Spectral polarization prediction method and system based on polarization bidirectional reflection distribution function

Abstract

The invention discloses a spectral polarization prediction method and system based on a polarization bidirectional reflection distribution function, and relates to the technical field of optical detection and remote sensing, and the method is characterized in that S1, a spectral intensity and linear polarization degree data set of a target coating in a visible light wave band is acquired, and the data set is preprocessed; s2, extracting characteristic values; and S3, constructing a prediction model. According to the method, curve prediction is creatively converted into characteristic value prediction, the generalization ability of the model to interpolation and extrapolation angles is remarkably improved while the known angle prediction precision is guaranteed, spectral polarization prediction which cannot be completed by a traditional method is achieved, the average relative error (MRE) is lower than 0.03, the determination coefficient (R) is higher than 0.99, and the method is suitable for being applied to spectral polarization prediction. The method is suitable for efficient polarization spectrum data acquisition in the fields of remote sensing, material analysis and the like.

Description

Technical Field

[0001] The present invention relates to the field of optical detection and remote sensing technology, and more specifically, it relates to a spectral polarization prediction method and system based on the polarization bidirectional reflectance distribution function. Background Art

[0002] I. Technical Requirements and Challenges of Polarization Spectral Detection

[0003] Polarization spectral detection can reveal the physical and chemical properties (such as refractive index, roughness, etc.) of the target surface by fusing light intensity, spectral, and polarization information, and has important value in remote sensing, atmospheric monitoring, and target recognition. However, the acquisition of multi-angle polarization spectral data is limited by detector performance, measurement complexity, and angular dependence:

[0004] Measurement Limitation: Existing polarization spectrometers (such as Gran-Thompson prism combined with ASD spectrometer) need to rotate the prism multiple times and collect multi-angle data, which is time-consuming and vulnerable to noise interference (especially in the low-wavelength region);

[0005] Angular Dependence: The polarization characteristics are strongly correlated with the detection angles (zenith angle, azimuth angle). Traditional methods need to rely on a large amount of measured data and it is difficult to cover unknown angle conditions in complex scenarios.

[0006] II. Deficiencies of Existing Polarization Modeling Methods

[0007] The polarization bidirectional reflectance distribution function (pBRDF) is the core model for describing the polarization scattering characteristics of the target surface, but its development faces the following bottlenecks:

[0008] Single-Wavelength Limitation: Traditional pBRDF models (such as Priest-Germer model, Hyde geometric optics model) mainly describe the spatial distribution at a single wavelength and lack the ability to model spectral behavior;

[0009] Inversion Accuracy Problem: The inversion of model parameters depends on optimization algorithms and prior data. The inversion results are vulnerable to noise interference, and the generalization ability significantly decreases at unknown angles;

[0010] Difficulty in Multi-Component Separation: Existing three-component models (specular reflection, directional diffuse reflection, ideal diffuse reflection) lack an adaptive mechanism for selecting the polynomial fitting order of the spectral response. High-order models are prone to overfitting, while low-order models cannot capture complex spectral changes.

[0011] III. Limitations of Existing Prediction Methods

[0012] To reduce the need for measured data, methods such as regression analysis and machine learning are used for spectral characteristic prediction, but there are the following defects:

[0013] Inefficient high-dimensional data processing: Spectral data (such as 361 wavelengths from 400 - 760 nm) are highly correlated. Directly predicting the full-spectrum curve leads to high computational complexity and is susceptible to interference from redundant wavelengths;

[0014] Insufficient generalization ability: Traditional methods (such as ridge regression and random forest) have high prediction accuracy (MRE < 0.05) at known angles, but their performance deteriorates significantly at interpolation or extrapolation angles (MRE increases to over 0.1 and R² is below 0.9);

[0015] Lack of polarization prediction: Existing methods can only predict spectral intensity ( ), and cannot be related to polarization characteristics (such as DoLP). The calculation of DoLP relies on non-linear transformations (such as the combination of Stokes parameters), which amplifies the prediction error.

[0016] IV. Noise and wavelength selection issues

[0017] Noise interference: In the low-wavelength region, due to the limitation of detector sensitivity, the noise of polarization components (I0, I 45 etc.) is significant, and it is further amplified after non-linear operations (such as the noise intensity of DoLP at 400 nm is 3 - 5 times higher );

[0018] Wavelength redundancy: Although traditional backward selection methods can eliminate interfering wavelengths, they ignore the synergistic effect between wavelengths, resulting in insufficient representativeness of eigenvalues.

[0019] Due to the above reasons, the present invention proposes a spectral polarization prediction method and system based on the polarization bidirectional reflectance distribution function. Summary of the invention

[0020] The purpose of the present invention is to provide a spectral polarization prediction method and system based on the polarization bidirectional reflectance distribution function to solve the above problems.

[0021] The above technical objective of the present invention is achieved through the following technical solutions:

[0022] The first aspect of the present invention provides a spectral polarization prediction method based on the polarization bidirectional reflectance distribution function, characterized in that it includes the following steps:

[0023] S1. Dataset preparation: Obtain the spectral intensity and degree of linear polarization datasets of the target coating at different detection angles, and preprocess the datasets;

[0024] S2. Extract eigenvalues: Construct a PSBRDF model, and through the inversion of Mueller matrix parameters based on the microfacet theory, decompose the preprocessed spectral intensity curve into an eigenvalue set composed of wavelength polynomial coefficients and weight parameters;

[0025] Optimize the eigenvalue set using the backward-forward iterative wavelength selection method;

[0026] S3. Construct a prediction model:

[0027] Establish a polynomial regression model, train and test the model by randomly dividing the training set and the test set at least 100 times, and select the optimal prediction model;

[0028] Input the optimized eigenvalue set into the optimal prediction model to obtain the predicted spectral intensity eigenvalue;

[0029] Substitute the predicted spectral intensity eigenvalue into the PSBRDF model to reconstruct the spectral intensity curve, and calculate the spectral linear polarization degree at the unknown detection angle in combination with the Stokes parameters.

[0030] In combination with the first aspect, the present invention is further configured as: in step S1, the detection angles include the incident zenith angle, the observation zenith angle, and the observation azimuth angle.

[0031] In combination with the first aspect, the present invention is further configured as: the range of the incident zenith angle is 30° - 50°, the range of the observation zenith angle is -60° to 60°, and the range of the observation azimuth angle is 0° - 180°.

[0032] In combination with the first aspect, the present invention is further configured as: in step S2, the mathematical expression of the PSBRDF model is:

[0033]

[0034] Among them, is the Gaussian distribution function of the microfacet inclination angle, is the geometric attenuation factor, are the 4×4 Mueller matrices of specular, directional diffuse reflection, and ideal diffuse reflection respectively, is the wavelength polynomial function, and the polynomial order is dynamically determined by the threshold of MRE < 0.05 and R² > 0.98.

[0035] In combination with the first aspect, the present invention is further configured as: the backward-forward iterative wavelength selection method includes:

[0036] Backward elimination: Eliminate wavelengths one by one, calculate the average relative error and the coefficient of determination of the inversion parameters of the remaining wavelengths, and retain the wavelengths that optimize the average relative error and the coefficient of determination;

[0037] Forward compensation: Backfill the eliminated wavelengths one by one, verify their contribution to the global accuracy, and dynamically adjust the retention set.

[0038] In combination with the first aspect, the present invention is further configured such that: the preprocessing is Savitzky-Golay filtering preprocessing with a window length of 21 and a polynomial order of 2, which is used to eliminate the polarization measurement noise amplification effect in the 400-450 nm band.

[0039] In combination with the first aspect, the present invention is further configured such that: in step S3, the number of times of randomly dividing the training set and the test set is at least 100 times.

[0040] The second aspect of the present invention further provides a spectral polarization prediction device / equipment / system based on the polarization bidirectional reflectance distribution function, including a memory, a processor, and a computer program stored on the memory, wherein the processor executes the computer program to implement the steps of any of the above methods.

[0041] The third aspect of the present invention further provides a computer-readable storage medium, on which a computer program / instructions are stored, wherein when the computer program / instructions are executed by a processor, the steps of any of the above methods are implemented.

[0042] The fourth aspect of the present invention further provides a computer program product, including a computer program / instructions, wherein when the computer program / instructions are executed by a processor, the steps of any of the above methods are implemented.

[0043] The principle and beneficial effects of this technical solution:

[0044] The core principle of the present invention is: by establishing a physical association between spectral intensity and polarization characteristics through the polarization spectral bidirectional reflectance distribution function (PSBRDF), combined with an adaptive wavelength selection and eigenvalue prediction model, efficient prediction of multi-angle spectral intensity ( ) and degree of linear polarization (DoLP) is achieved. It is specifically divided into the following three stages:

[0045] 1. Data-driven modeling: Based on the microfacet theory, a three-component PSBRDF model is constructed to respectively describe the spectral behaviors of specular reflection, directional diffuse reflection, and ideal diffuse reflection, and the wavelength response is fitted by a polynomial.

[0046] 2. Feature dimensionality reduction and optimization: The backward-forward wavelength selection method is used to eliminate noise and redundant wavelengths, and the PSBRDF parameters (such as reflection weight, surface roughness) are inverted as low-dimensional eigenvalues of spectral intensity.

[0047] 3. Angle-feature mapping: A regression model is trained with the detection angle as the input and the eigenvalue as the output to predict the eigenvalue at an unknown angle, and the DoLP is analyzed through the PSBRDF model.

[0048] Beneficial effects: High precision and generalization ability: When predicting S0RF at known angles, MRE ≤ 0.03 and R² ≥ 0.99; when predicting at unknown angles (interpolation / extrapolation), MRE ≤ 0.04 and R² ≥ 0.98;

[0049] Polarization characteristic prediction: For the first time, an end-to-end prediction from spectral intensity to DoLP is realized, and the MRE of DoLP prediction ≤ 0.03;

[0050] Improved computational efficiency: By wavelength selection, the spectral dimension is reduced from 361 to 102 - 241 dimensions, and the inversion speed is increased by 2 - 3 times. Description of the drawings

[0051] Figure 1 It is the framework diagram of the prediction model in Embodiment 1 of the present invention;

[0052] Figure 2 It is the physical diagram of the multi-angle polarization spectroscopy measurement device in Embodiment 1 of the present invention;

[0053] Figure 3 It is the schematic diagram of the measurement principle in Embodiment 1 of the present invention;

[0054] Figure 4 It is the spectral intensity ( ) curve of four types of coating samples in the main plane ( ) in Embodiment 1 of the present invention;

[0055] Figure 5 It is the degree of spectral polarization (DoLP) curve of four types of coating samples in the main plane in Embodiment 1 of the present invention;

[0056] Figure 6 It is the three-component reflection diagram based on the microfacet theory in the embodiment of the present invention;

[0057] Figure 7 It is the curve of the change of the description ability (MRE and R²) of the PSBRDF model with the polynomial order in the embodiment of the present invention;

[0058] Figure 8 It is in the embodiment of the present invention when , and S0RF measured and modeled in the order of the best samples I - IV (where the solid line and the dotted line with markers respectively represent the measured and modeled S O RF; different colors represent different types of samples);

[0059] Figure 9 It is the result diagram of backward - forward wavelength selection in Embodiment 1 of the present invention;

[0060] Figures 10 - 13It is a comparison chart of prediction effects under known angles, interpolation angles, and extrapolation angles in the embodiments of the present invention (wherein: the solid line is the measured value, and the dashed line is the predicted value, proving that the proposed method still maintains high precision under unknown angles; the predicted R² ≥ 0.98, and the DoLP predicted MRE ≤ 0.03).

[0061] In the figure: 1. Artificial light source system; 2. Polarizing lens; 3. ASD ground object spectrometer; 4. Angle measurement system; 5. Sample stage. Specific embodiments

[0062] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0063] Embodiment 1:

[0064] Multi-angle polarization spectroscopy measurement device: As Figure 2 shown, it includes an artificial light source system 1, a polarizing lens 2, an ASD ground object spectrometer 3, an angle measurement system 4, and a sample stage 5. The light source system uses a halogen lamp (power 100W) and a lens group to generate parallel natural light. The goniometer controls the detection zenith angle (range ±90°, accuracy 0.25°) and azimuth angle (range 0° - 360°, accuracy 0.25°). The effective wavelength range of the spectrometer (ASD FieldSpec®3) is 350nm - 2500nm, and the polarizing lens uses a Glan - Thompson prism (extinction ratio 10000:1, effective wavelength range 350nm - 2200nm).

[0065] A spectral polarization prediction method based on the polarization bidirectional reflectance distribution function specifically includes the following steps:

[0066] S1. Dataset preparation: Obtain the four - polarization light intensities ( ), calculate the reflectance factor ( ), and degree of polarization (DoLP) of the target coating at different incident angles ( ), and observation angles ( ), with an interval of 10°; ), with an interval of 15°) through the above - mentioned multi - angle polarization spectroscopy measurement device. The calculation formulas are as follows:

[0067]

[0068] where It is the Spectralon calibration coefficient (0.9284 - 0.9954). The data was preprocessed by Savitzky-Golay filtering (window length 21, polynomial order 2) to eliminate the polarization measurement noise amplification effect in the 400 - 450 nm band.

[0069] Table 1 Detailed description of the dataset

[0070]

[0071] S2. Extract eigenvalues:

[0072] As Figure 3 shown, a three-component PSBRDF model was constructed based on the microfacet theory, specifically:

[0073] Specular reflection component: Based on the microfacet theory, the geometric attenuation factor (GAF) and the Gaussian distribution surface roughness parameter σ were introduced, and the polarization characteristics were described by combining the Mueller matrix:

[0074]

[0075] Among them, is the wavelength-dependent Mueller matrix element, is the microfacet inclination distribution function.

[0076] Directional diffuse reflection component: The angular response was fitted with a Gaussian distribution and combined with the wavelength polynomial g(λ):

[0077]

[0078] Ideal diffuse reflection component: Through the Lambertian model combined with the wavelength polynomial h(λ):

[0079]

[0080] The final PSBRDF model is the weighted sum of the three components:

[0081]

[0082] The model parameters were optimized by backward-forward wavelength selection (such as Figure 4 ), and the key wavelengths were selected (such as 403 - 406 nm and 724 - 760 nm for sample I) to reduce the influence of redundant data on the inversion accuracy.

[0083] Eigenvalue extraction: The spectral curve was converted into eigenvalues ( etc.) through PSBRDF inversion. The optimal model order was determined by MRE < 0.05 and R² > 0.98 (such as Figure 5, the orders of Samples I - IV are 9, 5, 6, and 12 respectively).

[0084] S3. Construct a prediction model:

[0085] 3.1 Optimize the spectral data dimension using the backward - forward iterative wavelength selection method:

[0086] Backward elimination: Eliminate wavelengths one by one, calculate the mean relative error (MRE) and coefficient of determination (R²) of the inversion parameters for the remaining wavelengths, and retain the wavelengths that optimize MRE and R² (e.g., Figure 6 );

[0087] Forward compensation: Backfill the eliminated wavelengths one by one, verify their contribution to the global accuracy, and dynamically adjust the retained set;

[0088] The specific steps are as follows:

[0089] For each sample, under each detection angle condition, use 361 spectral data points (i = 400, 401, … 760) to perform parameter inversion. Record the original MRE and R 2 , denoted as MRE original and .

[0090] Remove the spectral data of 361 wavelengths one by one, and use the remaining 360 data points to perform parameter inversion again. Record the new MRE and R 2 , denoted as MRE backward and .

[0091] If MRE back < MRE original and > , then retain the data of this wavelength, denoted as ; otherwise, delete this wavelength, denoted as .

[0092] Construct a new retained data set y re, for all retained data points and a new deleted data set y el for all retained data points.

[0093] Perform parameter inversion using the spectral data in y re , and record the new MRE and R 2 , denoted as MRE new and .

[0094] Restore the data to y el , and then perform parameter inversion again. Record MRE and R 2 , denoted as MREforward and 。

[0095] If MRE forward <MRE new and > , the data at that wavelength is put back into the reserved dataset y re ; otherwise, the data is retained in the deleted dataset. Update it as the final inversion dataset and perform inversion using the updated y parameter. Record MRE and R 2 as the final result, denoted as MRE improved and 。

[0096] In the above steps, first eliminate the spectral data that affects the accuracy of parameter inversion through backward selection. Considering the possible common influence of different spectral data on the accuracy of parameter inversion, screen the spectral data again through forward selection to determine the final inversion dataset. The backward-forward iterative wavelength selection method ensures that the parameter inversion result can be used as the spectral eigenvalue describing the spectral behavior of S0RF. The wavelength selection results of the four samples are as Figure 9 shown, and the specific values are shown in Table 2

[0097] Table 2 MRE improved and selected wavelengths

[0098]

[0099] 3.2 Prediction model construction: Use polynomial regression to construct the model, input the detection angle ( ), and output the eigenvalue. The ratio of the training set to the test set is 4:1, and the optimal model is selected through 100 random divisions

[0100] Input the optimized eigenvalue set in step 3.1 into the optimal prediction model to obtain the predicted spectral intensity eigenvalue

[0101] Substitute the predicted spectral intensity eigenvalue into the PSBRDF model to reconstruct the spectral intensity curve, and calculate the degree of linear polarization (DoLP) of the spectrum at the unknown detection angle in combination with the Stokes parameters ( )

[0102]

[0103] It should be noted that

[0104] When predicting the extrapolation angle (such as = 70°), use the interpolation model to expand to ensure that MRE < 0.04 and R² > 0.98

[0105] In summary, the method proposed by the present invention solves the problem of poor generalization ability of traditional models at unknown angles through PSBRDF eigenvalue conversion, and for the first time realizes end-to-end prediction from spectral intensity to polarization spectrum.

[0106] Comparative Example 1:

[0107] The difference from Example 1 is that in step S3, ridge regression (RR) is used to construct the model.

[0108] Comparative Example 2:

[0109] The difference from Example 1 is that in step S3, linear regression (LR) is used to construct the model.

[0110] Comparative Example 3:

[0111] The difference from Example 1 is that in step S3, principal component regression (PCR) is used to construct the model.

[0112] Comparative Example 4:

[0113] The difference from Example 1 is that in step S3, random forest (RF) is used to construct the model.

[0114] Results of effect comparison:

[0115] Evaluation index:

[0116] Average relative error of the training set and average relative error of the test set

[0117]

[0118]

[0119] In the formula: represents the number of predicted values, represents the predicted value, represents the true value, and the subscripts tr and te represent the training set and the test set respectively.

[0120] Using different detection angles ( ) as the dependent variable and the eigenvalues as the independent variables for establishing the prediction model. The training and test sets are randomly assigned, with a ratio of 4:1. To prevent the randomness of the division, each training process is randomly divided 100 times, and the model with the lowest MRE in the test set is selected as the best model from the 100 trials.

[0121] Based on the specified splitting ratio and 100 random splits, the prediction results of Example 1 and Comparative Examples 1, 2, 3, and 4 on the training set and test set are shown in Table 3. Generally speaking, RF and MP are two relatively good methods, which have the best results in the training set or the test sets of different samples.

[0122] Table 3 Prediction Results of Different Methods on the Training Set and Test Set

[0123]

[0124] To visually compare the spectral curve prediction capabilities of several methods at known and unknown detection angles in the dataset (specifically divided into interpolation angles and extrapolation angles), at , , , 55° (interpolation angle) and 70° (extrapolation angle), the prediction capabilities of the spectral intensity curves are compared. It should be noted that the spectrum in the proposed method is restored through the predicted eigenvalues.

[0125] The evaluation metrics are MRE and R 2 , and are as follows:

[0126]

[0127]

[0128] In the formula: represents the number of predicted values, represents the predicted value, represents the true value, and the subscripts tr and te represent the training set and test set respectively

[0129] Under the condition of known detection angles ( ), the predicted spectrum As Figure 10 shown, the evaluation metrics are shown in Table 4.

[0130] Table 4 Evaluation Metrics MRE and R of Different Prediction Methods for Four Types of Samples 2

[0131]

[0132] From Figure 10As can be seen from Table 4, under the known detection angle conditions, the prediction results of the spectral curves and the evaluation indicators show that the best prediction results for Samples I - III are generated by RF, while for Sample IV, the best results are generated by LR. Although the proposed method is not optimal, it ensures that MRE and R² are maintained within a relatively ideal range, with MRE controlled below 0.03 and R² controlled above 0.99. The other three methods, RR, PCR, and PLSR, perform poorly. A possible reason is that RR suppresses the complexity of the model by introducing L2 regularization and fails to capture the non - linear patterns between the characteristic conditions and the spectral curves. At the same time, PCR and PLSR are also unable to capture the non - linear features in the data when extracting the principal components. Under the known detection angle conditions, the sacrifice in the prediction accuracy of the proposed method is predictable because the method transforms the prediction of the spectral curve into eigenvalue extraction. In eigenvalue extraction, accuracy has been sacrificed. To evaluate the ability of the prediction model, it is also necessary to analyze its ability to predict spectral data under unknown detection angle conditions. The predicted spectra under the interpolation detection angle conditions ( ) are as shown in Figure 10 , and the evaluation indicators are shown in Table 5.

[0133] Table 5 Evaluation indicators MRE and R of different prediction methods for four types of samples 2

[0134]

[0135] From Figure 11 the prediction results and evaluation indicators in Table 5, under the interpolation detection angle conditions, except that the best R2 value for Sample I is obtained by LR, the best prediction results for other samples are obtained by the proposed method. When , RF and LR provide better prediction results, but when predicting the spectra in the dataset under unknown conditions, their performance degrades, showing poor generalization ability. The method proposed in Example 1 can still control MRE below 0.03 and R 2 above 0.99 when predicting data at the interpolation angle. In addition, the prediction ability of the model for the spectra at the interpolation angle also needs to be discussed. To some extent, when establishing a prediction model, the derivation ability of this model is a more important concern. The prediction ability at the interpolation angle is used to improve the measured data, while the prediction ability at the derivation angle helps to expand and supplement the measured data. The predicted spectra under the derived detection angle conditions ( ) are as shown in Figure 12 , and the evaluation indicators are shown in Table 6.

[0136] Table 6 Evaluation indicators MRE and R of different prediction methods for four types of samples2

[0137]

[0138] From Figure 12 As can be seen from Table 6, under the derived detection angle conditions, the evaluation metrics of the predicted results and spectral curves show that the predicted spectra of all four samples at the derived angles are all optimal, further demonstrating that the proposed method has high generalization ability. Although the prediction accuracy decreases slightly compared with 60° and 55°, the same phenomenon occurs in both the LR and RF models, but the proposed method still maintains good accuracy, with the MRE controlled below 0.04 and the R 2 maintained above 0.98.

[0139] The ultimate goal of the prediction model is to use to predict the spectral DOLP. Through eigenvalue extraction, important wavelength selection, and the prediction model, the prediction of eigenvalues and spectra at different angles is achieved. By incorporating the eigenvalues into the PSBRDF model, the corresponding spectral DoLP at different angles can be calculated, which cannot be achieved by other methods. When , 60°, and 70°, the predicted spectral DoLP is as Figure 13 shown, and the evaluation metrics are shown in Table 7.

[0140] Table 7 Evaluation metrics MRE and R of spectral DoLP of four samples 2

[0141]

[0142] From Figure 13 the predicted results and evaluation metrics in Table 7, when , 60°, and 70°, the predicted spectral DoLP can basically retain the spectral characteristics of the measured DoLP, as well as the overall trend of the spectral DoLP changing with , that is, the trend that the spectral DoLP increases with the increase of . It should be noted that the performance of predicting the spectral DOLP is not as good as that of predicting the spectral . There are two main reasons for this: First, the eigenvalues of the predicted spectral SoRF calculated through the PSBRDF model require a non-linear calculation process, which amplifies the error between the predicted value and the measured value; Second, there is still room for improvement in the model itself in describing the polarization spectral characteristics. However, the method proposed in Example 1 still successfully controls the MRE in the DoLP prediction to be below 0.03, and the R 2 is above 0.98, whether for the known angles in the dataset or for the interpolated or extrapolated angles.

[0143] In summary, the method proposed in Embodiment 1 of the present invention performs eigenvalue decomposition on the spectral curve, transforming the prediction of the spectral curve into the prediction of eigenvalues. The comparison results show that although the accuracy of the predicted spectral intensity may slightly decrease in the dataset with known detection angles, the method proposed in Embodiment 1 exhibits strong generalization ability and significant advantages under the condition of predicting unknown detection angles, whether it is under interpolation or extrapolation angle conditions. More importantly, since the spectral intensity is transformed into eigenvalues, a connection is established between the predicted eigenvalues and the PSBR DF, thereby realizing the prediction of spectral polarization from the spectral intensity and maintaining the prediction accuracy within a good range.

[0144] Embodiment 2: Application of Spectral Polarization Prediction of Coating Materials

[0145] Taking four coating samples (I-IV) as examples, the implementation steps are as follows:

[0146] Data collection: At = 40°, measure and DoLP in the principal plane ( Figure 7 = 0° - 180°).

[0147] Model training: Use the 9th-order PSBRDF model for Sample I, and screen 102 key wavelengths; the prediction model uses Random Forest (RF), and the MRE of the test set is 0.0146.

[0148] Result verification: At = 60° (known angle) and = 70° (extrapolation angle), the MREs of the predicted DoLP are 0.0217 and 0.0362 respectively (as Figure 8 ).

[0149] Embodiment 3:

[0150] Provided is a spectral polarization prediction device / equipment / system based on the polarization bidirectional reflectance distribution function, including a memory, a processor, and a computer program stored on the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0151] Embodiment 4:

[0152] A computer-readable storage medium, on which a computer program / instructions are stored, wherein the computer program / instructions, when executed by a processor, implement the steps of the above method.

[0153] Embodiment 5:

[0154] A computer program product, comprising a computer program / instructions, characterized in that the steps of the above method are performed when the computer program / instructions are executed by a processor.

[0155] The above are only embodiments of the present invention. Well-known technical details such as polarization measurement and Savitzky-Golay filtering involved in the solution are not described in detail. It should be noted that those skilled in the art can make partial combinations or parameter adjustments without departing from the principle of the present invention, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A spectral polarization prediction method based on the polarized bidirectional reflectance distribution function, characterized in that: The steps are as follows: S1. Dataset preparation: Obtain the spectral intensity and linear polarization degree datasets of the target coating at different detection angles, and preprocess the datasets; S2. Extract eigenvalue: Construct a PSBRDF model, and through the inversion of Mueller matrix parameters based on the microfacet theory, decompose the preprocessed spectral intensity curve into an eigenvalue set composed of wavelength polynomial coefficients and weight parameters; Optimize the eigenvalue set by the backward-forward iterative wavelength selection method; S3. Construct a prediction model: Establish a polynomial regression model, randomly divide the training set and the test set, train and test the model, and select the optimal prediction model; Input the optimized eigenvalue set into the optimal prediction model to obtain the predicted spectral intensity eigenvalues; Substitute the predicted spectral intensity eigenvalues into the PSBRDF model to reconstruct the spectral intensity curve, and calculate and obtain the spectral linear polarization degree at an unknown detection angle in combination with Stokes parameters.

2. The spectral polarization prediction method according to claim 1, characterized in that: In step S1, the detection angles include the incident zenith angle, the observation zenith angle, and the observation azimuth angle.

3. The spectral polarization prediction method according to claim 2, wherein: The range of the incident zenith angle is 30° - 50°, the range of the observation zenith angle is -60° to 60°, and the range of the observation azimuth angle is 0° - 180°.

4. The spectral polarization prediction method according to claim 1, wherein: in In step S2, the mathematical expression of the PSBRDF model is: ； Among them, is the Gaussian distribution function of the microfacet inclination angle, is the geometric attenuation factor, are the 4×4 Mueller matrices of specular, directional diffuse, and ideal diffuse reflections respectively, is a wavelength polynomial function, and the polynomial order is dynamically determined by the thresholds of MRE < 0.05 and R² > 0.

98.

5. The spectral polarization prediction method according to claim 1, characterized in that: in In step S2, the backward-forward iterative wavelength selection method includes: Backward elimination: Eliminate wavelengths one by one, calculate the average relative error and the coefficient of determination of the inversion parameters of the remaining wavelengths, and retain the wavelengths that optimize the average relative error and the coefficient of determination; Forward compensation: Backfill the eliminated wavelengths one by one, verify their contribution to the global accuracy, and dynamically adjust the retention set.

6. The spectral polarization prediction method according to claim 1, wherein: in In step S1, the preprocessing is Savitzky-Golay filtering preprocessing with a window length of 21 and a polynomial order of 2, which is used to eliminate the polarization measurement noise amplification effect in the 400 - 450 nm band.

7. The spectral polarization prediction method according to claim 1, wherein: In step S3, the number of times of randomly dividing the training set and the test set is at least 100 times.

8. A spectral polarization prediction device / equipment / system based on the polarization bidirectional reflectance distribution function, comprising a memory, a processor, and a computer program stored on the memory, characterized in that, The processor executes the computer program to implement the steps of any one of claims 1 - 7.

9. A computer-readable storage medium having computer programs / instructions stored thereon, characterized in that , when the computer program / instructions are executed by the processor, the steps of any one of claims 1 - 7 are implemented.

10. A computer program product, comprising a computer program / instructions, characterized in that, , when the computer program / instructions are executed by the processor, the steps of any one of claims 1 - 7 are implemented.

Images