Model establishment method of lobster spectacle lens
By establishing a mathematical model of lobster-shaped eyeglass lenses based on point spread function kernel density estimation and error model, the problem of deviation between theoretical model and actual imaging performance was solved, and high-precision simulation and optimization of optical system were achieved.
Patent Information
- Application Number
- CN202511334315.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-18
- Publication Date
- 2026-01-02
AI Technical Summary
Existing lobster-themed eyeglass lens models are mainly based on theoretical geometric parameters, which makes it difficult to reflect errors in the actual manufacturing process. This leads to a discrepancy between the theoretical model and the actual imaging performance, affecting the accuracy of ray tracing simulation and image quality prediction.
By digitizing the inner wall of the micropores into a unified mathematical expression and combining it with the point spread function kernel density estimation distribution and error model of real imaging, a mathematical model of the lobster lens is established, including 24 matrix parameters to describe the geometric characteristics of the micropore array and correct errors in the theoretical model.
It achieves accurate modeling of the real geometric structure of lobster-shaped eyeglass lenses, improves the accuracy of ray tracing simulation and imaging performance prediction, and provides a reliable basis for optical system optimization and manufacturing precision.
Smart Images
Figure CN121256178A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of optical imaging technology for lobster eyes, and more particularly to a method for modeling lobster eyeglass lenses. Background Technology
[0002] Lobster-shaped lenses are a special type of lens with a biomimetic compound eye structure. They consist of a large number of closely packed square micropores, enabling focused imaging at a wide field of view, and have great application potential in time-domain astronomy. These lenses achieve light focusing through multiple reflections from the inner walls of the micropores, and their imaging performance is closely related to the geometry and spatial arrangement of the micropores.
[0003] However, existing lobster-themed eyeglass lens models are typically based solely on theoretical geometric parameters, such as micropore width, spacing, thickness, and radius of curvature. These parameters fail to adequately reflect errors encountered during actual lens manufacturing, leading to discrepancies between the theoretical model and actual imaging performance. This discrepancy not only affects the accuracy of ray tracing simulations but also limits the reliability of predicting the overall imaging quality of the optical system.
[0004] Currently, some studies attempt to calibrate and correct theoretical models through experiments, but most lack a unified mathematical framework and cannot simultaneously account for the overall characteristics of the micropore array and the error distribution of the inner wall of individual micropores. Therefore, there is an urgent need for a mathematical modeling method that can combine theoretical structural parameters with experimental imaging data to more accurately describe the true geometric structure of the lobster lens, providing a basis for optical simulation and performance optimization. Summary of the Invention
[0005] This invention provides a method for modeling lobster-shaped eyeglass lenses. By digitizing the inner wall of the micropores into a unified mathematical expression and combining it with the point spread function kernel density estimation distribution and error model of real imaging, the method achieves accurate modeling of the real geometric structure of the lobster-shaped eyeglass lenses. This overcomes the problem of large deviations between theoretical models and actual imaging performance in existing technologies, and provides a reliable basis for ray tracing simulation, imaging performance optimization, and processing accuracy evaluation.
[0006] To achieve the above objectives, the present invention provides the following technical solution:
[0007] A method for establishing a model of a lobster-shaped eyeglass lens involves establishing a mathematical model of the inner wall of the micropores in a spatial coordinate system. The origin of the spatial coordinate system is located at the theoretical curvature center of the lens, the Z-axis points to the theoretical center of the lens, the X-axis is parallel to the horizontal direction of the micropore array, and the Y-axis is parallel to the vertical direction of the micropore array.
[0008] The mathematical model consists of 24 matrix parameters, which are used to represent the point-normal equation parameters of the four inner wall planes of all micropores.
[0009] The set of 24 matrix parameters can be represented as {A} i B i C i ,X i ,Y i Z i |i∈up,down,left,right}, where (A i B i C i () represents the plane normal vector, (X) i ,Y i Z i ) represents a reference point on the plane; after the set is expanded, the 24 matrix parameters are specifically A up B up C up X up Y up Z up A down B down C down X down Y down Z down A left B left C left X left Y left Z left A right B right C right X right Y right Z right ;
[0010] The method for determining matrix parameters includes the following steps:
[0011] S1. Based on the micropore width, micropore spacing, number of micropores, lens thickness and radius of curvature of the lobster eyeglass lens, calculate the theoretical straight line equation of the central axis of each micropore. The straight line equation consists of a point on the XOY plane and a direction vector.
[0012] S2. Based on the actual imaging of the lobster lens under parallel or near-parallel light, obtain the kernel density estimation distribution map of the point spread function;
[0013] S3. Map the kernel density estimation distribution map to a spatial coordinate system, and correct the theoretical value of the point in the linear equation according to its probability density distribution. Combine the error model to obtain the true value of the point in the linear equation and the true value of the direction vector in the linear equation.
[0014] S4. Using the true values of the midpoints of the straight line equation as the mean, and combining this with the error model, calculate the reference points (X) of each inner wall plane.up Y up Z up )…(X right Y right Z right );
[0015] S5. Based on the true value of the direction vector in the linear equation, and combined with the angle subtended by a single micropore in the horizontal and vertical directions, calculate the median value of the plane normal vector; using the median value of the plane normal vector as the mean, and combining it with the error model, obtain the plane normal parameters (A) of each inner wall. up B up C up )…(A right B right C right ).
[0016] Furthermore, the method for determining the true value of a point in the linear equation is as follows: the kernel density estimation distribution map of the point spread function is scaled proportionally to the XOY plane according to the imaging pixel size and the position of the image plane in the spatial coordinate system, and the theoretical value of the point in the linear equation is corrected according to the scaled probability density distribution to obtain the true value of the point; the true value of the direction vector in the linear equation is obtained by introducing an error model on the basis of the theoretical vector.
[0017] Furthermore, the error model is selected and adjusted based on the processing characteristics and experimental data, and Gaussian distribution, statistical fitting correction, or least squares fitting method is adopted.
[0018] Furthermore, each of the 24 matrices contains M×N parameters, where M×N is the number of rows and columns of the micropore array.
[0019] Furthermore, the point-normal equations for the four inner wall planes of the micropore are as follows:
[0020] A up *(XX up )+B up *(YY up )+C up *(ZZ up ) = 0;
[0021] A down *(XX down )+B down *(YY down )+C down *(ZZ down ) = 0;
[0022] A left *(XX left )+B left*(YY left )+C left *(ZZ left ) = 0;
[0023] A right *(XX right )+B right *(YY right )+C right *(ZZ right ) = 0.
[0024] The method for establishing a model of a lobster eyeglass lens provided by the present invention, as described above, has the following beneficial effects:
[0025] (1) By introducing kernel density estimation and error model, the deviation generated by the lens in the actual processing can be truly reflected;
[0026] (2) The use of matrix-based mathematical expression can uniformly describe the geometric characteristics of the entire micropore array, which is convenient for numerical calculation and simulation.
[0027] (3) It can effectively improve the accuracy of ray tracing simulation and imaging performance prediction, and provide quantitative basis for lens optimization and processing quality control. Attached Figure Description
[0028] Figure 1 This is a flowchart illustrating the method for establishing the lobster-shaped eyeglass lens of the present invention.
[0029] Figure 2 This is a schematic diagram of the model space coordinate system of the lobster-shaped eyeglass lens of the present invention;
[0030] Figure 3 This is a schematic diagram of the inner wall of the micropores of the lobster-shaped eyeglass lens of the present invention;
[0031] Figure 4 This invention provides a true image of the lobster-shaped eyeglass lens.
[0032] Figure 5 This is a simulated imaging of a model of the lobster-shaped eyeglass lens of the present invention.
[0033] Explanation of reference numerals in the attached figures:
[0034] 101-Lobster eyeglass lens; 201-Micropore; 202-Upper plane of inner wall; 203-Lower plane of inner wall; 204-Left plane of inner wall; 205-Right plane of inner wall. Detailed Implementation
[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
[0036] It should also be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and / or processing steps closely related to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.
[0037] Additionally, it should be noted that the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.
[0038] This invention discloses a method for establishing a model of a lobster-shaped eyeglass lens. The method establishes a mathematical model of the inner wall of the micropores of the lens in a spatial coordinate system. The origin of the spatial coordinate system is located at the theoretical curvature center of the lens, the Z-axis points to the theoretical center of the lens, the X-axis is parallel to the horizontal direction of the micropore array, and the Y-axis is parallel to the vertical direction of the micropore array.
[0039] The mathematical model consists of 24 matrix parameters, which are used to represent the point-normal equation parameters of the four inner wall planes of all micropores.
[0040] The set of 24 matrix parameters can be represented as {A} i B i C i ,X i ,Y i Z i |i∈up,down,left,right}, where (A i B i C i () represents the plane normal vector, (X) i ,Y i Z i ) represents a reference point on the plane; after the set is expanded, the 24 matrix parameters are specifically A up B up C up X up Y up Z up A down B down C down X down Y down Z down A left B left C left X left Y left Z left Aright B right C right X right Y right Z right ;
[0041] Each of the 24 matrix parameters contains M×N parameters, where M×N is the number of rows and columns of the micropore array.
[0042] like Figure 1 As shown, the method for determining matrix parameters includes the following steps:
[0043] Step S1: Establish the theoretical straight line equation;
[0044] Based on the geometric design parameters of the lobster-shaped eyeglass lens, including the micropore width d, micropore spacing p, number of micropores M×N, lens thickness t, and radius of curvature R, the theoretical linear equation of the central axis of each micropore is determined.
[0045] like Figure 2 As shown, in the spatial coordinate system, let the center of curvature of the lobster-shaped eyeglass lens 101 be the origin O(0, 0, 0), and the XOY plane be the array arrangement plane. Then, the theoretical coordinates of the center point of the (m, n)th micropore can be expressed as:
[0046] P m,n =(x m ,y n ,z0),
[0047] in,
[0048] The theoretical direction vector of the micropore central axis points from the center of curvature O to P. m,n Its expression is:
[0049] v m,n =P m,n -O,
[0050] Thus, the theoretical linear equation of the central axis is obtained:
[0051]
[0052] Step S2: Obtain the kernel density estimation distribution map;
[0053] By placing the lobster-shaped lens under parallel or near-parallel light illumination, its true image is obtained, such as... Figure 4 As shown, kernel density estimation is performed based on the point spread function data of the actual image to obtain the probability density distribution map of the spot intensity.
[0054] Step S3: Correct the equation of the straight line;
[0055] The kernel density estimation distribution map is scaled according to the actual image pixel size and spatial coordinate ratio and mapped onto the XOY plane. The theoretical values of points in the linear equation are corrected based on its probability density distribution. Combined with the error model, the true values of the points in the linear equation and the true values of the direction vectors in the linear equation are obtained. Let the probability density function given by the kernel density estimation be f(x,y), then the true curvature center O′ corresponding to the (m,n)th micropore is... m,n The following formula is corrected:
[0056] O′ m,n =O+ΔO m,n ,ΔO m,n ~f(x,y),
[0057] Where ΔO m,n This is a correction factor, calculated from the probability distribution estimated by the kernel density.
[0058] The true center point P′ corresponding to the (m, n)th micropore m,n The following formula is corrected:
[0059] P′ m,n =P m,n +ΔP m,n ,
[0060] Where ΔP m,n It is generated by the error model.
[0061] The true value of the direction vector, i.e., the true direction vector v′ m,n for:
[0062] v′ m,n =P′ m,n -O′ m,n .
[0063] Step S4: Determine the plane reference point;
[0064] Based on the true center point P′ of the linear equation m,n The reference point (X) for each inner wall plane is obtained by combining the error model with the Gaussian distribution. up Y up Z up )…(X right Y right Z right These points, statistically speaking, satisfy P′ m,n It is a Gaussian distribution with mean .
[0065] Step S5: Determine the plane normal vector;
[0066] Based on the true direction vector v′ of the linear equation m,n Combining the angle θ of a single micropore in the horizontal and vertical directions x θy The median value of the plane normal vectors of the four inner walls is calculated. In this embodiment,
[0067]
[0068] The median value of the plane normal vector on the upper surface of the inner wall is the true direction vector v′. m,n Rotate clockwise around the Y-axis Then, after orthogonalizing with vector (0, 1, 0), the median value of the plane normal vector of the lower surface of the inner wall is obtained as the true direction vector v′. m,n Rotate negatively around the Y-axis Then, it is obtained by reversing the direction after being orthogonal to vector (0, 1, 0). The median value of the plane normal vector on the left surface of the inner wall is the true direction vector v′. m,n Rotate negatively around the X-axis Then, it is obtained by reversing the direction after being orthogonal to vector (1, 0, 0). The median value of the plane normal vector on the right surface of the inner wall is the true direction vector v′. m,n Rotate clockwise around the X-axis Then, it is obtained after being orthogonal to the vector (1, 0, 0).
[0069] The mean value of the median normal vectors of the four inner walls is used, and the normal parameters (A) of each inner wall plane are obtained by correcting the error using a Gaussian distribution model. up B up C up )…(A right B right C right These parameters statistically follow a Gaussian distribution with the mean of the plane normal vector.
[0070] like Figure 3 As shown, the point-normal equations (i.e., the plane equations of the four inner wall planes) of the micropore 201 are finally obtained:
[0071] The equation of plane 202 on the inner wall is:
[0072] A up *(XX up )+B up *(YY up )+C up *(ZZ up ) = 0;
[0073] The equation of the lower inner wall plane 203 is:
[0074] A down *(XX down )+B down *(YY down )+C down *(ZZdown ) = 0;
[0075] The equation for the left plane 204 of the inner wall is:
[0076] A left *(XX left )+B left *(YY left )+C left *(zz left ) = 0;
[0077] The equation of the right plane 205 of the inner wall is:
[0078] A right *(XX right )+B right *(YY right )+C right *(ZZ right ) = 0.
[0079] 24 matrix parameters (A) up B up C up X up Y up Z up …A right B right C right X right Y right Z right This is used to describe the geometric features of all micropores in the entire array.
[0080] The Gaussian distribution error model used in the above steps is only one specific implementation method. In this model establishment method, the specific error model used in each step can be selected according to the processing technology and experimental conditions. Specifically:
[0081] (1) When the process error conforms to a random distribution, a Gaussian distribution error model can be used;
[0082] (2) When the process error has a systematic deviation with position or direction, statistical fitting can be used for correction;
[0083] (3) When there is already reference measurement data, the theoretical value can be corrected by least squares fitting.
[0084] The model established by this method can be directly applied to X-ray ray tracing simulation. In the simulation, by calculating the intersection point and reflection direction of the X-ray incident ray with the aforementioned plane equation, the multiple reflection paths and final exit direction of the ray within the micro-aperture can be obtained. After setting the image plane position and pixel size, the simulated image can be calculated. Figure 5As shown, this allows for accurate prediction of the lens's focusing performance and imaging effect.
[0085] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.
Claims
1. A method for establishing a model of a lobster-shaped eyeglass lens, characterized in that: This method establishes a mathematical model of the inner wall of the micropores in a spatial coordinate system. The origin of the spatial coordinate system is located at the theoretical curvature center of the lens, the Z-axis points to the theoretical center of the lens, the X-axis is parallel to the horizontal direction of the micropore array, and the Y-axis is parallel to the vertical direction of the micropore array. The mathematical model consists of 24 matrix parameters, which are used to represent the point-normal equation parameters of the four inner wall planes of all micropores. The set of 24 matrix parameters can be represented as {A} i B i C i ,X i ,Y i Z i |i∈up,down,left,right}, where (A i B i C i () represents the plane normal vector, (X) i ,Y i Z i ) represents a reference point on the plane; after the set is expanded, the 24 matrix parameters are specifically A up B up C up X up Y up Z up A down B down C down X down Y down Z down A left B left C left X left Y left Z left A right B right C right X right Y right Z right ; The method for determining matrix parameters includes the following steps: S1. Based on the micropore width, micropore spacing, number of micropores, lens thickness and radius of curvature of the lobster eyeglass lens, calculate the theoretical straight line equation of the central axis of each micropore. The straight line equation consists of a point on the XOY plane and a direction vector. S2. Based on the actual imaging of the lobster lens under parallel or near-parallel light, obtain the kernel density estimation distribution map of the point spread function; S3. Map the kernel density estimation distribution map to a spatial coordinate system, and correct the theoretical value of the point in the linear equation according to its probability density distribution. Combine the error model to obtain the true value of the point in the linear equation and the true value of the direction vector in the linear equation. S4. Using the true values of the midpoints of the straight line equation as the mean, and combining this with the error model, calculate the reference points (X) of each inner wall plane. up Y up Z up )…(X right Y right Z right ); S5. Based on the true value of the direction vector in the linear equation, and combined with the angle subtended by a single micropore in the horizontal and vertical directions, calculate the median value of the plane normal vector; using the median value of the plane normal vector as the mean, and combining it with the error model, obtain the plane normal parameters (A) of each inner wall. up B up C up )…(A right B right C right ).
2. The method for establishing a model of a lobster eyeglass lens according to claim 1, characterized in that: The method for determining the true value of a point in the linear equation is as follows: the kernel density estimation distribution map of the point spread function is scaled proportionally to the XOY plane according to the imaging pixel size and the position of the image plane in the spatial coordinate system, and the theoretical value of the point in the linear equation is corrected according to the scaled probability density distribution to obtain the true value of the point; the true value of the direction vector in the linear equation is obtained by introducing an error model on the basis of the theoretical vector.
3. The method for establishing a model of a lobster eyeglass lens according to claim 1, characterized in that: The error model is selected and adjusted based on the processing characteristics and experimental data, and adopts Gaussian distribution, statistical fitting correction or least squares fitting method.
4. The method for establishing a model of a lobster eyeglass lens according to claim 1, characterized in that: Each of the 24 matrix parameters contains M×N parameters, where M×N is the number of rows and columns of the micropore array.
5. The method for establishing a model of a lobster eyeglass lens according to claim 1, characterized in that: The point-normal equations for the four inner wall planes of the micropore are as follows: A up *(X-X up )+B up *(Y-Y up )+C up *(Z-Z up )=0; A down *(X-X down )+B down *(Y-Y down )+C down *(Z-Z down )=0; A left *(X-X left )+B left *(Y-Y left )+C left *(Z-Z left )=0; A right *(X-X right )+B right *(Y-Y right )+C right *(Z-Z right )=0。