An anti-reflection film design method combined with a machine learning algorithm

Abstract

The present application relates to the technical field of optical element design, and particularly relates to an antireflection film design method combined with a machine learning algorithm, comprising the following steps: step 1, determining the material of each film layer and the thickness range of each film layer; step 2, sampling and screening a plurality of training samples to form a training data set; step 3, training a gradient boosting regression model by using the training data set to obtain a target gradient boosting regression model; step 4, obtaining a plurality of grid combinations, sorting all the grid combinations by using the target gradient boosting regression model, judging the grid combinations one by one, and obtaining a sample set comprising a plurality of qualified samples, and selecting the thickness of each film layer of the qualified sample with the smallest reflectivity difference in the sample set as the thickness of each film layer of the broadband antireflection film. The present application is at least beneficial to reducing the difficulty of parameter determination of the antireflection film.

Description

Technical Field

[0001] This invention belongs to the field of optical component design technology, and in particular relates to an antireflection coating design method that incorporates machine learning algorithms. Background Technology

[0002] Broadband antireflective coatings are key components in optical systems and are widely used in infrared optical systems, laser windows, imaging systems, and other fields. Traditional antireflective coating designs mainly rely on empirical formulas and manual optimization, making it difficult to achieve extremely low average reflectivity over a wide wavelength range. In particular, in the infrared band from 1μm to 12μm, due to the complexity of material dispersion and absorption characteristics, traditional design methods often cannot simultaneously meet the requirements of low average reflectivity and high spectral uniformity.

[0003] Currently, the design of antireflective coatings mainly uses the transfer matrix method to calculate optical performance and combines optimization algorithms to find the optimal film thickness. However, traditional optimization methods such as genetic algorithms and particle swarm optimization have problems such as slow convergence speed and easy getting trapped in local optima when dealing with multilayer film structures. In particular, under the strict condition that the average reflectivity is required to be less than 1%, traditional methods often require a lot of computation time and it is difficult to find a solution that meets the constraints.

[0004] With the development of machine learning technology, it has shown great potential in complex optimization problems. Ensemble learning methods such as gradient boosting and regression trees can effectively handle high-dimensional nonlinear problems, but their application in the field of antireflection coating design is still in the exploratory stage. There is a lack of systematic methods that organically combine the transfer matrix method with machine learning algorithms, especially effective solutions for optimization problems under strict reflectivity constraints. Summary of the Invention

[0005] In view of this, the present invention aims to provide an antireflection membrane design method that combines machine learning algorithms, which at least helps to reduce the difficulty of determining the parameters of the antireflection membrane.

[0006] To achieve the above objectives, the technical solution created by this invention is implemented as follows: This invention provides a method for designing antireflective coatings using machine learning algorithms, comprising: Step 1, determining the wavelength range, number of coating layers, total thickness constraint, and average reflectivity constraint, and determining the material of each coating layer and the thickness range of each coating layer based on the number of coating layers; Step 2, sampling and filtering multiple training samples within each coating layer thickness range that satisfy the total thickness constraint and average reflectivity constraint within the wavelength range to form a training dataset, each training sample including the thickness of each coating layer and the corresponding reflectivity difference; Step 3, training a gradient boosting regression model using the training dataset to obtain a target gradient boosting regression model; Step 4, obtaining multiple grid groups based on the coating layer thickness ranges in Step 1. Each grid combination includes the thickness of each film layer. A target gradient boosting regression model is used to predict the difference in predicted reflectance of each grid combination. All grid combinations are sorted from smallest to largest according to the magnitude of the predicted reflectance difference. Starting from the grid combination with the smallest predicted reflectance difference, each grid combination is judged one by one according to the sorting order. It is judged whether the grid combination meets the total thickness limit and average reflectance constraint within the wavelength range. If it meets the limit, it is considered a qualified sample. If it does not meet the limit, it is discarded. The judgment stops when the early termination condition is met, and a sample set including multiple qualified samples is obtained. The film layer thickness of the qualified sample with the smallest reflectance difference in the sample set is selected as the film layer thickness of the broadband antireflection film.

[0007] Furthermore, in step 1, determining the material and thickness range of each film layer based on the number of film layers includes: inputting the number of film layers into the parameter configuration system, and the parameter configuration system outputting the material and thickness range of each film layer. The parameter configuration system includes an optical prior experience mapping table, which includes the material and thickness of each film layer corresponding to different numbers of film layers.

[0008] Furthermore, in step 2, sampling within each film thickness range includes: when the average reflectance constraint is greater than or equal to 1%, training samples are obtained by alternating between normal and uniform distribution sampling within each film thickness range; when the average reflectance constraint is less than 1%, training samples are obtained by concentrated sampling in the low reflectance range of each film thickness range.

[0009] Furthermore, in step 2, selecting multiple training samples that satisfy the total thickness constraint and the average reflectivity constraint within the wavelength range to form the training dataset includes: after each training sample is sampled, determining whether the total thickness of the training sample is within the total thickness constraint; if not, discarding it; if so, retaining it. For training samples that meet the total thickness constraint, selecting four uniformly distributed wavelength points within the wavelength range and calculating the reflectivity of each wavelength point using the transfer matrix method, determining whether the reflectivity of each wavelength point is greater than 1.3 times the average reflectivity constraint; if the reflectivity of any wavelength point is greater than 1.3 times the average reflectivity constraint, discarding it; if the reflectivity of all wavelength points is less than or equal to 1.3 times the average reflectivity constraint, retaining it. For training samples with qualified reflectivity at four wavelength points, selecting N uniformly distributed wavelength points within the wavelength range and calculating the average reflectivity using the transfer matrix method, determining whether the average reflectivity satisfies the average reflectivity constraint; if not, discarding it; if satisfied, retaining it in the training dataset.

[0010] Furthermore, for step 2, when the average reflectance constraint is less than 1%, the target number of samples in the training dataset is 250,000; when the average reflectance constraint is in the range of 1% to 2%, the target number of samples in the training dataset is 180,000; and when the average reflectance constraint is greater than 2%, the target number of samples in the training dataset is 100,000.

[0011] Furthermore, in step 3, the gradient boosting regression model is trained using a training dataset to enable the model to learn the mapping relationship between the thickness of each film layer and the difference in reflectivity.

[0012] Furthermore, in step 3, training the gradient boosting regression model using the training dataset to obtain the target gradient boosting regression model includes: performing 5-fold cross-validation on the gradient boosting regression model using the training dataset to obtain the initial target gradient boosting regression model, and then training the initial target gradient boosting regression model using all training samples in the training dataset to obtain the target gradient boosting regression model.

[0013] Furthermore, the 5-fold cross-validation involves randomly dividing all training samples in the training dataset into 5 subsets. In each round, 4 subsets are selected for model training, and the remaining 1 subset is used for model testing. Different subsets are used for model testing in different rounds until 5 rounds of training are completed to obtain the initial target gradient boosting regression model.

[0014] Furthermore, in step 4, obtaining multiple mesh combinations based on the thickness range of each film layer in step 1 includes: determining the mesh step size according to the width of each film layer thickness range and the average reflectivity constraint in step 1; sampling multiple discrete thicknesses within each film layer thickness range based on the mesh step size; performing a Cartesian product on the multiple discrete thicknesses of each film layer to obtain multiple mesh combinations, which constitute a mesh search space; in step 4, a target gradient boosting regression model is used to predict the predicted reflectivity difference of all mesh combinations in the mesh search space, and then all mesh combinations are sorted from smallest to largest according to the magnitude of the predicted reflectivity difference; in step 4, determining whether the mesh combination meets the total thickness limit and the average reflectivity constraint within the wavelength range includes: determining whether the total thickness of the mesh combination meets the requirement of... For mesh combinations that meet the total thickness constraint, if not, discard; if yes, retain. For mesh combinations that meet the total thickness constraint, select three uniformly distributed wavelength points within the wavelength range and calculate the reflectivity of each wavelength point using the transfer matrix method. Determine if the reflectivity of each wavelength point is greater than 1.3 times the average reflectivity constraint. If the reflectivity of any wavelength point is greater than 1.3 times the average reflectivity constraint, discard; if the reflectivity of all wavelength points is less than or equal to 1.3 times the average reflectivity constraint, retain. For mesh combinations that meet the reflectivity of three wavelength points, select N uniformly distributed wavelength points within the wavelength range and calculate the average reflectivity using the transfer matrix method. Determine if the average reflectivity meets the average reflectivity constraint. If not, discard; if yes, retain as a qualified sample.

[0015] Furthermore, the early termination condition is that the number of qualified samples is greater than 100 and the minimum reflectance difference is less than 0.5%.

[0016] Compared with existing technologies, this invention achieves the following beneficial effects: The antireflection membrane design method combined with machine learning algorithms provided by this invention realizes intelligent optimization design of broadband antireflection membranes through the transfer matrix method and gradient boosting regression algorithm. In the step of generating training datasets, this invention adopts a constraint-aware data generation mechanism, that is, different sampling strategies are used for different reflectivity constraints. For strict reflectivity constraints, biased sampling is used, which significantly improves the generation efficiency of effective samples. In the optimization process, both the total thickness constraint and the average reflectivity constraint are considered. Compared with the traditional design mode that relies on manual or genetic / particle swarm optimization, it has the following advantages: First, relying on the constraint-aware hierarchical sampling mechanism, the conventional and biased sampling modes are switched according to the severity of reflectivity, and invalid samples are filtered out by rapid pre-screening after sampling, which greatly reduces the amount of computation and significantly improves the generation efficiency of training samples under the condition of strict low reflectivity constraints. Second, grid search combined with pre-sorting strategy, with the trained boosting regression model as a surrogate evaluator, prioritizes the selection of high-potential grid combinations. Combined with early termination conditions, it avoids the defects of slow convergence and easy getting trapped in local optima in traditional algorithms, which helps to shorten the optimization time of multilayer membranes. In summary, the antireflection coating design method combined with machine learning algorithms provided by this invention can significantly reduce the threshold for broadband antireflection coating design, and provide support for the development of high-performance film systems for devices such as infrared optical windows and laser components. Attached Figure Description

[0017] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 The flowchart illustrates the antireflection membrane design method incorporating machine learning algorithms as described in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0020] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0021] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0022] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] refer to Figure 1This invention provides a method for designing antireflective coatings using machine learning algorithms, comprising: Step 1, determining the wavelength range, number of coating layers, total thickness constraint, and average reflectivity constraint, and determining the material of each coating layer and the thickness range of each coating layer based on the number of coating layers; Step 2, sampling and filtering multiple training samples within each coating layer thickness range that satisfy the total thickness constraint and average reflectivity constraint within the wavelength range to form a training dataset, each training sample including the thickness of each coating layer and the corresponding reflectivity difference; Step 3, training a gradient boosting regression model using the training dataset to obtain a target gradient boosting regression model; Step 4, obtaining multiple grids based on the coating layer thickness ranges in Step 1. The grid combination, including the thickness of each film layer, is used to predict the difference in predicted reflectance of each grid combination using a target gradient boosting regression model. All grid combinations are sorted from smallest to largest based on the magnitude of the predicted reflectance difference. Starting with the grid combination with the smallest predicted reflectance difference, each grid combination is judged one by one according to the sorting order to determine whether it meets the total thickness limit and average reflectance constraint within the wavelength range. If it meets the constraint, it is considered a qualified sample; otherwise, it is discarded. The judgment stops when the early termination condition is met, and a sample set including multiple qualified samples is obtained. The thickness of each film layer of the qualified sample with the smallest reflectance difference in the sample set is selected as the thickness of each film layer of the broadband antireflection film.

[0024] The machine learning algorithm refers to the gradient boosting regression algorithm.

[0025] Furthermore, in step 1, determining the material of each film layer and the thickness range of each film layer based on the number of film layers includes: inputting the number of film layers into the parameter configuration system, and the parameter configuration system automatically outputting the material of each film layer and the thickness range of each film layer. The parameter configuration system includes an optical prior experience mapping table, which includes the material of each film layer and the thickness range of each film layer corresponding to different numbers of film layers.

[0026] In some embodiments, the wavelength range is from 1 μm to 12 μm, the number of film layers is from 3 to 6, the total thickness is typically less than 4000 nm, and the average reflectivity constraint is typically from 0.5% to 5%.

[0027] The parameter configuration system is configured in the data generator. The core logic of the parameter configuration system is: based on the number of film layers input by the user (e.g., 3 layers), it automatically searches and matches the corresponding material combination and the thickness of each layer from the pre-encoded optical prior experience mapping table, and finally outputs the material and thickness range of each film layer corresponding to the number of film layers. The parameter configuration system belongs to the templated design method commonly used in the field of optical thin film design, also known as rule-based design parameter initialization.

[0028] In the optical prior experience mapping table, the film materials and thickness ranges corresponding to different numbers of film layers are as follows: When the number of film layers is 3, the film materials and corresponding thickness ranges from the air side to the substrate side are as follows: YF3, [400, 2200] nm; ZnS, [10, 100] nm; Ge, [30, 1200] nm; When the number of film layers is 4, the film materials and corresponding thicknesses from the air side to the substrate side are as follows: YF3, [100, 1800] nm; ZnS, [10, 500] nm; Ge, [10, 100] nm; ZnS, [100, 800] nm; When the number of film layers is 5, the film materials and corresponding thicknesses from the air side to the substrate side are as follows: YF3, [100, 2000] nm; ZnS, [10, 900] nm; Ge, [10, 100] nm; ZnS, [10, 900] nm; Ge, [10, 100] nm; When the number of film layers is 6, the film materials and corresponding thicknesses from the air side to the substrate side are as follows: YF3, [100, 2000] nm; ZnS, [10, 700] nm; Ge, [10, 100] nm; ZnS, [10, 700] nm; Ge, [10, 100] nm; ZnS, [10, 700] nm.

[0029] Step 1 of this invention utilizes the difference in refractive index between YF3 (low refractive index), ZnS (medium refractive index), and Ge (high refractive index) in the infrared band to construct a gradient refractive index structure by combining high, low, and medium refractive index materials. In the wide infrared band of 1μm to 12μm, the initialization of parameters for 3 to 6 layers of antireflection film can be completed quickly, eliminating the tedious step of manually selecting materials layer by layer.

[0030] Furthermore, in step 2, sampling within each film thickness range includes: when the average reflectance constraint is greater than or equal to 1%, training samples are obtained by alternating between normal and uniform distribution sampling within each film thickness range to increase sample diversity; when the average reflectance constraint is less than 1%, concentrated sampling is performed in the low reflectance range of each film thickness range to obtain training samples.

[0031] The low reflectivity range refers to the film thickness subspace that is more likely to achieve low reflectivity within each film thickness range, determined through optical prior knowledge and experimental verification. The low reflectivity range is a thickness sub-range pre-specified by the optical prior experience mapping table, rather than being dynamically identified by the algorithm during operation.

[0032] Further, in step 2, selecting multiple training samples that satisfy the total thickness constraint and the average reflectivity constraint within the wavelength range to form the training dataset includes: after each training sample is sampled, determining whether the total thickness of the training sample is within the total thickness constraint; if not, discarding it; if so, retaining it. For training samples that meet the total thickness constraint, four uniformly distributed wavelength points are selected within the wavelength range, and the reflectivity of each wavelength point is calculated using the transfer matrix method. It is determined whether the reflectivity of each wavelength point is greater than 1.3 times the average reflectivity constraint. If the reflectivity of any wavelength point is greater than 1.3 times the average reflectivity constraint, discarding it; if the reflectivity of all wavelength points is less than or equal to 1.3 times the average reflectivity constraint, retaining it. For training samples with qualified reflectivity at four wavelength points, N uniformly distributed wavelength points are selected within the wavelength range, and the average reflectivity is calculated using the transfer matrix method. It is determined whether the average reflectivity satisfies the average reflectivity constraint. If not, discarding it; if satisfied, retaining it in the training dataset, where N is an integer in the range of 100 to 200.

[0033] In some examples, N is 150.

[0034] Furthermore, for step 2, when the average reflectance constraint is less than 1%, the target number of samples in the training dataset is 250,000; when the average reflectance constraint is in the range of 1% to 2%, the target number of samples in the training dataset is 180,000; and when the average reflectance constraint is greater than 2%, the target number of samples in the training dataset is 100,000.

[0035] Step 2 of this invention uses a constraint-aware sampling strategy to generate a training dataset. For low reflectivity constraints (less than 1%), a biased sampling method is used to prioritize sampling within the thickness range that is more likely to meet the low reflectivity requirement, which helps to improve sampling efficiency. For each sample obtained, the total thickness constraint and the calculation of four wavelength points are used to quickly pre-screen the sampled samples, retaining only the samples that meet the total thickness constraint and the reflectivity of the four wavelength points. After the quick pre-screening, the complete N-point calculation is then performed.

[0036] Among them, the four wavelength points can be the starting point of the band, the 1 / 3 quartile, the 2 / 3 quartile, and the ending point of the band.

[0037] Furthermore, in step 3, the gradient boosting regression model is trained using a training dataset to enable the model to learn the mapping relationship between the thickness of each film layer and the difference in reflectivity.

[0038] Furthermore, in step 3, training the gradient boosting regression model using the training dataset to obtain the target gradient boosting regression model includes: determining the hyperparameter search range, which includes the number of iterations in the range of 100 to 5000, the learning rate in the range of 0.01 to 0.3, and the maximum tree depth in the range of 3 to 15; randomly selecting a set of hyperparameters within the hyperparameter search range; using the selected hyperparameters to perform 5-fold cross-validation on the gradient boosting regression model to obtain the initial target gradient boosting regression model; and then using all the training samples in the training dataset to train the initial target gradient boosting regression model to obtain the target gradient boosting regression model.

[0039] Furthermore, the 5-fold cross-validation involves randomly dividing all training samples in the training dataset into 5 subsets. In each round, 4 subsets are selected for model training, and the remaining 1 subset is used for model testing. Different subsets are used for model testing in different rounds until 5 rounds of training are completed to obtain the initial target gradient boosting regression model.

[0040] It should be noted that the mean squared error (MSE) and coefficient of determination (R²) of the five training rounds can be obtained to evaluate the generalization performance and goodness of fit of the gradient boosting regression model. The smaller the MSE, the more accurate the gradient boosting regression model is in predicting the reflectivity difference of unseen samples. The coefficient of determination (R²) is used to measure the model's ability to explain data variation, and the closer the coefficient of determination (R²) is to 1, the better.

[0041] Furthermore, in step 4, obtaining multiple mesh combinations based on the thickness range of each film layer in step 1 includes: determining the mesh step size according to the width of the thickness range of each film layer in step 1 and the average reflectivity constraint; sampling multiple discrete thicknesses within the thickness range of each film layer based on the mesh step size; performing a Cartesian product on the multiple discrete thicknesses of each film layer to obtain multiple mesh combinations; and the multiple mesh combinations constitute the mesh search space.

[0042] In some embodiments, in step 4, the target gradient boosting regression model is used to predict the difference in predicted reflectance of all grid combinations in the grid search space, and then all grid combinations are sorted from smallest to largest according to the magnitude of the difference in predicted reflectance. In other embodiments, after generating the grid search space, since the number of grid combinations in the grid search space is usually very large, directly using the target gradient boosting regression model to predict all grid combinations is time-consuming. Therefore, the following method can be adopted: First, 10,000 grid combinations are randomly selected from the grid search space as sampled combinations. The target gradient boosting regression model is used to predict all sampled combinations to obtain the predicted reflectance difference corresponding to each sampled combination. Then, the 10,000 sampled combinations and their corresponding predicted reflectance differences are input into the k-nearest neighbor algorithm. The k-nearest neighbor algorithm fits the mapping relationship between the thickness vector of the sampled combination and the predicted reflectance difference. Subsequently, the fitted k-nearest neighbor algorithm is used to predict the remaining grid combinations in the grid search space to obtain the predicted reflectance difference corresponding to the remaining grid combinations. Finally, all grid combinations are sorted from smallest to largest according to the magnitude of the predicted reflectance difference. The k-nearest neighbor algorithm is used as an auxiliary interpolation tool in the sorting process to quickly estimate the reflectance difference of unsampled grid combinations to achieve sorting.

[0043] In some embodiments, step 4, determining whether the mesh combination meets the total thickness limit and average reflectivity constraint within the wavelength range includes: determining whether the total thickness of the mesh combination is within the total thickness constraint; if not, discarding it; if yes, retaining it; for mesh combinations that meet the total thickness constraint, selecting three uniformly distributed wavelength points within the wavelength range and calculating the reflectivity of each wavelength point using the transfer matrix method, determining whether the reflectivity of each wavelength point is greater than 1.3 times the average reflectivity constraint; if the reflectivity of any wavelength point is greater than 1.3 times the average reflectivity constraint, discarding it; if the reflectivity of all wavelength points is less than or equal to 1.3 times the average reflectivity constraint, retaining it; for mesh combinations with qualified reflectivity at three wavelength points, selecting N uniformly distributed wavelength points within the wavelength range and calculating the average reflectivity using the transfer matrix method, determining whether the average reflectivity meets the average reflectivity constraint; if not, discarding it; if yes, retaining it as a qualified sample.

[0044] Furthermore, the early termination condition is that the number of qualified samples is greater than 100 and the minimum reflectance difference is less than 0.5%.

[0045] In some embodiments, determining the grid step size based on the width of each film thickness range and the average reflectivity constraint in step 1 includes: determining the number of discrete sampling points within each film thickness range using a layering strategy based on the average reflectivity constraint, and then determining the grid step size, specifically as follows: when the average reflectivity constraint is less than 0.5%, a first preset number of discrete sampling points are set within each film thickness range; when the average reflectivity constraint is greater than or equal to 0.5% and less than 1%, a second preset number of discrete sampling points are set within each film thickness range; when the average reflectivity constraint is greater than or equal to 1%, a third preset number of discrete sampling points are set within each film thickness range, wherein the first preset number is greater than the second preset number, and the second preset number is greater than the third preset number.

[0046] Within each film thickness range, the difference between the upper and lower limits of the thickness range is used as the range width, and the number of discrete sampling points minus one is used as the interval number. The range width is divided by the interval number to obtain the spacing between adjacent discrete sampling points, which is the grid step size.

[0047] In other words, the stricter the average reflectance constraint, the more discrete sampling points there are, the smaller the grid step size, and the higher the grid density; the looser the average reflectance constraint, the fewer discrete sampling points there are, the larger the grid step size, and the lower the grid density.

[0048] In step 4, the grid step size is determined based on the width of each film layer thickness range and the average reflectivity constraint. This allows for dynamic adjustment of the grid density according to the strictness of the average reflectivity constraint; generally, the stricter the average reflectivity constraint, the denser the grid, resulting in a more refined search and more intelligent sorting. Simultaneously, step 4 uses a target gradient boosting regression model to predict reflectivity differences. All grid combinations are then sorted from smallest to largest based on the predicted reflectivity differences. Starting with the grid combination with the smallest predicted reflectivity difference, each grid combination is evaluated sequentially according to its order. Thus, the system does not traverse grid combinations in random order but instead uses the trained target gradient boosting regression model to sort the grid combinations. This prioritizes and calculates more promising regions. Furthermore, the sequential evaluation process follows an early termination condition, which helps to end the search early, saving computational resources and avoiding time-consuming precise optical calculations for each grid combination, thereby significantly improving search efficiency. In summary, step 4 can improve accuracy while maintaining low computational cost.

[0049] In some embodiments, in step four, after selecting the qualified sample with the smallest reflectance difference in the sample set, a complete spectral calculation is performed on the qualified sample with the smallest reflectance difference to generate a reflectance curve and to statistically analyze and archive key performance indicators, including average reflectance, minimum reflectance, maximum reflectance and reflectance difference, so as to realize the verification, analysis and visualization of the optimal solution.

[0050] This invention achieves intelligent optimization design of broadband antireflection coatings by combining the transfer matrix method and gradient boosting regression algorithm, showing significant advantages, especially under strict reflectivity constraints, and providing effective technical support for the development of high-performance optical systems.

[0051] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0052] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for designing antireflective membranes incorporating machine learning algorithms, characterized in that, include: Step 1: Determine the wavelength range, number of film layers, total thickness constraint, and average reflectivity constraint. Determine the material of each film layer and the thickness range of each film layer based on the number of film layers. Step 2: Sample within the thickness range of each film layer, and select multiple training samples that meet the total thickness constraint and average reflectivity constraint within the wavelength range to form a training dataset. Each training sample includes the thickness of each film layer and the corresponding reflectivity difference. Step 3: Train the gradient boosting regression model using the training dataset to obtain the target gradient boosting regression model; Step 4: Based on the thickness range of each film layer in Step 1, obtain multiple grid combinations. Each grid combination includes the thickness of each film layer. Use the target gradient boosting regression model to predict the predicted reflectance difference of each grid combination. Sort all grid combinations according to the magnitude of the predicted reflectance difference from smallest to largest. Starting from the grid combination with the smallest predicted reflectance difference, judge each grid combination one by one according to the sorting order. Determine whether the grid combination meets the total thickness limit and average reflectance constraint within the wavelength range. If it meets the limit, it is a qualified sample. If it does not meet the limit, it is discarded. Stop the judgment when the early termination condition is met and obtain a sample set including multiple qualified samples. Select the thickness of each film layer of the qualified sample with the smallest reflectance difference in the sample set as the thickness of each film layer of the broadband antireflection film.

2. The antireflective membrane design method combining machine learning algorithms according to claim 1, characterized in that, In step 1, determining the material and thickness range of each film layer based on the number of film layers includes: inputting the number of film layers into the parameter configuration system, and the parameter configuration system outputting the material and thickness range of each film layer. The parameter configuration system includes an optical prior experience mapping table, which includes the material and thickness of each film layer corresponding to different numbers of film layers.

3. The antireflective membrane design method combining machine learning algorithms according to claim 1, characterized in that, Step 2, sampling within each film thickness range includes: When the average reflectance constraint is greater than or equal to 1%, training samples are obtained by alternating sampling of normal and uniform distributions within each film layer thickness range. When the average reflectance constraint is less than 1%, concentrated sampling is performed in the low reflectance range of each film thickness range to obtain training samples.

4. The antireflective membrane design method combining machine learning algorithms according to claim 3, characterized in that, In step 2, multiple training samples that satisfy the total thickness constraint and the average reflectivity constraint within the wavelength range are selected to form the training dataset, which includes: After obtaining a training sample, determine whether the total thickness of the training sample is within the total thickness constraint. If not, discard it; if so, retain it. For training samples that meet the total thickness constraint, four uniformly distributed wavelength points are selected within the wavelength range, and the reflectivity of each wavelength point is calculated using the transfer matrix method. It is then determined whether the reflectivity of each wavelength point is greater than 1.3 times the average reflectivity constraint. If the reflectivity of any wavelength point is greater than 1.3 times the average reflectivity constraint, it is discarded. If the reflectivity of all wavelength points is less than or equal to 1.3 times the average reflectivity constraint, it is retained. For training samples with acceptable reflectivity at four wavelength points, select N uniformly distributed wavelength points within the wavelength range and calculate the average reflectivity using the transfer matrix method. Determine whether the average reflectivity meets the average reflectivity constraint. If it does not, discard the sample; if it does, retain it in the training dataset.

5. The antireflective membrane design method combining machine learning algorithms according to claim 4, characterized in that, For step 2, when the average reflectance constraint is less than 1%, the target number of samples in the training dataset is 250,000; when the average reflectance constraint is in the range of 1% to 2%, the target number of samples in the training dataset is 180,000; and when the average reflectance constraint is greater than 2%, the target number of samples in the training dataset is 100,000.

6. The antireflective membrane design method combining machine learning algorithms according to claim 1, characterized in that, In step 3, the gradient boosting regression model is trained using the training dataset to enable the model to learn the mapping relationship between the film thickness and reflectivity difference of each training sample.

7. The antireflective membrane design method combining machine learning algorithms according to claim 6, characterized in that, In step 3, training the gradient boosting regression model using the training dataset to obtain the target gradient boosting regression model includes: performing 5-fold cross-validation on the gradient boosting regression model using the training dataset to obtain the initial target gradient boosting regression model, and then training the initial target gradient boosting regression model using all training samples in the training dataset to obtain the target gradient boosting regression model.

8. The antireflective membrane design method combining machine learning algorithms according to claim 7, characterized in that, Five-fold cross-validation involves randomly dividing all training samples in the training dataset into five subsets. In each round, four subsets are selected for model training, and the remaining subset is used for model testing. Different subsets are used for model testing in different rounds until five rounds of training are completed to obtain the initial target gradient boosting regression model.

9. The antireflective membrane design method combining machine learning algorithms according to claim 1, characterized in that, In step 4, obtaining multiple mesh combinations based on the thickness range of each film layer in step 1 includes: determining the mesh step size according to the width of the thickness range of each film layer in step 1 and the average reflectivity constraint; sampling multiple discrete thicknesses within the thickness range of each film layer based on the mesh step size; performing a Cartesian product on the multiple discrete thicknesses of each film layer to obtain multiple mesh combinations; and the multiple mesh combinations constitute the mesh search space. In step 4, the target gradient boosting regression model is used to predict the difference in predicted reflectance of all grid combinations in the grid search space, and then all grid combinations are sorted from smallest to largest according to the magnitude of the difference in predicted reflectance. Step 4, determining whether the mesh combination meets the total thickness limit and average reflectivity constraint within the wavelength range includes: Determine whether the total thickness of the mesh combination is within the total thickness constraint. If not, discard it; if so, keep it. For mesh combinations with acceptable total thickness constraints, three uniformly distributed wavelength points are selected within the wavelength range, and the reflectivity of each wavelength point is calculated using the transfer matrix method. It is then determined whether the reflectivity of each wavelength point is greater than 1.3 times the average reflectivity constraint. If the reflectivity of any wavelength point is greater than 1.3 times the average reflectivity constraint, it is discarded. If the reflectivity of all wavelength points is less than or equal to 1.3 times the average reflectivity constraint, it is retained. For a grid combination with acceptable reflectivity at three wavelength points, select N uniformly distributed wavelength points within the wavelength range and calculate the average reflectivity using the transfer matrix method. Determine whether the average reflectivity meets the average reflectivity constraint. If it does not meet the constraint, discard the sample; if it does, retain it as a qualified sample. Here, N is an integer in the range of 100 to 200.

10. The antireflective membrane design method combining machine learning algorithms according to claim 9, characterized in that, Early termination is allowed when the number of qualified samples is greater than 100 and the minimum reflectance difference is less than 0.5%.

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