Spectral characteristic prediction method based on Tanassen matrix estimation

Abstract

The invention provides a spectral characteristic prediction method based on Tanassen matrix estimation, which adopts a deep learning model to obtain a Tanassen matrix, can quickly predict spectral characteristics and appearance color of a sample under any standard or non-standard illuminant, provides a powerful virtual simulation tool for industrial color matching, quality control, product development and the like, and is suitable for large-scale popularization and application. Actual measurement does not need to be carried out on each lighting condition; that is to say, the invention provides the spectral characteristic prediction method which is rapid, accurate and high in automation degree, and the method can efficiently estimate the complete Tanasenson matrix from limited spectral measurement data, is used for predicting the appearance performance of the material under any illumination, and has very high flexibility and practicability.

Description

Technical Field

[0001] This invention belongs to the field of spectral analysis and material characterization technology, and particularly relates to a method for predicting spectral properties based on Donaldson matrix estimation. Background Technology

[0002] In fields such as color science, materials science, and computer graphics, accurate characterization and prediction of the spectral properties of materials are crucial, especially for materials containing fluorescent components (such as fluorescent whitening paper, textiles, plastics, and coatings). These materials not only reflect incident light but also absorb light of specific wavelengths and emit it at longer wavelengths (fluorescence effect).

[0003] To fully describe this complex reflection and fluorescence phenomenon, academia and industry have introduced the two-dimensional Donaldson matrix. The Donaldson matrix provides a complete description of the sample's spectral response, capturing both its reflectance and fluorescence excitation-emission characteristics. Its diagonal elements describe the material's reflectance at various wavelengths, while the off-diagonal elements precisely quantify the fluorescence conversion efficiency from one excitation wavelength to another emission wavelength. It is a bispectral function D( λ em , λ ex ), associated with each excitation wavelength ( λ ex The incident light and each emitted wavelength ( λ em The emitted light from a material. Once the accurate Donaldson matrix of a material is obtained, the total emission spectrum of that material under any illuminator with a known spectral power distribution can theoretically be calculated, thereby obtaining its spectral radiance factor and chromaticity coordinates, and achieving accurate prediction of its appearance color.

[0004] The traditional and most accurate method for obtaining the Donaldson matrix is ​​the dual monochromator method. This technique involves systematically scanning a series of monochromatic excitation wavelengths and measuring the complete emission spectrum for each excitation. Although this method is considered the gold standard, it has significant drawbacks. Due to its sequential scanning nature, the method is very time-consuming and requires expensive and complex instrumentation (two monochromators, a calibration light source, and a detector), making it inefficient for high-throughput analysis or large-scale sample screening.

[0005] Therefore, there is an urgent need in this field for a technical solution that can overcome the shortcomings of traditional methods, such as long time consumption, high cost, and complex operation, in order to achieve rapid and accurate estimation of the Donaldson matrix of materials, thereby improving the efficiency and practicality of spectral characteristic prediction. Summary of the Invention

[0006] To address the problems of existing Donaldson matrix measurement methods being time-consuming, requiring sophisticated equipment, and being complex to operate, this invention provides a spectral characteristic prediction method based on Donaldson matrix estimation. This method enables rapid and accurate estimation of the optical characteristic matrix of materials, and predicts the spectral characteristics and appearance color of materials under different lighting conditions based on the optical characteristic matrix, thereby improving the efficiency and practicality of spectral characteristic prediction.

[0007] A method for predicting spectral properties based on Donaldson matrix estimation includes the following steps: S1: Input at least one set of data consisting of the excitation illumination spectrum and the total emission spectrum formed when the fluorescence sample under test is irradiated by the excitation illumination spectrum into the trained hybrid deep learning model, and then output a two-dimensional Donaldson prediction matrix characterizing the optical properties of the fluorescence sample under test from the hybrid deep learning model. ; S2: Transform the two-dimensional Donaldson prediction matrix Spectral vector of the target illuminator Matrix multiplication is performed to obtain the predicted total emission spectrum vector of the fluorescent sample under target illuminator illumination. ; S3: Based on the predicted total emission spectrum vector Obtain the spectral radiance factor and / or chromaticity coordinates of the fluorescent sample under the spectral illumination of the target illuminator.

[0008] Furthermore, the hybrid deep learning model includes an embedding and interaction layer, a local feature extraction module, a Transformer module, and a feature integration and output module; The embedding and interaction layer projects the excitation illumination spectrum and total emission spectrum in the data pair from the original spectral dimension to a higher-dimensional feature space, and multiplies the excitation illumination spectrum and total emission spectrum in the feature space element by element to obtain the fused spectral features. The local feature extraction module uses a series of cascaded one-dimensional convolutional layers to extract features from the fused spectral features, thereby obtaining local spectral features; among which, the local spectral features include the sharpness of spectral peaks, the position of peaks and valleys, and the local slope of the spectral curve; The Transformer module employs a self-attention mechanism to extract the long-range dependencies of local spectral features across the entire spectral range and global contextual information, thereby obtaining global spectral features. The feature integration and output module fuses local and global spectral features and outputs the fusion result as a two-dimensional Donaldson prediction matrix.

[0009] Furthermore, the loss function L used when training the hybrid deep learning model is: L = α ×L MSE + β × L GFC + γ × L smooth in, L MSE Two-dimensional Donaldson prediction matrix output by a hybrid deep learning model With the two-dimensional Donaldson truth matrix D true The square of the Frobenius norm of the difference between them L GFC The two-dimensional Donaldson prediction matrix after being flattened into a one-dimensional vector. With the two-dimensional Donaldson truth matrix D true Cosine similarity between them L smooth For the two-dimensional Donaldson prediction matrix Regularization loss with physical smoothness constraints applied. α , β , γ They are respectively L MSE , L GFC , L smooth The corresponding preset weights.

[0010] Furthermore, L MSE The calculation method is as follows:

[0011] in, A two-dimensional Donaldson prediction matrix of dimension M×N No. i Line 1 j Column elements, The two-dimensional Donaldson truth matrix of dimension M×N D true No. i Line 1 j Column elements; L GFC The calculation method is as follows:

[0012] in, For the first j Column weights To set penalties, Two-dimensional Donaldson prediction matrix No. j All elements of the column, The two-dimensional Donaldson truth matrix D true No. j All elements of the column, The two-dimensional Donaldson truth matrix D true No. j The maximum value among all elements in the column.

[0013] Furthermore, a tunable illumination system based on a digital micromirror device (DMD) is used to modulate the spectrum of a broadband light source, resulting in excitation illumination spectra with different peak wavelengths, bandwidths, and spectral shapes.

[0014] Furthermore, the tunable lighting system includes a light source 201, a first lens 202, a diffraction grating 203, a second lens 204, a digital micromirror device (DMD) 205, a third lens 206, an integrating sphere 207, and a spectrometer 209. The light beam emitted by the light source 201 is collimated by the first lens 202 to form a uniform light beam and illuminate the diffraction grating 203; The diffraction grating 203 splits the incident beam, and its first-order diffraction beam is converged and focused by the second lens 204 onto the effective area of ​​the digital micromirror device DMD 205. The DMD205 digital micromirror device selectively reflects first-order diffracted beams of different wavelengths by programming and controlling the deflection state of micromirrors at different positions on its internal micromirror array, thereby forming a modulated beam with a customized spectral distribution. The modulated beam, which is modulated and reflected by the digital micromirror device DMD205, is collected by the third lens 206 and converged before entering the interior of the integrating sphere 207 through the entrance port 207a. The integrating sphere 207 is used to homogenize the incident modulated beam. A sample port 207b is provided on the side wall of the integrating sphere 207 for placing the fluorescent sample 208 to be tested, and a detection port 207c is provided on the opposite side of the sample port 207b. When the homogenized modulated beam irradiates the fluorescent sample 208 to be tested, the fluorescent sample 208 is excited to emit fluorescence. The emitted fluorescence and part of the scattered modulated beam are collected by the spectrometer 209 through the detector port 207c, thereby measuring the total emission spectrum under a specific customized excitation illumination spectrum.

[0015] Furthermore, in step S3, the method for obtaining the spectral radiance factor and / or chromaticity coordinates of the fluorescent sample under the spectral illumination of the target illuminator is as follows: Predict the total emission spectral vector Normalization was performed to obtain the spectral radiance factor of the fluorescent sample under the spectral illumination of the target illuminator. The chromaticity coordinates of the fluorescent sample under irradiance by the target illuminator were calculated based on the spectral radiance factor.

[0016] Furthermore, the target illuminator spectrum is either a CIE standard illuminator spectrum or a user-defined non-standard illuminator spectrum.

[0017] Beneficial effects: 1. This invention provides a spectral characteristic prediction method based on Donaldson matrix estimation. It employs a deep learning model to obtain the Donaldson matrix, enabling rapid prediction of the spectral characteristics and appearance color of samples under any standard or non-standard illuminant. This provides a powerful virtual simulation tool for industrial color matching, quality control, and product development, eliminating the need for actual measurements under every illumination condition. In other words, this invention provides a fast, accurate, and highly automated spectral characteristic prediction method. This method can efficiently estimate the complete Donaldson matrix from limited spectral measurement data and use it to predict the appearance of materials under arbitrary illumination, exhibiting strong flexibility and practicality.

[0018] 2. This invention provides a spectral characteristic prediction method based on Donaldson matrix estimation. It extracts local features from the input spectral data using one or more convolutional neural network (CNN) layers. These local features are then input into a Transformer encoder module to capture long-range dependencies between spectral data and generate the final Donaldson matrix estimation result. In other words, this invention, by combining the local feature extraction capability of CNNs with the global dependency modeling capability of Transformers, constructs a hybrid model that provides a deeper understanding of the complex physical processes between excitation and emission. Furthermore, this invention employs an end-to-end deep learning model. Once trained, it only requires collecting a few sets of spectral data to complete the estimation of the entire Donaldson matrix in a very short time (usually within one minute), greatly improving measurement efficiency and achieving an order-of-magnitude speed improvement compared to traditional point-by-point scanning methods.

[0019] 3. This invention provides a spectral characteristic prediction method based on Donaldson matrix estimation, coupled with a specially designed composite loss function. The first term is a first spectral error loss used to minimize the difference between the total emission spectrum predicted by the Donaldson matrix estimated by the model and the actual measured total emission spectrum; the second term is a matrix error loss used to minimize the difference between the Donaldson matrix estimated by the model and the preset true Donaldson matrix; and the third term is a regularization loss used to impose physical smoothness constraints on the estimated Donaldson matrix. The loss function used in this invention ensures that the estimation results are numerically accurate, spectrally realistic, and physically smooth, and its accuracy is significantly better than that of traditional models or single-structure deep learning models. Attached Figure Description

[0020] Figure 1 A flowchart of a fluorescence Donaldson matrix estimation method based on deep learning provided for this invention; Figure 2 This is a schematic diagram of a light source device for generating customized excitation spectra provided by the present invention; Figure 3 The detailed architecture diagram of the hybrid CNN-Transformer deep learning model for estimating the Donaldson matrix provided by this invention shows the process of data flow through the embedding layer, convolutional module, Transformer encoder and fully connected layer. Detailed Implementation

[0021] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0022] A method for predicting spectral properties based on Donaldson matrix estimation first estimates the Donaldson matrix of a sample through measurement and a deep learning model, and then uses this matrix to predict the spectral properties of the sample under arbitrary target illumination. Figure 1 As shown, it includes the following steps: S1: Input at least one set of data consisting of the excitation illumination spectrum and the total emission spectrum formed when the fluorescence sample under test is irradiated by the excitation illumination spectrum into the trained hybrid deep learning model, and then output a two-dimensional Donaldson prediction matrix characterizing the optical properties of the fluorescence sample under test from the hybrid deep learning model. In this matrix, the diagonal elements represent the reflectance properties of the sample, while the off-diagonal elements represent the fluorescence conversion properties of the sample.

[0023] S2: Transform the two-dimensional Donaldson prediction matrix Spectral vector of the target illuminator Matrix multiplication is performed to obtain the predicted total emission spectrum vector of the fluorescent sample under target illuminator illumination. ; S3: Based on the predicted total emission spectrum vector Obtain the spectral radiance factor and / or chromaticity coordinates of the fluorescence sample to be tested under the illumination of a target illuminator, such as a CIE standard illuminator spectrum or a user-defined non-standard illuminator spectrum.

[0024] In other words, the present invention acquires at least one data pair consisting of the excitation illumination spectrum and the corresponding total emission spectrum. In a typical embodiment, this can be obtained by emitting a series of excitation lights with different broadband spectral power distributions (e.g., through different combinations of LEDs or filters) onto the sample and measuring the total emission spectrum produced by the sample under each excitation using a standard spectrometer.

[0025] Then, using these data pairs as input, a pre-trained computational model is used to directly estimate the two-dimensional Donaldson matrix characterizing the optical properties of the sample.

[0026] The following section details the specific implementation methods for each step.

[0027] Step S101: Use a DMD tunable light source to generate a set of preset, diverse excitation illumination spectra.

[0028] In this step, we utilize a tunable illumination system based on a digital micromirror device (DMD). This system, by precisely controlling the deflection states of millions of micromirrors on the DMD, can spectrally modulate a broadband light source (such as a xenon lamp), thereby flexibly and rapidly generating a series of excitation lights with different peak wavelengths, bandwidths, and spectral shapes. l 1, l 2, …, l n This diverse set of excitation spectra forms the basis for subsequent model training and accurate estimation. Its diversity ensures that the model can learn the sample's response under various excitation conditions.

[0029] Step S102: Irradiate the fluorescent sample with each excitation spectrum and collect the corresponding total emission spectrum to form a spectral data pair.

[0030] Each excitation illumination spectrum generated in step S101 is sequentially or according to a specific encoding method irradiated onto the fluorescence sample to be tested. For each excitation light... l i (i=1,…,n) uses a single spectral detector (such as a spectrometer) to simultaneously acquire the total emission spectrum emitted from the sample surface. s i The total emission spectrum is the superposition of the pure reflected light from the sample and the fluorescence generated after excitation. Each "excitation illumination spectrum" is paired with its corresponding "total emission spectrum" to form a set of spectral data pairs {(l 1, s 1), ( l 2, s 2), …, ( l n , s n This set of data will serve as input for subsequent deep learning models.

[0031] Step S103: Input the spectral data pairs into the CNN-Transformer hybrid deep learning model.

[0032] The multiple sets of spectral data obtained in step S102 are input into a pre-built hybrid deep learning model. The core architecture of this model integrates a convolutional neural network (CNN) and a Transformer encoder. The CNN layer extracts local features (such as the sharpness of spectral peaks and local shapes) from the excitation and emission spectra, while the Transformer encoder module utilizes its self-attention mechanism to capture long-range dependencies and global contextual information of the spectral data across the entire wavelength range. This step corresponds to the core content of claim 1.

[0033] Step S104: The model undergoes end-to-end processing and directly outputs the estimated Donaldson matrix.

[0034] Internally, the input excitation and emission spectra are first processed and fused in parallel, then sequentially passed through a CNN module and a Transformer encoder module to capture local spectral features and global contextual information, respectively. The entire model acts as an end-to-end mapping function, decoding the input series of spectral data into a two-dimensional matrix. This output two-dimensional matrix is ​​the estimated Donaldson matrix of the sample, denoted as Depred. According to its physical definition, the diagonal elements of this matrix represent the pure reflectance of the sample at different wavelengths, while the off-diagonal elements fully describe the fluorescence intensity produced at all other wavelengths under a certain excitation wavelength.

[0035] Step S105: Set the target illuminator spectrum.

[0036] Select one or more target illuminators based on actual application requirements. These illuminators can be standard illuminators defined by the International Commission on Illumination (CIE), such as the D65 illuminator simulating daylight or the A illuminator simulating incandescent light; or they can be any non-standard illuminator customized by the user according to the actual scenario, such as a specific model of LED light or mixed lighting for commercial shop windows. Represent the spectral power distribution of the selected illuminators as a vector. L target .

[0037] Step S106: Calculate the total emission spectrum based on the estimated Donaldson matrix.

[0038] The estimated Donaldson matrix D obtained in step S104 pred Compared with the target illuminator spectral vector set in step S105 L target Perform matrix multiplication to obtain the predicted total emission spectrum vector of the sample under the target illumination. S total :

[0039] This operation mathematically simulates the physical process of light-matter interaction, which is the sum of the contributions made by each wavelength component of the illumination spectrum at all emission wavelengths after interacting with the reflection and fluorescence conversion properties of the sample.

[0040] Step S107: Calculate the spectral radiance factor and chromaticity coordinates.

[0041] To obtain a standardized color metric, the total emission spectrum calculated in step S106 can be used. S total Divide by an ideal diffuse white board in the same illuminated body L target The reflection spectrum under the given conditions is used to obtain the spectral radiance factor β(λ).

[0042] After obtaining the spectral radiance factor β(λ), the tristimulus values ​​(XYZ) of the sample under the target illuminator and its chromaticity coordinates (e.g., L) in standard color spaces such as CIELAB can be further calculated according to the CIE color science standard formula. * , a * , b * By repeating steps S105 to S107, the appearance color of samples under various lighting conditions can be predicted quickly and in batches without any additional physical measurements, greatly improving efficiency and flexibility.

[0043] Further reference Figure 2 The diagram illustrates a schematic structural representation of a light source device 200 for generating a customized excitation spectrum according to an embodiment of the present invention. The device 200 is used for implementing… Figure 1 The data acquisition steps in the process. For example... Figure 2 As shown, the device 200 includes a light source 201, a first lens 202, a diffraction grating 203, a second lens 204, a digital micromirror device (DMD) 205, a third lens 206, an integrating sphere 207, and a spectrometer 209.

[0044] In one embodiment, the light source 201 may be a xenon lamp, the light beam of which is collimated by a first lens 202 (e.g., a plano-convex single lens made of fused silica) to form a uniform light beam and illuminate the diffraction grating 203.

[0045] The diffraction grating 203 splits the incident beam, and its first-order diffracted beam is converged and focused by the second lens 204 onto the effective area of ​​the DMD 205. In this way, light of different wavelengths is dispersed horizontally on the surface of the DMD 205.

[0046] The DMD 205 can selectively reflect light of different wavelengths by programming the deflection state of micromirrors at different positions on its internal micromirror array, thereby forming a modulated beam with a customized spectral distribution.

[0047] The beam modulated and reflected by DMD 205 is collected by the third lens 206 and converged before entering the interior of integrating sphere 207 through the entrance port 207a. Integrating sphere 207 is used to homogenize the incident modulated beam.

[0048] A sample port 207b is provided on the side wall of the integrating sphere 207 for placing the fluorescent sample 208 to be tested. A detector port 207c is provided on the opposite side of the sample port 207b.

[0049] When homogenized excitation light is irradiated onto the fluorescent sample 208, the sample 208 is excited to emit fluorescence. The emitted fluorescence (including partially scattered excitation light) is collected by a spectrometer 209 (e.g., a JETI spectrometer) through a detector port 207c, thereby measuring the total emission spectrum under a specific customized excitation spectrum.

[0050] Furthermore, in a preferred embodiment of the present invention, the computational model is a deep learning model, more specifically, a hybrid deep learning model. This model is designed to fully utilize the advantages of different network structures, and its steps for processing input spectral data are as follows: a) Local Feature Extraction: The input spectral data is first passed through one or more convolutional neural network (CNN) layers. CNN structures excel at capturing local correlations and patterns in the data, and are used in this step to effectively extract local shape features, peak and valley information, etc., from the spectral curve.

[0051] b) Global Relationship Modeling and Matrix Generation: Local features extracted from the CNN layers are fed into a Transformer encoder module. The core of the Transformer architecture is the self-attention mechanism, which captures long-range dependencies between any two positions in the input sequence. In this step, it is used to analyze the interactions between features in different bands and synthesize all information to ultimately generate an estimate of the entire two-dimensional Donaldson matrix. This direct generation method from the input spectrum to the output matrix achieves end-to-end estimation.

[0052] See details Figure 3 This diagram illustrates the detailed architecture of the hybrid CNN-Transformer deep learning model 300 used in this embodiment. One of the core components of this invention is this unique hybrid model, whose architecture executes on a processor and is designed to efficiently capture local and global spectral features. The specific structure and data processing flow are as follows: 1. Embedded and Interaction Layer: The collected n illumination spectra ( l 1, l 2, …, l n )301 and n emission spectra ( s 1, s 2, …, s n )302 projects the original spectral dimensions to a higher-dimensional feature space through independent learnable embedding layers 310a and 310b, respectively. To explicitly simulate the physical interaction between the excitation light and the sample response, the resulting embedding vectors of the illumination and emission spectra are fused in an interaction layer 320 via element-wise multiplication. This step is crucial for the model to learn the conditional relationship between the excitation and emission spectra.

[0053] 2. Local Feature Extraction Module (CNN Module): The fused high-dimensional feature representation is then fed into a CNN module consisting of a series of one-dimensional convolutional (Conv1D) layers 330a and 330b. These convolutional layers act as local feature extractors, effectively identifying feature patterns within small wavelength windows, such as the sharpness of spectral peaks, the location of peaks and valleys, and the local slope of spectral curves. This is similar to the principle by which CNNs identify local patterns such as edges and textures in image processing. Each convolutional layer is followed by a ReLU non-linear activation function by default to increase the model's non-linear expressive power.

[0054] 3. Transformer module (Global Context Modeling): After local features are extracted, the data is fed into the Transformer module to capture global information. The data sequence is first combined with a learnable positional encoding 340, which provides the model with information about the location (i.e., wavelength) of each data point in the sequence, crucial for spectral data. The sequence is then fed into a Transformer encoder 350, which utilizes its core self-attention mechanism. This mechanism allows the model to weigh the importance of all other wavelengths in the spectrum when processing each wavelength point, effectively capturing long-range dependencies and global context across the entire spectral range. This is particularly important for accurately modeling fluorescence phenomena, as excitation in one wavelength region can lead to emission in physically distant spectral regions (i.e., Stokes shift).

[0055] 4. Feature Integration and Output Module: The output from the Transformer encoder 350 (which already contains rich global context information) can be further processed by another Conv1D layer 360a to deeply integrate the local and global features learned in the preceding steps. To ensure that the elements of the output Donaldson matrix are non-negative, consistent with its physical meaning, a Softplus activation function 370a is applied before the output layer. Finally, the final two-dimensional estimated Donaldson matrix is ​​output. D pred ( λ em , λ ex 380.

[0056] To ensure that the aforementioned hybrid CNN-Transformer model can accurately estimate the Donaldson matrix from the input excitation-emission spectrum pairs, and to guarantee the accuracy and physical plausibility of the model's estimation results, supervised training of the model is necessary. One of the core innovations of this invention lies in employing a specially designed composite loss function to guide the model's training process, ensuring that the prediction results achieve high standards in numerical accuracy, spectral morphology, and physical realism.

[0057] It should be noted that the training dataset contains multiple sets of samples, each consisting of an input "spectral data pair" and its corresponding "ground value" Donaldson matrix. D true Composition. The "truth value" Donaldson matrix. D true It can be obtained in advance through high-precision physical model simulation or traditional scanning measurement methods.

[0058] During the research and development process, various combinations of loss functions were experimented with. The study found that using them alone... L MSEThis can lead to the loss of crucial fingerprint information for distinguishing different fluorescent substances in the reconstructed signal. Introducing... L GFC Afterwards, although the peak shape was significantly improved, spurious signals were easily generated in regions with low signal-to-noise ratios. Ultimately, it was found that it was necessary to... L MSE , L GFC and L smooth Only when these three factors are combined with specific weights can they work together to suppress noise, maintain peak shape, and ensure numerical accuracy, thus achieving a synergistic optimization effect.

[0059] Based on this, the present invention employs a composite loss function comprising three terms during the model training phase. L : L = α × L MSE + β × L GFC + γ × L smooth Here, α, β, and γ are preset weight hyperparameters used to balance the importance of different optimization objectives. The specific definitions and functions of these three loss terms are as follows: First item: Loss of spectral mean square error L MSE This loss term is used to compare the difference between "the total emission spectrum predicted by the Donaldson matrix estimated by the model" and "the total emission spectrum actually measured in the experiment". It ensures the accuracy of the model at the final application level (i.e., spectral prediction).

[0060] In other words, L MSE Used to ensure the numerical precision of the prediction matrix at the element-wise level. It calculates the prediction matrix... D pred With the truth matrix D true This is achieved by squared Frobenius norm of the difference between the predicted and actual values, ensuring that the predicted values ​​are as close as possible to the true values. Its form is:

[0061] in, A two-dimensional Donaldson prediction matrix of dimension M×N No. i Line 1 j Column elements, The two-dimensional Donaldson truth matrix of dimension M×N D true No.i Line 1 j Column elements; Second item: Matrix error loss L GFC The training dataset can include a “true” Donaldson matrix, precisely measured using conventional methods, as a supervisory label. This loss term directly compares the model-estimated Donaldson matrix with the true matrix (e.g., using mean squared error), thus fundamentally supervising the model to generate correct intermediate results.

[0062] In other words, L GFC The aim is to ensure that the predicted spectrum is highly similar to the true spectrum in shape and structure. The Goodness-of-Fit Coefficient (GFC) is essentially the cosine similarity between two vectors. This invention will... D pred and D true Flattened into a one-dimensional long vector, its GFC is calculated. The loss term is defined as 1-GFC, where GFC is 1 and loss is 0 when the two spectra are perfectly identical. This allows the model to accurately capture the position, relative intensity, and overall contour of spectral peaks, rather than simply matching absolute values. Its form is...

[0063] in, For the first j Column weights To set penalties, Two-dimensional Donaldson prediction matrix No. j All elements of the column, The two-dimensional Donaldson truth matrix D true No. j All elements of the column, The two-dimensional Donaldson truth matrix D true No. j The maximum value among all elements in the column.

[0064] Third item: Regularization loss L smooth This loss term imposes physical constraints on the estimated Donaldson matrix. For example, it encourages smooth matrix surfaces by calculating the differences between adjacent elements in the matrix, since real Donaldson matrices typically have good smoothness. This effectively suppresses noise and ensures that the output conforms to physical laws.

[0065] It should be noted that, L smoothThis is a physical prior regularization term used to ensure that the generated spectrum has physical smoothness. Real spectral curves are typically continuous and smooth. This loss term is implemented by penalizing the gradient or second-order difference (i.e., local curvature) between adjacent elements in the prediction matrix Dpred.

[0066] During training, the gradient of the composite loss function L with respect to all learnable parameters of the model is calculated using the backpropagation algorithm. Subsequently, the Adam optimizer is used to iteratively update the model parameters based on the calculated gradients, thereby collaboratively minimizing these three loss terms. After training, the model is optimized to generate Donaldson matrix estimation results that demonstrate excellent performance in terms of numerical value, shape, and smoothness.

[0067] In summary, this invention provides a method for predicting spectral characteristics based on Donaldson matrix estimation. It acquires a data pair consisting of the excitation illumination spectrum and the corresponding total emission spectrum; processes the data pair using a trained hybrid deep learning model to generate an estimated two-dimensional Donaldson matrix that fully characterizes the sample's reflectance and fluorescence properties in an end-to-end manner; then, it uses the estimated Donaldson matrix to calculate the spectral radiance factor and corresponding chromaticity coordinates of the sample under any preset illuminant. In a preferred embodiment, the model is trained using a composite loss function to simultaneously optimize the numerical accuracy, spectral shape similarity, and smoothness of the estimation results. This invention overcomes the time-consuming nature of traditional measurement methods, providing a practical tool for quickly and accurately estimating the Donaldson matrix and directly predicting the appearance color of fluorescent materials under various practical lighting scenarios, significantly improving analytical efficiency and application flexibility.

[0068] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for predicting spectral properties based on Donaldson matrix estimation, characterized in that, Includes the following steps: S1: Input at least one set of data consisting of the excitation illumination spectrum and the total emission spectrum formed when the fluorescence sample under test is irradiated by the excitation illumination spectrum into the trained hybrid deep learning model, and then output a two-dimensional Donaldson prediction matrix characterizing the optical properties of the fluorescence sample under test from the hybrid deep learning model. ; S2: Transform the two-dimensional Donaldson prediction matrix Spectral vector of the target illuminator Matrix multiplication is performed to obtain the predicted total emission spectrum vector of the fluorescent sample under target illuminator illumination. ; S3: Based on the predicted total emission spectrum vector Obtain the spectral radiance factor and / or chromaticity coordinates of the fluorescent sample under the spectral illumination of the target illuminator.

2. The spectral characteristic prediction method based on Donaldson matrix estimation as described in claim 1, characterized in that, The hybrid deep learning model includes an embedding and interaction layer, a local feature extraction module, a Transformer module, and a feature integration and output module; The embedding and interaction layer projects the excitation illumination spectrum and total emission spectrum in the data pair from the original spectral dimension to a higher-dimensional feature space, and multiplies the excitation illumination spectrum and total emission spectrum in the feature space element by element to obtain the fused spectral features. The local feature extraction module uses a series of cascaded one-dimensional convolutional layers to extract features from the fused spectral features, thereby obtaining local spectral features; among which, the local spectral features include the sharpness of spectral peaks, the position of peaks and valleys, and the local slope of the spectral curve; The Transformer module employs a self-attention mechanism to extract the long-range dependencies of local spectral features across the entire spectral range and global contextual information, thereby obtaining global spectral features. The feature integration and output module fuses local and global spectral features and outputs the fusion result as a two-dimensional Donaldson prediction matrix.

3. The spectral characteristic prediction method based on Donaldson matrix estimation as described in claim 1, characterized in that, The loss function L used when training a hybrid deep learning model is: L = α × L MSE + β × L GFC + γ × L smooth in, L MSE Two-dimensional Donaldson prediction matrix output by a hybrid deep learning model With the two-dimensional Donaldson truth matrix D true The square of the Frobenius norm of the difference between them L GFC The two-dimensional Donaldson prediction matrix after being flattened into a one-dimensional vector. With the two-dimensional Donaldson truth matrix D true Cosine similarity between them L smooth For the two-dimensional Donaldson prediction matrix Regularization loss with physical smoothness constraints applied. α , β , γ They are respectively L MSE , L GFC , L smooth The corresponding preset weights.

4. The spectral characteristic prediction method based on Donaldson matrix estimation as described in claim 3, characterized in that, L MSE The calculation method is as follows: in, A two-dimensional Donaldson prediction matrix of dimension M×N No. i Line 1 j Column elements, The two-dimensional Donaldson truth matrix of dimension M×N D true No. i Line 1 j Column elements; L GFC The calculation method is as follows: in, For the first j Column weights To set penalties, Two-dimensional Donaldson prediction matrix No. j All elements of the column, The two-dimensional Donaldson truth matrix D true No. j All elements of the column, The two-dimensional Donaldson truth matrix D true No. j The maximum value among all elements in the column.

5. The spectral characteristic prediction method based on Donaldson matrix estimation as described in claim 1, characterized in that, A tunable illumination system based on a digital micromirror device (DMD) was used to modulate the spectrum of a broadband light source, resulting in excitation and illumination spectra with different peak wavelengths, bandwidths, and spectral shapes.

6. The spectral characteristic prediction method based on Donaldson matrix estimation as described in claim 5, characterized in that, The tunable illumination system includes a light source (201), a first lens (202), a diffraction grating (203), a second lens (204), a digital micromirror device (DMD) (205), a third lens (206), an integrating sphere (207), and a spectrometer (209). The light beam emitted by the light source (201) is collimated by the first lens (202) to form a uniform light beam and illuminate the diffraction grating (203); The diffraction grating (203) splits the incident beam, and its first-order diffraction beam is converged and focused by the second lens (204) onto the effective area of ​​the digital micromirror device (DMD) (205). The digital micromirror device (DMD) (205) selectively reflects first-order diffracted beams of different wavelengths by programming and controlling the deflection state of micromirrors at different positions on its internal micromirror array, thereby forming a modulated beam with a customized spectral distribution. The modulated beam, which is modulated and reflected by the digital micromirror device DMD (205), is collected by the third lens (206) and converged before entering the interior of the integrating sphere (207) through the entrance port (207a). The integrating sphere (207) is used to homogenize the incident modulated beam. A sample port (207b) is provided on the side wall of the integrating sphere (207) for placing the fluorescent sample (208) to be tested, and a detection port (207c) is provided on the opposite side of the sample port (207b). When the homogenized modulated beam is irradiated onto the fluorescent sample (208) to be tested, the fluorescent sample (208) to be tested is excited to emit fluorescence. The emitted fluorescence and part of the scattered modulated beam are collected by the spectrometer (209) through the detector port (207c), thereby measuring the total emission spectrum under a specific customized excitation illumination spectrum.

7. The spectral characteristic prediction method based on Donaldson matrix estimation as described in claim 1, characterized in that, In step S3, the method for obtaining the spectral radiance factor and / or chromaticity coordinates of the fluorescent sample under the spectral illumination of the target illuminator is as follows: Predict the total emission spectral vector Normalization was performed to obtain the spectral radiance factor of the fluorescent sample under the spectral illumination of the target illuminator. The chromaticity coordinates of the fluorescent sample under irradiance by the target illuminator were calculated based on the spectral radiance factor.

8. The spectral characteristic prediction method based on Donaldson matrix estimation as described in claim 1, characterized in that, The target illuminator spectrum is either a CIE standard illuminator spectrum or a user-defined non-standard illuminator spectrum.

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