 its global and local continuity.

[0247] Deviation angle gradient The calculations are used to diagnose local performance problems on the lens surface, identify areas with drastic changes in light deviation, and locate the coordinates of these areas.

[0248] The module simultaneously performs statistical analysis on the mean and standard deviation of the deviation angles, providing global performance indicators. The analysis results serve as input to the optimization solution module, providing direction for lens geometry optimization.

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

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

[0251] The objective function is optimized by taking into account both the minimization of the deviation angle and the continuity constraint of the gradient. The optimization conditions are derived by variational method and numerical solution is achieved by combining the finite element discretization method.

[0252] The optimization process employs gradient descent to iterate parameters, gradually reducing the objective function value to ultimately generate an optimized lens surface model. The optimized lens surface significantly improves collimation performance while also meeting the requirements of actual manufacturing processes.

[0253] 5. Perform performance verification on 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 angular distribution of light deviation (such as mean and standard deviation) and evaluation of the uniformity of beam intensity distribution. Simultaneously, the module simulates the impact of manufacturing errors on lens performance, assessing the suitability of the design model for actual manufacturing.

[0256] The final evaluation results are output in a visual format, including a deviation angle distribution map, a beam intensity distribution map, and a manufacturing error impact map. Simultaneously, an optimization results report containing all performance indicators is generated, providing 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 the construction of the lens model to the performance verification, ensuring that the optimized double freeform surface lens model has excellent optical performance and practical manufacturing feasibility.

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

Claims

1. A simulation system based on a collimating lens design using a differential manifold with two freeform surfaces, characterized in that, include: The surface modeling module is used to construct a double freeform lens model based on a differential manifold. The double freeform lens model is represented by a parametric method, and the principal curvature, normal vector distribution, and optical refraction parameters are defined. The optical simulation module is used to simulate the propagation path of light on the curved surface of a lens and analyze the collimation performance after light refraction. The error analysis module is used to analyze the continuity and global changes of the deviation angle distribution in the light propagation path; The optimization solution module is used to perform iterative optimization on the lens surface based on the goal of minimizing light deviation, and adjust the geometry of the surface. The results evaluation module is used to evaluate the performance of the optimized lens surface, including the intensity distribution of the collimated beam, the deviation angle distribution, and the adaptability to manufacturing errors. The surface modeling module defines the lens surface using differential geometry. The surface is a two-dimensional differential manifold, and its local parametric form is expressed as follows: The coordinate values ​​of each point on the surface are described by two independent variables, and a first fundamental quantity and a second fundamental quantity are constructed to characterize the intrinsic geometric properties of the surface; the first fundamental quantity is used to describe the distance and angle relationships within the surface, and the second fundamental quantity is used to describe the changes in the surface normal vector. The normal vector of the curved surface is used to determine the direction of light propagation and the angle of refraction on the lens surface.

2. The simulation system based on the design of a double freeform collimating lens using a 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 direction of the light source and the refractive index of the material, thus satisfying the directional consistency required for collimated beams.

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

4. The simulation system based on the design of a double freeform collimating lens using a differential manifold according to claim 3, characterized in that, The refraction path of the light rays satisfies Snell's law, and the simulation module simulates the lens performance of different optical materials by adjusting the refraction parameters.

5. The simulation system based on the design of a double freeform collimating lens with a differential manifold according to claim 1, characterized in that, The error analysis module diagnoses local deviations in the lens surface design by calculating the continuity of the light deviation angular distribution, specifically including: A global analysis of the gradient distribution of the light deviation angle is performed. Regions with large angular gradients in the positioning deviation are used to assist in surface optimization.

6. The simulation system based on the design of a double freeform collimating lens with a differential manifold according to claim 1, characterized in that, The optimization solution module establishes an optimization objective function based on the goal of minimizing light deviation. The objective function includes: The objective is to minimize the deviation angle; The continuity constraint of the deviation angular distribution is used to avoid the phenomenon of uneven deviation.

7. The simulation system based on the design of a double freeform collimating lens using a differential manifold according to claim 6, characterized in that, The optimization solution module discretizes the surface model using the finite element method and uses the variational method to iteratively solve the shape of the lens surface, so that the light deviation of the entire lens surface reaches the global optimum.

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

9. A method for designing a double freeform collimating lens based on a differential manifold, based on the system described in any one of claims 1-8, characterized in that, Includes the following steps: A double freeform surface lens model based on a differential manifold is constructed. The surface is defined by a parametric method, including principal curvature distribution, normal vector distribution, and refractive index parameter. Based on the lens model, the propagation path of light on the curved surface is simulated, the propagation direction of light after refraction is calculated, and the collimation performance of light is analyzed. The optical simulation results are analyzed to obtain the light deviation distribution and calculate the gradient change of the deviation distribution to diagnose the local deviation and global continuity of the lens surface. Based on the global minimization objective of light deviation, the geometric parameters of the lens surface model are iteratively adjusted through an optimization algorithm to generate an optimized lens model. The optimized lens model is validated to assess its collimation performance, deviation distribution, and manufacturing adaptability, and the optimization results and design report are output.

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