Method for predicting surface shape and thickness change of multilayer element through multi-surface interference tomography learning

Abstract

The invention relates to the technical field of image processing, in particular to a method for predicting surface shape and thickness changes of a multilayer element through multi-surface interference tomography learning, and the method comprises the steps: constructing the surface shape distribution of each surface of two layers of elements through employing a Zernike polynomial; constructing a multi-surface interferogram based on an interference theory model; training the tomographic neural network model by using the initial multi-surface interferogram based on the two-layer element and the corresponding phase shift interferogram, and separating out a single-surface interferogram; and training the two-step phase-shift unsupervised learning model, further processing the two-frame phase-shift single-surface interferogram, and outputting a wrapped phase. The method has anti-noise performance, and can realize high-precision multi-layer optical element and even multi-layer film global measurement with a small number of interferograms.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to a method for predicting the surface shape and thickness changes of multilayer components using multi-surface interferometric tomography, which can be used for measuring the surface shape and thickness of multilayer structures such as precision optical components and thin films. Background Technology

[0002] Multilayer components are widely used in integrated circuits, semiconductor chips, and optical devices. The physical parameters such as the thickness and three-dimensional profile of each layer affect the performance and reliability of the components. Therefore, it is crucial to achieve high-precision, global measurement of the surface shape and thickness variation parameters in multilayer components.

[0003] Optical measurement methods have been applied to measure the surface shape or thickness of components. Based on different principles, classic methods mainly include: elliptic polarization, which uses the polarization change of reflected light after reflection from the component to analyze film thickness, optical constants, and interface characteristics; white light interferometry, which finds the peak of interference fringes by changing the optical path difference in the vertical direction, and reconstructs the surface morphology and thickness by solving for the relative height; and spectroscopic methods, which invert the optical constants and thickness changes by analyzing the spectrum of reflected or transmitted light from the component. To further improve detection accuracy, technological evolution and the integration of multiple methods have enabled effective measurements. While the above methods offer certain accuracy advantages under specific application conditions, they also have limitations: for example, elliptic polarization requires a complex experimental optical path and high system stability, and primarily focuses on thickness and refractive index; white light interferometry requires vertical scanning, has a slow measurement speed, and is sensitive to environmental vibrations; and spectroscopic methods are simple to operate, but their measurement accuracy is easily affected by environmental interference. Summary of the Invention

[0004] To address the shortcomings of existing methods, this invention proposes a method for predicting the surface shape and thickness variations of multilayer components using multi-surface interferometric tomography. This method detects two layers of components based on the principle of wavelength-tuned interferometry, constructs an end-to-end UNet network, and separates individual single-surface interferograms from the multi-surface interferogram. An unsupervised learning model is then constructed to recover the component phase. First, a multi-surface interferometric tomography neural network model is designed. It takes two frames of multi-surface phase-shift interferograms as input and outputs the separated single-surface component interference signals. Label-supervised loss function is used to iteratively optimize the error between the predicted and ground truth interferograms. Ultimately, the model can achieve tomographic interference signal separation from multi-surface interferograms. Next, a two-step phase-shift unsupervised learning model is trained. It takes two frames of single-surface phase-shift interferograms as input, reconstructs the interferogram using the wrapped phase and phase shift estimates calculated by the network, calculates the loss function with the input interferogram, and optimizes the network weights through backpropagation, achieving unsupervised learning based on a physical model. Based on these two models, the wrapped phase based on the component surface shape is recovered from the multi-surface interferogram.

[0005] The technical solution adopted in this invention is: a method for predicting the surface shape and thickness variations of multilayer components using multi-surface interferometric tomography includes the following steps: Step 1: Construct the surface shape distribution of each surface of the two-layer element using Zernike polynomials; construct a multi-surface interferogram based on the interference theory model; As a preferred embodiment of the present invention, the model formula for the multi-surface interference pattern is: (3) in, I 1( x , y () represents the initial multi-surface interferogram; A ( x , y )and B ( x , y () represents the background light intensity and modulation. m This indicates that there are six superimposed interference signals in the multi-surface interference signal of the two-layer element; λ 0 represents the initial wavelength.

[0006] As a preferred embodiment of the present invention, the interferogram is 6 sets of two-frame initial single-surface interferograms. The initial single-surface interferograms include: the reference surface and the front surface of the first element (element 1) interferogram, the reference surface and the contact surface interferogram, the reference surface and the rear surface of the second element (element 2) interferogram, the front surface of the first element and the contact surface interferogram, the front surface of the first element and the rear surface of the second element interferogram, and the contact surface of the two elements and the rear surface of the second element interferogram.

[0007] Step 2: Train the tomographic neural network model using the multi-surface interferograms of the two-layer elements and the corresponding multi-surface phase-shift interferograms to separate the interference signals of the single-surface elements; As a preferred embodiment of the present invention, the improved UNet network includes: The feature map is input into the convolutional extraction layer, mapping the number of channels to 64. Each downsampling layer is followed by a convolutional extraction layer. After five downsampling passes, the number of channels increases to 128, 256, 512, 1024, and 2048 respectively. After one convolutional extraction layer through the bottleneck layer, upsampling is performed. The upsampling output is concatenated and fused with the corresponding downsampling feature map through a skip connection. After concatenation, a convolutional extraction layer follows. After five upsampling passes, the number of channels decreases to 1024, 512, 256, 128, and 64 respectively. The output layer of a 1×1 convolution maps the number of channels to a 12-channel feature map.

[0008] In a preferred embodiment of the present invention, the convolutional extraction layer includes: the input feature map is passed sequentially through two stacked CBL modules and then residuals are extracted with the input feature map.

[0009] As a preferred embodiment of the present invention, the hybrid loss function formula of the layered neural network model (first improved UNet network model) is as follows:

[0010] in, , denoted as weight, MSE as mean squared error loss, and GL as gradient loss.

[0011] Step 3: Train a two-step phase-shift unsupervised learning model (second improved UNet network), further process the two-frame phase-shifted single-surface interferograms, and output the wrapped phase and phase shift estimates; As a preferred embodiment of the present invention, background light intensity is extracted from the initial interferogram. A ( x , y ) and adjustment system B ( x , y The interferogram is reconstructed using the estimated phase and phase shift values ​​of the package. I 1 ( x , y ), I 2 ( x , y ); Calculate the initial interference pattern of a single surface I 1'( x , y )and I 1 ( x , y Loss1 is used to calculate the phase-shifted interferogram. I 2'( x , y )and I 2 ( x , y The loss Loss2 is used to optimize the weights of the two-step phase-shift unsupervised learning model by backpropagation using the total Loss = Loss1 + Loss2.

[0012] As a preferred embodiment of the present invention, the RMS index is used to evaluate the two-step phase-shift unsupervised learning model.

[0013] As a preferred embodiment of the present invention, a system for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement a method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography.

[0014] As a preferred embodiment of the present invention, a computer-readable medium storing computer program code implements a method for predicting the surface shape and thickness variations of multilayer components by multi-surface interferometric tomography when executed by a processor.

[0015] The beneficial effects of this invention are: 1. This invention designs 6 different combinations of interference optical paths, with each group consisting of two frames to facilitate the input of the subsequent two phase shift steps; 2. The CBL module (Conv-BN-LeakyReLU) structure is used to extract and enhance local features. The residual connection helps to alleviate gradient decay and promote feature fusion. When used together, it ensures the global structure and detail recovery of the interferogram. It is suitable for detail-sensitive multi-surface interferograms and helps the network to reconstruct the interferometric information more accurately. 3. MSE loss is used to calculate the average of the squares of the differences between the model's predicted values ​​and the true values, which can ensure the accuracy of overall intensity recovery; GL loss calculates the gradient difference of the image in the x and y directions, emphasizing the alignment of the interference fringe edges with local structures, effectively improving the clarity of the phase boundary; by setting weights, a balance is achieved between the overall fitting accuracy and the local structure, satisfying the characteristics of the interferogram being smooth overall but sensitive at the edges.

[0016] 4. The two-step phase-shift unsupervised learning model simultaneously outputs phase and phase shift estimates E, realizing joint learning of phase and phase shift; the phase shift step is dynamically adjusted based on each pair of interferogram features to more accurately fit phase shift changes, and the accurate phase shift estimate further optimizes the phase reconstruction accuracy, forming a virtuous cycle; at the same time, this method overcomes the limitation of having good accuracy only for some phase shift values, and enhances the robustness and generalization ability to different experimental conditions. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography according to the present invention. Figure 2 This is a schematic diagram of an interferometric system; Figure 3 This is a schematic diagram showing the superposition of six interference signals in a two-layer element. Figure 4 This is a schematic diagram of the multi-surface interferogram separation process of the present invention; Figure 5 This is a diagram of the UNet network structure of the present invention; Figure 6 This is a schematic diagram of the two-step phase shift recovery package phase process of the present invention; Figure 7 This is a set of two frames of multi-surface phase-shifting interferometry layers analyzing and separating the interference signals of a single-surface element; Figure 8 This is the first set of test interferograms; Figure 9 This is the second set of test interferograms. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0019] like Figure 1 As shown, the method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography includes the following steps: This invention, based on Zernike polynomials and wavelength-tuned interferometry detection theory, generates two frames of multi-surface phase-shift interferograms based on two-layer element interference as input data, and six sets of two-frame phase-shift single-surface element interference signals as training labels. A multi-surface tomographic neural network model is constructed, with training parameters such as the number of training rounds, batch size, learning rate, loss function, and optimizer set. The difference between the network output and the labels is evaluated using a hybrid loss function (MSE+GL), and the network weights are updated using the AdamW optimization algorithm. The trained optimal model is used to tomographically separate the interference signals of each layer of elements. A two-step phase-shift unsupervised learning model is constructed, using an interference theory model to generate two frames of single-surface phase-shift interferograms, extracting background light intensity and contrast from the initial interferograms. The interferograms are reconstructed using the wrapping phase and phase shift estimates from the network output, and the loss function between the reconstructed interferograms and the input interferograms is calculated. Backpropagation optimizes the network weights, achieving unsupervised learning based on the interference physics model. Based on these two models, the system takes two frames of multi-surface phase-shift interferograms as input and outputs a wrapping phase based on the element surface shape.

[0020] Step 1: Analyze the interference of light in the two-layer components. Based on the wavelength tuning measurement principle, construct the surface shape distribution of each surface using Zernike polynomials; record the interference signals of light in the two-layer components; calculate the interference optical path difference; and construct the interference pattern based on the interference theory model. Simulated surface Z m The formula is as follows: (1) In the formula, Z i ( x , y () is a Zernike polynomial; C m Zernike coefficient, m The values ​​1, 2, and 3 represent the front surface of component 1, the contact surface between the two components, and the rear surface of component 2, respectively.N =20 represents the total coefficients of the Zernike polynomials used; Optical path difference of each interference based on simulated surface shape construction H ( x , y The theoretical structure is as follows: (2) Wherein, ΔZ( x , y ) represents the surface shape difference; h The cavity length is determined by the thicknesses d1 and d2 of two different elements; the refractive index... n= 1.5; Simulated interference fringe pattern; the surfaces involved in the interference are: reference surface, front surface of element 1, contact surface between the two elements and rear surface of element 2, and six types of interference fringes are generated by pairwise interference (parasitic fringes are not considered); Based on wavelength-tuned interferometry theory, the formula for simulating multi-surface interferograms is as follows: (3) (4) in, I 1( x , y )and I 2( x , y () represent the initial multi-surface interferogram and the phase-shifting interferogram, respectively; A ( x , y )and B ( x , y () represents the background light intensity and modulation. m =6 indicates that there are 6 superimposed interference signals in the multi-surface interference signal based on two-layer components; λ 0 represents the initial wavelength; Δ λ The change in wavelength is represented by a phase shift of π / 2, based on the change in the thickness of element 1.

[0021] A dataset was constructed based on an interferometric theory model, divided into a training set and a test set. Two frames of multi-surface phase-shifting interferograms were used as input, and six separate sets of two-frame initial single-surface interferograms and phase-shifting interferograms were used as labels, with each set corresponding to a specific target. Figure 3L1-L6 represent six single surfaces, including: L1 interference between the reference surface and the front surface of element 1, L2 interference between the reference surface and the contact surface, L3 interference between the reference surface and the rear surface of element 2, L4 interference between the front surface of element 1 and the contact surface, L5 interference between the front surface of element 1 and the rear surface of element 2, and L6 interference between the contact surface of the two elements and the rear surface of element 2. By changing the wavelength, the initial interference pattern and the corresponding phase-shifted interference pattern are obtained.

[0022] like Figure 2 The diagram shown is a schematic of the interference system.

[0023] like Figure 4 Step 2: Construct the first improved UNet network (multi-surface interference tomography neural network); like Figure 5 The main body of the network adopts a U-shaped structure, consisting of a downsampling layer, an upsampling layer, a convolutional extraction layer, a bottleneck layer, and an output layer; The downsampling layer reduces the feature map size through max pooling (2×2); The upsampling layer uses bilinear interpolation to restore the feature map size; The convolutional extraction layer (DoubleConv) consists of two 3×3 convolutions, batch normalization, and an activation function, which are applied to the input feature map to achieve feature fusion and extraction. The output layer uses a 1×1 convolution to map the upsampled feature map to 12 output channels.

[0024] The simulated interferogram is 128×128 pixels in size and is input to a convolutional extraction layer, mapping the number of channels to 64. Each downsampling layer is followed by a convolutional extraction layer, and the feature map size after five downsampling passes (2×2 max pooling field of view) is [size missing]. H / 32× W / 32, the number of channels increases sequentially to 128, 256, 512, 1024, and 2048; after one convolutional extraction at the bottleneck layer, it enters the upsampling stage. The upsampling layer uses bilinear interpolation to restore the feature map size. The output of the upsampling layer is concatenated and fused with the feature map of the corresponding downsampling stage through skip links. After concatenation, a convolutional extraction layer follows. After five upsampling operations, the number of channels decreases sequentially to 1024, 512, 256, 128, and 64, and the size is finally restored to 1024, 512, 256, 128, and 64. H × W The number of channels is mapped to 12 outputs through an output layer (1×1 convolution); The network outputs 12-channel feature maps, which correspond to 6 separate sets of two-frame phase-shifted single-surface element interferograms. Training the UNet network: First, the normalized training set is input into the UNet network; the data is processed layer by layer in the model through multiple downsampling, upsampling, convolution and other modules, and the interferogram prediction results of 12 frames are output; the prediction output is compared with the corresponding real label map, and the HybridLoss loss function is used to measure the difference between the prediction value and the real value.

[0025] The training rounds are set to 100; the batch size is 16; the initial learning rate is 0.001; and the AdamW optimization algorithm is used to adaptively update the network parameters to optimize the loss. Each iteration includes the following steps: First, forward propagation inputs the entire training set into the model in batches to calculate the multi-channel separation results. Then, loss calculation is performed, calculating MSE and GL, merging the losses of the two parts according to the set weights, and outputting the total loss. Next, backpropagation automatically calculates the gradients of all learnable parameters in the network based on the loss function. Finally, parameter updates are implemented by calling the AdamW optimizer to update the network weights and biases according to the current gradients.

[0026] Repeat the process until 100 loops are completed; each loop iterates through the entire training set once, continuously reducing the loss value on the training and validation sets; after training, the optimal model weights obtained can be used to separate and predict multi-surface interferograms.

[0027] The specific process for training the UNet network is as follows: 1. Data Reading: Input data and label data are stored in a specified location to achieve accurate loading; 2. Define the UNet network and define the initialization weight function; 3. Define the hybrid loss function HybridLoss, which consists of MSE and GL. The mathematical model expression is as follows: (5) in, I i ’ To estimate the phase shift value, I i This is the true phase shift value. n This represents the number of training samples.

[0028] (6)

[0029] in, x I ( i , j ), x I (i , j ) respectively represent in x and y Gradient of direction; N This represents the total number of pixels in the interferogram.

[0030] Total loss L Defined as: (7) The optimizer uses AdamW to adaptively adjust the learning rate to speed up convergence. In each iteration, forward propagation is used to obtain the network output, and after calculating the loss, the weights are updated through backpropagation.

[0031] MSE loss is used to calculate the average of the squared differences between the model's predicted values ​​and the true values, ensuring accurate overall intensity recovery; GL loss calculates the gradient difference in the image in the x and y directions, emphasizing the alignment of the interference fringe edges with local structures, effectively improving the clarity of phase boundaries; by setting weights, a balance is achieved between overall fitting accuracy and local structure, satisfying the characteristics of an interferogram that is smooth overall but sensitive at the edges.

[0032] 4. Set the number of iterations. In each round of training, repeat the forward propagation, loss calculation, backpropagation and parameter update steps until the predetermined number of iterations is reached. Each iteration will train the entire training dataset once. Until the model converges on the validation set, the optimal multi-surface interference tomography neural network model is finally obtained.

[0033] 5. Model saving: After each loop, the model parameters, current epoch number, training loss, and optimizer state are saved to a specified location for easy model recovery and performance verification.

[0034] The specific process for model testing is as follows: 1. Load the best model saved from training into the test.

[0035] 2. Regenerate the test set, input it into the optimal model, and output the six sets of two-frame phase-shifted single-surface element interferograms.

[0036] To further recover the surface shape and thickness variations of the element using the predicted two-frame single-surface phase-shifted interferograms, a two-step phase-shifting method is used to recover the wrapping phase. The specific training and testing process of the two-step phase-shifting unsupervised network model is as follows: Step 3: Simulate the single-surface phase-shifting interferogram; the theoretical model of single-surface interferometry is as follows: (8) (9) in, I 1'( x ,y ), I 2'( x , y () represent the initial interferogram and phase-shifted interferogram of a single surface, respectively; A ( x , y )and B ( x , y () represents the background light intensity and modulation. E This represents a random phase shift value; single-surface interference refers to any one of L1 to L6.

[0037] Using two frames of single-surface phase-shifted interferometric fringe patterns as input, a two-step unsupervised phase-shifted learning model (second improved UNet network) based on the UNet network is constructed, and the output wrapping phase and phase shift estimates are obtained. like Figure 6 The two-step phase-shift unsupervised learning model is improved on the multi-surface interferometric tomography neural network model by adding a phase-shift estimation module. This module extracts feature maps from downsampling, and after extracting features through activation functions and regularization, concatenates them to obtain the phase-shift value. E m Estimate, then first E m The values ​​are normalized from 0 to 1 and then multiplied by π to achieve a mapping from 0 to π. The model input consists of two 128×128 pixel single-surface phase-shifting interferograms. The output layer uses a 1×1 convolution and normalizes the wrapped phase to -π to π using the arctangent function. Finally, the wrapped phase and the estimated value are output together. E m Used for calculating the loss function during training.

[0038] Train a two-step phase-shift unsupervised learning model based on UNet.

[0039] During training, the physical interference model is reconstructed, and the loss function is calculated. The expression for the physical interference model is as follows: (10) (11) Extracting background light intensity from the initial interferogram A ( x , y ) and adjustment system B ( x , y Using package phase and estimated value E m Reconstructing the interferogram I 1 ( x , yPhase shift diagram I 2 ( x , y );calculate I 1 ’ ( x , y )and I 1 ( x , y Loss1 and I 2 ’ ( x , y )and I 2 ( x , y The loss is calculated as Loss2, and the total loss is the sum of Loss1 and Loss2 (Loss = Loss2). Backpropagation optimizes the network weights, achieving unsupervised learning based on the physical model. The optimized model only needs two frames of interferograms as input to directly output the wrapped phase. Specifically, the mathematical model of the loss function is expressed as follows: (12) (13) in, n The number of rows / columns in the interferogram. n = 128; By calculating the total loss value, the AdamW optimizer performs backpropagation based on this loss value, continuously updating the weights and bias parameters of the convolutional neural network.

[0040] Specifically, each iteration trains on all training data and calculates the total loss value. This process is repeated for 200 iterations, continuously reducing the loss value on both the training and validation sets, and automatically saving the current optimal model. After training, the resulting optimal model can be used to perform phase recovery wrapping on phase-shifting interferograms.

[0041] Test a two-step phase-shift unsupervised learning model.

[0042] The six sets of two-frame single-surface phase-shift interferograms obtained by separation are input into the optimal two-step phase-shift unsupervised learning model to output the wrapped phase; the error evaluation index of the real wrapped phase label of the calculation and simulation is used to evaluate the accuracy of the model.

[0043] Specifically, the simulated film thicknesses were 1 μm and 2 μm, generating multi-surface interferograms. Information about each individual surface was obtained by separating the data using a tomographic model and an unsupervised model. Multi-surface interferograms (128×128 pixels) with signal-to-noise ratios of 20 dB and 30 dB were tested respectively. Figure 7This is a set of single-surface element interference signals separated by analysis of two frames of multi-surface phase-shifting interferometry. Figure 7 a is the initial multi-surface interferogram, b is the multi-surface phase-shifting interferogram, ch is the 6 sets of initial single-surface element interference signals separated by a, and in is the 6 sets of phase-shifting single-surface element interference signals separated by b. Figure 8 The first set of test interferograms: a is the initial multi-surface interferogram, b is the multi-surface phase-shift interferogram, ch is the encapsulated phase based on the element thickness variation; c is the corresponding... Figure 3 Interference situation in L1, d corresponds to Figure 3 Interference situation in L2, e corresponds to Figure 3 Interference situation in L3, f corresponds to Figure 3 Interference situation in L4, g corresponds to Figure 3 Interference situation at L5, h corresponds to Figure 3 Interference situation at L6; Figure 9 The second set of test interferograms: a is the initial multi-surface interferogram, b is the multi-surface phase-shift interferogram, ch is the wrapping phase based on the element thickness variation; c is the corresponding... Figure 3 Interference situation in L1, d corresponds to Figure 3 Interference situation in L2, e corresponds to Figure 3 Interference situation in L3, f corresponds to Figure 3 Interference situation in L4, g corresponds to Figure 3 Interference situation at L5, h corresponds to Figure 3 Interference situation at L6; The RMS values ​​of the errors are compared as shown in Table 1 (accurate to 4 decimal places). The interferometric groups in the table are as follows: Figure 3 As shown.

[0044] Table 1 Analysis of Simulation Test Results

[0045] According to the test results in Table 1, the error between the wrapped phase output by the network and the root mean square value of the simulated real label phase is small, and the results are within the expected range. This indicates that the deep learning framework used in this study can accurately achieve the separation and phase recovery of multi-surface interferograms under different signal-to-noise ratio conditions, with a low error level.

[0046] This invention addresses the problem of high-precision detection of the thickness and morphology of transparent multilayer components by proposing a method for predicting the surface shape and thickness variations of multilayer components using multi-surface interferometric tomography. First, based on the principle of wavelength-tuned interferometry and the recording of interference signals from multilayer components, Zernike polynomials are used to represent the phase, generating two-frame phase-shifted multi-surface interferograms based on the interference of two layers of components. A neural network training framework is constructed. By setting the learning rate, loss function, and optimizer, the optimal multi-surface interferometric tomography neural network model is trained to achieve high-precision separation of the two-frame multi-surface phase-shifted interferograms. Further, a two-step unsupervised phase-shift learning model is established, using the calculated wrapping phase and phase shift estimates to reconstruct the interferogram, and calculating the loss function with the input interferogram to achieve unsupervised optimization of the network weights. The optimal model is tested, recovering the wrapping phase from the separated two-frame phase-shifted single-surface interferograms. Experimental results show that this method can achieve high-precision detection of multilayer components and has good noise resistance.

[0047] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography, characterized in that, Includes the following steps: Step 1: Construct the surface shape distribution of each surface of the two-layer element using Zernike polynomials; construct a multi-surface interferogram based on the interference theory model; Step 2: Train the tomographic neural network model using the interferograms of the two-layer elements and the corresponding phase-shift interferograms to separate the interference signals of the single-surface elements; Step 3: Train a two-step phase-shift unsupervised learning model, further process the two-frame phase-shifted single-surface interferograms, and output the wrapped phase and phase shift estimates.

2. The method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography according to claim 1, characterized in that, The model formula for interferograms is: (3) in, I 1( x , y () represents the initial multi-surface interferogram; A ( x , y )and B ( x , y () represents the background light intensity and modulation. m This indicates that there are six superimposed interference signals in the multi-surface interference signal of the two-layer element; λ 0 represents the initial wavelength.

3. The method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography according to claim 1, characterized in that, The layered neural network model includes: The feature map is input into the convolutional extraction layer, mapping the number of channels to 64. Each downsampling layer is followed by a convolutional extraction layer. After five downsampling passes, the number of channels increases to 128, 256, 512, 1024, and 2048 respectively. After one convolutional extraction layer through the bottleneck layer, upsampling is performed. The upsampling output is concatenated and fused with the corresponding downsampling feature map through a skip connection. After concatenation, a convolutional extraction layer follows. After five upsampling passes, the number of channels decreases to 1024, 512, 256, 128, and 64 respectively. The output layer of a 1×1 convolution maps the number of channels to a 12-channel feature map.

4. The method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography according to claim 3, characterized in that, The convolutional extraction layer consists of: the input feature map passing through two stacked CBL modules (Conv-BN-LeakyReLU) in sequence and then performing residual extraction with the input feature map.

5. The method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography according to claim 1, characterized in that, The formula for the hybrid loss function of the tonal neural network model is: in, , denoted as weight, MSE as mean squared error loss, and GL as gradient loss.

6. The method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography according to claim 1, characterized in that, Extracting background light intensity from the initial interferogram A ( x , y ) and adjustment system B ( x , y The interferogram is reconstructed using the estimated phase and phase shift values ​​of the package. I 1 ( x , y ), I 2 ( x , y ); Calculate the initial interference pattern of a single surface I 1'( x , y )and I 1 ( x , y Loss1 is used to calculate the phase-shifted interferogram. I 2'( x , y )and I 2 ( x , y The loss Loss2 is used to optimize the weights of the two-step phase-shift unsupervised learning model by backpropagation using the total Loss = Loss1 + Loss2.

7. The method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography according to claim 1, characterized in that, The root mean square error (RMS) metric is used to evaluate a two-step phase-shift unsupervised learning model.

8. The method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography according to claim 1, characterized in that, The interferogram consists of six sets of two-frame initial single-surface interferograms, including: the interferogram between the reference surface and the front surface of the first element, the interferogram between the reference surface and the contact surface, the interferogram between the reference surface and the rear surface of the second element, the interferogram between the front surface of the first element and the contact surface, the interferogram between the front surface of the second element and the rear surface of the second element, and the interferogram between the contact surface of the two elements and the rear surface of the second element.

9. A system for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography, characterized in that, include: Memory is used to store instructions that can be executed by the processor; A processor for executing instructions to implement the method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography as described in any one of claims 1-8.

10. A computer-readable medium storing computer program code, characterized in that, The computer program code, when executed by a processor, implements the method for predicting surface shape and thickness variations of multilayer components using multi-surface interferometric tomography as described in any one of claims 1-8.

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