A fractal iteration-based optical lens pattern generation method and system

Abstract

The application relates to the technical field of intelligent manufacturing of optical lenses, and discloses an optical lens pattern generation method and system based on fractal iteration, which adopts an IFS fractal iteration algorithm, establishes a transformation system composed of four affine transformation functions based on a Barnsley fern model, performs iterative calculation through a probability weight random selection mechanism, generates a complex fractal pattern with self-similarity characteristics, and applies the complex fractal pattern to optical path difference regulation of myopia prevention control lenses. Specifically, an affine transformation system is established, transformation parameters and probability weights are set, iterative calculation parameters are initialized, starting conditions and storage structures are set, a probability selection mechanism is executed, transformation functions are randomly selected, affine transformation results are calculated, new iteration point coordinates are generated, iteration states are stored and updated, pattern data is accumulated, iteration convergence conditions are judged, the calculation process is controlled, lens pattern coordinate data is generated, and physical coordinate mapping is completed.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology for optical lenses, and more specifically, to a method and system for generating optical lens patterns based on fractal iteration. Background Technology

[0002] With the continued rise in the global incidence of myopia, myopia control technology has become an important research direction in ophthalmology and optical engineering. Traditional myopia control lenses mainly employ periodic pattern designs, such as regular geometric patterns like concentric rings, grids, or stripes. These patterns create a defocus effect by forming a specific optical path difference distribution on the lens surface, thereby inhibiting abnormal axial elongation. These traditional methods did demonstrate some effectiveness in myopia control in initial applications and have been widely used in clinical practice. However, existing technologies generally suffer from limitations such as limited pattern complexity and insufficient design flexibility, making it difficult to meet the growing trend of personalized myopia control needs.

[0003] The most critical problem facing current myopia control lens technology is drug resistance, namely the gradual decline in control effectiveness during long-term wear. The root cause of this problem lies in the strong adaptive mechanism of the human visual system. When continuously exposed to the same visual stimulus pattern, the visual cortex gradually reduces its sensitivity to that stimulus, causing the originally effective optical intervention to gradually fail. Traditional periodic patterns, due to their regularity and predictability, are particularly prone to triggering adaptive responses in the visual system. Furthermore, traditional pattern generation methods also suffer from technical problems such as large storage space requirements, high manufacturing costs, and difficulties in personalized customization, limiting their application and development in the era of precision medicine.

[0004] To address the aforementioned technical challenges, there is an urgent need to develop a novel pattern generation technology capable of generating highly complex, non-periodic patterns with adaptive properties. An ideal solution should possess the following characteristics: the pattern should have sufficient complexity and unpredictability to effectively resist the adaptive mechanisms of the visual system; the pattern generation algorithm should be efficient and parametric, facilitating personalized design and industrial production; and the generated pattern should possess natural characteristics, conforming to human visual perception habits and providing a comfortable wearing experience. The development of fractal geometry theory has provided new insights into solving this technical challenge, particularly the unique advantages exhibited by iterative function systems (IFS) in complex pattern generation, laying the theoretical foundation for the development of next-generation myopia control lens technology. Summary of the Invention

[0005] This invention provides a method and system for generating optical lens patterns based on fractal iteration, solving technical problems such as the difficulty of personalized customization in related technologies.

[0006] This invention provides a method for generating optical lens patterns based on fractal iteration, comprising the following steps:

[0007] Obtain the design requirements parameters for myopia lenses; process the lens design requirements parameters using a quaternary affine transformation matrix construction method to obtain the IFS iterative function system;

[0008] Based on the IFS iterative function system, the initialization requirements are calculated using a precision adaptive configuration method to obtain the set of iterative calculation initialization parameters.

[0009] Based on the iterative calculation of the initial parameter set, the Monte Carlo random selection method is used to perform fractal iterative calculation to generate a set of fractal points.

[0010] Based on the generated set of fractal points, the fractal points are processed using the optical path difference distribution calculation method to obtain optical path difference distribution data;

[0011] Based on the optical path difference distribution data, the defocus amount distribution calculation method is used to process the conversion from optical path difference to defocus amount, and the defocus amount distribution data is obtained.

[0012] Based on the defocus distribution data and the convergence judgment threshold, a multi-convergence condition judgment method is used to perform iterative convergence judgment, and the iterative control decision results and complete optical fractal point set are obtained.

[0013] Based on the complete optical fractal point set, the coordinates of the fractal point set are processed by the coordinate normalization mapping method and the optical path difference distribution matrix is ​​constructed to obtain complete optical pattern data for the manufacture of myopia control lenses.

[0014] In a preferred embodiment, the step of processing lens design requirement parameters using the four-element affine transformation matrix construction method includes:

[0015] Configure the affine transformation function, which consists of a transformation matrix and a translation vector. The transformation matrix contains coefficients that control the scaling of the horizontal coordinate, the coupling of the horizontal and vertical coordinates, the coupling of the horizontal and vertical coordinates, and the scaling of the vertical coordinate.

[0016] The first affine transformation function is set to generate the stem part and produce the central focus area, and the second affine transformation function is used to generate the main leaves to form the defocus area.

[0017] A third affine transformation function is set to generate the left lobule, and a fourth affine transformation function is set to generate the balanced optical distribution of the right lobule.

[0018] The probability weight distributions of the first, second, third, and fourth affine transformation functions are optimized according to optical performance requirements and then summed to obtain the cumulative probability distribution.

[0019] In a preferred embodiment, the step of calculating the initialization requirements using the precision adaptive configuration method includes:

[0020] The fractal point density is calculated based on the manufacturing precision requirements, and the point density requirement is determined based on the lens area, coverage, and minimum feature size.

[0021] The target number of iterations is determined based on point density, safety factor, and calculations from optical diffraction theory.

[0022] Configure a high-precision random number generator, using the Mersenne Twister algorithm, with the hash value of the lens serial number and timestamp as the seed;

[0023] Establish an optical data structure, including a fractal point coordinate array, an optical path difference distribution matrix that determines the resolution based on the minimum feature size, a defocus distribution array, and optical quality evaluation parameters;

[0024] Set convergence thresholds, including the minimum number of points for point density convergence, the standard deviation threshold for optical uniformity convergence, and the area requirement for coverage convergence.

[0025] In a preferred embodiment, the step of performing fractal iterative calculations using the Monte Carlo random selection method includes:

[0026] The iteration start point is initialized to the coordinates of the lens center; a high-precision random number generator is called to generate uniformly distributed random numbers.

[0027] The transformation function is selected based on the cumulative probability distribution, and the corresponding transformation function is determined by comparing the random number with the cumulative probability value.

[0028] Perform affine transformations to calculate new iteration points and monitor convergence conditions in real time;

[0029] Store the valid fractal points that satisfy the lens boundary conditions, and record the iteration number and the number of the transformation function to which each point belongs.

[0030] In a preferred embodiment, the step of processing fractal points using the optical path difference distribution calculation method includes:

[0031] Initialize the optical path difference distribution matrix; for each point in the fractal point set, calculate its optical path difference value;

[0032] Map the fractal points to the grid indices and assign the optical path difference to the corresponding matrix elements;

[0033] The optical performance of the optical path difference distribution matrix is ​​verified, including checking the optical path difference range, coverage, and numerical stability.

[0034] In a preferred embodiment, the step of processing the conversion from optical path difference to defocus amount using the defocus amount distribution calculation method includes:

[0035] For each grid point in the optical path difference distribution matrix, calculate the defocus value for each grid point;

[0036] Construct the defocus distribution matrix and calculate the statistical properties of the defocus distribution;

[0037] Perform optical performance verification of defocus distribution; output complete defocus distribution data, including defocus distribution matrix, grid point defocus value array, effective defocus area, and standard deviation of defocus distribution.

[0038] In a preferred embodiment, the step of using a multiple convergence condition judgment method to perform iterative convergence judgment includes:

[0039] Multiple convergence criteria are used, including convergence criteria based on the number of iterations, optical coverage, and defocus effect uniformity.

[0040] Execute convergence judgment logic. When all conditions are met, output convergence completed status. When only the iteration count condition is met, output forced termination status. When the condition is not met, output continue iteration status.

[0041] Generate corresponding output data based on the convergence status. When convergence is complete, organize the complete fractal point set. When forced termination occurs, output the currently available fractal point set and record warning information.

[0042] Calculate optical performance evaluation metrics, including coverage efficiency and defocus effect uniformity.

[0043] In a preferred embodiment, the step of processing the coordinates of the fractal point set using a coordinate normalization mapping method includes:

[0044] The fractal point set is normalized, and the physical coordinates are calculated based on the normalized coordinates, lens diameter, and pattern scale adjustment coefficient.

[0045] Construct a high-resolution optical path difference distribution matrix and calculate the optical path difference for each point in the grid.

[0046] Perform optical performance verification, including coverage check, defocus effect uniformity check, and pattern integrity check;

[0047] Output complete optical lens pattern data, including the final optical path difference distribution matrix, physical coordinate point set, actual coverage, and optical quality indicators.

[0048] In a preferred embodiment, the complete optical pattern data includes:

[0049] The optical path difference distribution matrix is ​​used to define the optical path difference value at each point on the lens surface;

[0050] The physical coordinate point set contains the position of each fractal point in the lens's physical coordinate system and the corresponding defocus value;

[0051] Actual coverage rate indicates the effective coverage of the fractal pattern on the lens surface;

[0052] Optical quality indicators are used to evaluate the optical performance and myopia control effectiveness of lenses.

[0053] In a preferred embodiment, an optical lens pattern generation system based on fractal iteration is used to perform the steps of the above-described optical lens pattern generation method based on fractal iteration, including:

[0054] The quaternary affine transformation matrix construction module obtains the design requirement parameters for myopia lenses; the quaternary affine transformation matrix construction method is used to process the lens design requirement parameters to obtain the IFS iterative function system;

[0055] The precision adaptive configuration module, based on the IFS iterative function system, uses the precision adaptive configuration method to calculate the initialization requirements and obtain the set of iterative calculation initialization parameters.

[0056] The Monte Carlo fractal iteration module initializes the parameter set based on iterative calculations and performs fractal iterative calculations using the Monte Carlo random selection method to generate a set of fractal points.

[0057] The optical path difference distribution calculation module processes the fractal points based on the generated set of fractal points using the optical path difference distribution calculation method to obtain optical path difference distribution data.

[0058] The defocus amount distribution calculation module, based on the optical path difference distribution data, uses the defocus amount distribution calculation method to process the conversion from optical path difference to defocus amount, and obtains the defocus amount distribution data;

[0059] The convergence judgment module, based on the defocus distribution data and the convergence judgment threshold, uses a multi-convergence condition judgment method to perform iterative convergence judgment, and obtains the iterative control decision results and the complete optical fractal point set.

[0060] The coordinate normalization mapping module, based on a complete set of optical fractal points, uses a coordinate normalization mapping method to process the coordinates of the fractal point set and construct an optical path difference distribution matrix to obtain complete optical pattern data for the manufacture of myopia control lenses.

[0061] The beneficial effects of this invention are as follows:

[0062] The patterns generated by the IFS fractal iterative algorithm possess infinite complexity and aperiodicity, fundamentally solving the drug resistance problem of traditional myopia control lenses. The fractal patterns exhibit rich detail at different scales, forming a hierarchical complexity distribution. When the visual system adapts to features at a certain scale, features at other scales can still maintain an effective stimulating effect, thus preserving the overall control effect.

[0063] Parametric pattern generation methods achieve significant improvements in storage space and computational efficiency. Traditional pattern generation methods require storing large amounts of pixel data or complex geometric description information, while the IFS algorithm only needs 28 numerical parameters to fully describe complex fractal patterns, thus reducing storage requirements. Attached Figure Description

[0064] Figure 1 This is a flowchart of an optical lens pattern generation method based on fractal iteration according to the present invention;

[0065] Figure 2 This is a block diagram of an optical lens pattern generation system based on fractal iteration according to the present invention;

[0066] Figure 3 This is a diagram of the iterative convergence process of the present invention. Detailed Implementation

[0067] 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.

[0068] At least one embodiment of the present invention discloses a method for generating optical lens patterns based on fractal iteration, such as... Figure 1 As shown, it includes the following steps:

[0069] S1, obtain the design requirements parameters for myopia lenses; use the four-element affine transformation matrix construction method to process the lens design requirements parameters and obtain the IFS iterative function system;

[0070] Specifically, the design requirements for myopia lenses include: lens diameter D; target defocus amount. Optical path difference modulation depth Pattern coverage Minimum feature size ;

[0071] Processing procedure: Based on the optical principles of myopia control, the relationship between defocus effect and optical path difference is established. For any coordinate point (x, y) on the lens surface, the optical path difference is calculated according to the following formula:

[0072]

[0073] in, This represents the optical path difference at coordinate point (x, y) on the lens surface; The value represents the defocus amount of the target; x and y represent the horizontal and vertical coordinates of the coordinate points on the lens surface, respectively; n represents the refractive index of the lens material, with a value of 1.586. This represents the equivalent focal length of the human eye, and its value is 22.3 mm.

[0074] An improved Barnsley fractal system suitable for optical lenses is constructed. The general expression for the IFS affine transformation is:

[0075]

[0076] in, Let x and y represent the x-coordinate and y-coordinate after the (n+1)th iteration, respectively; Let x and y represent the x and y coordinates of the nth iteration, respectively. Let represent the first, second, third, and fourth linear transformation coefficients of the i-th affine transformation function, respectively; Let e ​​and f represent the e-th and f-th components of the translation vector of the i-th affine transformation function, respectively.

[0077] Specific transformation function configuration:

[0078] First transformation function probability It is responsible for generating the stem part and creating the central focal area.

[0079] Second transformation function probability It is responsible for generating the main blades and forming the main defocus area.

[0080] The third transformation function probability It is responsible for generating the small leaves on the left, increasing the complexity of the pattern.

[0081] The fourth transformation function probability It is responsible for generating the right leaflet and balancing the optical distribution.

[0082] Cumulative probability distribution with weights: Calculate the cumulative probability distribution based on the probability weights of each transformation function. .

[0083] Output the complete IFS iterative function system It contains: four affine transformation matrices and its transformation parameters ; corresponding probability weight distribution Cumulative probability distribution array Parameters for optical path difference calculation formula: lens material refractive index n=1.586, equivalent focal length of human eye. millimeters;

[0084] S2, based on the IFS iterative function system, uses a precision adaptive configuration method to calculate the initialization requirements and obtain the set of iterative calculation initialization parameters;

[0085] Calculate the required fractal point density based on the manufacturing process requirements of the optical lens. Lens radius R = D / 2, fractal point density... ,in This represents the number of fractal points required per unit area.

[0086] Determine the number of iterations to ensure optical performance; target number of iterations. The larger value is chosen from the safety factor calculated based on point density and the value calculated based on optical diffraction theory.

[0087] Set convergence conditions related to optical performance: Point density convergence: Current number of points Optical uniformity convergence: standard deviation of local defocus Refractive power; Coverage convergence: Effective coverage area ;

[0088] Initialize the data structures related to optical calculations: fractal point coordinate array : Stores the x and y coordinates of all fractal iteration points; optical path difference distribution matrix Based on minimum feature size A two-dimensional matrix that determines the resolution; an array of defocus distributions. : An array storing the defocus values ​​at each point; Optical quality assessment parameters: MTF calculation grid, wavefront error statistics, Indicates the target number of iterations;

[0089] Configure a high-precision random number generator: Algorithm used: Mersenne Twister MT19937-64; Seed: Hash value based on lens serial number and timestamp; Precision: 64-bit floating-point number to ensure optical calculation accuracy;

[0090] Output the complete set of initialization parameters for the iterative calculation, including: the target number of iterations. (Calculated based on point density and optical diffraction theory); Triple convergence threshold set Point density threshold (Calculated from fractal point density), optical uniformity threshold Diopter (set based on optical performance requirements), coverage threshold (Calculated from lens design parameters); Initialized optical data structures: fractal point coordinate array P, optical path difference distribution matrix Defocus distribution array The configured high-precision random number generator RNG (MT19937-64 algorithm, 64-bit floating-point precision) is complete.

[0091] S3, based on the iterative calculation of the initial parameter set, uses the Monte Carlo random selection method to perform fractal iterative calculation and generate a set of fractal points;

[0092] Initialize the iteration start point The coordinates are the center coordinates of the lens.

[0093] Execute the Monte Carlo iteration loop. For the nth iteration, Generate random numbers According to the cumulative probability distribution Select the appropriate transformation function :when Time selection ,when Time selection ,when Time selection ,when Time selection .

[0094] Perform affine transformation to calculate new iteration points .

[0095] Real-time monitoring of convergence conditions: Check point density convergence: Check optical uniformity convergence: Refractive error; check coverage convergence:

[0096] Storing valid fractal points: satisfying lens boundary conditions The coordinates of the iteration points are stored in the fractal point coordinate array P, and the iteration number and the number of the transformation function to which each point belongs are recorded.

[0097] Output a complete set of fractal points, including: valid fractal point coordinate data. (satisfies boundary conditions) ); Iteration number of each point (Record generation order) and the corresponding transformation function number (Record the transformation function used); Geometric statistics of the fractal point set. Total points Actual coverage area Spatial distribution density ;

[0098] S4. Based on the generated set of fractal points, the fractal points are processed using the optical path difference distribution calculation method to obtain optical path difference distribution data.

[0099] Calculate the optical path difference value corresponding to each fractal point and construct a complete optical path difference distribution matrix.

[0100] Initialize optical path difference distribution matrix The matrix size is For each valid point in the set of fractal points. Calculate its optical path difference:

[0101]

[0102] in, This represents the optical path difference at the i-th fractal point; Indicates the amount of the target out of focus; Let x and y represent the x and y coordinates of the i-th fractal point, respectively; n represents the refractive index of the lens material, with a value of 1.586. This represents the equivalent focal length of the human eye, and its value is 22.3 mm. This indicates the design wavelength, with a value of 550 nanometers.

[0103] Mapping fractal points to grid indexes And assign the optical path difference to the corresponding matrix element. .

[0104] Optical performance verification of the optical path difference distribution matrix: Check the optical path difference range; Check the coverage: Effective coverage area. Numerical stability was checked: all optical path differences were finite numbers.

[0105] Output complete optical path difference distribution data, including: optical path difference distribution matrix. (size is) ); Fractal point optical path difference array Effective coverage area and standard deviation of optical path difference distribution ;

[0106] S5. Based on the optical path difference distribution data, the defocus amount distribution calculation method is used to process the conversion from optical path difference to defocus amount, and the defocus amount distribution data is obtained.

[0107] Based on the optical path difference distribution matrix, the corresponding defocus distribution is calculated, and a complete defocus distribution matrix is ​​constructed.

[0108] For the optical path difference distribution matrix For each grid point (u, v) in the graph, calculate the corresponding defocus value:

[0109]

[0110] in, This represents the defocus value at grid point (u,v); n represents the refractive index of the lens material, with a value of 1.586. This represents the equivalent focal length of the human eye, and its value is 22.3 mm. This represents the optical path difference at grid point (u,v) in the optical path difference distribution matrix; These represent the x-coordinate and y-coordinate of the physical coordinates corresponding to the grid point (u,v), respectively.

[0111] Construct the defocus distribution matrix And calculate the statistical characteristics of the defocus distribution.

[0112] Perform optical performance verification of defocus distribution: Check the defocus range: Refractive power; check distribution uniformity: Diopter; Inspection coverage: effective defocus area ;

[0113] Output complete defocus distribution data, including: defocus distribution matrix. (size is) ); Array of grid point defocus values (Defocus values ​​of all valid grid points in the corresponding matrix); Area of ​​the effective defocus region and the standard deviation of the defocus distribution .

[0114] S6. Based on the defocus distribution data and the convergence judgment threshold, a multi-convergence condition judgment method is used to perform iterative convergence judgment, and the iterative control decision results and complete optical fractal point set are obtained.

[0115] Based on the defocus distribution data and the convergence threshold, it is determined whether to terminate the iteration process.

[0116] Multiple convergence criteria are used to determine convergence: iteration number convergence condition; optical coverage convergence condition; defocus effect uniformity convergence condition.

[0117] Execute convergence judgment logic:

[0118]

[0119] Generate corresponding output data based on the convergence status: When convergence is complete: organize the complete fractal point set. When forced termination occurs: output the currently available fractal point set and record a warning message; when iteration continues: update the iteration counter. Return to step S3; calculate optical performance evaluation indicators. :

[0120]

[0121] Output the iterative control decision results, including: iterative control signals (convergence complete, forced termination, or continued iteration); and the complete fractal point set. (When convergence occurs, the coordinates and defocus of all valid iteration points are included); Optical coverage efficiency and the uniformity of the final defocus effect ;

[0122] When the iterative control signal indicates convergence completion or forced termination, the iterative control decision provides a complete fractal geometric data basis for the generation of the final optical pattern in the next step; when the signal indicates continued iteration, the updated iterative state is passed back to S3 to continue iterative calculation.

[0123] S7, based on the complete optical fractal point set, uses the coordinate normalization mapping method to process the coordinates of the fractal point set and constructs the optical path difference distribution matrix to obtain complete optical pattern data for the manufacture of myopia control lenses;

[0124] Based on the complete fractal point set, the fractal coordinates are converted into the physical coordinates of the lens to generate the final optical pattern data.

[0125] Perform coordinate normalization on the fractal point set:

[0126]

[0127] in, Let x and y represent the x and y coordinates of the i-th fractal point in the lens physical coordinate system, respectively, in millimeters; Let x and y represent the normalized x and y coordinates of the i-th fractal point, respectively, with values ​​ranging from 0 to 1. D indicates the lens diameter; This represents the pattern scale adjustment coefficient, with a value of 0.95.

[0128] Construct a high-resolution optical path difference distribution matrix and calculate the optical path difference for each point in the grid.

[0129] Perform optical performance verification: Check coverage; check defocus effect uniformity. Diopter; Check pattern integrity: Ensure all fractal points are within the effective area of ​​the lens;

[0130] Output complete optical lens pattern data, including: final optical path difference distribution matrix. (size is) ); physical coordinate point set Actual coverage and optical quality indicators ;

[0131] Optical lens pattern data can be directly used in the precision manufacturing of myopia control lenses, realizing the complete application of the optical lens pattern generation method based on fractal iteration.

[0132] In one embodiment of the present invention, an optical lens pattern generation system based on fractal iteration is provided, such as... Figure 2 As shown, it includes:

[0133] The quaternary affine transformation matrix construction module obtains the design requirement parameters for myopia lenses; the quaternary affine transformation matrix construction method is used to process the lens design requirement parameters to obtain the IFS iterative function system;

[0134] The precision adaptive configuration module, based on the IFS iterative function system, uses the precision adaptive configuration method to calculate the initialization requirements and obtain the set of iterative calculation initialization parameters.

[0135] The Monte Carlo fractal iteration module initializes the parameter set based on iterative calculations and performs fractal iterative calculations using the Monte Carlo random selection method to generate a set of fractal points.

[0136] The optical path difference distribution calculation module processes the fractal points based on the generated set of fractal points using the optical path difference distribution calculation method to obtain optical path difference distribution data.

[0137] The defocus amount distribution calculation module, based on the optical path difference distribution data, uses the defocus amount distribution calculation method to process the conversion from optical path difference to defocus amount, and obtains the defocus amount distribution data;

[0138] The convergence judgment module, based on the defocus distribution data and the convergence judgment threshold, uses a multi-convergence condition judgment method to perform iterative convergence judgment, and obtains the iterative control decision results and the complete optical fractal point set.

[0139] The coordinate normalization mapping module, based on a complete set of optical fractal points, uses a coordinate normalization mapping method to process the coordinates of the fractal point set and construct an optical path difference distribution matrix to obtain complete optical pattern data for the manufacture of myopia control lenses.

[0140] In one embodiment of the present invention, a design example of a lens for preventing and controlling myopia in teenagers is provided, as follows:

[0141] Design parameters: Lens diameter: 70 mm; Target defocus: 2.50 diopters; Maximum optical path difference: 1.5 microns; Minimum feature size: 50 microns; Target age group: Adolescents aged 8-16.

[0142] Barnsley fractal parameter configuration:

[0143] Transformation T1 (Stalk Transformation - Main Defocus Area): The affine transformation coefficients are set as follows: First linear coefficient = 0.00, Second linear coefficient = 0.00, Third linear coefficient = 0.00, Fourth linear coefficient = 0.16, First translation coefficient = 0.00, Second translation coefficient = 0.00, and Selection probability = 0.01. This transformation is mainly responsible for generating the stalk structure of the fractal pattern, corresponding to the main defocus functional area of ​​the lens.

[0144] Transformation T2 (Left Leaf Transformation - Auxiliary Defocus Area): The affine transformation coefficients are set as follows: First linear coefficient = 0.85, Second linear coefficient = 0.04, Third linear coefficient = -0.04, Fourth linear coefficient = 0.85, First translation coefficient = 0.00, Second translation coefficient = 1.60, and Selection probability = 0.85. This transformation generates a fractal pattern on the left leaf structure, corresponding to the auxiliary defocus area of ​​the lens, which has the highest selection probability.

[0145] Transformation T3 (Right Leaf Transformation - Auxiliary Defocus Area): The affine transformation coefficients are set as follows: First linear coefficient = 0.20, Second linear coefficient = -0.26, Third linear coefficient = 0.23, Fourth linear coefficient = 0.22, First translation coefficient = 0.00, Second translation coefficient = 1.60, and Selection probability = 0.07. This transformation generates the right leaf structure of the fractal pattern, which, together with the left leaf transformation, constitutes the auxiliary defocus area.

[0146] Transformation T4 (Top Transformation - Central Sharp Visual Area): The affine transformation coefficients are set as follows: First linear coefficient = -0.15, Second linear coefficient = 0.28, Third linear coefficient = 0.26, Fourth linear coefficient = 0.24, First translation coefficient = 0.00, Second translation coefficient = 0.44, and Selection probability = 0.07. This transformation generates the top structure of the fractal pattern, corresponding to the central sharp visual area of ​​the lens.

[0147] Iteration results: Total iterations: 50,000; Number of effective optical points: 47,832; Final optical coverage: 68.3%; Final MTF value: 0.72 (at 30 line pairs / mm); Defocus effect uniformity: 0.15 diopters;

[0148] Manufacturing process results: Laser etching depth range: 0.2 μm to 0.9 μm; Surface roughness: 6.8 nm (meets the requirement of less than 10 nm); Edge sharpness: 25 μm; Optical accuracy: ±0.03 wavelength (better than the design requirement of ±0.05 wavelength).

[0149] Clinically validated results: Myopia progression control rate: 67.4% (compared to traditional monofocal lenses); Wearing comfort score: 8.6 out of 10; Visual quality retention rate: 94.2%; No drug resistance observed during 6-month follow-up;

[0150] The execution data table is shown in Table 1:

[0151] Table 1 Execution Data

[0152]

[0153] Table 2 shows a comparative analysis of traditional periodic patterns:

[0154] Table 2 Comparative Analysis of Traditional Periodic Patterns

[0155]

[0156] like Figure 3 The figure illustrates the iterative convergence process of the IFS fractal algorithm in practical applications. The number of fractal points rapidly increases from an initial 4,523 (5,000 iterations) to 18,947 (20,000 iterations), then steadily rises to 36,782 (40,000 iterations), finally reaching a convergence state of 47,832 fractal points at 50,000 iterations. This convergence curve exhibits typical logarithmic growth characteristics, indicating that the algorithm rapidly generates the main structure in the early stages and refines and perfects the detailed features in the later stages. The final 47,832 fractal points provide sufficient pattern density for myopia control lenses for teenagers.

[0157] 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 generating optical lens patterns based on fractal iteration, characterized in that, Includes the following steps: Obtain the design requirements parameters for myopia lenses; The lens design requirements parameters are processed using a quaternary affine transformation matrix construction method, resulting in the IFS iterative function system; including: Configure the affine transformation function, which consists of a transformation matrix and a translation vector. The transformation matrix contains coefficients that control the scaling of the horizontal coordinate, the coupling of the horizontal and vertical coordinates, the coupling of the horizontal and vertical coordinates, and the scaling of the vertical coordinate. The first affine transformation function is set to generate the stem part and produce the central focus area, and the second affine transformation function is used to generate the main leaves to form the defocus area. A third affine transformation function is set to generate the left lobule, and a fourth affine transformation function is set to generate the balanced optical distribution of the right lobule. The probability weight distributions of the first, second, third, and fourth affine transformation functions are optimized according to optical performance requirements and then summed to obtain the cumulative probability distribution. Based on the IFS iterative function system, the initialization requirements are calculated using a precision adaptive configuration method to obtain the set of iterative calculation initialization parameters, including: calculating the fractal point density according to manufacturing precision requirements, and determining the point density requirements based on lens area, coverage, and minimum feature size. The target number of iterations is determined based on point density, safety factor, and calculations from optical diffraction theory. Configure a high-precision random number generator, using the Mersenne Twister algorithm, with the hash value of the lens serial number and timestamp as the seed; Establish an optical data structure, including a fractal point coordinate array, an optical path difference distribution matrix that determines the resolution based on the minimum feature size, a defocus distribution array, and optical quality evaluation parameters; Set convergence thresholds, including the minimum number of points for point density convergence, the standard deviation threshold for optical uniformity convergence, and the area requirement for coverage convergence. Based on the initial parameter set calculated iteratively, a Monte Carlo random selection method is used to perform fractal iterative calculations to generate a set of fractal points, including: The iteration start point is initialized to the coordinates of the lens center; a high-precision random number generator is called to generate uniformly distributed random numbers. The transformation function is selected based on the cumulative probability distribution, and the corresponding transformation function is determined by comparing the random number with the cumulative probability value. Perform affine transformations to calculate new iteration points and monitor convergence conditions in real time; Store the valid fractal points that satisfy the lens boundary conditions, and record the iteration number and the number of the transformation function to which each point belongs; Based on the generated set of fractal points, the fractal points are processed using the optical path difference distribution calculation method to obtain optical path difference distribution data; Based on the optical path difference distribution data, the defocus amount distribution calculation method is used to process the conversion from optical path difference to defocus amount, and the defocus amount distribution data is obtained. Based on the defocus distribution data and convergence threshold, a multiple convergence condition judgment method is used for iterative convergence judgment to obtain the iterative control decision results and the complete optical fractal point set; including: Multiple convergence criteria are used, including convergence criteria based on the number of iterations, optical coverage, and defocus effect uniformity. Execute convergence judgment logic. When all conditions are met, output convergence completed status. When only the iteration count condition is met, output forced termination status. When the condition is not met, output continue iteration status. Generate corresponding output data based on the convergence status. When convergence is complete, organize the complete fractal point set. When forced termination occurs, output the currently available fractal point set and record warning information. Calculate optical performance evaluation metrics, including coverage efficiency and defocus effect uniformity; Based on the complete optical fractal point set, the coordinates of the fractal point set are processed by the coordinate normalization mapping method and the optical path difference distribution matrix is ​​constructed to obtain complete optical pattern data for the manufacture of myopia control lenses.

2. The method for generating optical lens patterns based on fractal iteration according to claim 1, characterized in that, The steps for processing fractal points using the optical path difference distribution calculation method include: Initialize the optical path difference distribution matrix; for each point in the fractal point set, calculate its optical path difference value; Map the fractal points to the grid indices and assign the optical path difference to the corresponding matrix elements; The optical performance of the optical path difference distribution matrix is ​​verified, including checking the optical path difference range, coverage, and numerical stability.

3. The method for generating optical lens patterns based on fractal iteration according to claim 1, characterized in that, The steps for processing the conversion from optical path difference to defocus amount using the defocus amount distribution calculation method include: For each grid point in the optical path difference distribution matrix, calculate the defocus value for each grid point; Construct the defocus distribution matrix and calculate the statistical properties of the defocus distribution; Perform optical performance verification of defocus distribution; output complete defocus distribution data, including defocus distribution matrix, grid point defocus value array, effective defocus area, and standard deviation of defocus distribution.

4. The method for generating optical lens patterns based on fractal iteration according to claim 1, characterized in that, The steps for processing fractal point set coordinates using the coordinate normalization mapping method include: The fractal point set is normalized, and the physical coordinates are calculated based on the normalized coordinates, lens diameter, and pattern scale adjustment coefficient. Construct a high-resolution optical path difference distribution matrix and calculate the optical path difference for each point in the grid. Perform optical performance verification, including coverage check, defocus effect uniformity check, and pattern integrity check; Output complete optical lens pattern data, including the final optical path difference distribution matrix, physical coordinate point set, actual coverage, and optical quality indicators.

5. The method for generating optical lens patterns based on fractal iteration according to claim 1, characterized in that, The complete optical pattern data includes: The optical path difference distribution matrix is ​​used to define the optical path difference value at each point on the lens surface; The physical coordinate point set contains the position of each fractal point in the lens's physical coordinate system and the corresponding defocus value; Actual coverage rate indicates the effective coverage of the fractal pattern on the lens surface; Optical quality indicators are used to evaluate the optical performance and myopia control effectiveness of lenses.

6. A fractal iteration-based optical lens pattern generation system, used to perform the steps in the fractal iteration-based optical lens pattern generation method as described in any one of claims 1-5, characterized in that, include: The quaternary affine transformation matrix construction module obtains the design requirement parameters for myopia lenses; the quaternary affine transformation matrix construction method is used to process the lens design requirement parameters to obtain the IFS iterative function system; The precision adaptive configuration module, based on the IFS iterative function system, uses the precision adaptive configuration method to calculate the initialization requirements and obtain the set of iterative calculation initialization parameters. The Monte Carlo fractal iteration module initializes the parameter set based on iterative calculations and performs fractal iterative calculations using the Monte Carlo random selection method to generate a set of fractal points. The optical path difference distribution calculation module processes the fractal points based on the generated set of fractal points using the optical path difference distribution calculation method to obtain optical path difference distribution data. The defocus amount distribution calculation module, based on the optical path difference distribution data, uses the defocus amount distribution calculation method to process the conversion from optical path difference to defocus amount, and obtains the defocus amount distribution data; The convergence judgment module, based on the defocus distribution data and the convergence judgment threshold, uses a multi-convergence condition judgment method to perform iterative convergence judgment, and obtains the iterative control decision results and the complete optical fractal point set. The coordinate normalization mapping module, based on a complete set of optical fractal points, uses a coordinate normalization mapping method to process the coordinates of the fractal point set and construct an optical path difference distribution matrix to obtain complete optical pattern data for the manufacture of myopia control lenses.

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