Dispersion model parameter prediction method for a material
By using deep learning methods to extract features and classify scattering cross-section spectra, the problem of the inability to reverse-engineer material parameters in traditional methods is solved. This enables fast and stable material type identification and parameter inversion, reduces computational costs and equipment requirements, and improves the accuracy and ease of measurement.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2026-03-16
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies struggle to directly measure or derive material particle parameters and refractive index dispersion parameters using mathematical and physical methods when dealing with uncertain or novel materials. This is especially true when refractive index dispersion and absorption are present, as traditional methods cannot achieve reverse solutions.
By employing deep learning methods, we first determine the material type by extracting and classifying features from the scattering cross-section spectrum. Then, we use the corresponding regression model to predict the geometric parameters and dispersion model parameters of the material. This includes training the classification model and the regression model, and constructing a two-stage deep learning inversion framework to reduce the difficulty of regression space.
It enables rapid and stable inversion of particle parameters and refractive index dispersion parameters under material uncertainty, reduces computational costs, avoids complex sample preparation and high-threshold measurements, and improves the accuracy and simplicity of measurement.
Smart Images
Figure CN122201554A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of optical AI reverse engineering technology, and more specifically, relates to a method for predicting dispersion model parameters of materials. Background Technology
[0002] The Mie scattering problem refers to the scattering of plane electromagnetic waves on spherical particles. For a non-absorbing, constant refractive index dielectric sphere, Mie provided an analytical solution in 1908; and pointed out that the scattering cross section is determined by at least four key parameters: particle radius, incident wavelength, particle refractive index, and ambient refractive index, etc., and that when the particle size is on the same order of magnitude as the wavelength, the response of the scattering cross section to the wavelength is highly nonlinear.
[0003] The inverse Mie scattering problem is to infer the particle parameters from a given scattering cross-section spectrum. Existing work has attempted to find the inverse using functional analysis or numerical methods, but these methods often assume a refractive index constant or simplify the process. In practical engineering, most materials, especially in the visible light range, exhibit significant refractive index dispersion, and metals also exhibit absorption (extinction coefficient). Furthermore, traditional mathematical physics methods cannot directly achieve the inverse solution.
[0004] Existing methods are suitable for obtaining physically interpretable "forward simulations" based on analytical or numerical solutions. They can be solved relatively accurately and conveniently when the refractive index is fixed, there is no absorption, and the parameter dimension is low. However, the following problems exist: (1) The refractive index of the real medium changes with the wavelength, and the refractive index and extinction coefficient of the metal need to be predicted at the same time; mathematical physics methods cannot be directly reversed. (2) Directly measuring the refractive index requires the material to be tested to be made into a smooth and flat film using an ellipsometer, and the surface accuracy of the film requires professional technicians and professional equipment, which makes it difficult to be widely used. (3) The dispersion model structures and the number of parameters of metals and media are different; if the material type is not determined first, the subsequent regression model will have problems such as inconsistent target space and unstable training.
[0005] Therefore, when the material is uncertain or contains mixed materials, it is difficult to directly and accurately measure or derive and solve the particle parameters and refractive index and dispersion parameters of the material through mathematical physics methods. Summary of the Invention
[0006] In view of the shortcomings of related technologies, the purpose of this invention is to provide a method for predicting the dispersion model parameters of materials, which aims to solve the problem in the prior art that it is difficult to directly and accurately measure or derive and solve the particle parameters and refractive index dispersion parameters of materials through mathematical and physical methods when the material is uncertain or when dealing with new materials.
[0007] To achieve the above objectives, the present invention provides a method for predicting the dispersion model parameters of materials, comprising: Feature extraction of the original scattering cross-section spectrum of the material under test: The original scattering cross-section spectrum is discretely sampled and normalized to obtain a normalized spectrum sequence; Features of the normalized spectrum sequence are extracted, and the obtained features are concatenated with the normalized spectrum sequence in the channel dimension to obtain a scattering cross-section spectrum feature sequence; The scattering cross-section spectrum feature sequence is input into a pre-trained classification model to obtain the material type of the material to be tested; The scattering cross-section spectrum feature sequence is input into the pre-trained regression model corresponding to the material type to predict the geometric parameters and dispersion model parameters of the particles corresponding to the material under test. Each material type corresponds to a regression model, and its training samples are the scattering cross-section spectrum feature sequences obtained by extracting the features from the scattering cross-section spectra of the material samples of the corresponding material type; the corresponding labels are the geometric parameters and dispersion model parameters of the particles of the corresponding material samples.
[0008] Optional, also includes: The visualized dispersion curve is obtained by solving the dispersion model parameters. The analytical solution of forward Mie scattering is obtained based on the geometric parameters and dispersion model parameters, and used as the reconstructed scattering cross-section spectrum. The absolute error between the reconstructed scattering cross-section spectrum and the original scattering cross-section spectrum is then calculated.
[0009] Optionally, the scattering cross-section spectrum of the material sample is calculated using Mie scattering theory based on the determined material particle set parameters and dispersion model parameters.
[0010] Optionally, extracting features from the normalized spectral sequence includes: Extract the derivative features of the normalized spectral sequence: take the difference between the values of adjacent wavelength points on the normalized spectral sequence to obtain the derivative features; Extract the accumulation and features of the normalized spectral sequence: perform cumulative summation on the normalized spectral sequence to obtain the accumulation and features.
[0011] Optionally, the classification model includes cascaded LSTM neural networks and fully connected networks.
[0012] Optionally, the material type includes metals, low refractive index media with a refractive index range of 1.3 to 1.7, medium refractive index media with a refractive index range of 2.3 to 2.8, and high refractive index media with a refractive index range of 2.4 to 4.3.
[0013] Optionally, when the material type is a medium, the dispersion model includes a normal dispersion model; the geometric parameter is the particle radius, and the dispersion model parameters include the initial refractive index. and the magnitude of the decrease in refractive index ; When the material type is metal, the dispersion model includes the Drude–Lorentz model; the geometric parameter is the particle radius, and the dispersion model parameters include the refractive index. With extinction coefficient .
[0014] Optionally, the refractive index and wavelength satisfy The normal dispersion model is expressed as: ; in, For the wavelength in free space, , , , For custom wavelengths.
[0015] Optionally, the complex permittivity is calculated using the Drude–Lorentz model based on the dispersion model. Then convert it into the complex refractive index of the metal. ; ; in, The wavelength in free space is represented by the abscissa of the scattering cross-section spectrum. The speed of light in a vacuum. The imaginary unit, and for The real and imaginary parts, It is the high-frequency limiting dielectric constant. For plasma frequency, Drude damping / collision frequency, This is the Lorentz resonant angular frequency. For the Lorentz oscillator strength, Lorentz damping; For refractive index, is the extinction coefficient.
[0016] Compared with the prior art, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: 1. This invention provides a method for predicting dispersion model parameters of materials. It decomposes the complex inverse Mie scattering problem into a "classification followed by regression" approach, significantly reducing the difficulty of the regression space. Experimental data is first input into a classification model to classify the material. Then, based on the classification results, a regression model is selected to calculate the parameters required for the dispersion model, thereby retrieving the dispersion parameters and obtaining a visualized dispersion curve and an accurate scattering cross-section spectrum. This solves the problem of difficulty in directly and accurately measuring or deriving particle parameters and refractive index dispersion parameters when dealing with uncertain materials or new materials. It accurately solves for the particle radius and dispersion model parameters of the material, thereby retrieving the particle parameters and refractive index dispersion parameters.
[0017] 2. This invention provides a method for predicting dispersion model parameters of materials. By breaking down the problem, the computational cost is reduced, enabling the system to run on a standard computer without relying on a computing cluster, thereby expanding the application scenarios of the method.
[0018] 3. The embodiments of the present invention provide a method for predicting the dispersion model parameters of materials. It can realize material classification, parameter inversion and dispersion curve recovery based solely on the scattering cross-section spectrum. It avoids the complex sample preparation and high-threshold precision measurement process in traditional methods, reduces the requirements for equipment and personnel, and has the advantages of being easy to use, simple process and convenient implementation. Attached Figure Description
[0019] Figure 1 This is a schematic diagram of the training process of a material dispersion model parameter prediction method provided in an embodiment of the present invention.
[0020] Figure 2 This is a flowchart illustrating a method for predicting dispersion model parameters of materials according to an embodiment of the present invention.
[0021] Figure 3 For regression models; comparison chart of actual and predicted refractive indices of the medium; comparison chart of actual and predicted model parameters of the metal.
[0022] Figure 4 This is a table of various evaluation indicators and a confusion matrix for the classification results in this embodiment of the invention. Detailed Implementation
[0023] 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 embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0024] The following description, in conjunction with a preferred embodiment, illustrates the content involved in the above embodiments.
[0025] Example 1 Addressing existing technologies, this paper addresses how to rapidly, stably, and reliably invert particle parameters and refractive index dispersion parameters from a given scattering cross-section spectrum in more realistic scenarios involving refractive index dispersion or even absorption (in metals); and how to accurately identify materials between metals and media with different refractive index ranges, and then call the corresponding parameter space regressor based on the identification results to achieve an end-to-end automated inversion process. This solution proposes a method for predicting dispersion model parameters of materials, including: Feature extraction of the original scattering cross-section spectrum of the material under test: The original scattering cross-section spectrum is discretely sampled and normalized to obtain a normalized spectrum sequence; Features of the normalized spectrum sequence are extracted, and the obtained features are concatenated with the normalized spectrum sequence in the channel dimension to obtain a scattering cross-section spectrum feature sequence; The scattering cross-section spectrum feature sequence is input into a pre-trained classification model to obtain the material type of the material to be tested; The scattering cross-section spectrum feature sequence is input into the pre-trained regression model corresponding to the material type to predict the geometric parameters and dispersion model parameters of the particles corresponding to the material under test. Each material type corresponds to a regression model, and its training samples are the scattering cross-section spectrum feature sequences obtained by extracting the features from the scattering cross-section spectra of the material samples of the corresponding material type; the corresponding labels are the geometric parameters and dispersion model parameters of the particles of the corresponding material samples.
[0026] This solution can be summarized into three parts. The first part is to train the classification model and the regression model to build a two-stage deep learning inversion framework. The second part is to measure the scattering spectrum of the material under test, and then classify it according to the test data through the regression model. The corresponding geometric parameters and dispersion model parameters are obtained through the regression model. The third part is to solve for the dispersion curve based on the calculated dispersion model parameters, and then invert and deduce the reconstructed scattering cross-section data of the material under test based on the geometric parameters and dispersion model parameters, so as to carry out engineering acceptance or confidence assessment.
[0027] like Figure 1As shown, the first part specifically includes: To ensure that the training data meets the needs of both the classification and regression models, a unified principle is adopted when generating the training data. All training data in this scheme is generated from the defined material particle geometric parameters and dispersion model parameters through analytical solutions of forward Mie scattering. During training, feature engineering for functional spectra is introduced (mentioned later). During inference, the corresponding regression model output particle radius and dispersion model parameters are automatically selected based on the classification results. Specifically, the incident light wavelength, material refractive index, and material particle refractive index are defined, and PyMieScat is used to calculate the scattering cross-section spectrum to construct a supervised learning dataset. The material types include metals, low-refractive-index media with a refractive index range of 1.3 to 1.7, medium-refractive-index media with a refractive index range of 2.3 to 2.8, and high-refractive-index media with a refractive index range of 2.4 to 4.3.
[0028] Particle geometry parameters (particle radius) setting requirements: Sampling should be performed within a preset range to ensure the scattering cross section (SCS) spectrum exhibits a resonance peak in the 500–1000 nm band (facilitating inversion); the scattering cross section spectrum should resonate within the preset particle radius range and conform to typical material scales. Material dispersion parameters setting requirements: Based on the normal dispersion of the medium. , Or random sampling of the Drude–Lorentz parameters of the metal.
[0029] After setting the material particle geometry parameters and dispersion model parameters, the scattering cross section spectrum (SCS(λ)) was calculated using Mie scattering theory. The wavelength range of 500–1000 nm was selected, and each spectrum was represented by 51 discrete points. The spectrum was then normalized. The material category (or refractive index range) used in generating the scattering cross section spectrum was used as the classification label, and the particle radius and dispersion model parameters used during generation were used as the regression labels.
[0030] To address the inconsistency in regression target spaces caused by differences in the structure and parameter dimensions of dispersion models for metals and dielectrics, a classification model is employed to categorize material types. The input is a scattering cross-section spectrum sequence, and the output is the material type category.
[0031] A classification model is used to divide the materials corresponding to the scattering cross-section spectrum sequence into four categories: metals, low refractive index media, medium refractive index media, and high refractive index media. Among them, low refractive index media, medium refractive index media, and high refractive index media share the same normal dispersion model and similar parameter forms in physics. However, since the parameter range of real materials is relatively wide, grouping them according to the refractive index interval allows each type of regressor to face a narrower parameter distribution, thus making it easier to train a lighter, faster-converging, and more stable sub-model.
[0032] The training dataset construction includes: normalizing and feature engineering the calculated scattering cross-section spectrum to obtain a scattering cross-section spectrum feature sequence. The input for each data sample is a normalized 51-point sequence representing the variation of the scattering cross-section spectrum in the wavelength range of 500 to 1000 nanometers.
[0033] To further improve the model's learning performance, additional features, such as derivative and integral features, are generated based on the original scattering cross-section spectrum. These features increase the model's sensitivity to local trends and overall changes in the scattering spectrum. Specifically, the calculated scattering cross-section spectrum is discretized and normalized to obtain a normalized spectral sequence. Based on this normalized sequence, the values at adjacent wavelengths are differencing to obtain a first-order derivative approximation, used to characterize local slope / turning point trends. This derivative feature reflects local trends and improves training efficiency. Since the length is one less after differencing, zeros are padded at the starting point to ensure a uniform length. The normalized sequence is then summed to obtain a global cumulative feature similar to a distribution function.
[0034] Furthermore, let the discrete scattering spectrum before normalization be... ( In this scheme, the preferred option is... Then the normalized cumulative sum characteristic is defined as: ; in, This feature gives the spectral sequence a "distribution function" shape, which is used to introduce long-range contextual information. This accumulation and feature can help the model capture long context and accelerate training convergence.
[0035] Furthermore, the normalized spectral sequence, derivative features, and cumulative sum features are concatenated by channel to obtain the scattering cross section spectral feature sequence, which is used as input data.
[0036] The training dataset for the classification model contains four categories: metals, low-refractive-index media, medium-refractive-index media, and high-refractive-index media. In practical applications, due to the large number of metal samples in the dataset, the classification model may misclassify low-refractive-index media, especially when the spectra of low-refractive-index media are similar to those of metals. Therefore, overrepresentation of metal samples may lead to a small number of misclassifications, such as misclassifying low-refractive-index media as metals. However, this misclassification has a very small impact on the overall classification accuracy and does not significantly affect the model's performance in real-world applications.
[0037] The goal of the regression model is to predict the geometric parameters and dispersion model parameters of the particles using the input scattering cross-section spectrum sequence, specifically the dispersion model parameters of the particle radius and refractive index.
[0038] The construction of the training dataset for regression models differs from that for classification models. Regression tasks require not only processing the scattering cross-section spectrum but also extracting labels related to physical properties. The training dataset for regression models comes from the same data foundation (calculated scattering cross-section spectra), but in data selection, the material type is first predicted using a classification model (e.g., metal, low-refractive-index medium, high-refractive-index medium, etc.). Then, an appropriate regression model is selected for training based on the predicted classification results (material type). Therefore, the training of regression models is based on the classification results. Specifically, after classification, one of four regression models is selected: a metal regression model, a low-refractive-index medium regression model, a medium-refractive-index medium regression model, and a high-refractive-index medium regression model, each corresponding to a specific material type. The training samples are the scattering cross-section spectrum feature sequences obtained by extracting features from the scattering cross-section spectra of material samples corresponding to the material type; the corresponding labels are the geometric parameters and dispersion model parameters of the particles in the corresponding material sample.
[0039] The labels for regression tasks include multi-objective regression values; for media materials, the label is the particle radius. Initial refractive index and the magnitude of refractive index change Parameters; for metallic materials, regression labels include particle radius. And the parameters of the Drude-Lorentz model (the refractive index of the metal can be derived from the parameters of the Drude-Lorentz model). and extinction coefficient In constructing the regression dataset through forward computation, to improve the efficiency of model training and the stability of the fit, it is necessary to ensure a uniform distribution of data from different media types. The training set for each regression model contains approximately 80% of that type of spectrum for training, with the remaining 20% used for validation and testing.
[0040] The uniform distribution of regression data ensures a smoother training process for each regression model and effectively avoids training instability caused by an excessive or insufficient number of samples in one class. In this way, the model can not only accurately classify materials but also accurately predict the corresponding physical parameters after classification, thus achieving efficient and accurate inverse Mie scattering inversion.
[0041] When the classification result is "medium", the dispersion model adopts the normal dispersion model; the geometric parameters output by the regression model are the particle radii, and the output dispersion model parameters are the initial refractive indices. and the magnitude of the decrease in refractive index .
[0042] For many media, the change in refractive index with wavelength can be described using normal dispersion. Furthermore, through variable substitution, a more interpretable parametric form that satisfies boundary constraints can be obtained, making the learning objective of the regression model: the initial refractive index. and the magnitude of the decrease in refractive index Therefore, the output of the regression model is the dispersive model parameters, rather than an uncontrollable free curve.
[0043] For dielectric materials, the refractive index follows normal dispersion characteristics with wavelength. Its empirical model can be written as: (1) in, For wavelengths in free space, this scheme replaces the learning objective with more interpretable parameters through boundary constraints. and : (2) (3) From the above formula, in formula (1) Written Functions: (4) (5) in, , For a custom wavelength, in a specific embodiment, it can be... , It is considered a constant. Therefore, the media regression model only needs to predict... (or its equivalent parameter) can restore the complete Dispersion curve.
[0044] When the classification result is metal, the Drude–Lorentz model is used for the dispersion model; the geometric parameters output by the regression model are particle radii, and the output dispersion model parameters are refractive indices. With extinction coefficient .
[0045] For metallic materials, the refractive index must be considered simultaneously. With extinction coefficient Or equivalently derived from the real / imaginary part of the dielectric constant. Therefore, the output of the metal regression model is the Drude–Lorentz model parameter. The complex permittivity is calculated using the Drude–Lorentz model. Then convert it into the complex refractive index of the metal. .
[0046] (6) in, The wavelength in free space is represented by the abscissa of the scattering cross-section spectrum. The speed of light in a vacuum. The imaginary unit, and for The real and imaginary parts, It is the high-frequency limiting dielectric constant. For plasma frequency, Drude damping / collision frequency, This is the Lorentz resonant angular frequency. For the Lorentz oscillator strength, Lorentz damping; For refractive index, is the extinction coefficient.
[0047] Therefore, the output of the metal regression model is The Drude–Lorentz parameter set, which can then be used to recover and .
[0048] Training the classification and regression models is an offline process: labeled scattering spectrum datasets are synthesized in batches based on the forward Mie analytical solution, the classification and regression losses are minimized using supervised learning, the network weights are updated through backpropagation, and the trained classifiers and the weights of each class regressor are fixed and saved.
[0049] The classification model training strategy includes: using an LSTM neural network and a fully connected network, and selecting a preset number of LSTM layers and the number of nodes per layer by adjusting the parameters; wherein, in a preferred embodiment, two LSTM layers and 64 nodes per layer are set.
[0050] The regression model training strategy includes: after material type identification is completed through the classification model, the same input spectrum (scattering cross-section spectrum feature sequence) is fed into the regression model of the corresponding category. The classification network outputs posterior probability vectors for four categories for the input spectrum. and prediction categories (Take the maximum value of p). When When determining that the material is a metal, the metal regression model is invoked. Output particle radius and Drude–Lorentz parameters; when When determining that the material is a medium, the corresponding medium regression model is invoked. Output particle radius and normal dispersion model parameters (e.g., The selection of the regression model is entirely automated based on the classification results, ensuring that different material groups enter a matching parameter space and avoiding regression instability caused by inconsistent model structures. This results in a narrower parameter range for each regressor, consistent dispersion model structures, more stable training, and easier lightweight deployment.
[0051] like Figure 2 As shown, the second part specifically includes: keeping the network weights fixed, performing normalization, feature construction, classification forward calculation, model routing and regression forward calculation only on the input scattering cross-section spectrum data, and outputting the particle radius and dispersion model parameters of the material under test.
[0052] The original scattering cross-section spectrum of the particles in the test material is obtained through experimental measurement or simulation. In one specific embodiment, a confocal spectrometer can be used to measure the scattering spectrum of the test material to obtain its original scattering cross-section spectrum. The original scattering cross-section spectrum is then discretized and normalized to output a normalized spectral sequence, i.e., a discretized 51-point spectral vector. (Corresponding to the 500–1000 nm wavelength band). The normalized spectral sequence undergoes feature engineering processing, and the output is a scattering cross-section spectral feature sequence, i.e., a multi-channel sequence tensor. The channels can include: the original spectral channel, the differential derivative channel, and the normalized cumulative sum channel, corresponding to the normalized spectral sequence, derivative feature, and cumulative sum feature, respectively. The multi-channel sequence tensor... The input to the trained classification model is a four-class probability vector. With prediction category The classification network is implemented using a combination of LSTM and a fully connected network. Based on the classification results (i.e., the predicted category)... Select the corresponding regression model when For low / medium / high, select the corresponding medium regression model respectively. When considering metal, choose the metal regression model. Then convert the multi-channel sequence tensor... The input to the selected regression model is the particle radius of the material under test. And the parameters of the dispersion model. The output of the medium regression model is... (and equivalent form) and formulas (1) to (5) restore the refractive index The metal regression model outputs a set of Drude–Lorentz parameters and the refractive index can be recovered using formula (6). and extinction coefficient .
[0053] Part Three specifically includes: The visualized dispersion curve is obtained by solving the dispersion model parameters; specifically, when the material is a medium, the dispersion curve is obtained by... or equivalent Determine the entire line Curve; when the material is metallic, it is first obtained from the parameters of the Drude–Lorentz model. Then convert to With extinction coefficient One set of parameters can generate a refractive index (or complex refractive index) curve at any wavelength. This scheme can directly predict the complete dispersion model parameters and obtain the refractive index at each wavelength.
[0054] By solving the analytical solution of forward Mie scattering based on the geometric parameters and dispersion model parameters, the reconstructed scattering cross-section spectrum is obtained. The absolute error is then obtained by comparing the reconstructed scattering cross-section spectrum with the original scattering cross-section spectrum. This calculated absolute error can be used for engineering acceptance or confidence assessment.
[0055] In one specific embodiment, the classification network of this scheme has extremely high performance. Referring to Table 1, the macro-average index is close to 1, and it is pointed out that even if there is class imbalance, the index is not lower than 99.8%. The errors mainly come from the bias caused by the low refractive index medium being similar to the metal spectrum at certain radii and the excessive number of metal samples.
[0056] Table 1
[0057] As can be seen from the above data, this scheme decomposes the complex inverse problem into "classification first, regression second", which results in accurate classification and significantly reduces the difficulty of regression space.
[0058] like Figure 3 As shown, the results of the regression model are primarily presented. Figure 3 (a) shows the refractive index dispersion diagrams of three media with low, medium and high refractive indices. It can be seen that all three media exhibit a normal dispersion trend that decreases slowly with increasing wavelength. The predicted points basically match the real curves, indicating that the model has a good recovery effect on the media refractive index curves. Figure 3 (b) shows a comparison of the actual and predicted model parameters for the metal. Overall, the predicted curves and the actual curves show consistent trends. The fit is good. It can also follow its changing trends relatively well. like Figure 4 As shown, this primarily displays the metrics of the classification model. The table on the left presents the regression metrics for four types of materials, including MAE, RMSE, and... The results show that the errors for the low-refractive-index, medium-refractive-index, and high-refractive-index media are relatively small, with coefficients of determination reaching 0.973, 0.913, and 0.877 respectively, indicating that the regression of the medium parameters is generally accurate; the low-refractive-index media performs best. Metals have the highest MAE and RMSE. The value of 0.640 indicates that regression of metal parameters is relatively more difficult, and the fitting accuracy is significantly lower than that of the medium. The confusion matrix on the right shows the four-class classification results. The values on the main diagonal are all close to 100%, indicating very good classification performance: the accuracy rate for metal recognition is 99.95%, for low refractive index it is 99.61%, for medium refractive index it is 99.97%, and for high refractive index it is 99.82%. The misclassification rates between each category are very low, indicating that the classification model can almost stably distinguish between metals and media with different refractive index ranges.
[0059] For nano-optical devices requiring specific scattering responses, resonance positions, or spectral line shapes, a target scattering cross-section spectrum can be first defined. This target spectrum can then be input into the method provided in this scheme to obtain the material type, particle radius, and dispersion model parameters that may achieve the scattering response. Since this scheme does not directly output isolated refractive index values at a specific wavelength, but rather outputs model parameters that can recover the entire dispersion curve, it is more suitable for reverse engineering under real material constraints, providing an initial solution for subsequent device structure material selection and parameter optimization.
[0060] In this embodiment of the invention, the complex inverse Mie scattering problem is decomposed into "classification first, regression second", which significantly reduces the difficulty of regression space. By first inputting experimental data / simulation data into the classification model to classify materials, and then selecting a regression model based on the classification results to calculate the parameters required for the dispersion model, the dispersion parameters are inverted, and a visualized dispersion curve and an accurate scattering cross-section spectrum are obtained. Thus, even when the material is uncertain, the particle parameters and refractive index dispersion parameters of the material can still be accurately solved.
[0061] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for predicting dispersion model parameters of a material, characterized in that, include: Feature extraction of the original scattering cross-section spectrum of the material under test: The original scattering cross-section spectrum is discretely sampled and then normalized to obtain a normalized spectrum sequence; The features of the normalized spectral sequence are extracted, and the obtained features are concatenated with the normalized spectral sequence in the channel dimension to obtain the scattering cross section spectral feature sequence. The scattering cross-section spectrum feature sequence is input into a pre-trained classification model to obtain the material type of the material to be tested; The scattering cross-section spectrum feature sequence is input into the pre-trained regression model corresponding to the material type to predict the geometric parameters and dispersion model parameters of the particles corresponding to the material under test. Each material type corresponds to a regression model, and its training samples are the scattering cross-section spectrum feature sequences obtained by extracting the features from the scattering cross-section spectra of the material samples of the corresponding material type; the corresponding labels are the geometric parameters and dispersion model parameters of the particles of the corresponding material samples.
2. The prediction method as described in claim 1, characterized in that, Also includes: The visualized dispersion curve is obtained by solving the dispersion model parameters. The analytical solution of forward Mie scattering is obtained based on the geometric parameters and dispersion model parameters, and used as the reconstructed scattering cross-section spectrum. The absolute error between the reconstructed scattering cross-section spectrum and the original scattering cross-section spectrum is then calculated.
3. The prediction method as described in claim 1, characterized in that, The scattering cross-section spectrum of the material sample was calculated using Mie scattering theory based on the determined material particle set parameters and dispersion model parameters.
4. The prediction method as described in claim 1, characterized in that, The extraction of features from the normalized spectral sequence includes: Extract the derivative features of the normalized spectral sequence: take the difference between the values of adjacent wavelength points on the normalized spectral sequence to obtain the derivative features; Extract the accumulation and features of the normalized spectral sequence: perform cumulative summation on the normalized spectral sequence to obtain the accumulation and features.
5. The prediction method as described in claim 1, characterized in that, The classification model includes cascaded LSTM neural networks and fully connected networks.
6. The prediction method as described in claim 1, characterized in that, The material types include metals, low refractive index media with a refractive index range of 1.3 to 1.7, medium refractive index media with a refractive index range of 2.3 to 2.8, and high refractive index media with a refractive index range of 2.4 to 4.
3.
7. The prediction method as described in claim 6, characterized in that, When the material type is a medium, the dispersion model includes a normal dispersion model; the geometric parameter is the particle radius, and the dispersion model parameters include the initial refractive index. and the magnitude of the decrease in refractive index ; When the material type is metal, the dispersion model includes the Drude–Lorentz model; the geometric parameter is the particle radius, and the dispersion model parameters include the refractive index. With extinction coefficient .
8. The prediction method as described in claim 7, characterized in that, The refractive index and wavelength satisfy The normal dispersion model is expressed as: ； in, For the wavelength in free space, , , , For custom wavelengths.
9. The prediction method as described in claim 7, characterized in that, The dispersion model was used to calculate the complex permittivity using the Drude–Lorentz model. Then convert it into the complex refractive index of the metal. ; ； in, The wavelength in free space is represented by the abscissa of the scattering cross-section spectrum. The speed of light in a vacuum. The imaginary unit, and for The real and imaginary parts, It is the high-frequency limiting dielectric constant. For plasma frequency, Drude damping / collision frequency, This is the Lorentz resonant angular frequency. For the Lorentz oscillator strength, Lorentz damping; For refractive index, is the extinction coefficient.