A multi-interface morphology super-resolution measurement method

Abstract

This invention discloses a multi-interface topography super-resolution measurement method, comprising: constructing a swept-frequency interferometric signal dataset; constructing swept-frequency interferometric signal labels using the sparsity of the swept-frequency interferometric signal spectrum; normalizing the swept-frequency interferometric signal data; constructing and training a super-resolution spectrum prediction model based on the normalized swept-frequency interferometric signal data; predicting the super-resolution spectrum of the measured surface using the optimized super-resolution spectrum prediction model; tracing the phase spectrum of the measured surface using the predicted super-resolution spectrum; and reconstructing the topography field using the traced phase spectrum of the measured surface. This invention constructs a swept-frequency interferometric signal dataset; then utilizes a data-driven model to learn the sparsity characteristics of the swept-frequency interferometric signals in the dataset, achieving super-resolution measurement in the depth direction. This invention requires no additional parameter calculations, and the obtained model has good robustness, overcoming the problems of traditional physical modeling methods that require parameter design and have weak anti-interference capabilities.

Description

Technical Field

[0001] This invention relates to the technical field of multi-interface topography measurement, and more particularly to a super-resolution measurement method for multi-interface topography. Background Technology

[0002] Sweep-frequency interferometry is a distance measurement technique based on the principle of optical coherent interference. It offers advantages such as high precision and non-contact measurement, and is commonly used to measure the surface morphology and thickness of optical devices (e.g., lenses, thin films, and lenses). To measure the morphology of multiple interfaces, the swept-frequency interferometric signal obtained by the system typically needs to be converted to the frequency domain for processing. However, the limited bandwidth of the laser source in the measurement system reduces the system's resolution in the depth direction, leading to aliasing between interfaces.

[0003] To overcome this problem, Autoregressive Spectrum Estimation (AR) can be used to physically model the signal. This method establishes an autoregressive model of the signal, estimates the parameters of the model, and obtains the autoregressive coefficients of the signal to obtain its power spectrum estimate, thus improving the depth resolution of swept-frequency interferometry. However, AR spectrum estimation generally cannot solve for the phase information of the interface, resulting in an inability to measure the morphological distribution of the interface layer with high sensitivity; moreover, the choice of the order of the AR model has a significant impact on the results, and its accuracy decreases when there is high noise. Later, with the rapid development of machine learning technology, data-driven methods were applied to optical measurement. Researchers used convolutional neural networks (CNNs) or generative adversarial networks (GANs) to train neural network models from aliased images to dealiased images, in order to learn the features and patterns of aliased signals in the image, thereby achieving signal aliasing removal and improved depth resolution. However, traditional data-driven methods only focus on the end-to-end mapping relationship, ignoring the physical nature of the limited depth resolution of swept-frequency interferometry signals due to the bandwidth of the light source, and do not pay attention to the physical characteristics of the swept-frequency interferometry signals themselves, thus limiting the degree of improvement in depth resolution.

[0004] In summary, existing physical modeling-based or traditional data-driven methods have limitations in improving the resolution of multi-interface topography, thus requiring further exploration of multi-interface super-resolution topography measurement technology. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a super-resolution measurement method for multi-interface morphology.

[0006] To achieve the above objectives, the technical solutions provided by the present invention are:

[0007] A multi-interface morphology super-resolution measurement method includes:

[0008] Construct a swept-frequency interferometric signal dataset;

[0009] A sweep frequency interference signal label is constructed by utilizing the sparsity of the sweep frequency interference signal spectrum;

[0010] Normalize the frequency sweep interferometric signal data;

[0011] A super-resolution spectrum prediction model was constructed and trained based on normalized swept frequency interferometric signal data;

[0012] The optimized super-resolution spectrum prediction model is used to predict the super-resolution spectrum of the measured surface;

[0013] The phase spectrum of the measured surface is traced using the predicted super-resolution spectrum.

[0014] The topographic field of the measured surface is reconstructed using the phase spectrum obtained by tracking.

[0015] Furthermore, a swept-frequency interferometric signal dataset is constructed, including:

[0016] In frequency sweep interferometry, after eliminating the DC and self-coherent components in the frequency sweep interferometric signal, the multi-surface scanning frequency sweep interferometric signal acquired according to the principle of optical interference is represented in the time domain t as follows:

[0017]

[0018] Where M is the number of surfaces participating in the interference; I R , I m The reflected light intensities of the reference surface and the measured surface, Λ, are respectively. m The optical path difference between the reference surface and the measured surface is given by Δk, where Δk is the laser wavenumber scanning range and k0 is the initial wavenumber of the swept light source. The frequency generated when the reflected light from the reference surface and the measured surface interferes. The initial phase of the interference between the reflected light from the reference surface and the surface under test;

[0019] In a noisy environment, the sampled frequency sweep interference signal can be represented as follows:

[0020]

[0021] Formula (2) is equivalent to formula (1) for superimposed noise; where N is the number of sampling points of the swept frequency interference signal, M is the number of surfaces participating in the interference, Re[·] represents taking the real part of the complex number, and f i ∈[-0.5,0.5) indicates that the signal sampling frequency is F. s The frequency α is the frequency generated when the reflected light from the reference surface and the measured surface interferes with each other at 1Hz. i ∈[0,1) represents the amplitude of the frequency generated by the interference between the reflected light from the reference surface and the measured surface. The initial phase of the interference between the reflected light from the reference surface and the measured surface is given by z[t], where z[t] is the Gaussian noise in the environment.

[0022] According to formula (2), change the frequency f i Amplitude α i Phase Obtain a rich variety of swept-frequency interferometric signals, and f i The sampling follows a Gaussian distribution, α i and The sampling must satisfy a uniform distribution;

[0023] An analytical signal corresponding to the swept-frequency interference signal is created, and its real and imaginary coefficients are used to form the network input.

[0024]

[0025] The analytic signal of the swept frequency interference signal in the complex domain is obtained according to formula (3). The real part and imaginary part of each signal are extracted to form a matrix. Re[·] and Im[·] represent taking the real and imaginary parts of a complex number, respectively; the Input matrix has a size of 2×N and is used as training data.

[0026] Furthermore, when constructing the frequency-sweeping interferometric signal tag, all frequencies f1, f2, ..., f generated when the reflected light from the reference surface and the measured surface interfere with each other are included. M The smoothed spectrum corresponding to the swept frequency interference signal is obtained by inputting the Gaussian kernel function;

[0027] The Gaussian kernel function is expressed as:

[0028]

[0029] N is the length of the sampled sweep interference signal; K(x) is a smoothing function, where x is the independent variable of the function. Its characteristics are: when x→0, K(x)=1; when x≠0, K(x) drops rapidly to 0, that is, there is a sharp peak at x=0;

[0030] The smoothed spectrum F(u) of the swept-frequency interference signal is obtained by inputting the spectrum of the Gaussian kernel function:

[0031]

[0032] Where u∈[-0.5,0.5) is the sampling frequency F s The spectral sampling points of the discrete Fourier transform at 1 Hz, where M is the number of surfaces participating in the interference, and f i The frequency generated when the reflected light from the reference surface and the measured surface interfere with each other.

[0033] Furthermore, the formula for normalizing the frequency sweep interferometric signal data is as follows:

[0034]

[0035] Where, x i The frequency sweep interferometric data before normalization, The normalized frequency sweep interference data is given by N, which is the length of the sampled frequency sweep interference signal. When the matrix Input is normalized, the sum of squares of all frequency sweep interference signal values ​​in the matrix is ​​calculated and the mean is taken. Then, the mean after the square root is used as the normalization factor of this matrix. All signal values ​​are divided by the normalization factor to obtain the normalized data.

[0036] Furthermore, the constructed super-resolution spectrum prediction model includes a CVSwinFreq model as its basic framework, comprising a complex-valued filtering module and a super-resolution module.

[0037] The complex value filtering module includes a CVLinear layer and a CVConv2d layer.

[0038] In the CVLinear layer, the linear_r and linear_i attributes each store a real-valued linear layer for linear operations on the real and imaginary parts of the data. When complex data enters the CVLinear, the real and imaginary parts pass through the corresponding real-valued linear layers, and the results are obtained through the mapping relationship and stored in the newly created CVTensor object.

[0039] In the CVConv2d layer, the conv_r and conv_i attributes store a one- or two-dimensional real-valued convolutional layer, which is used for convolution operations on the real and imaginary parts of the data. When complex data enters the CVConv2d layer, the real and imaginary parts pass through the corresponding real-valued convolutional layers, and the results are obtained through the mapping relationship and stored in the newly created CVTensor object.

[0040] Furthermore, the super-resolution module includes a complex-valued signal shift window attention module, a CVConv1d layer, and an UPConvld layer;

[0041] The complex-valued signal shift window attention module includes a signal shift window attention layer and a CVConv1d layer, with residual connections at the input and the CVConv1d layer;

[0042] The signal shift window attention layer includes a layer normalization layer, a multi-head shift window attention mechanism operation layer, and a multilayer perceptron;

[0043] After the signal passes through the layer normalization layer, a shift window attention calculation is performed. Then, after the residual connection, it passes through the layer normalization layer and the multilayer perceptron again. Finally, the output is obtained after the residual connection.

[0044] Furthermore, the multi-head shift window attention mechanism of the multi-head shift window attention mechanism operation layer is as follows:

[0045] When the signal enters the attention layer of the odd-numbered signal shift window, the signal is divided into two parts by the shift window, and then attention calculation is performed.

[0046] Q = ZP Q K = ZP K V = ZP V (7)

[0047]

[0048] In formula (7), Q, K, and V are referred to as the query vector, key vector, and value vector, respectively, in the attention operation; P Q , P K , P V These are the query weight matrix, key weight matrix, and value weight matrix, respectively, which are the parameters involved in training and learning; Z is the signal after window segmentation;

[0049] In formula (8), atten(·) is the attention calculation operation, d is the built-in dimension of the multi-head shift window attention, and B is the learnable relative position encoding;

[0050] In formula (9), σ(·) is the softmax operation, which performs exponential weighting on the data, x i The independent variable for softmax calculation is n, which is the number of windows for segmenting the signal.

[0051] When the signal enters the attention layer of the even-numbered signal shift window, the signal is divided into three parts by the shift window, and then attention is calculated according to formulas (7), (8), and (9), and so on.

[0052] Furthermore, when using the optimized super-resolution spectrum prediction model to predict the super-resolution spectrum of the measured surface, the acquired swept-frequency interferometric signal is converted into an analytic signal in the complex domain. The transformation formula is as follows:

[0053]

[0054] Where H[·] is the Hilbert transform operator, and I(t) is the swept-frequency interference signal; the interference signal obtains its corresponding analytic signal after undergoing the Hilbert transform. However, since the analytic signal is in the complex domain, it is necessary to obtain the imaginary part of the analytic signal after transformation as the imaginary part of the interference signal.

[0055]

[0056] The real and imaginary parts of the swept-frequency interference signal are combined to form a 2×N matrix. N is the length of the interference signal.

[0057] Furthermore, the phase spectrum of the measured surface is traced using the predicted super-resolution spectrum, including:

[0058] The relationship between the phase of the swept-frequency interference signal and the optical path difference from the reference plane to the measured plane can be expressed as follows:

[0059]

[0060] in, Let Λ be the phase corresponding to the frequency generated by the interference between the reflected light from the reference surface and the measured surface, and k0 = 2π / λ0 be the initial wavenumber of the light source; i The optical path difference is between the reference surface and the measured surface.

[0061] Euler's formula is used to transform the interference signal from the real domain to the complex domain.

[0062]

[0063] Among them, w i The angular frequency generated by the interference between the reflected light from the reference surface and the measured surface. ω represents the phase corresponding to the angular frequency, and N is the length of the interference signal;

[0064] Formula (13) can be written in matrix form:

[0065] I = AX, (14)

[0066] Where I is the value of the interference signal after discrete sampling. It is an N×2 matrix; It is a 2×1 matrix;

[0067] After matrix operations, the phase P corresponding to the measured surface angular frequency is obtained as follows:

[0068] X = (A T A) -1 A T I,(15)

[0069]

[0070] Where X(1) represents taking the first term in the matrix; by combining formulas (15), (16) and (12), the phase spectrum of the measured surface can be traced.

[0071] Compared with existing technologies, the principles and advantages of this technical solution are as follows:

[0072] This technical solution fully considers the characteristics of super-resolution swept-frequency interferometric signals and constructs a swept-frequency interferometric signal dataset accordingly. Then, a data-driven model is used to learn the sparsity characteristics of the swept-frequency interferometric signals in the dataset, achieving super-resolution measurement in the depth direction. This technical solution requires no additional parameter calculations, and the resulting model exhibits good robustness, overcoming the problems of traditional physical modeling methods that require parameter design and have weak anti-interference capabilities. Furthermore, compared to traditional data-driven methods, a neural network with higher depth resolution and stronger generalization ability is obtained. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the services required in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0074] Figure 1 This is a flowchart illustrating the principle of a multi-interface topography super-resolution measurement method according to the present invention.

[0075] Figure 2 This is a structural diagram of the super-resolution spectral prediction model in the multi-interface topography super-resolution measurement method of the present invention;

[0076] Figure 3 This is a schematic diagram illustrating the computational principle of the CVLinear layer in a super-resolution spectrum prediction model.

[0077] Figure 4 A schematic diagram of the multi-head shifting window attention mechanism;

[0078] Figure 5 This is a schematic diagram of multi-surface stacking;

[0079] Figure 6 Interface phase diagram;

[0080] Figure 7 Comparison of the original image and the super-resolution image, and the corresponding rolled-up phase map;

[0081] Figure 8 This is a comparison diagram of the winding phase and the unwinding phase. Detailed Implementation

[0082] The present invention will be further described below in conjunction with specific embodiments:

[0083] like Figure 1 As shown in this embodiment, a multi-interface topography super-resolution measurement method includes the following steps:

[0084] S1. Construct a swept-frequency interferometric signal dataset;

[0085] In frequency sweep interferometry, after eliminating the DC and self-coherent components in the interference signal, the multi-surface interference signal acquired by the system, according to the principle of optical interference, is represented in the time domain t as follows:

[0086]

[0087] Where M is the number of surfaces participating in the interference; I R , I m The reflected light intensities of the reference surface and the measured surface, Λ, are respectively. m The optical path difference between the reference surface and the measured surface is given by Δk, where Δk is the laser wavenumber scanning range and k0 is the initial wavenumber of the swept light source. The frequency generated when the reflected light from the reference surface and the measured surface interferes. The initial phase is the interference of the reflected light from the reference surface and the surface under test. It can be seen from formula (1) that the point-to-point vertical distance between the reference surface and the surface under test is related to their optical path difference. Therefore, as long as the spectrum of the interference signal is obtained, the reconstruction of the surface topography field can be achieved.

[0088] Meanwhile, from formula (1), it can be seen that the sweep frequency interference light intensity is actually the superposition of multiple sinusoidal signals; and considering that a large amount of experimental data cannot be obtained in real-world situations, this method constructs a simulation dataset based on the characteristics of the sweep frequency interference signal. In a noisy environment, the general form of the sampled sweep frequency interference signal can be expressed as:

[0089]

[0090] Equation (2) is equivalent to Equation (1) for superimposed noise. Where N is the number of sampling points of the interference signal, Re[·] represents taking the real part of the complex number, and f i ∈[-0.5,0.5) indicates that the signal sampling frequency is F. s The frequency α is the frequency generated when the reflected light from the reference surface and the measured surface interferes with each other at 1Hz. i ∈[0,1) represents the amplitude of the frequency generated by the interference between the reflected light from the reference surface and the measured surface. Let z[t] be the initial phase when the reflected light from the reference surface and the measured surface interfere with each other, and z[t] be the Gaussian noise in the environment. The frequency f is changed according to formula (2). i Amplitude α i Phase This allows for the acquisition of a rich variety of swept-frequency interference signals, and f i The sampling (referring to sampling within the interval [-0.5, 0.5), different from sampling of interference signals) follows a Gaussian distribution, α i and The sampling (as above, referring to sampling within a specified range) must satisfy a uniform distribution.

[0091] It is important to note that the model used in the proposed method is designed for processing complex domain data. When constructing the dataset, the analytic signal corresponding to the swept-frequency interferometric signal can be directly created, and its real and imaginary coefficients can be used to form the network input.

[0092]

[0093] Based on the above formula, the analytic signal of the interference signal in the complex domain can be obtained. The real and imaginary parts of each signal are extracted to form a matrix. Re[·] and Im[·] represent taking the real and imaginary parts of a complex number, respectively; the Input matrix has a size of 2×N and is used as training data.

[0094] S2. Construct sweep frequency interference signal labels using the sparsity of the sweep frequency interference signal spectrum;

[0095] The spectrum of a swept-frequency interferometric signal is sparse, specifically manifested as the superposition of multiple impulse functions. However, abrupt changes in the spectrum can cause gradient explosion when the network calculates the error gradient. Therefore, the labels need to be smoothed during data labeling. This embodiment uses all frequencies f1, f2, ..., f generated when the reflected light from the reference surface and the measured surface interfere with each other. M The smoothed spectrum of the interference signal is obtained by inputting the Gaussian kernel function. The Gaussian kernel function can be expressed as:

[0096]

[0097] Here, K(x) is a smooth function, and x is the independent variable of the function. Its characteristics are: as x→0, K(x)=1; when x≠0, K(x) drops rapidly to 0, that is, there is a sharp peak at x=0.

[0098] The smoothed spectrum F(u) is obtained by inputting the spectrum of the interference signal into the Gaussian kernel function.

[0099]

[0100] Where u∈[-0.5,0.5) can be analogized to the sampling frequency F s The spectral sampling points of the discrete Fourier transform at 1Hz, f i Let F(u) be the frequency generated when the reflected light from the reference surface and the measured surface interfere with each other. From formula (4), it can be seen that F(u) is related to the frequency generated when the reflected light from the reference surface and the measured surface interfere with each other. i There is a sharp peak at a certain point, which then rapidly decays to 0. Thus, according to formulas (3) and (5), a high-quality dataset based on the sparse features of tomographic interferometry spectrum can be obtained for model training.

[0101] S3. Normalize the swept frequency interference signal data;

[0102] The normalization formula is as follows:

[0103]

[0104] Where, x i The frequency sweep interferometric data before normalization, This is the normalized swept-frequency interferometric data. When normalizing the Input matrix, the sum of squares of all interferometric signal values ​​in the matrix is ​​calculated, and then the mean is taken. This mean, obtained by applying the square root, is used as the normalization factor for the matrix. All signal values ​​are then divided by this normalization factor to obtain the normalized data. Normalization makes the data distribution more uniform, accelerates the network training process, and improves network performance.

[0105] S4. Construct and train a super-resolution spectrum prediction model based on the normalized swept frequency interferometric signal data;

[0106] The super-resolution spectrum prediction model is based on the CVSwinFreq model and consists of two parts: a complex-valued filtering module (MF Module) and a super-resolution module (SR Module), as shown in the figure. Figure 2 As shown;

[0107] right Figure 2 The terms appearing in the network structure are explained as follows:

[0108] CVLinear: A linear layer used for complex numerical computation;

[0109] CVConv1d: A one-dimensional convolutional layer used for complex numerical computation;

[0110] CVConv2d: A two-dimensional convolutional layer used for complex numerical computation;

[0111] UPConvld: Real-valued one-dimensional transpose convolutional layer;

[0112] CVSSTB: Signal shift window attention mechanism module for complex numerical computation;

[0113] CVSSTL: Signal shift window attention mechanism layer for complex numerical computation;

[0114] LN: Layer Normalization;

[0115] MSA: Multi-head shift window attention mechanism operation;

[0116] MLP: Multilayer Perceptron Figure 2 The perceptron layer in the network model is 2;

[0117] The model's complex-valued filtering module consists of one complex-valued linear layer and one complex-valued two-dimensional convolutional layer. The super-resolution module consists of three complex-valued signal shift window attention modules (CVSSTB), one complex-valued one-dimensional convolutional layer, and one transposed convolutional layer. Residual connections are performed at the input of the super-resolution module and the complex-valued one-dimensional convolutional layer to prevent gradient vanishing during training. The complex-valued signal shift window attention module consists of two signal shift window attention layers and one complex-valued one-dimensional convolutional layer, also with residual connections at the input and the complex-valued one-dimensional convolutional layer. The signal shift window attention layer consists of two layer normalization layers, one multi-head shift window attention computation layer, and one two-layer perceptron, with two residual connections. After layer normalization, the signal undergoes one shift window attention computation, then passes through layer normalization and the multi-layer perceptron again after residual connections, and finally, the output is obtained after residual connections.

[0118] The weights of a neural network are all in the real number domain, but by creating a CVTensor object related to complex vectors, it is possible to incorporate the weights into the complex number domain for computation. A CVTensor stores the real and imaginary parts of the data in the `real` and `imag` properties, respectively, and has the same methods and functions as a real vector object.

[0119] Figure 2 All complex number computation modules appearing in the network model are based on CVTensor, which will be explained in detail below:

[0120] CVLinear: The `linear_r` and `linear_i` attributes each store a real-valued linear layer (the weights of the linear layers are in the linear layer object), used for linear operations on the real and imaginary parts of the data. When complex data enters a CVLinear, the real and imaginary parts pass through their corresponding real-valued linear layers, and then the results are obtained through a certain mapping relationship and stored in a new CVTensor. To illustrate this process more intuitively, the flow is as follows: Figure 3 As shown.

[0121] CVCon1d / CVConv2d: Similar to CVLinear, the conv_r and conv_i attributes store a one- or two-dimensional real-valued convolutional layer, used for convolution operations on the real and imaginary parts of the data. When complex data enters CVCon1d / CVConv2d, the real and imaginary parts pass through their corresponding real-valued convolutional layers, and the results are obtained through a certain mapping relationship and stored in a new CVTensor. The process is similar. Figure 3 .

[0122] MSA: Uses CVLinear to store query weights, key weights, and value weights, and still returns a CVTensor after attention calculation.

[0123] The operation process of other modules such as LN and MLP is similar to CVLi near, and returns CVTensor.

[0124] By utilizing the characteristics of the swept-frequency interferometric signal itself, the signal can be placed in the complex domain, bringing more prior information to the network model, which is beneficial to further improve the depth resolution of swept-frequency interferometric measurements.

[0125] Multi-head shift window attention mechanism:

[0126] The multi-head shift window attention mechanism is an innovation of the traditional self-attention mechanism. By introducing a shift window, different sequence data segments can interact through the shift window, which improves both the computation speed and the performance of the network model.

[0127] Multi-head shift window attention mechanism, such as Figure 4 As shown in the figure; the signal length is 200, and the shift window length is 100. When the signal enters the odd-numbered CVSSTL layer, the signal is divided into two parts by the shift window, each with a length of 100, and then attention calculation is performed.

[0128] Q = ZP Q K = ZP K V = ZP V (7)

[0129]

[0130] In formula (7), Q, K, and V are referred to as the query vector, key vector, and value vector, respectively, in the attention operation; P Q , P K , P V The query weight matrix, key weight matrix, and value weight matrix are the parameters involved in training and learning; Z is the signal after window segmentation. In formula (8), atten(·) is the attention calculation operation, d is the built-in dimension of multi-head shift window attention, and B is the learnable relative position encoding; in formula (9), σ(·) is the softmax operation, which exponentially weights the data, x i The independent variable for softmax calculation is n, which is the number of windows for segmenting the signal.

[0131] When the signal enters the even-numbered CVSSTL layer, the signal is divided into three parts by a shift window with lengths of 50, 100 and 50 respectively. Attention is then calculated according to formulas (7), (8) and (9), and so on.

[0132] As can be seen from the principle of the multi-head shift window attention mechanism, when using it to extract features of swept frequency interference signals, the higher attention scores at the peak and envelope peaks indicate that it tends to focus more on the peak and envelope of the signal, or in other words, it focuses more on the characteristics of the signal itself, which are the features that determine the signal frequency. The multi-head shift window attention mechanism not only solves the problem of long-distance dependence of sequence data, but also brings better feature extraction capabilities to the network.

[0133] Hyperparameter settings

[0134] Model hyperparameters are parameters that need to be specified in advance when training a model. These parameters are usually not learned from training data, but need to be set manually. They play a role in adjusting and controlling the model's structure and learning process.

[0135] The network hyperparameter settings are as follows:

[0136] n_epochs (number of network training iterations): 100;

[0137] lr (learning rate): 0.003, which is the step size when the network performs gradient backpropagation;

[0138] optim_type(optimizer): adamw, the optimizer is the gradient backpropagation optimization algorithm;

[0139] fr_size (tag length): 4096. The higher this value, the higher the spectral resolution.

[0140] inner_dim (embedding dimension): 512. The embedding dimension refers to the dimension of the data in the feature space after encoding.

[0141] upsampling (the stride of the transposed kernel): 8;

[0142] n_filters(number of neurons in the linear layer of the filtering module): 32;

[0143] kernel_size (kernel length): 3;

[0144] kernel_out(transposed kernel length): 18;

[0145] window_size (length of the shifted window): 32;

[0146] It is important to note that in order to ensure that the network input length and output length match, fr_size must be equal to inner_dim upsampling.

[0147] Network model training:

[0148] According to step S1, the dataset constructed based on the sparse characteristics of tomographic interferometry spectra includes a training set (640,000 swept interferometric signals and their spectra) and a validation set (12,800 swept interferometric signals and their spectra). The number of surfaces participating in the interferometry is set to a maximum of 10. The training set is then input... Figure 2 The super-resolution spectrum prediction model shown is trained, and the mean variance (MSE) is used as the loss function for backpropagation. The evaluation index of the super-resolution spectrum prediction model is obtained by comparing the output obtained by inputting the validation set into the network with the mean standard deviation of the validation set spectrum.

[0149] The super-resolution spectrum prediction model converged after about 40 iterations, with each iteration taking about 20 minutes, and the verification error was about 0.3.

[0150] S5. The optimized super-resolution spectrum prediction model is used to predict the super-resolution spectrum of the measured surface. During the process, the acquired swept frequency interferometric signal is converted into an analytic signal in the complex domain. The transformation formula is as follows:

[0151]

[0152] Where H[·] is the Hilbert transform operator, and I(t) is the swept-frequency interference signal; the interference signal obtains its corresponding analytic signal after undergoing the Hilbert transform. However, since the analytic signal is in the complex domain, it is necessary to obtain the imaginary part of the analytic signal after transformation as the imaginary part of the interference signal.

[0153]

[0154] The real and imaginary parts of the swept-frequency interference signal are combined to form a 2×N matrix.

[0155] The specific prediction process is as follows:

[0156] 1) Obtain experimental data. Since the length of the experimental data may not match the input length of the network, the data must first be truncated. At the same time, the truncation operation further reduces the resolution of the image.

[0157] 2) Normalize the truncated data.

[0158] 3) Input normalized data into the super-resolution spectrum prediction model to obtain the super-resolution spectrum corresponding to the low-resolution data.

[0159] S6. Use the predicted super-resolution spectrum of the measured surface to trace its phase spectrum.

[0160] The accuracy of the topography field obtained by spectral reconstruction is far inferior to that obtained by phase spectrum reconstruction. To obtain a more accurate topography field, the phase spectrum of the surface under test can be traced using the spectrum of the surface under test, and then the topography field can be reconstructed. The relationship between the phase of the swept-frequency interference signal and the optical path difference between the reference surface and the surface under test can be expressed as follows:

[0161]

[0162] in Let k0 be the phase corresponding to the frequency generated by the interference between the reflected light from the reference surface and the measured surface, and k0 = 2π / λ0 be the initial wavenumber of the light source; since the order of magnitude of k0 is in the order of 10... -6 Therefore, the topography field reconstructed from the phase spectrum has high accuracy. Λ i Let be the optical path difference between the reference surface and the surface under test. From formula (12), it can be seen that the phase generated by the interference of the reflected light from the reference surface and the surface under test is proportional to the corresponding optical path difference. Therefore, as long as the phase spectrum of the surface under test is calculated, its morphological field can be reconstructed.

[0163] To trace the phase spectrum of the surface under test, the interference signal must first be transformed from the real domain to the complex domain using Euler's formula.

[0164]

[0165] Among them, w i The angular frequency generated by the interference between the reflected light from the reference surface and the measured surface. Let be the phase corresponding to the angular frequency, and N be the length of the interference signal. The above equation can be written in matrix form as follows:

[0166] I = AX, (14)

[0167] Where I is the value of the interference signal after discrete sampling. It is an N×2 matrix; It is a 2×1 matrix. After matrix operations, the phase P corresponding to the angular frequency of the measured surface can be obtained.

[0168] X = (A T A) -1 A T I,(15)

[0169]

[0170] Where X(1) represents taking the first term in the matrix. Combining formulas (15), (16) and (12), the phase spectrum of the measured surface can be traced.

[0171] S7. Reconstruct the topography field of the measured surface using the phase spectrum obtained from the tracking.

[0172] To verify the practicality and superiority of the method described in this embodiment, the following experiment was conducted:

[0173] Two acrylic sheets are stacked together, creating a gap in the middle. A piece of paper is clamped between each end of the gap and pressure is applied, causing the upper and lower surfaces of the upper acrylic sheet (interfaces 1 and 2) and the lower acrylic sheet (interfaces 3 and 4) to overlap, resulting in the following effect: Figure 5 As shown.

[0174] The phase diagrams corresponding to interfaces 1, 2, 3, and 4 are as follows: Figure 6 As shown.

[0175] from Figure 6 A disordered phase fringe phenomenon can be observed. This is a result of spectral aliasing causing incorrect estimation of the interface position, which in turn leads to an error in the topographic field reconstruction.

[0176] Will Figure 5 The corresponding swept-frequency interferometric signal is truncated and normalized, then input into the obtained model to obtain its super-resolution spectrum; the aliased interface in the original image is extracted and compared with the corresponding part of the high-resolution image, and the result is as follows. Figure 7 As shown.

[0177] from Figure 7 It can be seen that the model successfully separated the four aliased interface layers, improving the depth resolution of the swept-frequency interferometry.

[0178] The winding and unwinding phases of the original image interface layer and the high-resolution image interface layer are compared, such as... Figure 8 As shown.

[0179] from Figure 8 It was found that the super-resolution image accurately estimated the interface location, and clear phase fringes could be seen, indicating that the reconstructed topography field would be more accurate.

[0180] The embodiments described above are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, any changes made based on the shape and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-interface morphology super-resolution measurement method, characterized in that, include: Construct a swept-frequency interferometric signal dataset; A sweep frequency interference signal label is constructed by utilizing the sparsity of the sweep frequency interference signal spectrum; Normalize the frequency sweep interferometric signal data; A super-resolution spectrum prediction model was constructed and trained based on normalized swept frequency interferometric signal data; The optimized super-resolution spectrum prediction model is used to predict the super-resolution spectrum of the measured surface; The phase spectrum of the measured surface is traced using the predicted super-resolution spectrum. The topography field of the measured surface is reconstructed using the phase spectrum obtained from the tracking. The constructed super-resolution spectrum prediction model includes a CVSwinFreq model as its basic framework, comprising a complex-valued filtering module and a super-resolution module. The complex value filtering module includes a CVLinear layer and a CVConv2d layer. In the CVLinear layer, the linear_r and linear_i attributes each store a real-valued linear layer for linear operations on the real and imaginary parts of the data. When complex data enters the CVLinear, the real and imaginary parts pass through the corresponding real-valued linear layers, and the results are obtained through the mapping relationship and stored in the newly created CVTensor object. In the CVConv2d layer, the conv_r and conv_i attributes store a one- or two-dimensional real-valued convolutional layer, which is used for convolution operations on the real and imaginary parts of the data. When complex data enters the CVConv2d layer, the real and imaginary parts pass through the corresponding real-valued convolutional layers, and the results are obtained through the mapping relationship and stored in the newly created CVTensor object. The super-resolution module includes a complex-valued signal shift window attention module, a CVConv1 d layer, and an UPConvld layer; The complex-valued signal shift window attention module includes a signal shift window attention layer and a CVConv1 d layer, with residual connections at the input and the CVConv1 d layer; The signal shift window attention layer includes a layer normalization layer, a multi-head shift window attention mechanism operation layer, and a multilayer perceptron; After the signal passes through the layer normalization layer, a shift window attention calculation is performed. Then, after the residual connection, it passes through the layer normalization layer and the multilayer perceptron again. Finally, the output is obtained after the residual connection. The multi-head shift window attention mechanism of the computational layer is as follows: When the signal enters the attention layer of the odd-numbered signal shift window, the signal is divided into two parts by the shift window, and then attention calculation is performed. Q=ZP Q ,K=ZP K ,V=ZP V ,(7) In formula (7), Q, K, and V are referred to as the query vector, key vector, and value vector, respectively, in the attention operation; P Q , P K , P V These are the query weight matrix, key weight matrix, and value weight matrix, respectively, which are the parameters involved in training and learning; Z is the signal after window segmentation; In formula (8), atten(·) is the attention calculation operation, d is the built-in dimension of the multi-head shift window attention, and B is the learnable relative position encoding; In formula (9), σ(·) is the softmax operation, which performs exponential weighting on the data, X i The independent variable for softmax calculation is n, which is the number of windows for segmenting the signal. When the signal enters the attention layer of the even-numbered signal shift window, the signal is divided into three parts by the shift window, and then attention is calculated according to formula (7), formula (8), and formula (9), and so on. Construct a swept-frequency interferometric signal dataset, including: In frequency sweep interferometry, after eliminating the DC and self-coherent components in the frequency sweep interferometric signal, the multi-surface scanning frequency sweep interferometric signal acquired according to the principle of optical interference is represented in the time domain t as follows: Where M is the number of surfaces participating in the interference; I R , I m The reflected light intensities of the reference surface and the measured surface, Λ, are respectively. m The optical path difference between the reference surface and the measured surface is given by Δk, where Δk is the laser wavenumber scanning range and k0 is the initial wavenumber of the swept light source. The frequency generated when the reflected light from the reference surface and the measured surface interferes. The initial phase of the interference between the reflected light from the reference surface and the surface under test; In a noisy environment, the sampled frequency sweep interference signal can be represented as follows: Formula (2) is equivalent to formula (1) for superimposed noise; where N is the number of sampling points of the swept frequency interference signal, M is the number of surfaces participating in the interference, Re[·] represents taking the real part of the complex number, and f i ∈[-0.5,0.5) indicates that the signal sampling frequency is F. s The frequency α is the frequency generated when the reflected light from the reference surface and the measured surface interferes with each other at 1Hz. i ∈[0,1) represents the amplitude of the frequency generated by the interference between the reflected light from the reference surface and the measured surface. The initial phase of the interference between the reflected light from the reference surface and the measured surface is given by z[t], where z[t] is the Gaussian noise in the environment. According to formula (2), change the frequency f i Amplitude α i Phase Obtain a rich variety of swept-frequency interferometric signals, and f i The sampling follows a Gaussian distribution, α i and The sampling must satisfy a uniform distribution; An analytical signal corresponding to the swept-frequency interference signal is created, and its real and imaginary coefficients are used to form the network input. The analytic signal of the swept frequency interference signal in the complex domain is obtained according to formula (3). The real part and imaginary part of each signal are extracted to form a matrix. Re[·] and Im[·] represent taking the real and imaginary parts of a complex number, respectively; the Input matrix is ​​2×N in size and is used as training data; The formula for normalizing the frequency sweep interferometric signal data is as follows: Where, x i The frequency sweep interferometric data before normalization, For the normalized frequency sweep interference data, N is the length of the sampled frequency sweep interference signal. When the matrix Input is normalized, the sum of squares of all frequency sweep interference signal values ​​in the matrix is ​​calculated and the mean is taken. Then, the mean after the square root is used as the normalization factor of this matrix. All signal values ​​must be divided by the normalization factor to obtain the normalized data. When using the optimized super-resolution spectrum prediction model to predict the super-resolution spectrum of the measured surface, the acquired swept interferometric signal is converted into an analytic signal in the complex domain. The transformation formula is as follows: Where H[·] is the Hilbert transform operator, and I(t) is the swept-frequency interference signal; the interference signal obtains its corresponding analytic signal after undergoing the Hilbert transform. However, since the analytic signal is in the complex domain, it is necessary to obtain the imaginary part of the analytic signal after transformation as the imaginary part of the interference signal. The real and imaginary parts of the swept-frequency interference signal are combined to form a 2×N matrix. N is the length of the interference signal.

2. The multi-interface topography super-resolution measurement method according to claim 1, characterized in that, When constructing a frequency-sweeping interferometric signal tag, all frequencies f1, f2, ..., f generated when the reflected light from the reference surface and the surface under test interfere with each other are considered. M The smoothed spectrum corresponding to the swept frequency interference signal is obtained by inputting the Gaussian kernel function; The Gaussian kernel function is expressed as: N is the length of the sampled sweep interference signal; K(x) is a smoothing function, where x is the independent variable of the function. Its characteristics are: when x→0, K(x)=1; when x≠0, K(x) drops rapidly to 0, that is, there is a sharp peak at x=0; The smoothed spectrum F(u) of the swept-frequency interference signal is obtained by inputting the spectrum of the Gaussian kernel function: Where u∈[-0.5,0.5) is the sampling frequency F s The spectral sampling points of the discrete Fourier transform at 1 Hz, where M is the number of surfaces participating in the interference, and f i The frequency generated when the reflected light from the reference surface and the measured surface interfere with each other.

3. The multi-interface topography super-resolution measurement method according to claim 1, characterized in that, The phase spectrum of the measured surface is traced using the predicted super-resolution spectrum, including: The relationship between the phase of the swept-frequency interference signal and the optical path difference from the reference plane to the measured plane can be expressed as follows: in, Let Λ be the phase corresponding to the frequency generated by the interference between the reflected light from the reference surface and the measured surface, and k0 = 2π / λ0 be the initial wavenumber of the light source; i The optical path difference is between the reference surface and the measured surface. Euler's formula is used to transform the interference signal from the real domain to the complex domain. Among them, w i The angular frequency generated by the interference between the reflected light from the reference surface and the measured surface. ω represents the phase corresponding to the angular frequency, and N is the length of the interference signal; Formula (13) can be written in matrix form: I = AX, (14) Where I is the value of the interference signal after discrete sampling. It is an N×2 matrix; It is a 2×1 matrix; After matrix operations, the phase P corresponding to the measured surface angular frequency is obtained as follows: X=(A T A) -1 A T I,(15) Where X(1) represents taking the first term in the matrix; by combining formulas (15), (16) and (12), the phase spectrum of the measured surface can be traced.

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