Lens arrangement method and system with Fermat spiral golden angle deviation

Abstract

The invention relates to the technical field of optical lens design, and discloses a Fermat spiral golden angle offset lens arrangement method and system.The method comprises the steps that lens parameters are obtained, a curved surface polar coordinate system is established, a Fermat spiral model is adopted to generate an initial dot matrix, uniformity is evaluated through Voronoi space subdivision, and a final lens array is obtained. Self-adaptive offset optimization is carried out in a golden angle critical range, a central vision protection area is applied to constrain and restore the uniformity of an inner ring, a pre-distortion compensation mechanism is adopted when curved surface projection mapping is executed, optical parameters of the microstructure are configured according to the radial position, and finally a digital processing file is generated. According to the invention, high-uniformity isotropic arrangement of the microstructures can be realized on the curved surface of the lens, and the technical problems that the existing periodic arrangement generates structured artifacts and the existing non-periodic arrangement lacks adaptive optimization capability are solved.

Description

Technical Field

[0001] This invention relates to the field of optical lens design technology, and more specifically, to a lens arrangement method and system based on the Fermat spiral golden angle offset. Background Technology

[0002] In the field of ophthalmic optical lens design, the spatial arrangement of microstructural units on the curved surface of the lens directly affects the uniformity of optical performance and visual quality. Existing periodic arrangement methods, such as honeycomb or concentric ring layouts, although simple to design and easy to standardize, will produce structured diffraction artifacts in the optical system due to their inherent periodicity. These artifacts appear as regular halos or spots, interfering with visual quality.

[0003] To address the shortcomings of periodic arrangement, some technical solutions employ non-periodic arrangement methods, such as Poisson disk sampling or random dot matrix generation. These methods can reduce structured artifacts to some extent, but they suffer from poor local density consistency, easily leading to microstructure overlap or large visual holes, resulting in uneven distribution of defocus energy. Furthermore, existing non-periodic arrangement methods typically use fixed divergence angle parameters, failing to adaptively optimize for parameters such as the radius of curvature and optical area size of different lenses, and lacking the ability to compensate for projection distortion of the lens surface.

[0004] When the microstructure lattice is projected from planar polar coordinates onto the three-dimensional curved surface of a lens, the geometric properties of the surface introduce a nonlinear transformation in spatial scale, causing the edge regions to become sparse due to surface divergence, thus disrupting the uniformity of the arrangement. Existing technologies lack effective pre-distortion compensation mechanisms and adaptive optimization capabilities, making it difficult to achieve a highly uniform and isotropic arrangement of microstructures on the curved surface of a lens. Summary of the Invention

[0005] This invention provides a lens arrangement method and system with Fermat spiral golden angle offset, which solves the technical problems of structured artifacts generated by existing periodic arrangements and poor surface uniformity caused by the lack of adaptive optimization capability of existing non-periodic arrangements in related technologies.

[0006] This invention provides a lens arrangement method based on the Fermat spiral golden angle offset, comprising the following steps: S1. Collect lens prescription parameters and surface data, establish a curved surface geodesic polar coordinate system, determine projection distortion characteristics through surface curvature analysis, and obtain the lens parameter set; S2, receive the lens parameter set, use the area matching method to initialize the scaling constant and initial value of the golden angle of the Fermat spiral, and generate the initial lattice data and spiral parameters through analytical expression; S3. Based on the initial lattice data, the golden angle adaptive offset optimization is performed with Voronoi cell area uniformity and minimum point spacing as the two objectives to obtain the optimal golden angle, the optimal scaling constant, and the optimized lattice. S4: Obtain optimized dot matrix data and central protection zone radius parameters, calculate and determine the center points to be removed, restore uniformity to the inner circle area after removal, and output an effective dot matrix that meets the visual center protection constraint. S5 receives the valid point array, adjusts the polar radius distribution through the pre-distortion compensation mechanism, maps the polar coordinates to the three-dimensional curved surface of the lens using the geodesic projection algorithm, and outputs three-dimensional spatial coordinates and surface Voronoi subdivision data. S6 acquires three-dimensional coordinates and surface Voronoi data, partitions the optical region according to the radial position, and uses a radial gradient configuration strategy to configure defocusing intensity and aperture parameters for the microstructures in different regions, integrating them to generate digital processing files.

[0007] In a preferred embodiment, S1 includes: The lens prescription parameters include the outer radius of the lens optical area, the radius of the central clear vision protection zone, the peripheral defocus power value, and the surface parameters of the lens substrate. The origin of the geodesic polar coordinate system is located at the optical center of the lens, the polar radius is defined as the arc length measured along the geodesic line on the curved surface from the optical center, and the polar angle is defined as the azimuth angle relative to the reference direction. The lens parameter set includes optical region parameters, curvature distribution function, and total number of target microstructures.

[0008] In a preferred embodiment, S2 includes: The calculation process of the area matching method is as follows: the effective arrangement area is determined to be a ring, the total area of ​​the ring is calculated, and according to the space filling characteristics of the Fermat spiral, the total area of ​​the ring is divided by the total number of target microstructures to obtain the average area of ​​the unit. The initial estimated value of the scaling constant is obtained by solving the inverse operation of the square relationship. The initial value of the golden angle is set by analyzing the curvature distribution function to calculate the projection scaling ratio of the edge region. When the ratio indicates that there is obvious divergence at the edge, the initial value of the golden angle is set to be slightly smaller than the standard value. When the curvature distribution is uniform, the standard value is used.

[0009] In a preferred embodiment, S3 includes: The golden angle adaptive offset optimization uses the Voronoi spatial partitioning method to quantify the spatial uniformity of the lattice. The standard deviation of the area of ​​all Voronoi cells is used as the first optimization objective, and the minimum spacing between all point pairs in the lattice is used as the second optimization objective. The minimum spacing is required to be greater than a preset minimum spacing threshold. The two objectives are combined into a comprehensive evaluation function through a weighted method.

[0010] In a preferred embodiment, S3 further includes: An incremental Voronoi update algorithm is adopted to improve the optimization calculation efficiency. The incremental Voronoi update algorithm identifies points whose positions have moved beyond a preset displacement threshold due to parameter changes and marks them as affected points. For each affected point, its neighboring points in the previous Voronoi partition are identified. The local point set formed by the affected points and their neighboring points is reconstructed by Voronoi. The local reconstruction result is then joined with the global Voronoi partition by boundary stitching. The golden section search method is used to optimize within the preset critical range of the golden angle. Two trial points are selected within the search interval according to the golden ratio. The search interval is gradually narrowed by comparing the objective function values ​​of the trial points until the interval width is less than the preset accuracy threshold.

[0011] In a preferred embodiment, S3 further includes: The scaling constant is simultaneously optimized using a binary search method. The optimization goal is to make the point with the largest polar radius in the dot matrix exactly located at the outer radius of the optical region. Convergence is determined when the error between the largest polar radius and the outer radius of the target is less than a preset error threshold. The two-parameter optimization of the golden angle and scaling constant adopts a nested loop structure. The outer loop is a golden section search for the golden angle, and the inner loop is a binary search for the scaling constant given the golden angle.

[0012] In a preferred embodiment, S4 includes: By utilizing the ordered nature of the Fermat spiral lattice, the exclusion range is determined in batches by calculating the critical number corresponding to the radius of the protected area. The calculation of the critical number is achieved through the inverse operation of the Fermat spiral formula. A radial diffusion fine-tuning mechanism is used to restore the uniformity of the inner circle region. Inner circle points with a polar radius smaller than the radius of the protected area plus a preset buffer distance are identified. Points whose ratio of Voronoi unit area to global average area is greater than a preset area ratio threshold are radially shifted outward. The outward shift distance is proportional to the difference between its area ratio and the threshold.

[0013] In a preferred embodiment, S5 includes: The pre-distortion compensation mechanism analyzes the local geometric characteristics of the surface at different radial positions based on the curvature distribution function, calculates the local projection scaling factor of the surface at that location, and performs nonlinear scaling on the polar radius of each point in the lattice. The scaling rule is to divide the polar radius by the scaling factor at the corresponding position. The geodesic projection algorithm uses spherical trigonometric geometry to project onto spherical lenses, and uses numerical integration to discretize the geodesic path into several tiny arc segments for projection onto aspherical lenses. After projection, the points on the 3D surface are subjected to Voronoi subdivision under surface metric to verify the effect of pre-distortion compensation.

[0014] In a preferred embodiment, S6 includes: The radial partitioning strategy divides the peripheral annular optical region of the lens into three sub-regions: an inner ring region, a middle ring region, and an outer ring region. The microstructure of the inner ring region is configured with nominal defocus power, the middle ring region adopts a gradually increasing power configuration strategy, and the outer ring region is configured with maximum power. The aperture parameter of the microstructure is determined based on the area of ​​the surface Voronoi element of the microstructure. The effective aperture of the microstructure is set as the equivalent circle diameter of its Voronoi element area multiplied by the filling factor.

[0015] In a preferred embodiment, setting the initial value of the golden angle in S2 further includes: By analyzing the curvature distribution function, the projection scaling ratio of the edge region is calculated. When the ratio indicates that there is significant divergence at the edge, the initial value of the golden angle is set to be slightly smaller than the standard value, so that the planar lattice is slightly compact in the angular direction and is stretched to a uniform state by the surface divergence effect after projection. When the curvature distribution is uniform or the lens is close to a plane, the initial value of the golden angle is a standard value; the setting of the initial value of the golden angle provides the initial parameter for coarse compensation in the subsequent precise optimization in S3.

[0016] In a preferred embodiment, the preset critical range of the golden angle in S3 is determined by the following method: For typical parameter ranges of lens curvature radius and optical region outer radius, numerical simulations are performed on the surface Voronoi uniformity index under different golden angle values ​​to determine the fluctuation range of the optimal golden angle relative to the standard golden angle. The fluctuation range is used as the optimization interval of the golden section search method. The optimization interval covers a preset degree range above and below the standard golden angle to include the optimal solution of most lens parameter combinations.

[0017] In a preferred embodiment, S3 further includes: Once the golden section search converges, a point spacing constraint check is performed on the optimized point matrix. The Euclidean distance between all point pairs is calculated, and the minimum distance value is identified. When the minimum distance is less than a preset minimum spacing threshold, a local position perturbation is applied to one point in a point pair that is too close. The perturbation direction is radial or tangential away from the other point, and the perturbation amplitude is set to make the distance between the two points exactly reach the minimum spacing threshold. The local position perturbation only affects a few points and does not destroy the uniformity of the overall point matrix.

[0018] In a preferred embodiment, S5 further includes: The surface normal vector at each point on the three-dimensional surface is calculated. For a spherical lens, the normal vector points towards the center of the sphere. For an aspherical lens, the normal vector is obtained by normalizing the gradient vector after performing partial derivative calculations on the surface equation at that point. The surface normal vector is used to determine the optical axis direction of the corresponding microlens, so that the axis of symmetry of the microlens coincides with the surface normal vector. The surface normal vector is output to S6 as a component of the three-dimensional point matrix data.

[0019] In a preferred embodiment, the radial partitioning strategy in S6 further includes: The defocus illumination configuration in the middle ring area is smoothly transitioned radially using linear interpolation. The illumination of the microstructure inside the middle ring is equal to the nominal defocus illumination. The illumination of the microstructure outside the middle ring is increased by a preset first illumination increment based on the nominal value. The illumination of the microstructure inside the middle ring is determined by linear interpolation. The microstructure of the outer ring region is incremented by a second pre-set increment based on the nominal defocus intensity, and the second increment is greater than the first increment. The increment compensates for the physiological characteristic that the sensitivity of the peripheral retina to defocus stimulation decreases with increasing eccentricity, so that each region produces a consistent effective defocus stimulation intensity on the retina.

[0020] In a preferred embodiment, a lens arrangement system with Fermat spiral golden angle offset is used to perform the steps in the above-described lens arrangement method with Fermat spiral golden angle offset, including: The parameter acquisition module is used to collect lens prescription parameters and surface data, establish a curved surface geodesic polar coordinate system, determine projection distortion characteristics through surface curvature analysis, and obtain a set of lens parameters. The dot matrix initialization module is used to receive the lens parameter set, initialize the scaling constant and initial value of the golden angle of the Fermat spiral using the area matching method, and generate the initial dot matrix data and spiral parameters analytically. The Golden Angle Optimization Module is used to perform adaptive offset optimization of the golden angle based on the initial lattice data, with Voronoi cell area uniformity and minimum point spacing as the two objectives, to obtain the optimal golden angle, the optimal scaling constant, and the optimized lattice. The visual protection constraint module is used to acquire optimized dot matrix data and central protection zone radius parameters, calculate and determine the center points to be removed, restore uniformity to the inner circle area after removal, and output an effective dot matrix that meets the visual center protection constraint. The curved surface projection module is used to receive the effective point array, adjust the polar radius distribution through the pre-distortion compensation mechanism, and use the geodesic projection algorithm to map the polar coordinates to the three-dimensional curved surface of the lens, and output three-dimensional spatial coordinates and curved surface Voronoi subdivision data. The optical parameter configuration module is used to acquire three-dimensional coordinates and surface Voronoi data, divide the optical region into partitions according to the radial position, and use a radial gradient configuration strategy to configure defocusing intensity and aperture parameters for the microstructures in different regions, and integrate them to generate digital processing files.

[0021] The beneficial effects of this invention are as follows: By performing adaptive offset optimization within the critical range of the golden angle and combining it with Voronoi space partitioning to evaluate uniformity, the golden angle parameters can be dynamically adjusted according to the characteristics of the lens curvature radius, optical area size, etc. This enables the arrangement algorithm to adapt to different lens design parameters, achieving a highly uniform and isotropic arrangement of microstructures on the lens surface. Compared with the fixed golden angle method, it improves the surface uniformity and significantly reduces edge density deviation. A pre-distortion compensation mechanism is adopted to adjust the polar radius distribution. By introducing spatial modulation in the plane stage in the opposite direction to the surface distortion, the two distortions cancel each other out during the projection process. Combined with the geodesic projection algorithm, the polar coordinates are mapped to the three-dimensional surface of the lens, ensuring that the mapped lattice still maintains spatial uniformity under the surface measurement. This solves the density gradient problem introduced by the geometric characteristics of the surface when the planar lattice is directly projected onto the surface. Attached Figure Description

[0022] Figure 1 This is a flowchart of a lens arrangement method based on the Fermat spiral golden angle offset of the present invention; Figure 2 This is a block diagram of a lens arrangement system with Fermat spiral golden angle offset according to the present invention. Detailed Implementation

[0023] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, some features described in the examples may be combined in other examples.

[0024] At least one embodiment of the present invention discloses a lens arrangement method with Fermat spiral golden angle offset, such as Figures 1 to 2 As shown, it includes the following steps: S1. Collect lens prescription parameters and surface data, establish a curved surface geodesic polar coordinate system, determine projection distortion characteristics through surface curvature analysis, and obtain the lens parameter set; The system receives raw prescription parameters from the lens design system as input data. These parameters include, but are not limited to, the outer radius of the lens's optical region, the radius of the central clear vision protection zone, the peripheral defocus power, and the surface profile parameters of the lens substrate. For reading the surface profile parameters, this invention supports processing both spherical and aspherical lenses. When the lens is spherical, the surface profile parameter is simplified to a single radius of curvature value, which defines the spherical geometry of the front or rear surface of the lens. When the lens is aspherical, the surface profile parameter uses a standard mathematical expression of quadratic surface plus higher-order aspherical terms, requiring the reading of quadratic surface coefficients and aspherical coefficients of various orders. After obtaining the above parameters, the core processing step is to establish a geodesic polar coordinate system on the lens surface suitable for subsequent Fermat spiral generation. The origin of this coordinate system is located at the optical center of the lens, the polar radius is defined as the arc length measured along the geodesic line from the optical center, and the polar angle is defined as the azimuth angle relative to a reference direction.

[0025] To provide the necessary geometric information for subsequent surface projection processing, this step requires extracting the curvature distribution characteristics of the lens surface. Specifically, multiple points are sampled at equal intervals along the radial direction in polar coordinates. For each sampled point, the principal curvature of the surface at that location is calculated. The principal curvature is obtained by performing second-order partial derivative operations on the surface shape equation. The sampled discrete curvature data points are then used to construct a continuous curvature distribution function using cubic spline interpolation. This function describes the variation of curvature with radial position and will be used in subsequent steps to analyze the degree of spatial density distortion after the planar point lattice is projected onto the surface. For spherical lenses, the curvature distribution function is constant; for aspherical lenses, the curvature distribution function exhibits a non-linear variation from the center to the edge. This variation causes points that are equally spaced in planar polar coordinates to appear non-equally spaced after being projected onto the surface, generating a density gradient in the edge region.

[0026] In determining the total number of microstructures, this step employs a calculation method based on optical design specifications. The ideal aperture of a single microlens is determined according to the defocusing power. Generally, the higher the defocusing power, the smaller the required aperture to ensure optical performance. The aperture range is typically between 0.8 mm and 2.0 mm. Then, the area of ​​the effective arrangement region is calculated. This region is annular, with its inner radius being the radius of the central protection zone and its outer radius being the outer radius of the optical region. The annular area is calculated using the formula for the area of ​​a circular ring. Finally, the total annular area is divided by the cross-sectional area of ​​a single microlens and multiplied by the filling factor to obtain an estimated value for the total number of target microstructures. The range of 0.75 to 0.85 for the fill factor is determined as follows: a fill factor that is too small will result in excessive gaps between microstructures, reducing the effective optical area; a fill factor that is too large will result in microstructure edges being too close, potentially causing edge fusion during processing. Given that the minimum feature size of a femtosecond laser processing system is approximately 50 micrometers, and considering the heat-affected zone and edge roughness of adjacent microstructures during processing, the edge processing error of each microstructure is approximately 30 to 50 micrometers. Therefore, the safe gap between two adjacent microstructures should be no less than 0.1 millimeters, or 100 micrometers, to ensure sufficient physical separation even under the worst-case scenario where both sides have an error of 50 micrometers. Based on this, a reasonable range for the fill factor is calculated to be 0.75 to 0.85. The parameter set output in this step provides complete boundary conditions and target constraints for subsequent Fermat spiral generation.

[0027] S2, receive the lens parameter set, use the area matching method to initialize the scaling constant and initial value of the golden angle of the Fermat spiral, and generate the initial lattice data and spiral parameters through analytical expression; This step receives the lens parameter set output from the previous step as input, including the geometric boundaries of the optical region, curvature distribution characteristics, and the total number of target microstructures. The core task of this step is to initialize two key parameters of the Fermat spiral mathematical model: the scaling constant and the initial value of the golden angle, and to generate an initial polar coordinate lattice for subsequent optimization. The basic mathematical form of the Fermat spiral in polar coordinates is that the polar radius is proportional to the square root of the microstructure number, and the polar angle is proportional to the product of the number and the golden angle. This mathematical model originates from the optimal filling principle of sunflower seed inflorescences in nature, and its core characteristic is that it can theoretically achieve uniform filling of planar space without producing radial or angular periodic features.

[0028] The scaling constant is initialized using an area matching method. The physical basis of this method is to ensure that the lattice generated by the Fermat spiral precisely covers the target optical region given the specified total number of microstructures. The specific calculation process involves first determining the effective arrangement region as a ring, with its outer radius being the outer radius of the optical region and its inner radius being the radius of the central protection zone, and then calculating the total area of ​​this ring. Then, based on the spatial filling characteristics of the Fermat spiral, the area controlled by the nth point in the lattice is approximately equal to the increment of the ring area from point n minus 1 to point n. By differentiating the Fermat spiral formula, the controlled area of ​​a single point is approximately proportional to the square of the scaling constant. Dividing the total area of ​​the ring by the total number of target microstructures yields the average area of ​​the unit, and then solving the inverse operation of this square relationship gives the initial estimated value of the scaling constant. This method ensures that the radial coverage of the initial lattice basically matches the design requirements, avoiding significant adjustments during subsequent optimization.

[0029] The initial value of the golden angle needs to consider the influence of the lens surface characteristics on the projection of the planar dot matrix. When the dot matrix is ​​projected from the planar polar coordinates onto the curved surface, the curvature introduces nonlinear spatial stretching, especially in the edge region of the lens where the degree of divergence of the curved surface relative to the plane increases, causing the originally uniform angular spacing to become sparse after projection. To compensate for this distortion before projection, this step calculates the projection stretching ratio of the edge region by analyzing the curvature distribution function output in step 1. When this ratio indicates that there is significant divergence at the edge, the initial value of the golden angle is set slightly less than the standard value of 137.508 degrees, for example, set between 136 and 137 degrees, so that the planar dot matrix is ​​slightly denser in the angular direction, and after projection, it is stretched to a uniform state by the surface divergence effect. When the curvature distribution is uniform or the lens is close to the plane, the initial value of the golden angle uses the standard value. It should be noted that the initialization of the golden angle in this step is based on a coarse compensation of the curvature distribution, and the subsequent step 3 will further optimize this parameter through precise optimization.

[0030] After parameter initialization, this step uses an analytical method to generate an initial polar coordinate matrix. For each microstructure number n, from 1 to the total number of target microstructures, a iterative calculation is performed. The polar radius corresponding to each number n is calculated by multiplying the scaling constant by the square root of n, and the polar angle is calculated by multiplying the number n by the initial value of the golden angle and taking the modulus of 360 degrees. This analytical generation method has a linear computational complexity of O(N), which offers a certain efficiency advantage in high-density layout scenarios compared to the iterative trial-and-error mechanism of Poisson disk sampling. The generated initial matrix is ​​structured as a two-dimensional array, with each row storing the polar coordinates of one microstructure.

[0031] S3. Based on the initial lattice data, the golden angle adaptive offset optimization is performed with Voronoi cell area uniformity and minimum point spacing as the two objectives to obtain the optimal golden angle, the optimal scaling constant, and the optimized lattice. The core task of this invention, which receives the initial polar coordinate lattice and initial spiral parameters from the previous step as input, is to determine the optimal golden angle and scaling constant values ​​for the lattice space distribution under the current lens parameters using an adaptive optimization algorithm. This step is the core innovation that distinguishes this invention from existing technologies. Existing technologies directly use a fixed golden angle of 137.508 degrees without considering the influence of different lens parameters on the optimal divergence angle. While methods using Poisson disks or Penrose tessellation have non-periodicity, they lack parameterized optimization capabilities tailored to lens characteristics. The inventiveness of this invention lies in transforming the golden angle from a fixed constant into an optimizable parameter, establishing a quantitative correlation between the golden angle and lens optical performance indicators, namely Voronoi uniformity and dot spacing. Through adaptive optimization, the arrangement algorithm adapts to different lens design parameters, a technique not disclosed in existing technologies. The physical mechanism of optimizing the golden angle offset lies in the fact that the combination of different lens curvature radii, optical region sizes, and the total number of microstructures affects the angular density distribution characteristics of the lattice after projection onto a curved surface. By fine-tuning the golden angle in the planar stage, the angular non-uniformity introduced by the curved surface projection can be pre-compensated, so that the final lattice distribution on the curved surface reaches the optimal uniformity. Specifically, when the lens curvature radius is small, the divergence effect of the curved surface relative to the plane is enhanced, causing the angular spacing after projection to be stretched in the edge region. In this case, the golden angle needs to be set slightly smaller than the standard value to pre-compress the angular spacing in the planar stage. When the optical region size is large, the cumulative effect of projection distortion in the edge region is more obvious, and the offset of the optimal golden angle increases accordingly. By establishing a quantitative correlation between the golden angle and lens parameters, this invention achieves adaptive optimization of the arrangement algorithm for different lens designs.

[0032] To quantify the spatial uniformity of the lattice, this step employs the Voronoi spatial partitioning method. This method divides the planar space into multiple control regions, each corresponding to a point, where the distance from any point within that region to that point is less than the distance to any other point. Voronoi partitioning geometrically reflects the spatial occupancy of the lattice. When the lattice is completely uniform, all Voronoi cell areas are equal; when the lattice exhibits local clustering or sparseness, the Voronoi cell areas of the corresponding regions deviate from the average. Therefore, this step uses the standard deviation of all Voronoi cell areas as the first optimization objective; a smaller standard deviation indicates a more uniform lattice. To avoid processing difficulties caused by excessively close point pairs during the optimization process, this step also uses the minimum spacing between all point pairs in the lattice as a second optimization objective. This minimum spacing is required to be greater than a preset threshold set to 0.5 mm to 0.8 mm. This threshold range is determined based on the minimum spacing requirements of the femtosecond laser processing system for adjacent microstructures; excessively small spacing can lead to overlapping heat-affected zones during processing. The two objectives are synthesized into a comprehensive evaluation function using a weighted method, with the weighting coefficients set according to actual engineering requirements.

[0033] To improve the computational efficiency of optimization, this step employs two algorithmic optimization strategies. The first is an incremental Voronoi update algorithm. In traditional global Voronoi partitioning, after each parameter fine-tuning, the partitioning structure needs to be recalculated for all points. Its computational complexity is on the order of the number of points multiplied by the logarithm of the number of points. When the number of points reaches more than 2000 and dozens of parameter trials are required, the total computation time is quite long. The principle of the incremental algorithm is that when the golden angle changes slightly, the neighborhood topology of most points in the lattice remains unchanged, and only the points in the boundary region are affected. Therefore, the algorithm only recalculates the Voronoi cell boundaries for the affected local regions, while the unaffected regions directly reuse the results of the previous calculation. In its implementation, the algorithm first identifies points whose position shifts exceed a threshold set to 10% of the average point spacing due to parameter changes, and marks these points as affected points. Then, for each affected point, it identifies its neighboring points in the previous Voronoi partition, i.e., points sharing the Voronoi boundary, and reconstructs the local point set formed by the affected point and its neighbors using Voronoi. Finally, it concatenates the local reconstruction result with the global Voronoi partition. This incremental update method is a well-known technique in computational geometry and can reduce the average computational cost of a single Voronoi update to less than one-tenth of the global computation.

[0034] The second optimization strategy is to use the golden section search method to find the optimal value within the critical range of the golden angle. The determination of this range is based on the following analysis: the standard golden angle of 137.508 degrees corresponds to the theoretical optimal value of uniform plane filling. However, the curved projection of the lens surface will introduce an angular stretching effect, causing the actual optimal angle to deviate from the standard value. By performing numerical simulations on typical lens parameters with curvature radii of 60 mm to 120 mm and outer radius of optical area of ​​15 mm to 20 mm, the Voronoi uniformity index of the curved surface under different golden angles was calculated for each set of parameters in the range of 134 degrees to 141 degrees with a step size of 0.5 degrees. It was found that the fluctuation range of the optimal golden angle is 3 to 4 degrees above and below the standard value. Therefore, setting the optimization range to 134 degrees to 141 degrees can cover the optimal solution for most combinations of lens parameters. This step employs the golden section search method to optimize the golden angle within its critical range of 134 to 141 degrees. This method is a highly efficient algorithm for unimodal function optimization. Its principle is to select two trial points within the search interval according to the golden ratio, and gradually narrow the search interval by comparing the objective function values ​​of the trial points until the interval width is less than a preset accuracy threshold. For a golden angle accuracy requirement of 0.1 degrees, the golden section method converges in approximately 8 to 10 iterations. In each iteration, a Fermat spiral lattice is regenerated for the current candidate golden angle value. The standard deviation of the Voronoi cell area and the minimum inter-cell spacing of the lattice are calculated using an incremental Voronoi algorithm. These two indicators are then combined with preset weights to form a comprehensive objective function value, which is used to update the search interval.

[0035] While optimizing the golden angle, this step simultaneously optimizes the scaling constant. The scaling constant directly controls the radial expansion rate of the Fermat spiral, affecting the radial coverage of the lattice. The optimization goal is to ensure that the point with the largest polar radius in the lattice is located precisely at the outer radius of the optical region, ensuring that the microstructure fully covers the effective area without exceeding the boundary. The scaling constant is optimized using a binary search method. Given a golden angle, this method iteratively adjusts the scaling constant and calculates the corresponding maximum polar radius of the lattice. Convergence is determined when the error between the maximum polar radius and the target outer radius is less than 0.01 mm. The adjustment range of the scaling constant is typically within ±5% of the initial value. This adjustment ensures a precise match between the radial coverage of the lattice and the optical region. The dual-parameter optimization of the golden angle and scaling constant employs a nested loop structure. The outer loop performs a golden section search for the golden angle, while the inner loop performs a binary search for the scaling constant given the golden angle. This nested structure ensures that the scaling constant achieves an optimal match for each candidate value of the golden angle.

[0036] Once the golden section search converges, this step obtains the optimal golden angle and corresponding optimal scaling constant that minimize the comprehensive objective function. These parameters are then used to regenerate the final optimized point matrix. A point spacing constraint check is performed on this optimized point matrix. The Euclidean distance between all point pairs is calculated, and the minimum distance value is identified. If this minimum distance is greater than a preset minimum spacing threshold, the check passes; otherwise, it indicates that there are too-close point pairs that need to be addressed. The addressing method involves applying a small positional perturbation to one point in each too-closed pair. The perturbation direction is radial or tangential away from the other point, and the perturbation amplitude is set so that the distance between the two points just reaches the minimum spacing threshold. This treatment is local and only affects a few points, without disrupting the overall uniformity of the point matrix. This step ultimately outputs an optimized polar coordinate point matrix that has undergone multi-objective optimization, satisfies uniformity requirements and minimum spacing constraints, and also outputs the optimal golden angle and optimal scaling constant parameters. These parameters and the point matrix data will serve as input for the next step of visual protection zone constraint processing.

[0037] S4: Obtain optimized dot matrix data and central protection zone radius parameters, calculate and determine the center points to be removed, restore uniformity to the inner circle area after removal, and output an effective dot matrix that meets the visual center protection constraint. Receives the optimized polar coordinate matrix and the radius of the central clear vision protection zone from the previous step as input. Its core task is to address the vision center protection requirements in lens design. Myopia control lenses require the central area, typically within a diameter of 3 to 5 millimeters, to remain completely transparent and free of any microstructures to ensure the wearer's central vision is clear and unaffected by defocusing. Technically, this translates to the arrangement algorithm being able to handle annular arrangement areas with a central circular restricted zone. The Fermat spiral's inherent characteristic is that it spirals outward from the origin, resulting in a dense concentration of points in its central area, directly conflicting with the vision protection zone requirement. Therefore, this step needs to identify and remove points located within the protection zone.

[0038] The method for determining point removal involves traversing each point in the optimized point matrix and comparing its polar radius with the radius of the central protected area. Points with a polar radius smaller than the protected area radius are marked as points to be removed, while points with a polar radius greater than or equal to the protected area radius are marked as valid points to be retained. To improve computational efficiency, this step utilizes the ordered nature of the Fermat spiral point matrix. Since the polar radius monotonically increases with the number, the removal range can be determined in batches by calculating the critical number corresponding to the protected area radius. The calculation of the critical number is achieved through the inverse operation of the Fermat spiral formula, that is, dividing the protected area radius by the scaling constant and squaring the result to obtain the critical number. All points with a number smaller than this critical number are located within the protected area and need to be removed, while points with a number greater than or equal to this critical number are located within the annular valid area and are retained. This method avoids point-by-point distance judgment and reduces the computational complexity from O(N) to O(1) for number threshold calculation plus O(N_valid) for valid point extraction.

[0039] After removing the central points, this step requires evaluating the impact of this operation on the overall uniformity of the lattice. Specifically, this involves performing Voronoi subdivision on the remaining valid lattice, focusing on the area distribution of Voronoi cells in the inner region, i.e., points whose radial positions are close to the boundary of the protected area. Theoretically, the lattice generated by the Fermat spiral under unconstrained conditions has global uniformity. However, when the central points are removed, points originally located at the edge of the protected area lose their inner neighbors, causing their Voronoi cells to expand towards the center. This results in an abnormally large control area for these inner points, leading to localized disruption of uniformity. To repair this non-uniformity, this step employs a radial diffusion fine-tuning mechanism. This mechanism simulates the physical repulsive force effect, causing the inner points to move radially outwards in small increments, moving them away from the protected area boundary and thus reducing their Voronoi cell area.

[0040] The specific algorithm for radial diffusion fine-tuning is as follows: First, identify the inner circle points, defined as points whose polar radius is less than the radius of the protected area plus a buffer distance. The buffer distance is set to 10% to 20% of the radius of the protected area. This range is determined based on the spatial range analysis of the inner circle points affected by the center removal. Too small a buffer distance cannot cover all affected points, while too large a buffer distance will cause unnecessary disturbance to points that do not need adjustment. For each inner circle point, calculate the ratio of its current Voronoi cell area to the global average area. If the ratio is greater than a set threshold, such as 1.3, it is determined to be a point that needs adjustment. Apply radial outward movement to the points that need adjustment. The outward movement distance is proportional to the difference between its area ratio and the threshold. The larger the ratio, the more severe the non-uniformity and the larger the outward movement distance. After one round of outward movement, recalculate the Voronoi subdivision and area distribution. If the inner circle uniformity index still does not meet the standard, proceed to the next iteration. After 3 to 5 iterations, the uniformity of the inner circle lattice can be restored to the same level as the overall lattice. This fine-tuning process only affects a few points in the inner circle, while the main structure of the lattice remains unchanged. This step outputs an effective polar coordinate lattice that has undergone central protection zone constraint processing and inner circle uniformity restoration. The polar radius of all points in the lattice is greater than or equal to the radius of the central protection zone, and the standard deviation of the Voronoi cell area of ​​the entire lattice meets the uniformity requirements.

[0041] S5 receives the valid point array, adjusts the polar radius distribution through the pre-distortion compensation mechanism, maps the polar coordinates to the three-dimensional curved surface of the lens using the geodesic projection algorithm, and outputs three-dimensional spatial coordinates and surface Voronoi subdivision data. The core task of this invention is to accurately map the optimized point matrix in the planar polar coordinate system onto the three-dimensional surface of the lens, while ensuring that the mapped point matrix maintains spatial uniformity and isotropy under surface metric. This is achieved by receiving the effective polar coordinate lattice that satisfies the visual center protection constraint from the previous step, and the lens curvature distribution function from the first step. The technical challenge lies in the fact that the lens surface, especially aspherical or high-curvature spherical surfaces, has uneven radial curvature distribution. When the planar point matrix is ​​directly projected onto the surface, the geometric properties of the surface introduce a nonlinear transformation in spatial scale, causing the originally uniform planar distribution to exhibit a density gradient on the surface. Specifically, the edge regions become sparse due to the divergence of the surface relative to the plane. It should be noted that although the concept of pre-distortion compensation has been applied in optical system design, its application to the spatial coordinate optimization of microstructure arrangement, especially in the scenario of projecting a Fermat spiral point matrix onto a surface, is the innovation of this invention. Existing microstructure arrangement methods typically involve directly projecting the planar design onto a curved surface without considering the impact of projection distortion on uniformity, or they employ post-processing adjustments. In contrast, this invention achieves feedforward distortion cancellation through pre-distortion compensation, ensuring high uniformity of the curved surface lattice.

[0042] To compensate for the aforementioned projection distortion, this step performs pre-distortion compensation processing on the polar coordinate lattice before actual projection. The physical basis of this processing is to introduce spatial modulation in the plane stage, opposite to the direction of surface distortion, so that the two types of distortion cancel each other out during projection, ultimately achieving a uniform distribution on the surface. It should be noted that this pre-distortion compensation addresses the radial density gradient problem, which is a different technical dimension from the angular uniformity problem addressed by the golden angle optimization in the previous steps. The two work together to ensure the overall uniformity of the surface lattice. The calculation method for pre-distortion compensation is based on analyzing the local geometric characteristics of the surface at different radial positions according to the curvature distribution function. For a point at a radial position r, the local projection scaling factor of the surface at that location is calculated. This factor is defined as the ratio of the planar polar coordinate arc length to the unit geodesic arc length on the surface. For a sphere, the scaling factor is proportional to the sine of the spherical angle. Specifically, it is calculated based on the polar radius r and the radius of curvature. Calculate spherical angles Then the scaling factor is For aspherical surfaces, the scaling factor is calculated by first resolving the equations of the aspherical surface. The slope of the tangent is obtained by taking the first derivative radially, then the surface normal vector at that point is calculated, and finally the scaling factor is calculated based on the ratio of surface arc length elements to plane arc length elements in differential geometry. This calculation method belongs to the standard application of differential geometry. After obtaining the scaling factor at each radial position, the polar radius of each point in the lattice is nonlinearly scaled. The scaling rule is that the polar radius is divided by the scaling factor at the corresponding position. After this pre-scaling, the lattice exhibits a distribution with a loose center and tight edges on the plane. This distribution characteristic is exactly the opposite of the divergence effect of curved surface projection.

[0043] After completing pre-distortion compensation, this step performs a projection mapping from polar coordinates to a 3D surface. This mapping uses a geodesic projection algorithm to ensure that the polar radius in polar coordinates corresponds to the actual geodesic arc length on the surface, rather than a straight-line distance in Euclidean space. For spherical lenses, the geodesic is a great circle arc, and the projection formula uses spherical trigonometric geometry. Given the polar radius r and polar angle θ, the corresponding spherical angle is first calculated. ,in Let the radius of curvature be denoted, and then the three-dimensional Cartesian coordinates are calculated using the spherical coordinate transformation formula. , The z-coordinate represents the height of the surface at that point relative to the lens reference plane. For aspherical lenses, since the curvature varies radially, the geodesic is no longer a circular arc, requiring a numerical integration method to solve. Specifically, the geodesic path from the center to the target point is discretized into several small arc segments. For each arc segment, the spatial increment is calculated based on the local curvature, and all increments are accumulated to obtain the three-dimensional coordinates.

[0044] After projection, this step performs Voronoi subdivision of the points on the 3D surface using surface metrics to verify the effectiveness of pre-distortion compensation. The difference between surface Voronoi subdivision and planar Voronoi subdivision lies in the distance metric: it uses geodesic distances on the surface instead of Euclidean distances. The algorithm needs to calculate the Voronoi cell boundaries on the surface manifold. This step employs an approximation algorithm based on surface discretization, representing the surface as a triangular mesh. Approximate geodesic distances are calculated on the mesh, and Voronoi subdivision is performed. The surface area of ​​the subdivided surface Voronoi cells is calculated by summing the areas of the triangular faces within the cell. The standard deviation of the area of ​​all surface Voronoi cells is calculated and compared with the standard deviation before pre-distortion compensation. If the standard deviation decreases after compensation, the compensation is effective. If the standard deviation does not meet the target requirement, the pre-distortion compensation parameters are iteratively adjusted and reprojected. After 2 to 3 iterations, the uniformity of the surface point lattice can reach a level comparable to that of the optimized planar point lattice.

[0045] This step also requires calculating the normal vector of each point on the surface. The normal vector defines the perpendicular direction of the surface at that point and will be used in subsequent steps to determine the optical axis direction of the microlens, ensuring that the symmetry axis of the microlens coincides with the surface normal vector to guarantee optical performance. The normal vector is calculated by performing a partial derivative operation on the lens surface equation at that point. For spherical lenses, the normal vector points towards the center of the sphere; for aspherical lenses, the normal vector is obtained by normalizing the gradient vector of the surface equation. This step ultimately outputs the lattice data of the three-dimensional surface. The data format is a set of values ​​corresponding to each microstructure, including three-dimensional Cartesian coordinates x, y, and z, the three components of the surface normal vector, and the area of ​​the surface Voronoi unit at that point. This data provides a complete geometric basis for configuring the optical parameters of the microstructure in the next step.

[0046] S6: Acquire three-dimensional coordinates and surface Voronoi data, partition the optical region according to the radial position, use the radial gradient configuration strategy to configure defocusing intensity and aperture parameters for the microstructures in different regions, and integrate to generate digital processing files; Receives the 3D surface coordinate data, normal vector data, and Voronoi section data from the previous step as input. Its core task is to configure the optical functional parameters for each microstructure with a defined spatial location and integrate all geometric and optical information into a standard digital file that can be used to drive the processing equipment. The optical functional parameters of the microstructure mainly include defocus intensity and microstructure aperture. These two parameters directly determine the microstructure's ability to focus or diverge incident light and its effective aperture range. It should be noted that the optical parameter configuration strategy described in this step is a preferred embodiment of the present invention; other optical parameter configuration methods can also be used according to actual needs. The core innovation of this invention lies in the uniform spatial arrangement of the microstructures achieved in the aforementioned steps. The key technical point of this step is to differentiate the configuration based on the radial position of the microstructures on the lens to adapt to the different response characteristics of the peripheral retina to defocus stimuli at different eccentric positions.

[0047] The optical parameter configuration employs a radial partitioning strategy, which divides the peripheral annular optical region of the lens radially into three sub-regions: an inner ring, a middle ring, and an outer ring. The boundaries of these regions are determined based on the radial span of the optical region. Assuming the inner radius of the effective annular region is the radius of the central protection zone and the outer radius is the outer radius of the optical region, this radial span is trisected or divided according to a preset ratio, such as 3:4:3, to determine the radial positions of the outer boundaries of the inner and middle rings. For each microstructure, its radial distance relative to the optical center of the lens is calculated using its three-dimensional coordinates. This distance is defined on the curved surface using the geodesic arc length, and the partition to which the microstructure belongs is determined based on this radial distance.

[0048] The inner ring region is configured with a nominal defocus power for its microstructures. This power value is derived from the lens prescription parameters and is typically a positive power, such as 2.50D or 3.00D, indicating that the focal point produced by this microstructure is located at the corresponding distance in front of the retina. The middle ring region, considering the curvature of the retina and the characteristics of the eye's optical system in the peripheral region, adopts a gradually increasing power configuration strategy. The power of the microstructures inside the middle ring is equal to the nominal value, while the power of the microstructures outside the middle ring increases by 0.25D to 0.50D from the nominal value. The power of the microstructures inside the middle ring is determined by linear interpolation, ensuring a smooth radial transition in power. The outer ring region is configured with the maximum power, which is increased by 0.50D to 0.75D from the nominal power. This design compensates for the physiological characteristic that the peripheral retina's sensitivity to defocus stimuli decreases with increasing eccentricity, ensuring that the physiological response of the defocus signal intensity on the retina in the outer ring region is consistent with that in the inner ring region. The determination of the above-mentioned incremental values ​​of added power is based on ocular optical models and clinical research data. Studies have shown that the sensitivity of the peripheral retina to defocused stimuli decreases by about 15% to 25% in the range of eccentric angles of 10 to 20 degrees. To compensate for this decrease in sensitivity, it is necessary to increase the defocused power accordingly to keep the intensity of the effective stimulus received by the retina consistent. According to ocular optical models and clinical validation data, a decrease in sensitivity of 15% to 25% corresponds to an increase in added power compensation of 0.25D to 0.50D. In the range of eccentric angles above 20 degrees, the sensitivity decreases further, requiring an increase in added power compensation of 0.50D to 0.75D to ensure that the intensity of the effective defocused signal received by the peripheral retina remains consistent.

[0049] The aperture parameters of the microstructure are determined based on the area of ​​the curved Voronoi elements of the microstructure. The Voronoi elements geometrically define the spatial control region of the microstructure. To ensure no optical crosstalk between adjacent microstructures and to fully utilize the available area, the effective aperture of the microstructure is set as the equivalent circle diameter of its Voronoi element area multiplied by a fill factor. The equivalent circle diameter is calculated by dividing the Voronoi element area by pi, taking the square root, and then multiplying by 2. The fill factor ranges from 0.75 to 0.85, maximizing the effective optical area while ensuring necessary processing clearance between microstructures. Since the previous step ensured the uniformity of the curved Voronoi element area, the aperture of the microstructure calculated using this method also exhibits a uniform spatial distribution, avoiding optical inhomogeneities introduced by aperture differences.

[0050] After configuring the optical parameters of all microstructures, this step integrates the geometric and optical information to generate a standardized digital fabrication file. This file employs a hierarchical data structure. The top layer contains global lens parameters, including lens identification, surface parameters, and optical region definitions. The second layer contains microstructure array data, storing the complete definition of each microstructure in a structured array format. Each microstructure's data record includes its microstructure number, 3D coordinates, normal vector, aperture parameter, defocusing power, and optional processing parameters such as toolpath or exposure dose. The file format supports common optical design exchange formats or proprietary formats directly adapted to specific processing equipment. The digital fabrication file output in this step can be directly used to drive laser direct-write systems, femtosecond laser processing systems, or photolithography mask fabrication equipment to achieve the physical fabrication of microstructures on the lens surface.

[0051] In one embodiment of the present invention, a lens arrangement system with Fermat spiral golden angle offset is provided, such as Figure 2 As shown, it includes: The parameter acquisition module is used to collect lens prescription parameters and surface data, establish a curved surface geodesic polar coordinate system, determine projection distortion characteristics through surface curvature analysis, and obtain a set of lens parameters. The dot matrix initialization module is used to receive the lens parameter set, initialize the scaling constant and initial value of the golden angle of the Fermat spiral using the area matching method, and generate the initial dot matrix data and spiral parameters analytically. The Golden Angle Optimization Module is used to perform adaptive offset optimization of the golden angle based on the initial lattice data, with Voronoi cell area uniformity and minimum point spacing as the two objectives, to obtain the optimal golden angle, the optimal scaling constant, and the optimized lattice. The visual protection constraint module is used to acquire optimized dot matrix data and central protection zone radius parameters, calculate and determine the center points to be removed, restore uniformity to the inner circle area after removal, and output an effective dot matrix that meets the visual center protection constraint. The curved surface projection module is used to receive the effective point array, adjust the polar radius distribution through the pre-distortion compensation mechanism, and use the geodesic projection algorithm to map the polar coordinates to the three-dimensional curved surface of the lens, and output three-dimensional spatial coordinates and curved surface Voronoi subdivision data. The optical parameter configuration module is used to acquire three-dimensional coordinates and surface Voronoi data, divide the optical region into partitions according to the radial position, and use a radial gradient configuration strategy to configure defocusing intensity and aperture parameters for the microstructures in different regions, and integrate them to generate digital processing files.

[0052] This invention focuses on the industrial design and application of high-end aspheric myopia control lenses. Taking a batch of myopia control lenses for teenagers received by a lens manufacturer as an example, the prescription parameters of this batch of lenses are -6.00D myopia correction in the central optical zone and +3.00D anterior defocus in the peripheral ring area. The lenses adopt an aspheric design to adapt to the visual needs of high-prescription wearers. The microstructure layout design is carried out using the method of this invention, and the specific data are shown in Table 1: Table 1, Example of Input Parameters

[0053] The complete design process was executed using the method of this invention. In the lens parameter acquisition step, the total number of target microstructures was calculated to be 1850. In the Fermat spiral initialization step, the initial scaling constant was determined to be 0.42, and the initial golden angle to be 136.8 degrees. Since the lens uses an aspherical design and has a relatively small radius of curvature (85.0 mm), according to the curvature compensation mechanism in step 2, the initial golden angle was set to 136.8 degrees, slightly less than the standard value, to pre-compensate for the edge divergence effect of the curved surface projection. In the golden angle offset optimization step, through nine rounds of golden section search iterations, the optimal golden angle was finally determined to be 137.12 degrees, and the optimal scaling constant was 0.436. In the visual protection zone constraint step, points numbered 1 to 18 at the center were removed, and points numbered 19 to 45 in the inner circle were radially diffused and fine-tuned, with an outward shift distance ranging from 0.15 mm to 0.38 mm. In the curved surface projection step, pre-distortion compensation was used, and the edge region polar radius scaling factor was 0.92. After projection, the Voronoi uniformity of the curved surface met the standard.

[0054] Table 2 shows an example of output indicators.

[0055] This application example demonstrates the application process and output results of the method of this invention in a real industrial design scenario, verifying the effectiveness and computational efficiency of the method in handling high-density, large optical area, and complex curved surface lens designs. The generated digital processing file is used to drive a femtosecond laser processing system to manufacture a microlens array on the rear surface of the lens. After optical performance testing, the spatial uniformity and isotropy of the peripheral retinal defocus energy distribution of the manufactured lens meet the clinical requirements for myopia prevention and control.

[0056] To verify the technical effectiveness of the method of the present invention, a comparative experiment was conducted. Using the same lens parameters and the same initial golden angle of 137.508 degrees, the control group used the fixed golden angle method, i.e., without optimizing the golden angle, directly using the initial value for subsequent steps. The experimental group used the adaptive golden angle method of the present invention to optimize the golden angle and then used the optimal value for subsequent steps. The comparison results are shown in Table 3.

[0057] Table 3. Comparison of Technical Effects

[0058] Comparative data shows that the method of this invention improves surface uniformity by 42% and reduces edge density deviation by 82% compared to the fixed golden angle method, while only increasing computation time by 3 seconds, verifying the technical effectiveness of the adaptive golden angle offset optimization mechanism. While the fixed golden angle method can achieve uniform distribution in the planar stage, it results in a significant density gradient in the edge region after projection onto the curved surface due to the lack of consideration for the surface's geometric characteristics. This invention, through a dual mechanism of adaptive golden angle optimization and pre-distortion compensation, effectively solves the problem of surface projection distortion, achieving highly uniform arrangement under curved surface measurements.

[0059] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A method for arranging lenses with a Fermat spiral golden angle offset, characterized in that, Includes the following steps: S1. Collect lens prescription parameters and surface data, establish a curved surface geodesic polar coordinate system, determine projection distortion characteristics through surface curvature analysis, and obtain the lens parameter set; S2, receive the lens parameter set, use the area matching method to initialize the scaling constant and initial value of the golden angle of the Fermat spiral, and generate the initial lattice data and spiral parameters through analytical expression; S3. Based on the initial lattice data, the golden angle adaptive offset optimization is performed with Voronoi cell area uniformity and minimum point spacing as the two objectives to obtain the optimal golden angle, the optimal scaling constant, and the optimized lattice. S4: Obtain optimized dot matrix data and central protection zone radius parameters, calculate and determine the center points to be removed, restore uniformity to the inner circle area after removal, and output an effective dot matrix that meets the visual center protection constraint. S5 receives the valid point array, adjusts the polar radius distribution through the pre-distortion compensation mechanism, maps the polar coordinates to the three-dimensional curved surface of the lens using the geodesic projection algorithm, and outputs three-dimensional spatial coordinates and surface Voronoi subdivision data. S6 acquires three-dimensional coordinates and surface Voronoi data, partitions the optical region according to the radial position, and uses a radial gradient configuration strategy to configure defocusing intensity and aperture parameters for the microstructures in different regions, integrating them to generate digital processing files.

2. The lens arrangement method with Fermat spiral golden angle offset according to claim 1, characterized in that, S1 includes: The lens prescription parameters include the outer radius of the lens optical area, the radius of the central clear vision protection zone, the peripheral defocus power value, and the surface parameters of the lens substrate. The origin of the geodesic polar coordinate system is located at the optical center of the lens, the polar radius is defined as the arc length measured along the geodesic line on the curved surface from the optical center, and the polar angle is defined as the azimuth angle relative to the reference direction. The lens parameter set includes optical region parameters, curvature distribution function, and total number of target microstructures.

3. The lens arrangement method with Fermat spiral golden angle offset according to claim 1, characterized in that, S2 includes: The calculation process of the area matching method is as follows: the effective arrangement area is determined to be a ring, the total area of ​​the ring is calculated, and according to the space filling characteristics of the Fermat spiral, the total area of ​​the ring is divided by the total number of target microstructures to obtain the average area of ​​the unit. The initial estimated value of the scaling constant is obtained by solving the inverse operation of the square relationship. The initial value of the golden angle is set by analyzing the curvature distribution function to calculate the projection scaling ratio of the edge region. When the ratio indicates that there is obvious divergence at the edge, the initial value of the golden angle is set to be slightly smaller than the standard value. When the curvature distribution is uniform, the standard value is used.

4. The lens arrangement method with Fermat spiral golden angle offset according to claim 1, characterized in that, S3 includes: The golden angle adaptive offset optimization uses the Voronoi spatial partitioning method to quantify the spatial uniformity of the lattice. The standard deviation of the area of ​​all Voronoi cells is used as the first optimization objective, and the minimum spacing between all point pairs in the lattice is used as the second optimization objective. The minimum spacing is required to be greater than a preset minimum spacing threshold. The two objectives are combined into a comprehensive evaluation function through a weighted method.

5. The lens arrangement method with Fermat spiral golden angle offset according to claim 4, characterized in that, S3 further includes: An incremental Voronoi update algorithm is adopted to improve the optimization calculation efficiency. The incremental Voronoi update algorithm identifies points whose positions have moved beyond a preset displacement threshold due to parameter changes and marks them as affected points. For each affected point, its neighboring points in the previous Voronoi partition are identified. The local point set formed by the affected points and their neighboring points is reconstructed by Voronoi. The local reconstruction result is then joined with the global Voronoi partition by boundary stitching. The golden section search method is used to optimize within the preset critical range of the golden angle. Two trial points are selected within the search interval according to the golden ratio. The search interval is gradually narrowed by comparing the objective function values ​​of the trial points until the interval width is less than the preset accuracy threshold.

6. The lens arrangement method with Fermat spiral golden angle offset according to claim 5, characterized in that, S3 further includes: The scaling constant is simultaneously optimized using a binary search method. The optimization goal is to make the point with the largest polar radius in the dot matrix exactly located at the outer radius of the optical region. Convergence is determined when the error between the largest polar radius and the outer radius of the target is less than a preset error threshold. The two-parameter optimization of the golden angle and scaling constant adopts a nested loop structure. The outer loop is a golden section search for the golden angle, and the inner loop is a binary search for the scaling constant given the golden angle.

7. The lens arrangement method with Fermat spiral golden angle offset according to claim 1, characterized in that, S4 includes: By utilizing the ordered nature of the Fermat spiral lattice, the exclusion range is determined in batches by calculating the critical number corresponding to the radius of the protected area. The calculation of the critical number is achieved through the inverse operation of the Fermat spiral formula. A radial diffusion fine-tuning mechanism is used to restore the uniformity of the inner circle region. Inner circle points with a polar radius smaller than the radius of the protected area plus a preset buffer distance are identified. Points whose ratio of Voronoi unit area to global average area is greater than a preset area ratio threshold are radially shifted outward. The outward shift distance is proportional to the difference between its area ratio and the threshold.

8. The lens arrangement method with Fermat spiral golden angle offset according to claim 1, characterized in that, S5 includes: The pre-distortion compensation mechanism analyzes the local geometric characteristics of the surface at different radial positions based on the curvature distribution function, calculates the local projection scaling factor of the surface at that location, and performs nonlinear scaling on the polar radius of each point in the lattice. The scaling rule is to divide the polar radius by the scaling factor at the corresponding position. The geodesic projection algorithm uses spherical trigonometric geometry to project onto spherical lenses, and uses numerical integration to discretize the geodesic path into several tiny arc segments for projection onto aspherical lenses. After projection, the points on the 3D surface are subjected to Voronoi subdivision under surface metric to verify the effect of pre-distortion compensation.

9. The lens arrangement method for Fermat spiral golden angle offset according to claim 1, characterized in that, S6 includes: The radial gradient configuration strategy divides the peripheral annular optical region of the lens into three sub-regions: an inner ring region, a middle ring region, and an outer ring region. The microstructure configuration of the inner ring region is set with nominal defocus power, the middle ring region adopts a gradually increasing power configuration strategy, and the outer ring region is configured with maximum power. The aperture parameter of the microstructure is determined based on the area of ​​the surface Voronoi element of the microstructure. The effective aperture of the microstructure is set as the equivalent circle diameter of its Voronoi element area multiplied by the filling factor.

10. The lens arrangement method with Fermat spiral golden angle offset according to claim 3, characterized in that, The setting of the initial value of the golden angle in S2 also includes: By analyzing the curvature distribution function, the projection scaling ratio of the edge region is calculated. When the ratio indicates that there is significant divergence at the edge, the initial value of the golden angle is set to be slightly smaller than the standard value, so that the planar lattice is slightly compact in the angular direction and is stretched to a uniform state by the surface divergence effect after projection. When the curvature distribution is uniform or the lens is close to a plane, the initial value of the golden angle is a standard value; the setting of the initial value of the golden angle provides the initial parameter for coarse compensation in the subsequent precise optimization in S3.

11. The lens arrangement method with Fermat spiral golden angle offset according to claim 5, characterized in that, The preset critical range of the golden angle in S3 is determined in the following way: For typical parameter ranges of lens curvature radius and optical region outer radius, numerical simulations are performed on the surface Voronoi uniformity index under different golden angle values ​​to determine the fluctuation range of the optimal golden angle relative to the standard golden angle. The fluctuation range is used as the optimization interval of the golden section search method. The optimization interval covers a preset degree range above and below the standard golden angle to include the optimal solution of most lens parameter combinations.

12. The lens arrangement method with Fermat spiral golden angle offset according to claim 6, characterized in that, S3 further includes: Once the golden section search converges, a point spacing constraint check is performed on the optimized point matrix. The Euclidean distance between all point pairs is calculated, and the minimum distance value is identified. When the minimum distance is less than a preset minimum spacing threshold, a local position perturbation is applied to one point in a point pair that is too close. The perturbation direction is radial or tangential away from the other point, and the perturbation amplitude is set to make the distance between the two points exactly reach the minimum spacing threshold. The local position perturbation only affects a few points and does not destroy the uniformity of the overall point matrix.

13. The lens arrangement method with Fermat spiral golden angle offset according to claim 8, characterized in that, The S5 also includes: The surface normal vector at each point on the three-dimensional surface is calculated. For a spherical lens, the normal vector points towards the center of the sphere. For an aspherical lens, the normal vector is obtained by normalizing the gradient vector after performing partial derivative calculations on the surface equation at that point. The surface normal vector is used to determine the optical axis direction of the corresponding microlens, so that the axis of symmetry of the microlens coincides with the surface normal vector. The surface normal vector is output to S6 as a component of the three-dimensional point matrix data.

14. The lens arrangement method with Fermat spiral golden angle offset according to claim 9, characterized in that, The radial partitioning strategy in S6 also includes: The defocus illumination configuration in the middle ring area is smoothly transitioned radially using linear interpolation. The illumination of the microstructure inside the middle ring is equal to the nominal defocus illumination. The illumination of the microstructure outside the middle ring is increased by a preset first illumination increment based on the nominal value. The illumination of the microstructure inside the middle ring is determined by linear interpolation. The microstructure of the outer ring region is increased by a preset second increment based on the nominal defocus intensity, and the second increment is greater than the first increment. The outer ring region is configured with maximum intensity to compensate for the physiological characteristic that the sensitivity of the peripheral retina to defocus stimulation decreases with increasing eccentricity, so that each region produces a consistent effective defocus stimulation intensity on the retina.

15. A lens arrangement system with Fermat spiral golden angle offset, used to perform the steps in the lens arrangement method with Fermat spiral golden angle offset as described in any one of claims 1-14, characterized in that, include: The parameter acquisition module is used to collect lens prescription parameters and surface data, establish a curved surface geodesic polar coordinate system, determine projection distortion characteristics through surface curvature analysis, and obtain a set of lens parameters. The dot matrix initialization module is used to receive the lens parameter set, initialize the scaling constant and initial value of the golden angle of the Fermat spiral using the area matching method, and generate the initial dot matrix data and spiral parameters analytically. The Golden Angle Optimization Module is used to perform adaptive offset optimization of the golden angle based on the initial lattice data, with Voronoi cell area uniformity and minimum point spacing as the two objectives, to obtain the optimal golden angle, the optimal scaling constant, and the optimized lattice. The visual protection constraint module is used to acquire optimized dot matrix data and central protection zone radius parameters, calculate and determine the center points to be removed, restore uniformity to the inner circle area after removal, and output an effective dot matrix that meets the visual center protection constraint. The curved surface projection module is used to receive the effective point array, adjust the polar radius distribution through the pre-distortion compensation mechanism, and use the geodesic projection algorithm to map the polar coordinates to the three-dimensional curved surface of the lens, and output three-dimensional spatial coordinates and curved surface Voronoi subdivision data. The optical parameter configuration module is used to acquire three-dimensional coordinates and surface Voronoi data, divide the optical region into partitions according to the radial position, and use a radial gradient configuration strategy to configure defocusing intensity and aperture parameters for the microstructures in different regions, and integrate them to generate digital processing files.

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