A method for predicting surface characteristic parameters of an ultra-smooth optical element

Abstract

The application discloses a kind of super smooth optical element surface characteristic parameter prediction methods, it is related to optical element measurement technical field, comprising: the value range of each surface parameter is determined and sampling accuracy;Scattering rate distribution database is constructed, and preprocessing is carried out;Classification-parameter prediction two-step neural network is constructed, and training is carried out;Obtain the integral scattering rate distribution data of super smooth optical element, carry out surface PSD statistical distribution prediction and surface characteristic parameter prediction.The application realizes the accurate classification of surface PSD statistical distribution of super smooth optical element, and the high-precision prediction and evaluation of key parameters such as surface roughness, autocorrelation length, to provide a kind of brand-new solution for the performance evaluation and quality control of super smooth optical element.

Description

Technical Field

[0001] This invention relates to the field of optical element measurement technology, and specifically to a method for predicting surface characteristic parameters of ultra-smooth optical elements. Background Technology

[0002] With advancements in gravitational wave detection technology, the surface quality of ultra-smooth optical components has become a key factor affecting system performance. Spaceborne gravitational wave telescopes need to be both transceiver and receiver-based, but the gravitational wave signals to be measured are extremely weak, thus placing extremely stringent requirements on the stray light levels of these telescopes. The stray light levels of spaceborne telescopes are primarily constrained by the surface characteristics of ultra-smooth optical components, which typically require sub-nanometer-level surface roughness and extremely low optical loss. Any minute surface defects or scattering can lead to signal attenuation and increased stray light, severely impacting the measurement accuracy and reliability of gravitational wave telescopes.

[0003] However, the detection of surface properties of ultra-smooth optical components still faces significant challenges: on the one hand, a unified measurement standard and evaluation system has not yet been established; on the other hand, traditional characterization methods have limitations in terms of detection efficiency, accuracy, and non-destructive comprehensive evaluation, making it difficult to meet the demand for high-precision and rapid measurement of surface morphology, scattering distribution, and loss parameters.

[0004] Among various optical characterization methods, the Generalized Beckmann-Kirchhoff (GBK) scalar scattering theory can accurately describe the scattering characteristics of ultrasmooth optical elements, including bidirectional scattering distribution, angular-resolved scattering, and integrated scattering rate. However, its input depends on the power spectral density (PSD) and characteristic parameters of the element's surface. It is worth noting that while the cavity ring-down method, as a highly sensitive optical loss measurement technique, can reflect the overall loss characteristics of the element, it is difficult to directly obtain the surface morphology and its related parameters. Therefore, there is an urgent need to develop a new method that combines high precision and high efficiency, and enables multi-parameter non-destructive testing and prediction. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a method for predicting surface characteristic parameters of ultra-smooth optical elements, which solves the performance deficiencies of existing technologies in terms of detection efficiency, accuracy, and non-destructive comprehensive evaluation.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] A method for predicting surface characteristic parameters of ultra-smooth optical components includes the following steps:

[0008] S1. Based on prior knowledge of ultra-smooth optical elements, determine the value range and sampling accuracy of various surface parameters;

[0009] S2. Based on the experimental principle of scattering measurement using the cavity ring-down method, a scattering rate distribution database is constructed using the GBK scalar scattering model theory and preprocessed.

[0010] S3. Based on the value range and sampling accuracy of various surface parameters, a two-step neural network for classification and parameter prediction is constructed and trained using a preprocessed scattering rate distribution database.

[0011] S4. Through the cavity ring-down scattering measurement experiment, the integral scattering rate distribution data of the ultra-smooth optical element is obtained. The trained classification-parameter prediction two-step neural network is used to predict the statistical distribution of surface PSD and the surface characteristic parameters.

[0012] Furthermore, the surface parameters in S1 and their value ranges are as follows:

[0013] Roughness, ranging from 0.1 to 1 nm;

[0014] Autocorrelation length, ranging from 1 to 20 μm;

[0015] Slope, ranging from 2.0 to 2.5;

[0016] Cutoff frequency, with a value range of 5 × 10⁻⁶. -4 Up to 0.1μm -1 .

[0017] Further, S2 includes the following steps:

[0018] S21. Based on the experimental principle of scattering measurement using the cavity ring-down method, and using the GBK scalar scattering model theory, calculate the integral scattering rate distribution data of ultra-smooth optical elements under three surface PSD statistical distributions (Gaussian, fractal, and Cauchy-Lorentz) at different spatial solid angles, and form a scattering rate distribution database.

[0019] S22. Perform data normalization on the scattering rate distribution database, randomly shuffle the order, and perform preprocessing to divide it into training and validation sets.

[0020] Furthermore, in S21, the expression for the integral scattering rate distribution of the ultra-smooth optical element at different spatial solid angles is: ,

[0021] in, The integral scattering rate, For the bidirectional reflection distribution function of an ultra-smooth optical element, The angle of incidence in spherical coordinates. Let be the scattering angle in spherical coordinates, and cos be the cosine function. For the integral solid angle.

[0022] Furthermore, in S21, the expression for the bidirectional reflection distribution function of the ultra-smooth optical element under a Gaussian distribution is: , ,

[0023] in, This represents the bidirectional reflection distribution function of an ultra-smooth optical element under a Gaussian distribution. The angle of incidence in spherical coordinates. The incident azimuth angle in spherical coordinates. The scattering angle in spherical coordinates. The scattering azimuth angle in spherical coordinates. For roughness, The incident light wavelength, For surface reflectivity related to polarization, It is a natural exponential function. Infinite For convergent series, ! is the factorial operator. The PSD function is under a Gaussian distribution. Pi The autocorrelation length, for Spatial frequency in the direction, for Spatial frequency in the direction, These are intermediate parameters for the GBK scalar scattering model;

[0024] The expression for the bidirectional reflection distribution function of an ultra-smooth optical element under a fractal distribution is: , ,

[0025] in, This represents the bidirectional reflection distribution function of an ultrasmooth optical element under a fractal distribution. The PSD function under fractal distribution. The first parameter of the fractal distribution is... The second parameter of the fractal distribution. The third parameter of the fractal distribution;

[0026] The expression for the bidirectional reflection distribution function of an ultra-smooth optical element under the Cauchy-Lorentz distribution is: , ,

[0027] in, This represents the bidirectional reflection distribution function of an ultrasmooth optical element under the Cauchy-Lorentz distribution. The PSD function is given by the Cauchy-Lorentz distribution. Let be the first parameter of the Cauchy-Lorentz distribution. is the cutoff frequency of the Cauchy-Lorentz distribution.

[0028] Furthermore, the intermediate parameters of the GBK scalar scattering model The expression is:

[0029] ,

[0030] in, The refractive index of the incident medium is... The refractive index of the exit medium, For the relevant surface roughness;

[0031] The expression is: ,

[0032] in, This is the cutoff frequency for integrating spatial frequencies. For and The PSD function is the independent variable; Spatial frequency in direction The expression is: ,

[0033] Where sin is the sine function and cos is the cosine function;

[0034] Spatial frequency in direction The expression is:

[0035] .

[0036] Furthermore, the classification-parameter prediction two-step neural network of S3 includes:

[0037] A classification neural network is used to analyze the statistical distribution of the surface PSD of an ultra-smooth optical element based on the integral scattering rate distribution data, determining whether it belongs to Gaussian, fractal, or Cauchy-Lorentz distribution.

[0038] A Gaussian distribution parameter prediction network is used to predict roughness and autocorrelation length for integral scattering rate distribution data of ultra-smooth optical elements with Gaussian distribution.

[0039] A fractal distribution parameter prediction network is used to predict roughness, autocorrelation length, and slope for integral scattering rate distribution data of ultra-smooth optical elements with fractal distribution types.

[0040] A Cauchy-Lorentz distribution parameter prediction network is used to predict roughness, autocorrelation length, and cutoff frequency for integrated scattering rate distribution data of ultra-smooth optical elements with Cauchy-Lorentz distribution.

[0041] Furthermore, the classification neural network, Gaussian distribution parameter prediction network, fractal distribution parameter prediction network, and Cauchy-Lorenz distribution parameter prediction network have the same structure, all including a first convolutional block, a second convolutional block, a third convolutional block, a multi-scale pooling layer, a fully connected layer, and an output layer connected in sequence.

[0042] The first convolutional block and the second convolutional block have the same structure, both including two convolutional layers and a max pooling layer connected in sequence;

[0043] The third convolutional block is a convolutional layer;

[0044] The multi-scale pooling layer consists of two parallel pooling branches, each comprising: a global average pooling layer and a fully connected sub-layer connected in sequence; and a global max pooling layer and a fully connected sub-layer connected in sequence.

[0045] The fully connected layer comprises three fully connected sub-layers connected in sequence;

[0046] The output layer is a fully connected sublayer.

[0047] Furthermore, S3 uses the cross-entropy loss function to train the classification neural network; and uses the MSE (Mean Squared Error) loss function to train the Gaussian distribution parameter prediction network, the fractal distribution parameter prediction network, and the Cauchy-Lorentz distribution parameter prediction network.

[0048] The beneficial effects of this invention are as follows: By integrating the cavity ring-down method and GBK scalar scattering theory, this invention utilizes a neural network to construct an intelligent mapping model from cavity ring-down experimental data to the surface quality parameters of the component, thereby achieving accurate classification of the statistical distribution of PSD on the surface of ultra-smooth optical components, as well as high-precision prediction and evaluation of key parameters such as surface roughness and autocorrelation length, thus providing a brand-new solution for the performance evaluation and quality control of ultra-smooth optical components. Attached Figure Description

[0049] Figure 1 This is a flowchart of a method for predicting surface characteristic parameters of an ultra-smooth optical element according to an embodiment of the present invention;

[0050] Figure 2 This is a diagram illustrating the internal structure of the classification-parameter prediction two-step neural network according to an embodiment of the present invention.

[0051] Figure 3This is an internal structure diagram of the classification neural network, Gaussian distribution parameter prediction network, fractal distribution parameter prediction network, and Cauchy-Lorentz distribution parameter prediction network in an embodiment of the present invention.

[0052] Figure 4 This is an experimental result of the training accuracy of the classification neural network according to an embodiment of the present invention;

[0053] Figure 5 The figure shows the experimental results of the classification neural network training loss function in an embodiment of the present invention.

[0054] Figure 6 This is a confusion matrix diagram of the classification neural network test set in an embodiment of the present invention;

[0055] Figure 7 The figure shows the experimental results of the training loss function of the Gaussian distribution parameter prediction network in an embodiment of the present invention.

[0056] Figure 8 This is an experimental result of the roughness prediction using a Gaussian distribution parameter prediction network according to an embodiment of the present invention.

[0057] Figure 9 This is an experimental result of the autocorrelation length prediction of the Gaussian distribution parameter prediction network according to an embodiment of the present invention.

[0058] Figure 10 This is an experimental result of the training loss function of the fractal distribution parameter prediction network according to an embodiment of the present invention;

[0059] Figure 11 This is an experimental result of roughness prediction using a fractal distribution parameter prediction network according to an embodiment of the present invention.

[0060] Figure 12 This is an experimental result of the autocorrelation length prediction of the fractal distribution parameter prediction network according to an embodiment of the present invention.

[0061] Figure 13 This is an experimental result of the slope prediction of the fractal distribution parameter prediction network according to an embodiment of the present invention.

[0062] Figure 14 This is an experimental result of the training loss function of the Cauchy-Lorentz distribution parameter prediction network according to an embodiment of the present invention;

[0063] Figure 15 This is an experimental result of the roughness prediction using the Cauchy-Lorentz distribution parameter prediction network according to an embodiment of the present invention.

[0064] Figure 16 This is an experimental result of the autocorrelation length prediction network of the Cauchy-Lorentz distribution parameter prediction network in an embodiment of the present invention.

[0065] Figure 17This is an experimental result of the Cauchy-Lorentz distribution parameter prediction network predicting the cutoff frequency in an embodiment of the present invention. Detailed Implementation

[0066] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0067] like Figure 1 As shown, a method for predicting surface characteristic parameters of ultra-smooth optical components includes the following steps:

[0068] S1. Based on prior knowledge of ultra-smooth optical elements, determine the value range and sampling accuracy of various surface parameters.

[0069] The surface parameters in S1 and their value ranges are as follows:

[0070] Roughness, ranging from 0.1 to 1 nm;

[0071] Autocorrelation length, ranging from 1 to 20 μm;

[0072] Slope, ranging from 2.0 to 2.5;

[0073] Cutoff frequency, with a value range of 5 × 10⁻⁶. -4 Up to 0.1μm -1 .

[0074] S2. Based on the experimental principle of scattering measurement using the cavity ring-down method, a scattering rate distribution database is constructed using the GBK scalar scattering model theory and preprocessed.

[0075] S2 includes the following steps:

[0076] S21. Based on the experimental principle of scattering measurement using the cavity ring-down method, and using the GBK scalar scattering model theory, calculate the integral scattering rate distribution data of ultra-smooth optical elements under three surface PSD statistical distributions (Gaussian, fractal, and Cauchy-Lorentz) at different spatial solid angles, and form a scattering rate distribution database.

[0077] S22. Perform data normalization on the scattering rate distribution database, randomly shuffle the order, and perform preprocessing to divide it into training and validation sets.

[0078] In the experimental principle of cavity ring-down scattering measurement, the statistical distribution of PSD of ultra-smooth optical elements is usually classified into Gaussian distribution, fractal distribution and Cauchy-Lorentz distribution.

[0079] According to the GBK scalar scattering model theory, the expression for the BRDF (Bidirectional Reflectance Distribution Function) of an ultra-smooth optical element under a Gaussian distribution is as follows: , ,

[0080] in, This represents the bidirectional reflection distribution function of an ultra-smooth optical element under a Gaussian distribution. The angle of incidence in spherical coordinates. The incident azimuth angle in spherical coordinates. The scattering angle in spherical coordinates. The scattering azimuth angle in spherical coordinates. For roughness, The incident light wavelength, For surface reflectivity related to polarization, It is a natural exponential function. Infinite For convergent series, ! is the factorial operator. The PSD function is under a Gaussian distribution. Pi The autocorrelation length is the length of the autocorrelation. l c It is the half-width of the autocorrelation function at a height of 1 / e, where e is the natural constant. for Spatial frequency in the direction, for Spatial frequency in the direction, These are intermediate parameters for the GBK scalar scattering model;

[0081] Spatial frequency in direction The expression is: ,

[0082] Where sin is the sine function and cos is the cosine function;

[0083] Spatial frequency in direction The expression is:

[0084] ;

[0085] Intermediate parameters of the GBK scalar scattering model The expression is:

[0086] ,

[0087] in, The refractive index of the incident medium is... The refractive index of the exit medium, For the relevant surface roughness;

[0088] The expression is:

[0089] ,

[0090] in, This is the cutoff frequency for integrating spatial frequencies. For and The PSD function is the independent variable;

[0091] The BRDF function expression for an ultra-smooth optical element under a fractal distribution is: , ,

[0092] in, The BRDF function of an ultrasmooth optical element under fractal distribution. The PSD function under fractal distribution. The first parameter of the fractal distribution is... The second parameter of the fractal distribution. The third parameter of the fractal distribution;

[0093] First parameter of fractal distribution The second parameter of fractal distribution The third parameter of fractal distribution is determined by roughness and autocorrelation length. For spatial frequency greater than The slope of the time-spectral power density;

[0094] First parameter of fractal distribution With roughness The relation is:

[0095]

[0096] In the formula This represents the gamma function. In the third parameter... When, the second parameter It can be determined by the autocorrelation length With the third parameter express:

[0097] ,

[0098] The BRDF expression for an ultra-smooth optical element under the Cauchy-Lorentz distribution is: , ,

[0099] in, BRDF function of ultra-smooth optical elements under Cauchy-Lorentz distribution The PSD function is given by the Cauchy-Lorentz distribution. The first parameter of the Cauchy-Lorentz distribution Determined by roughness, This is the cutoff frequency of the Cauchy-Lorentz distribution. It is the spatial frequency that determines the critical point at which the PSD curve begins to decline significantly (roll-off).

[0100] The relationship between the first parameter of the Cauchy-Lorentz distribution and roughness and the first parameter of the fractal distribution With roughness The relationship is the same.

[0101] After obtaining the BRDF of ultra-smooth optical elements with different surface PSD statistical distributions, the corresponding scattering rate distribution as a function of solid angle can be theoretically calculated: ,

[0102] in, The integral scattering rate, For the element's angular-resolved scattering distribution, For the bidirectional reflection distribution function of an ultra-smooth optical element, The angle of incidence in spherical coordinates. Let be the scattering angle in spherical coordinates, and cos be the cosine function. For the integral solid angle.

[0103] S3. Based on the value range and sampling accuracy of various surface parameters, a two-step neural network for classification and parameter prediction is constructed and trained using a preprocessed scattering rate distribution database.

[0104] like Figure 2 As shown, the classification-parameter prediction two-step neural network includes:

[0105] A classification neural network is used to analyze the statistical distribution of the surface PSD of an ultra-smooth optical element based on the integral scattering rate distribution data, determining whether it belongs to Gaussian, fractal, or Cauchy-Lorentz distribution.

[0106] A Gaussian distribution parameter prediction network is used to predict roughness and autocorrelation length for integral scattering rate distribution data of ultra-smooth optical elements with Gaussian distribution.

[0107] A fractal distribution parameter prediction network is used to predict roughness, autocorrelation length, and slope for integral scattering rate distribution data of ultra-smooth optical elements with fractal distribution types.

[0108] A Cauchy-Lorentz distribution parameter prediction network is used to predict roughness, autocorrelation length, and cutoff frequency for integrated scattering rate distribution data of ultra-smooth optical elements with Cauchy-Lorentz distribution.

[0109] In this embodiment, the scattering rate distribution data of the ultra-smooth optical element under 10 different solid angles is obtained by cavity ring-down scattering measurement in the previous step S2. The GBK scalar scattering model is used to calculate the scattering rate distribution of the ultra-smooth optical element under different parameter conditions at 10 different solid angles with different PSD statistical distributions. This data is used as a database, and the number of input nodes of the neural network is 10. The number of output layer nodes varies depending on the network function, as shown in Table 1.

[0110] Table 1 Number of nodes in the output layer of the neural network

[0111] Output parameters Number of output layer nodes Classification Neural Network 3 types of category tags 3 Gaussian distribution parameter prediction network Roughness, autocorrelation length 2 Fractal Distribution Parameter Prediction Network Roughness, autocorrelation length, slope 3 Cauchy-Lorenz distribution parameter prediction network Roughness, autocorrelation length, cutoff frequency 3

[0112] Since the integrated scattering rate distribution data of the ultra-smooth optical element input in this embodiment is one-dimensional time-series data, a one-dimensional convolutional neural network is selected for classification and parameter prediction.

[0113] Therefore, classification neural networks, Gaussian distribution parameter prediction networks, fractal distribution parameter prediction networks, and Cauchy-Lorentz distribution parameter prediction networks have the same structure, such as... Figure 3 As shown, each layer includes a first convolutional block, a second convolutional block, a third convolutional block, a multi-scale pooling layer, a fully connected layer, and an output layer connected in sequence.

[0114] The first convolutional block and the second convolutional block have the same structure, both including two convolutional layers and a max pooling layer connected in sequence;

[0115] The third convolutional block is a convolutional layer;

[0116] The multi-scale pooling layer consists of two parallel pooling branches, each comprising: a global average pooling layer and a fully connected layer connected in sequence; and a global max pooling layer and a fully connected sub-layer connected in sequence.

[0117] The fully connected layer comprises three fully connected sub-layers connected in sequence;

[0118] The output layer is a fully connected sublayer.

[0119] However, in this embodiment, the classification neural network uses different network parameters than the other three parameter prediction networks.

[0120] For classification neural networks:

[0121] First convolutional block: convolutional layer (64, [3×1], Leaky), convolutional layer (64, [3×1], Leaky), and max pooling layer (2).

[0122] Second convolutional block: convolutional layer (128, [3×1], Leaky), convolutional layer (128, [3×1], Leaky) and max pooling layer (2);

[0123] Third convolutional block: convolutional layer (256, [3×1], Leaky);

[0124] The parameters within parentheses for each convolutional layer are explained as follows: number of kernels, kernel size, and activation function.

[0125] The parameters in parentheses for each maximum pooling layer are interpreted as: pooling layer stride.

[0126] Multi-scale pooling layer:

[0127] Both parallel pooling branches have fully connected sublayers of (256, Leaky), with the parameters in parentheses representing the number of neurons and the activation function, respectively.

[0128] Fully connected layer: Fully connected sublayer (512, Leaky, 0.5); Fully connected sublayer (256, Leaky, 0.4); Fully connected sublayer (128, Leaky, 0.3); The parameters in parentheses are: number of neurons, activation function, and dropout rate, respectively.

[0129] Output layer: Fully connected sublayer (3, Softmax); the parameters in parentheses are: number of neurons and activation function, respectively.

[0130] For the prediction network with the other three parameters:

[0131] First convolutional block: convolutional layer (64, [3×1], Leaky), convolutional layer (64, [3×1], Leaky), and max pooling layer (2).

[0132] Second convolutional block: convolutional layer (128, [3×1], Leaky), convolutional layer (128, [3×1], Leaky) and max pooling layer (2);

[0133] Third convolutional block: Convolutional layer (256, [3×1], Leaky); The parameters in parentheses for each convolutional layer are explained as follows: number of kernels, size, and activation function;

[0134] The parameters in parentheses for each maximum pooling layer are interpreted as: pooling layer stride.

[0135] Multi-scale pooling layer: The fully connected sublayers of the two parallel pooling branches are both fully connected sublayers (256, Leaky); the parameters in parentheses are interpreted as the number of neurons and the activation function, respectively.

[0136] Fully connected layers: fully connected sublayer (512, Relu, 0.5), fully connected sublayer (256, Relu, 0.4), and fully connected sublayer (128, Relu, 0.3); the parameters in parentheses are respectively: number of neurons, activation function, and dropout rate.

[0137] Output layer: Fully connected sublayer (3), the parameter in parentheses means: number of neurons.

[0138] Step S3 uses the cross-entropy loss function to train the classification neural network; and uses the MSE loss function to train the Gaussian distribution parameter prediction network, the fractal distribution parameter prediction network, and the Cauchy-Lorentz distribution parameter prediction network.

[0139] In this embodiment, as Figure 4 , Figure 5 , Figure 6 As shown, the classification neural network, with cross-entropy as the loss function, can achieve a total training accuracy of 98.93%. Figure 6 In the diagram, the numbers represent the number of samples, the percentages below the numbers represent the proportion of the total number of samples in the test set, the green percentage represents the proportion of correctly classified samples, and the red percentage represents the proportion of misclassified samples. As can be seen, the classification accuracy of the three PSD statistical distributions can all reach over 96%, and they can accurately predict Gaussian and Cauchy-Lorenz distributions.

[0140] like Figures 7 to 17 As shown in the figure (R) 2 The coefficient of determination (MSE) and root mean squared error (RMSE) are used to predict parameters in a three-parameter neural network. With MSE as the loss function, the neural network can achieve high accuracy in parameter prediction under three different surface PSD statistical distributions. The correlation index of each parameter prediction on the test set can reach above 0.99, and the validation set is consistent with the training set, with no overfitting.

[0141] S4. Through the cavity ring-down scattering measurement experiment, the integral scattering rate distribution data of the ultra-smooth optical element is obtained. The trained classification-parameter prediction two-step neural network is used to predict the statistical distribution of surface PSD and the surface characteristic parameters.

[0142] In summary, this invention integrates the cavity ring-down method with GBK scalar scattering theory and uses a neural network to construct an intelligent mapping model from cavity ring-down experimental data to the surface quality parameters of the component. This enables accurate classification of the statistical distribution of PSD on the surface of ultra-smooth optical components, as well as high-precision prediction and evaluation of key parameters such as surface roughness and autocorrelation length. Thus, it provides a novel solution for the performance evaluation and quality control of ultra-smooth optical components.

[0143] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., 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 surface characteristic parameters of ultra-smooth optical elements, characterized in that, Includes the following steps: S1. Based on prior knowledge of ultra-smooth optical elements, determine the value range and sampling accuracy of various surface parameters; S2. Based on the experimental principle of scattering measurement using the cavity ring-down method, a scattering rate distribution database is constructed using the GBK scalar scattering model theory and preprocessed. S3. Based on the value range and sampling accuracy of various surface parameters, a two-step neural network for classification and parameter prediction is constructed and trained using a preprocessed scattering rate distribution database. S4. Through the cavity ring-down scattering measurement experiment, the integral scattering rate distribution data of the ultra-smooth optical element was obtained. The trained classification-parameter prediction two-step neural network was used to predict the statistical distribution of surface PSD and the surface characteristic parameters. The classification-parameter prediction two-step neural network of S3 includes: A classification neural network is used to analyze the statistical distribution of the surface PSD of an ultra-smooth optical element based on the integral scattering rate distribution data, determining whether it belongs to Gaussian, fractal, or Cauchy-Lorentz distribution. A Gaussian distribution parameter prediction network is used to predict roughness and autocorrelation length for integral scattering rate distribution data of ultra-smooth optical elements with Gaussian distribution. A fractal distribution parameter prediction network is used to predict roughness, autocorrelation length, and slope for integral scattering rate distribution data of ultra-smooth optical elements with fractal distribution types. A Cauchy-Lorentz distribution parameter prediction network is used to predict roughness, autocorrelation length, and cutoff frequency for integrated scattering rate distribution data of ultra-smooth optical elements with Cauchy-Lorentz distribution.

2. The method for predicting surface characteristic parameters of ultra-smooth optical elements according to claim 1, characterized in that, The surface parameters in S1 and their value ranges are as follows: Roughness, ranging from 0.1 to 1 nm; Autocorrelation length, ranging from 1 to 20 μm; Slope, ranging from 2.0 to 2.5; Cutoff frequency, with a value range of 5 × 10⁻⁶. -4 Up to 0.1μm -1 .

3. The method for predicting surface characteristic parameters of ultra-smooth optical elements according to claim 1, characterized in that, S2 includes the following steps: S21. Based on the experimental principle of scattering measurement using the cavity ring-down method, and using the GBK scalar scattering model theory, calculate the integral scattering rate distribution data of ultra-smooth optical elements under three surface PSD statistical distributions (Gaussian, fractal, and Cauchy-Lorentz) at different spatial solid angles, and form a scattering rate distribution database. S22. Perform data normalization on the scattering rate distribution database, randomly shuffle the order, and perform preprocessing to divide it into training and validation sets.

4. The method for predicting surface characteristic parameters of ultra-smooth optical elements according to claim 3, characterized in that, In S21, the integral scattering rate distribution expression of the ultra-smooth optical element at different spatial solid angles is as follows: , in, The integral scattering rate, For the bidirectional reflection distribution function of an ultra-smooth optical element, The angle of incidence in spherical coordinates. Let be the scattering angle in spherical coordinates, and cos be the cosine function. For the integral solid angle.

5. The method for predicting surface characteristic parameters of ultra-smooth optical elements according to claim 4, characterized in that, In S21, the bidirectional reflection distribution function expression of the ultra-smooth optical element under a Gaussian distribution is: ， ， in, This represents the bidirectional reflection distribution function of an ultra-smooth optical element under a Gaussian distribution. The angle of incidence in spherical coordinates. The incident azimuth angle in spherical coordinates. The scattering angle in spherical coordinates. The scattering azimuth angle in spherical coordinates. For roughness, The incident light wavelength, For surface reflectivity related to polarization, It is a natural exponential function. Infinite For a convergent series, ! is the factorial operator. The PSD function is under a Gaussian distribution. Pi The autocorrelation length, for Spatial frequency in the direction, for Spatial frequency in the direction, These are intermediate parameters for the GBK scalar scattering model; The expression for the bidirectional reflection distribution function of an ultra-smooth optical element under a fractal distribution is: ， ， in, This represents the bidirectional reflection distribution function of an ultrasmooth optical element under a fractal distribution. PSD function under fractal distribution The first parameter of the fractal distribution is... The second parameter of the fractal distribution. The third parameter of the fractal distribution; The expression for the bidirectional reflection distribution function of an ultra-smooth optical element under the Cauchy-Lorentz distribution is: ， ， in, This represents the bidirectional reflection distribution function of an ultrasmooth optical element under the Cauchy-Lorentz distribution. The PSD function is given by the Cauchy-Lorentz distribution. Let be the first parameter of the Cauchy-Lorentz distribution. is the cutoff frequency of the Cauchy-Lorentz distribution.

6. The method for predicting surface characteristic parameters of ultra-smooth optical elements according to claim 5, characterized in that, The intermediate parameters of the GBK scalar scattering model The expression is: , in, The refractive index of the incident medium is... The refractive index of the exit medium, For the relevant surface roughness; The expression is: , in, This is the cutoff frequency for integrating spatial frequencies. For and The PSD function is the independent variable; Spatial frequency in direction The expression is: , Where sin is the sine function and cos is the cosine function; Spatial frequency in direction The expression is: .

7. The method for predicting surface characteristic parameters of ultra-smooth optical elements according to claim 1, characterized in that, The classification neural network, Gaussian distribution parameter prediction network, fractal distribution parameter prediction network and Cauchy-Lorentz distribution parameter prediction network have the same structure, all including a first convolutional block, a second convolutional block, a third convolutional block, a multi-scale pooling layer, a fully connected layer and an output layer connected in sequence; The first convolutional block and the second convolutional block have the same structure, both including two convolutional layers and a max pooling layer connected in sequence; The third convolutional block is a convolutional layer; The multi-scale pooling layer consists of two parallel pooling branches, each comprising: a global average pooling layer and a fully connected layer connected in sequence; and a global max pooling layer and a fully connected sub-layer connected in sequence. The fully connected layer comprises three fully connected sub-layers connected in sequence; The output layer is a fully connected sublayer.

8. The method for predicting surface characteristic parameters of ultra-smooth optical elements according to claim 1, characterized in that, S3 uses the cross-entropy loss function to train the classification neural network; and uses the MSE loss function to train the Gaussian distribution parameter prediction network, the fractal distribution parameter prediction network, and the Cauchy-Lorentz distribution parameter prediction network.

Images