A method and system for optimizing parameters of multilayer coating on optical lenses

Abstract

This invention relates to a method and system for optimizing parameters of multilayer coatings for optical lenses, belonging to the field of digital data distribution optimization processing for optical thin film processes. It includes: a data initialization step to obtain target spectral indices and material physical constants; constructing a multi-objective evaluation function composed of spectral performance and manufacturing tolerance terms, wherein the manufacturing tolerance term is obtained by weighted summation of the partial derivatives of spectral performance with respect to the thickness of each film layer using the transfer matrix method as a sensitivity operator; using the spectral performance and manufacturing tolerance terms as optimization objectives, a multi-objective optimization algorithm is used for global search to obtain the Pareto optimal solution set; based on the film thickness monitoring accuracy of the coating equipment, a thickness deviation statistical model is set, and Monte Carlo virtual manufacturing simulation is performed on the candidate schemes of the Pareto optimal solution set to obtain the predicted yield values ​​of the statistical schemes. This invention achieves a synergistic improvement in theoretical optical performance and actual manufacturing stability, effectively improving the mass production yield and process consistency of optical lens coatings.

Description

Technical Field

[0001] This invention belongs to the field of digital data distribution optimization processing in optical thin film lens technology, and specifically relates to a method and system for optimizing parameters of multilayer coating of optical lenses. Background Technology

[0002] Precision optical thin film technology is a key support for fields such as semiconductor processing, laser medicine, and high-end imaging. The design precision and manufacturing quality of multilayer film systems directly determine the performance of optical components. As application scenarios continue to demand higher optical performance, parameter optimization for multilayer interference film systems has become a research focus in the field of optical manufacturing.

[0003] Optimization of parameters for multilayer coatings on optical lenses aims to iteratively optimize the thickness distribution of the coating layer through mathematical models, so that the spectral response of the coating system approximates the target function. This is a key step in realizing high-performance filters, antireflective coatings, and mirrors.

[0004] However, existing coating parameter design schemes still have the following shortcomings: First, the optimization objectives are relatively singular, mostly using the minimization of spectral deviation as the evaluation criterion. The designed film systems have theoretically superior performance, but are highly sensitive to process errors in the actual coating process. Second, the modeling of manufacturing environment disturbance factors is insufficient. The random influence of evaporation source rate fluctuations and changes in coating uniformity in the vacuum chamber on film thickness is difficult to quantify effectively in the design stage, and the optimization solution is prone to falling into the sharp extremum region of the parameter space. Third, there is a lack of systematic analysis of the sensitivity of each film layer, making it difficult to achieve an effective balance between theoretical performance and engineering tolerance.

[0005] The aforementioned problems, to some extent, restrict the yield and process consistency of high-precision optical lenses during mass production, and are technical issues that urgently need attention in the field of precision optical manufacturing. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for optimizing the parameters of multilayer coatings for optical lenses, which can effectively solve the problems mentioned in the background art. Addressing the technical difficulties in the physical vapor deposition manufacturing process of precision optical components, such as spectral curve drift caused by deviations in the actual film thickness due to process disturbances, low mass production yield, and the lack of robust evaluation mechanisms in existing design methods, this invention constructs a multi-objective evaluation function that includes manufacturing tolerance terms, and combines it with Monte Carlo virtual manufacturing simulation for in-depth optimization and screening, achieving a synergistic improvement in both theoretical optical performance and actual manufacturing stability.

[0007] To achieve the above objectives, this invention proposes a method for optimizing the parameters of multilayer coatings on optical lenses, comprising the following steps: The data initialization step involves obtaining the target spectral parameters and the material physical constants of the coating layer to be coated. The steps for constructing the multi-objective evaluation function are as follows: A multi-objective evaluation function composed of a spectral performance term and a manufacturing tolerance term is constructed. The manufacturing tolerance term is constructed as follows: Based on the transfer matrix method in thin-film interferometry, a characteristic matrix model of the film system is established. The partial derivatives of the spectral performance index with respect to the physical thickness of each film layer are used as sensitivity operators, and the sensitivity operators of each film layer are weighted and summed to construct the manufacturing tolerance term. The spectral performance index is the root mean square of the deviation between the reflectance or transmittance at all sampling wavelength points within the preset working band and the target value. The Pareto optimal solution set search steps take spectral performance and manufacturing tolerance as optimization objectives, and use a multi-objective optimization algorithm to perform a global search to obtain a Pareto optimal solution set consisting of multiple candidate solutions; The virtual manufacturing simulation steps involve setting a statistical distribution model for thickness deviation based on the film thickness monitoring accuracy of the coating equipment, performing Monte Carlo virtual manufacturing simulation on each candidate scheme in the Pareto optimal solution set to generate a virtual production sample of each candidate scheme under thickness perturbation, and statistically analyzing the yield prediction value of each candidate scheme. The robustness screening step uses the yield prediction value as the primary screening criterion to select the final coating parameter combination from the Pareto optimal solution set.

[0008] Furthermore, in the multi-objective evaluation function construction step, the construction of the manufacturing tolerance term further includes: Based on the transfer matrix method, the partial derivatives of the characteristic matrices of each film layer in the characteristic matrix model of the film system with respect to its phase thickness are calculated. Combined with the derivative relationship between the phase thickness and the physical thickness, the partial derivatives of the spectral performance index with respect to the physical thickness of each film layer are calculated using the differential rule of matrix multiplication, and used as the sensitivity operator of the film layer.

[0009] Furthermore, the Pareto optimal solution set search steps specifically include: The population initialization sub-step randomly generates an initial thickness value for each film layer within a preset thickness variation range to form an initial population. The multi-objective value calculation sub-step concurrently calculates the spectral performance term value and manufacturing tolerance term value for each individual in the population; The non-dominated sorting sub-step performs a population stratification operation based on the spectral performance term value and manufacturing tolerance term value of each individual, dividing the population into multiple non-dominated levels, and using the set of individuals in the first non-dominated level as the Pareto front of the current population. The adaptive evolution sub-step calculates the average Euclidean distance of all individuals in the current population's Pareto front in the target space, and dynamically adjusts the variable asynchrony length to generate the next generation population based on the comparison between the average Euclidean distance and the preset aggregation threshold; the target space consists of the coordinate axes of the spectral performance term and the manufacturing tolerance term. The iteration termination sub-step outputs all individuals in the first non-dominated level of the final population as the Pareto optimal solution set when the iteration termination condition is met.

[0010] Furthermore, in the adaptive evolution sub-step, the dynamic adjustment of the variable asynchronous length specifically involves: When the average Euclidean distance is less than the clustering threshold, the variable asynchronous length is adjusted to twice the initial variable asynchronous length; when the average Euclidean distance is greater than the clustering threshold, the variable asynchronous length is adjusted to 0.5 times the initial variable asynchronous length.

[0011] Furthermore, the virtual manufacturing simulation steps specifically include: The statistical distribution setting sub-step sets the actual thickness deviation of each film layer to a normal distribution with a mean of zero, based on the monitoring accuracy of the quartz crystal oscillator film thickness monitor in the coating equipment. The virtual sample generation sub-step, for each candidate scheme, independently generates a random deviation amount that conforms to a normal distribution for each membrane layer, and superimposes the deviation amount onto the design thickness of the membrane layer to form a preset number of virtual production samples; The qualification determination sub-step calculates the spectral response of each virtual production sample and compares the calculated spectral curve with the preset industrial qualification threshold to determine whether the sample is qualified. The yield statistics sub-step counts the number of qualified virtual production samples in each candidate solution and divides it by the total number of virtual production samples generated by that solution to obtain the predicted yield value of that candidate solution.

[0012] Furthermore, in the statistical distribution setting sub-step, when there is no historical production data, 1% of the theoretical design thickness is used as the default setting value for the standard deviation of the normal distribution.

[0013] Furthermore, the robustness screening steps specifically include: The hard threshold elimination sub-step sets a hard minimum threshold for spectral performance and eliminates candidate solutions whose theoretical spectral performance values ​​in the Pareto optimal solution set are greater than the hard minimum threshold. In the yield-priority screening sub-step, the scheme with the highest predicted yield value is selected as the candidate output from the remaining candidate schemes. When there are multiple schemes whose highest yield and second highest yield are less than the preset yield tolerance threshold, the yields of these schemes are determined to be in the same tier. The stability screening sub-step selects the candidate scheme with the smallest comprehensive stability index from the candidate schemes with the same yield rate as the candidate output. The comprehensive stability index is the arithmetic mean of the standard deviation of spectral performance at all sampling wavelength points. The worst-case performance screening sub-step selects the scheme with the smallest worst-case performance index from the candidate schemes with the same overall stability index as the final coating parameter combination. The worst-case performance index is the maximum absolute value of the deviation between the mean spectral performance at all sampling wavelength points and the target spectral value.

[0014] Furthermore, the robustness screening step also includes: in the virtual manufacturing simulation step, for each candidate scheme, based on the spectral curves of all virtual production samples, calculating the statistical mean and standard deviation of the spectral performance index at each sampling wavelength point to generate a comprehensive stability index and a worst-case performance index.

[0015] Furthermore, the data initialization step, obtaining the material physical constants of the layer to be coated, further includes: The refractive index dispersion curves of high-refractive-index material titanium dioxide and low-refractive-index material silicon dioxide were obtained, and the refractive index dispersion curves were mathematically expressed using the Cauchy dispersion formula; and the refractive index data of the substrate material and the surface roughness statistical characteristics were obtained.

[0016] An optical lens multilayer coating parameter optimization system, used to implement the above method, includes: The data acquisition module is used to obtain the target spectral indicators, the material physical constants of the coating layer, and the process fluctuation parameters of the production line; The evaluation function construction module, connected to the data acquisition module, is used to construct a multi-objective evaluation function composed of spectral performance terms and manufacturing tolerance terms. The evaluation function construction module includes an optical analysis engine, which is used to establish a film system characteristic matrix model based on the transfer matrix method, and to generate a sensitivity operator by calculating the partial derivatives of the spectral performance index with respect to the physical thickness of each film layer, thereby constructing the manufacturing tolerance term. The multi-objective optimization module is used to perform a global search using a multi-objective optimization algorithm with spectral performance and manufacturing tolerance as optimization objectives to obtain the Pareto optimal solution set. The virtual manufacturing simulation module is used to set a statistical distribution model of thickness deviation based on the hardware accuracy of the coating equipment, and to perform Monte Carlo sampling simulation on each candidate solution in the Pareto optimal solution set to generate a yield prediction value for each candidate solution. The robustness screening module, connected to the process fluctuation simulation module, is used to select the final coating parameter combination from the Pareto optimal solution set, with the yield prediction value as the primary screening criterion.

[0017] Technical Effects: In summary, this invention fundamentally solves the problem of the disconnect between theory and practice in optical coating parameter design through multi-dimensional technological innovation. By using sensitivity analysis-guided parameter optimization, virtual manufacturing verification combined with statistical laws, and robust screening based on maximizing yield, this invention not only achieves precise control of spectral performance but also makes significant technological progress in ensuring manufacturing yield, reducing production costs, and improving product consistency, providing a complete technical solution for the high-efficiency and high-reliability production of precision optical components. Attached Figure Description

[0018] Figure 1 This is an overall schematic diagram of the method for optimizing the parameters of multilayer coating on optical lenses; Figure 2 This is a schematic diagram of the construction of a multi-objective evaluation function that takes into account both spectral performance and manufacturing tolerance. Figure 3 It is a logic diagram for searching the Pareto optimal solution set using a multi-objective optimization algorithm; Figure 4 This is a logic diagram of Monte Carlo virtual manufacturing simulation and robustness assessment screening; Figure 5 This is a schematic diagram of the multi-level interaction relationships and data flow in an optical lens multi-coating parameter optimization system. Detailed Implementation

[0019] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following description is provided in conjunction with the appendix. Figure 1-5 The following is a detailed description of the specific implementation methods, structures, features, and effects of the present invention, as well as preferred embodiments.

[0020] First, this embodiment describes in detail a method for optimizing parameters of multilayer coatings for optical lenses. This method addresses the problem of spectral curve drift caused by random disturbances in the process environment during physical vapor deposition (PVD) manufacturing of precision optical components. It proposes a deep optimization path that balances theoretical performance and manufacturing tolerance, and is implemented according to the following steps.

[0021] The first step is S1, the data initialization stage. The system first performs a data initialization operation to obtain the target spectral index and the material physical constants of the coating layer, providing basic data support for subsequent optical modeling and optimization.

[0022] Step S101: Obtain the target spectral index, which includes the target transmittance or target reflectance value at each sampling wavelength point within a preset working band. The working band is set according to the actual application scenario of the optical lens, for example, it is set to 380 nm to 780 nm in a visible light imaging system, and the sampling wavelength interval is set to 5 nm or 10 nm.

[0023] The target spectral parameters further include an incident angle distribution parameter, which defines the range of angles at which light is incident on the lens surface, including single normal incidence or a continuous angular range from 0 to 30 degrees. A polarization state parameter distinguishes the target responses of s-polarized and p-polarized light, while a phase delay parameter defines the target value of the phase difference between two orthogonally polarized components in the transmitted or reflected light.

[0024] The above-mentioned refined parameters are all input into the system in the form of numerical lists or function expressions, serving as the calculation benchmark for spectral performance terms in subsequent optimization processes.

[0025] Step S102: Obtain the physical constants of the film material. In this embodiment, the film to be coated is composed of alternating high-refractive-index titanium dioxide and low-refractive-index silicon dioxide. The physical constants of the material are obtained by pre-determining using an elliptic polarization spectrometer in the visible light region from 380 nm to 780 nm, resulting in a refractive index dispersion curve.

[0026] The refractive index dispersion curve is mathematically expressed in the form of the Cauchy dispersion formula, as follows: ; in, Indicates the material at wavelength The refractive index at that point, λ is the wavelength of light in a vacuum, measured in nanometers. , , These are the material characteristic coefficients obtained by fitting data measured using an elliptic polarization spectrometer. For titanium dioxide, these coefficients... , , The coefficients are set to 2.32, -0.012, and 0.0003 respectively; for silicon dioxide materials, the coefficients are set to 1.46, -0.003, and 0.0001 respectively.

[0027] Simultaneously, it is also necessary to obtain the non-zero absorption characteristics of the extinction coefficient in the short-wavelength band. It is expressed in a similar formula to describe the absorption loss of materials in the short-wavelength band of 380 nm to 450 nm, ensuring that subsequent simulation models can accurately account for the real physical losses.

[0028] The refractive index data of the substrate material and the surface roughness statistics were also collected as input variables. The roughness statistics were represented by the root mean square roughness value and were used to correct the interface scattering loss in the film system feature matrix.

[0029] Thus far, step S1 has completed the initialization of three key data categories: target spectral indicators, film material properties, and substrate physical parameters, constructing an initial physical model that conforms to actual working conditions, providing complete and accurate input conditions for the subsequent establishment of multi-objective evaluation functions.

[0030] For step S2, the system performs a multi-objective evaluation function construction operation, which is composed of a spectral performance term and a manufacturing tolerance term, and is used to simultaneously evaluate theoretical optical accuracy and process manufacturing stability in subsequent optimization.

[0031] Step S201: The system establishes a characteristic matrix model of the film system based on the transfer matrix method in thin-film interference theory. For a film system composed of multiple layers, the system constructs a characteristic matrix for each layer. The standard form of this characteristic matrix is: ; in The phase thickness of film j is determined by the physical thickness of the film, its refractive index, the angle of refraction of light in the layer, and the current wavelength. For the effective optical admittance of film layer j, The imaginary unit is used. Effective optical admittance. Calculate based on the polarization state of the light wave: For s-polarized light, For p-polarized light, ,in Let j be the refractive index of the film layer. Let be the angle of refraction of light in film j, which is determined by the angle of incidence and the refractive index of the film using Snell's law.

[0032] The system performs layer-by-layer multiplication of the feature matrices of all film layers according to their physical stacking order to obtain the overall feature matrix of the entire film system. During the multiplication process, for adjacent film layer interfaces with interfacial roughness, the system uses the Nevot-Croce factor to correct the interfacial reflection coefficient. The correction formula is as follows: ; in, The reflection coefficient of an ideal smooth interface. This is the corrected reflection coefficient. The root mean square roughness is... The refractive index of the incident side film is... The angle of refraction of light in the incident side film layer. Let λ be the wavelength of light in a vacuum. Based on this correction factor, the system adjusts the effective admittance parameter in the characteristic matrix accordingly to account for the influence of the rough interface on the light field distribution.

[0033] Based on the corrected total characteristic matrix, and combining the optical admittance of the substrate material and the optical admittance of the incident medium, the system can calculate the reflectivity and transmittance of the film system at different wavelengths, thereby establishing an accurate mapping relationship between the film thickness parameter and the total spectral response.

[0034] In step S202, the system introduces the calculation logic of a sensitivity operator to quantify the thickness fluctuation risk during the manufacturing process. The system uses the root mean square of the deviation between the reflectance or transmittance at all sampling wavelength points within the preset working band and the target value as the spectral performance index. The calculation formula is: ; in This represents the total number of sampling wavelength points within the preset working band. For the k-th sampling wavelength, For the system at wavelength The actual reflectance or transmittance calculated at that point Let be the target reflectance or transmittance at the corresponding wavelength. For any film layer in the film system, its sensitivity operator is defined as the partial derivative of the spectral performance index with respect to the physical thickness of the film layer, i.e. ,in Let j be the physical thickness of the film layer.

[0035] The partial derivative is solved using the chain rule of the transfer matrix method. Let the overall characteristic matrix of the entire membrane system be: ,in This represents the total number of membrane layers. For the first The characteristic matrix of the film layer. For the first... Physical thickness of the film The partial derivative of the total characteristic matrix with respect to the thickness is calculated using the following expansion: ; in, Further decomposed using the chain rule: , For the first Phase thickness of the film, , The phase thickness is obtained from the analytical partial derivative of the characteristic matrix with respect to it, i.e.: The system calculates the partial derivatives of the total characteristic matrix with respect to the physical thickness of each film layer based on the above expansion formula. Then, combining the optical admittance of the substrate and the optical admittance of the incident medium, it solves the partial derivative relationship of the spectral performance index (reflectivity or transmittance) with respect to the total characteristic matrix through the optical admittance method or matrix method, and finally obtains the partial derivatives of the spectral performance index with respect to the physical thickness of each film layer. ; The partial derivative is the sensitivity operator of the film. The larger the value, the more sensitive the film is to process errors. That is, even a small thickness deviation can cause a significant deterioration in spectral performance.

[0036] Step S203: The system constructs a multi-objective evaluation function. The system defines the weighted deviation between the spectral response obtained in step S201 and the preset target spectral index as the spectral performance term. The calculation formula is as follows: ; in The weighting coefficient for the k-th sampling wavelength point is preset by the user based on spectral sensitivity, assigning greater weight to key bands or sensitive wavelength points.

[0037] The system performs a weighted summation of the sensitivity operators of each film layer calculated in step S202, which is defined as the manufacturing tolerance term. The calculation formula is as follows: ; in This represents the total number of membrane layers. Let j be the sensitivity operator for film layer. is the tolerance weighting coefficient for film layer j. This coefficient is preset based on the thickness control accuracy of each film layer during the physical vapor deposition process. The lower the thickness control accuracy of the film layer, the larger its weighting coefficient.

[0038] The system weights and combines the spectral performance term and the manufacturing tolerance term using a balancing coefficient to form a multi-objective evaluation function. The calculation formula is as follows: ; in This is a balance coefficient, set by the user based on actual process stability requirements. Its value ranges from a real number greater than 0. A larger value indicates that the optimization process focuses more on improving manufacturing stability. The technical logic of this function is that the subsequent optimization process not only seeks the combination of film parameters that minimizes spectral deviation, but also seeks the parameter region that minimizes the sum of the sensitivities of each film layer, that is, to find a smooth solution space that combines theoretical accuracy and process tolerance.

[0039] In summary, through step S2, the system completes the construction of a multi-objective evaluation function that combines spectral performance constraints with manufacturing tolerance constraints. This function expands the traditional single spectral deviation optimization objective into a comprehensive evaluation system with "performance-stability" dual dimensions, providing a unified quantitative basis for subsequent multi-objective optimization and ensuring that the optimization process can guide the membrane parameters towards convergence towards theoretically superior performance and strong process robustness.

[0040] The next step, S3, involves the system performing a Pareto optimal solution set search to find a set of candidate solutions in the membrane parameter space that balances spectral performance and manufacturing stability. This step is based on the multi-objective evaluation function constructed in step S2 and employs a multi-objective optimization algorithm for global search.

[0041] Step S301: The system initializes the membrane system parameter space and generates an initial population. The system sets the encoding length of each individual according to the total number of layers in the membrane system to be optimized, and each individual corresponds to a complete sequence of membrane layer thicknesses.

[0042] The system randomly generates an initial thickness value for each film layer within a preset thickness variation range. The thickness variation range is set according to the design law of quarter-wavelength optical thickness in thin film optics theory. The center wavelength is taken as the median wavelength of the working band of the film system. When the working band of visible light is 380 nm to 780 nm, the center wavelength is taken as 580 nm. Then the physical thickness range corresponding to the quarter-wavelength optical thickness is 10 nm to 300 nm. The upper and lower limits of this range are determined according to the difference in refractive index between high refractive index materials and low refractive index materials.

[0043] The population size is set according to the complexity of the membrane system, generally 5 to 10 times the number of membrane layers, to ensure that the initial population has sufficient diversity.

[0044] In step S302, the system concurrently calculates the multi-objective values ​​for each individual in the population. The system uses the spectral performance term and manufacturing tolerance term constructed in step S203 as two optimization objectives. For each individual, the system calls the optical calculation model in step S201 to obtain its spectral response, and calculates the values ​​of the spectral performance term and manufacturing tolerance term for that individual using the formula in step S203.

[0045] The system adopts a parallel computing architecture, which distributes individuals in the population to multiple computing cores to perform the above calculations simultaneously, thereby shortening the optimization cycle.

[0046] In step S303, the system performs a population stratification operation based on non-dominated ranking. The system uses the two target values ​​calculated in step S302 as the evaluation criteria for each individual. For any two individuals in the population, if individual A is not inferior to individual B in either of the two target dimensions, and is superior to individual B in at least one target dimension, then individual A is determined to dominate individual B.

[0047] The system divides the population into multiple non-dominated levels based on this dominance relationship. The first level is the set of individuals that are not dominated by any other individuals, which constitutes the Pareto front of the current population. The second level is the set of individuals that are dominated only by individuals in the first level, and so on.

[0048] In step S304, the system introduces an adaptive mutation operator for iterative evolution. In each generation, the system dynamically adjusts the mutation length based on the current population density in the target space. Specifically, the system calculates the average Euclidean distance of all individuals in the Pareto front in the target space, which consists of the coordinate axes of the spectral performance term and the manufacturing tolerance term. The formula for calculating the average Euclidean distance is: ; in The number of individuals in the Pareto front. and These are the values ​​for the spectral performance term and the manufacturing tolerance term for the i-th individual, respectively.

[0049] System preset aggregation threshold This threshold is set to one-tenth of the average Euclidean distance of all individuals in the initial population in the target space. When the calculated... Less than When this indicates that the population is tending to cluster, the system will adjust the variable asynchronous length to twice the initial variable asynchronous length to expand the search range; when Greater than At this time, the system will adjust the variable asynchronous length to 0.5 times the initial variable asynchronous length to perform local fine-grained search.

[0050] The system simultaneously employs a tournament selection strategy to select parent individuals from the current population, generates offspring individuals through simulated binary crossover operations, and then combines the aforementioned adaptive mutation operations to generate new candidate solutions, forming the next generation population.

[0051] Step S305: The system determines the iteration termination condition and outputs the Pareto optimal solution set. The system sets two termination conditions: first, the number of generations reaches the user-preset maximum number of generations, which is set according to the complexity of the membrane system, generally between 100 and 500 generations; second, the average generational displacement of the Pareto front over 10 consecutive generations is less than a preset tolerance threshold. The average generational displacement is calculated by averaging the minimum Euclidean distances in the target space between all individuals in the current generation's Pareto front and all individuals in the previous generation's Pareto front, i.e.: ; in Let be the number of individuals in the Pareto front of generation t. Let be the number of individuals in the Pareto front of generation t-1. and denoted as , respectively, the values ​​of the spectral performance term and the manufacturing tolerance term for the i-th individual in the t-th generation.

[0052] Preset tolerance threshold The value is set to one percent of the range of values ​​for the spectral performance term and the manufacturing tolerance term in the target space. The system terminates the iteration when either of the above two conditions is met. The system outputs all individuals in the first non-dominated level of the final population as the Pareto optimal solution set. Each solution in this set achieves the optimal trade-off between spectral performance and manufacturing stability, i.e., no other solution is better than both objectives simultaneously.

[0053] In summary, through step S3, the system completes a multi-objective optimization search of the membrane parameter space. This process retains multiple candidate solutions with different trade-offs through a non-dominated sorting mechanism, avoiding the shortcomings of traditional single-objective optimization that easily gets trapped in extremely sensitive parameter regions. At the same time, the adaptive mutation operator balances the ability of global exploration and local refinement, ensuring that the search process can converge to a parameter region that combines theoretical accuracy and manufacturing tolerance, providing diverse candidate inputs for subsequent virtual manufacturing simulation and robustness screening.

[0054] In step S4, the system performs Monte Carlo virtual manufacturing simulation on the candidate schemes in the Pareto optimal solution set output in step S3. This simulation is used to simulate the impact of thickness fluctuations on spectral performance in a real physical vapor deposition process environment, thereby evaluating the manufacturing stability and expected yield of each candidate scheme in actual production.

[0055] Step S401: The system sets the statistical distribution model for film thickness deviation. Based on the actual monitoring accuracy of the quartz crystal oscillator film thickness monitor in the coating equipment and the long-term stability data of the electron beam evaporation source, combined with the process fluctuation parameters of the production line, the system determines the statistical distribution type and distribution parameters of the thickness deviation.

[0056] The process fluctuation parameters of the production line include the rate fluctuation coefficient caused by electron beam power fluctuations. Non-uniformity factor caused by planetary gear carrier rotation Among them, the rate fluctuation coefficient Characterizing the instantaneous rate change of the evaporation source during the coating process, the non-uniformity factor. This characterizes the difference in film thickness distribution at different locations on the lens due to workpiece holder rotation. The system converts the above fluctuation parameters into standard deviation contributions for each film thickness deviation, and the formula for synthesizing the total standard deviation is: ; in, This represents the standard deviation corresponding to the monitoring accuracy of the quartz crystal oscillator film thickness monitor. Rate fluctuation coefficient The converted standard deviation of thickness deviation Non-uniformity factor Standard deviation of thickness deviation after conversion.

[0057] Specifically, the system sets the actual thickness deviation of each membrane layer to a normal distribution with a mean of zero. When historical production data exists, the system statistically analyzes the distribution of deviations between the actual measured values ​​and design values ​​of each membrane layer thickness in historical production, and uses the standard deviation of this distribution as the set value.

[0058] When no historical data is available, the system uses 1% of the theoretical design thickness as the default standard deviation. This default value is determined based on the thickness control accuracy corresponding to a process capability index CpK greater than 1.33 for typical electron beam evaporation coating equipment. Users can also directly input the standard deviation percentage, which ranges from 0.5% to 5% of the theoretical design thickness.

[0059] In step S402, the system generates a virtual production sample for each candidate solution in the Pareto optimal solution set. For the membrane thickness sequence included in each candidate solution, the system independently generates a random deviation that conforms to the statistical distribution framework set in step S401 for each membrane layer, and adds the deviation to the design thickness of the membrane layer to form a thickness sequence of a virtual production sample.

[0060] The system repeatedly performs the above random sampling and overlay operations to generate a preset number of virtual production samples for each candidate scheme. The preset number is set according to the confidence level required for Monte Carlo simulation. When the error of the simulation result at a 95% confidence level is required to be no more than 1%, the required number of samples is no less than 10,000. When only preliminary evaluation is required, the number of samples can be set to 1,000.

[0061] In step S403, the system calculates the spectral response of each virtual production sample and determines its qualification. For each virtual production sample generated in step S402, the system calls the optical calculation model established in step S201 and calculates its reflectance or transmittance spectral curve within a preset working wavelength band based on the film thickness sequence of the sample. The system compares the calculated spectral curve with a preset industrial qualification threshold wavelength by wavelength.

[0062] The industrial acceptance threshold is set as follows: Based on the spectral performance item constructed in step S203, the user specifies the allowable relative deviation tolerance or absolute deviation tolerance. When using a relative deviation tolerance, the acceptance boundary is a certain percentage fluctuation above and below the target spectral curve value, which is usually set to 2% to 5%. When using an absolute deviation tolerance, the acceptance boundary is a fixed value added to or subtracted from the target spectral curve value above and below it, which is usually set to 0.5% to 2%.

[0063] For example, for narrowband filters, the industrial acceptable threshold is set as follows: the transmittance reduction at the center wavelength must not exceed 1% of the theoretical value, and the average background noise at the cutoff band must not exceed 0.1%.

[0064] If the spectral curve of a virtual sample falls within the acceptable boundary range at all sampling wavelengths, the sample is deemed acceptable; otherwise, it is deemed unacceptable.

[0065] Step S404: The system calculates the yield prediction index for each candidate solution. For each candidate solution, the system counts the number of virtual production samples that were determined to be qualified in step S403, and divides this number by the total number of virtual production samples generated for that solution to obtain the yield prediction value for that solution. This yield prediction value reflects the expected yield of the solution in actual production in a probabilistic form.

[0066] In step S405, the system calculates the statistical characteristics of the spectral performance of each candidate scheme under thickness perturbation and generates a composite index for robustness evaluation. For each candidate scheme, the system calculates the statistical mean and standard deviation of the spectral performance index at each sampling wavelength point based on the spectral curves of all virtual production samples obtained in step S403.

[0067] At each sampling wavelength point, the system sums the reflectance or transmittance values ​​of all virtual samples at that wavelength point and divides the sum by the total number of samples to obtain the mean spectral performance at that wavelength point. The system further calculates the sum of squares of the deviations of each sample's value at that wavelength point from the mean, divides the sum by the total number of samples, and takes the square root to obtain the standard deviation of the spectral performance at that wavelength point.

[0068] The system calculates the arithmetic mean of the standard deviations at all sampling wavelength points to obtain the comprehensive stability index of the candidate scheme; the maximum absolute value of the deviation between the mean of all sampling wavelength points and the target spectral value is used as the worst-case performance index of the candidate scheme under disturbance. The comprehensive stability index and the worst-case performance index together constitute the basis for evaluating the robustness of the candidate scheme under process fluctuations, and are used for multi-level screening in the subsequent step S5.

[0069] In summary, step S4 above completes the virtual manufacturing simulation and performance evaluation of each candidate scheme in the Pareto optimal solution set. This process establishes a quantitative correlation between theoretical design parameters and mass production process capabilities by introducing a statistical perturbation model based on the accuracy of real equipment; it obtains the predicted yield values ​​of each scheme through large-scale Monte Carlo sampling and spectral compliance judgment; and it quantifies the performance center and dispersion of each scheme under process fluctuations by calculating the statistical mean and standard deviation. The above evaluation results provide a complete quantitative basis for the final scheme selection based on robustness in the subsequent step S5, ensuring that the finally selected coating parameters have both high yield and high stability in the mass production stage.

[0070] Finally, for step S5, the system performs a robust optimal coating parameter screening operation based on the performance distribution index of each candidate scheme obtained in step S4, in order to select the final parameter combination that has both high yield and high stability in the mass production stage from the Pareto optimal solution set.

[0071] In step S501, the system sets a hard minimum threshold for spectral performance to eliminate candidate solutions with insufficient theoretical performance. This threshold is set based on the spectral performance item constructed in step S203. The user determines the maximum allowable spectral deviation value according to the actual application scenario of the optical lens, and the system uses this value as the hard threshold.

[0072] When the user does not actively set the threshold, the system uses the default threshold. The default threshold is determined based on the distribution of the weight coefficients of each sampling wavelength point in the spectral performance item in step S203. Specifically, the system calculates the numerical distribution of all individuals in the initial population on the spectral performance item and uses the median value of the distribution as the default hard threshold.

[0073] When the spectral performance value of a candidate scheme calculated at the theoretical design thickness is greater than the user-preset or system-default hard threshold, the scheme is directly eliminated and will not enter the subsequent screening stage.

[0074] In step S502, the system uses the yield prediction index as the primary screening criterion among the remaining candidate solutions after the screening in step S501. The system compares the yield prediction values ​​of each candidate solution calculated in step S404 and selects the solution with the highest yield prediction value as the candidate output.

[0075] When multiple yield predictions are identical, or the difference between the highest and second-highest yields among multiple solutions is less than a preset yield tolerance threshold, the system determines that these solutions belong to the same yield tier and proceeds to the next screening step. The default value for the yield tolerance threshold is 1%, but users can adjust this threshold according to mass production quality targets, with a range of 0.5% to 3%.

[0076] In step S503, among candidate schemes with yield prediction indicators in the same tier, the system uses the comprehensive stability index as a secondary screening criterion. The system compares the comprehensive stability index of each candidate scheme calculated in step S405. The comprehensive stability index is the arithmetic mean of the standard deviation of spectral performance at all sampling wavelength points. The smaller the value, the lower the sensitivity of the scheme to process fluctuations.

[0077] The system selects the scheme with the smallest overall stability index as the candidate output. When multiple schemes have the same overall stability index, or when the difference between the smallest and second smallest index among multiple schemes is less than 5% of the overall stability index value, the system determines that these schemes are in the same tier of overall stability and proceeds to the next screening step.

[0078] In step S504, among the candidate schemes with similar comprehensive stability indices, the system further uses the worst-case performance index as an auxiliary screening criterion. The system compares the worst-case performance indices of each candidate scheme calculated in step S405. The worst-case performance index is the maximum absolute value of the deviation between the mean spectral performance at all sampling wavelength points and the target spectral value. The smaller this value, the higher the lower limit of the scheme's performance under process fluctuations.

[0079] The system selects the solution with the smallest worst-case performance index as the candidate output. When multiple solutions have the same worst-case performance index, the system randomly selects one of them as the final output to ensure that the selection result is unique.

[0080] In step S505, the system outputs the final selected combination of coating parameters. The system outputs the film thickness sequence corresponding to the candidate schemes determined through the above multi-level screening as the final optimization result, which can be directly used for setting coating parameters in the physical vapor deposition process.

[0081] Meanwhile, the system outputs the predicted yield, comprehensive stability index, and worst-case performance index corresponding to the scheme, which serve as a reference for evaluating mass production process capabilities.

[0082] In summary, through step S5, the system completes the entire process of selecting the robust optimal coating parameters from the Pareto optimal solution set. This selection mechanism first eliminates solutions with unacceptable design specifications based on theoretical performance thresholds. Then, it performs multi-level selection according to a priority order: yield first, stability second, and worst performance third. Clear tolerance criteria are set at each level to ensure the determinism of the selection process and the uniqueness of the results. The final selected parameter combination, while meeting theoretical performance requirements, possesses the highest mass production yield, optimal process stability, and the most reliable performance lower limit.

[0083] At this point, all the core steps of the optical lens multilayer coating parameter optimization method proposed in this invention have been completed, achieving closed-loop optimization from design to mass production adaptation.

[0084] On the other hand, this embodiment focuses on an optical lens multilayer coating parameter optimization system. This system, through highly integrated software modules, achieves a closed-loop process from raw data acquisition to final robust parameter output.

[0085] The first layer of the system is the data acquisition module. This module is equipped with a high-speed data interface for real-time acquisition of target spectral indicators, material physical constants, and process fluctuation parameters of the production line. In actual operation, this module not only receives the spectral curves from the design task, but also, through connection with the coating machine monitoring system, can obtain the measured deviation distribution of film thickness from historical production data, providing a realistic error modeling basis for subsequent simulations.

[0086] The evaluation function construction module, serving as the system's core computing engine, connects to the data acquisition module at its input. This module integrates a sophisticated optical analysis engine. Its operational logic strictly adheres to the principles of energy conservation and boundary condition continuity in wave optics. When processing multilayer dielectric structures, the module treats each film layer as an electromagnetic transmission unit. By analyzing the reflection and refraction behavior of electromagnetic waves at different refractive index interfaces, it constructs and calculates the transmission matrix of the multilayer structure in real time. Notably, this module possesses partial derivative calculation capabilities, automatically identifying film thickness as the independent variable and calculating its derivative with respect to the final transmittance function, thereby generating a sensitivity operator. This process is entirely based on analytical logic, avoiding the computational bias and significant overhead that can arise from traditional numerical difference methods.

[0087] The multi-objective optimization module is responsible for executing search strategies within a vast parameter space. To handle the complex parameter combinations of dozens of layers in precision optical films, this module employs a parallel computing architecture. The system distributes the initial population of individuals to multiple independent computing cores, estimating the evaluation function in parallel. During the optimization process, the module performs non-dominated ranking based on the performance of candidate solutions in the spectral accuracy and sensitivity dimensions. This module also possesses adaptive evolutionary features, automatically adjusting crossover probabilities and mutation intensity based on the distribution density of the Pareto front, thereby significantly shortening the optimization cycle while ensuring the quality of the solutions.

[0088] The process variation simulation module serves as a bridge between design and manufacturing. This module simulates thickness evolution during actual physical vapor deposition (PVD) processes by performing large-scale Monte Carlo sampling simulations. Unlike simple static design, this module supports multi-dimensional perturbation modeling. In addition to basic physical thickness deviations, the module can incorporate temperature gradients within the vacuum chamber, minute refractive index shifts caused by residual gas pressure fluctuations, and non-uniformity scaling factors at different deposition locations into the random sampling. By simulating tens of thousands of virtual deposition processes with complex perturbations, the module generates a spectral performance envelope reflecting real-world production conditions, allowing designers to visually see the performance baseline under worst-case process variations.

[0089] The robustness assessment and screening module is located at the top layer of the system. It performs in-depth analysis of the massive statistical data output by the process fluctuation simulation module. This module first calculates the predicted yield for each scheme, i.e., the probability that the spectral indicators fall within the allowable tolerance band. Subsequently, it analyzes the correlation between performance fluctuations and process deviations, identifying parameter combinations with extremely strong immunity to manufacturing errors. This module also provides a visual interactive interface to dynamically display the distribution of the Pareto front. Operators can observe the trade-off between performance superiority and manufacturing stability of different schemes through the interface and select the final mass production coating parameters accordingly.

[0090] Through this systematic architectural design, the present invention transforms the tolerance analysis that originally relied on experience into precise statistical calculations, which significantly improves the performance consistency of precision optical lenses when facing complex manufacturing environments.

[0091] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects.

[0092] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for optimizing parameters of multilayer coating on optical lenses, characterized in that, Includes the following steps: The data initialization step involves obtaining the target spectral indicators, the material physical constants of the coating layer to be coated, and the process fluctuation parameters of the production line. The multi-objective evaluation function is constructed by combining a spectral performance term and a manufacturing tolerance term. The manufacturing tolerance term is constructed as follows: a characteristic matrix model of the film system is established based on the transfer matrix method in thin-film interference theory using optical analytical logic. The partial derivatives of the spectral performance index with respect to the physical thickness of each film layer are used as sensitivity operators, and the sensitivity operators of each film layer are weighted and summed to construct the manufacturing tolerance term. The spectral performance index is the root mean square of the deviation between the reflectance or transmittance at all sampling wavelength points within the preset working band and the target value. The multi-objective optimization search step takes the spectral performance term and the manufacturing tolerance term as optimization objectives, and uses a multi-objective optimization algorithm to perform a global search to obtain a Pareto optimal solution set composed of multiple candidate solutions; The virtual manufacturing simulation steps involve setting a statistical distribution model for thickness deviation based on the film thickness monitoring accuracy of the coating equipment and the process fluctuation parameters of the production line. Monte Carlo virtual manufacturing simulation is then performed on each candidate scheme in the Pareto optimal solution set to generate a virtual production sample of each candidate scheme under thickness perturbation, and the yield prediction value of each candidate scheme is statistically calculated. The robustness screening step uses the yield prediction value as the primary screening criterion to select the final coating parameter combination from the Pareto optimal solution set.

2. The method for optimizing the parameters of multilayer coating on optical lenses according to claim 1, characterized in that, In the process of constructing a multi-objective evaluation function, the construction of the manufacturing tolerance term further includes: Based on the transfer matrix method, the partial derivatives of the characteristic matrices of each film layer in the characteristic matrix model of the film system with respect to its phase thickness are calculated. Combined with the derivative relationship between the phase thickness and the physical thickness, the partial derivatives of the spectral performance index with respect to the physical thickness of each film layer are calculated using the differential rule of matrix multiplication, and used as the sensitivity operator of the film layer.

3. The method for optimizing the parameters of multilayer coating on optical lenses according to claim 1, characterized in that, The specific steps for searching the Pareto optimal solution set include: The population initialization sub-step randomly generates an initial thickness value for each film layer within a preset thickness variation range to form an initial population. The multi-objective value calculation sub-step concurrently calculates the spectral performance term value and manufacturing tolerance term value for each individual in the population; The non-dominated sorting sub-step performs a population stratification operation based on the spectral performance term value and manufacturing tolerance term value of each individual, dividing the population into multiple non-dominated levels, and using the set of individuals in the first non-dominated level as the Pareto front of the current population. The adaptive evolution sub-step calculates the average Euclidean distance of all individuals in the current population's Pareto front in the target space, and dynamically adjusts the variable asynchrony length to generate the next generation population based on the comparison between the average Euclidean distance and the preset aggregation threshold; the target space consists of the coordinate axes of the spectral performance term and the manufacturing tolerance term. The iteration termination sub-step outputs all individuals in the first non-dominated level of the final population as the Pareto optimal solution set when the iteration termination condition is met.

4. The method for optimizing the parameters of multilayer coating on optical lenses according to claim 3, characterized in that, In the adaptive evolution sub-step, the dynamic adjustment of the variable asynchronous length is specifically as follows: When the average Euclidean distance is less than the clustering threshold, the variable asynchronous length is adjusted to twice the initial variable asynchronous length; when the average Euclidean distance is greater than the clustering threshold, the variable asynchronous length is adjusted to 0.5 times the initial variable asynchronous length.

5. The method for optimizing the parameters of multilayer coating on optical lenses according to claim 1, characterized in that, The specific steps of virtual manufacturing simulation include: The statistical distribution setting sub-step sets the actual thickness deviation of each film layer to a normal distribution with a mean of zero, based on the monitoring accuracy of the quartz crystal oscillator film thickness monitor in the coating equipment. The virtual sample generation sub-step, for each candidate scheme, independently generates a random deviation amount that conforms to a normal distribution for each membrane layer, and superimposes the deviation amount onto the design thickness of the membrane layer to form a preset number of virtual production samples; The qualification determination sub-step calculates the spectral response of each virtual production sample and compares the calculated spectral curve with the preset industrial qualification threshold to determine whether the sample is qualified. The yield statistics sub-step counts the number of qualified virtual production samples in each candidate solution and divides it by the total number of virtual production samples generated by that solution to obtain the predicted yield value of that candidate solution.

6. The method for optimizing the parameters of multilayer coating on optical lenses according to claim 5, characterized in that, In the statistical distribution setting sub-step, when there is no historical production data, 1% of the theoretical design thickness is used as the default setting value for the standard deviation of the normal distribution.

7. The method for optimizing the parameters of multilayer coating on optical lenses according to claim 1, characterized in that, The robustness screening steps specifically include: The hard threshold elimination sub-step sets a hard minimum threshold for spectral performance and eliminates candidate solutions whose theoretical spectral performance values ​​in the Pareto optimal solution set are greater than the hard minimum threshold. In the yield-priority screening sub-step, the scheme with the highest predicted yield value is selected as the candidate output from the remaining candidate schemes. When the difference between the highest yield and the second highest yield is less than the preset yield tolerance threshold, the yield tiers of the two schemes are determined to be in the same tier. The stability screening sub-step selects the candidate scheme with the smallest comprehensive stability index from the candidate schemes with the same yield rate as the candidate output. The comprehensive stability index is the arithmetic mean of the standard deviation of spectral performance at all sampling wavelength points. The worst-case performance screening sub-step selects the scheme with the smallest worst-case performance index from the candidate schemes with the same overall stability index as the final coating parameter combination. The worst-case performance index is the maximum absolute value of the deviation between the mean spectral performance at all sampling wavelength points and the target spectral value.

8. The method for optimizing the parameters of multilayer coating on optical lenses according to claim 7, characterized in that, The robustness screening step also includes: in the virtual manufacturing simulation step, for each candidate scheme, based on the spectral curves of all virtual production samples, calculating the statistical mean and standard deviation of the spectral performance index at each sampling wavelength point to generate a comprehensive stability index and a worst performance index.

9. The method for optimizing the parameters of multilayer coating on optical lenses according to claim 1, characterized in that, In the data initialization step, obtaining the material physical constants of the layer to be coated further includes: The refractive index dispersion curves of high-refractive-index material titanium dioxide and low-refractive-index material silicon dioxide were obtained, and the refractive index dispersion curves were mathematically expressed using the Cauchy dispersion formula; and the refractive index data of the substrate material and the surface roughness statistical characteristics were obtained.

10. A system for optimizing parameters of multilayer coating on optical lenses, used to implement the method described in any one of claims 1-9, characterized in that, include: The data acquisition module is used to obtain the target spectral indicators, the material physical constants of the coating layer, and the process fluctuation parameters of the production line; The evaluation function construction module, connected to the data acquisition module, is used to construct a multi-objective evaluation function composed of spectral performance terms and manufacturing tolerance terms. The evaluation function construction module includes an optical analysis engine, which is used to establish a film system characteristic matrix model based on the transfer matrix method, and to generate a sensitivity operator by calculating the partial derivatives of the spectral performance index with respect to the physical thickness of each film layer, thereby constructing the manufacturing tolerance term. The multi-objective optimization module is used to perform a global search using a multi-objective optimization algorithm with spectral performance and manufacturing tolerance as optimization objectives to obtain the Pareto optimal solution set. The virtual manufacturing simulation module is used to set a statistical distribution model of thickness deviation based on the hardware accuracy of the coating equipment, and to perform Monte Carlo sampling simulation on each candidate solution in the Pareto optimal solution set to generate a yield prediction value for each candidate solution. The robustness screening module, connected to the process fluctuation simulation module, is used to select the final coating parameter combination from the Pareto optimal solution set, with the yield prediction value as the primary screening criterion.

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