Convolutional neural network based multi-surface interferogram prediction method

Abstract

The application relates to an interference phase shift technology, in particular to a multi-surface interference graph prediction method based on a convolutional neural network, which comprises the following steps: step one, generating a plurality of frames of simulated multi-surface interference graphs; step two, taking the first sixth as input data and the last fifth sixth as label data, and the input data and the label data correspond to each other; step three, constructing a multi-surface phase shift interference graph prediction model based on a convolutional neural network; step four, inputting the first sixth frame into the convolutional neural network, training the multi-surface phase shift interference graph prediction model based on the convolutional neural network, and iteratively obtaining an optimal model; and step five, predicting the multi-surface phase shift interference graph by using the optimal model. The multi-surface phase shift interference graph prediction method has noise resistance and can solve the problem that in some special cases, the required multi-frame multi-surface phase shift interference graph cannot be collected due to the range limitation of laser wavelength tuning in actual collection.

Description

Technical Field

[0001] This application relates to interferometric phase-shifting techniques, and more particularly to a method for predicting multi-surface interferograms based on convolutional neural networks. Background Technology

[0002] In optical multi-surface interferometry, the accurate extraction of phase information from the front and back surfaces, as well as the thickness, is crucial. Phase-shifting interferometry is a widely used and effective phase extraction method in interferometry, achieving high-precision phase recovery by recording multiple frames of phase-shifting interferograms.

[0003] Currently, to achieve high-precision multi-surface interferometry, there are many classic multi-surface phase retrieval algorithms, such as the nineteen-frame phase retrieval algorithm, the least-squares-based multi-surface iterative algorithm, and the weighted thirty-six-step phase shift retrieval algorithm. Among them, the weighted thirty-six-step phase shift retrieval algorithm requires only thirty-six interferograms to achieve simultaneous measurement of each surface. It only needs to determine the length of the interferometric cavity and the thickness of the measured object to obtain good measurement results. Therefore, the weighted thirty-six-step phase shift retrieval algorithm will be used as a verification method in the following sections.

[0004] To meet the requirements of multi-surface phase retrieval algorithms, a wavelength-tuned interferometer is needed to acquire multiple frames of phase-shifted interferograms. The smaller the thickness of the measured component and the more interferogram frames acquired, the larger the required wavelength tuning range. However, due to the limited range of laser output wavelength (approximately 0.2633 nm), it is impossible to obtain multi-surface phase-shifted interferograms that meet the above conditions. Summary of the Invention

[0005] The technical problem to be solved by this invention is that existing surface phase retrieval algorithms have difficulty obtaining a sufficient number of interferograms within a limited wavelength range.

[0006] Therefore, the present invention provides a method for predicting multi-surface interferograms based on convolutional neural networks.

[0007] The technical solution adopted by this invention to solve its technical problem is: A method for predicting multi-surface interferograms based on convolutional neural networks includes the following steps: Step 1: Generate a simulated multi-surface interference pattern; Step 2: Take the first one-sixth as input data and the last five-sixths as label data, with the input data corresponding to the label data; Step 3: Construct a multi-surface phase-shifting interferogram prediction model based on a convolutional neural network; Step 4: Divide the input data into N / 6 channels and input them into a convolutional neural network. Train a multi-surface phase-shifting interferogram prediction model based on the convolutional neural network and iterate to obtain the optimal model. Step 5: Use the optimal model to predict the multi-surface phase-shift interferogram.

[0008] Furthermore, the multi-surface phase-shifting interferogram prediction model based on convolutional neural networks includes multiple downsampling blocks, multiple upsampling blocks, and an output layer. Each downsampling block consists of 3 convolutional layers + activation functions and 1 max pooling layer. Each upsampling block consists of 1 upsampling layer and 3 convolutional layers + activation functions. The downsampling blocks are used to gradually reduce the image size and extract features. The upsampling blocks are used to restore the feature images extracted from the downsampling part to the size of the original input image. The upsampling layers are combined with the convolutional layers to combine features of different resolutions.

[0009] Furthermore, the output layer uses 5N / 6 1×1 convolutional kernels to convert the 256×256 64-channel feature map output from the upsampled part into a 256×256 5N / 6-channel multi-surface phase-shift interferogram, which is the final output of the neural network.

[0010] Furthermore, the training process of the multi-surface phase-shifting interferogram prediction model based on a convolutional neural network includes: S4.1 Input the training data (the first one-sixth frame of multi-surface phase-shifting interferograms) into the neural network framework, and generate the prediction results through network calculation; S4.2 compares the predicted results with the labels (true values) and uses the mean squared error loss function (MSE) to measure the difference between the predicted multi-surface phase-shifting interferogram and the true multi-surface phase-shifting interferogram.

[0011] S4.3 determines the direction of parameter adjustment by calculating the gradient of the loss function with respect to the model parameters. This gradient information is passed back from the output layer to the input layer, updating the parameters layer by layer. The Adam optimization algorithm updates the weights and biases based on the calculated gradient information, so that the loss function gradually decreases.

[0012] S4.4 Training Loop: Iterates over the dataset in a certain number of rounds. Each iteration trains the entire training dataset once to gradually optimize the model's performance.

[0013] Furthermore, in step S4.1, the first one-sixth of the multi-surface phase-shifting interferogram is shuffled by DataLoader and the number of data transmitted in a single pass is increased before being input into the neural network framework.

[0014] Furthermore, in step S4.3, a loss function is set, and the average of the squared errors is calculated to measure the difference between the predicted multi-surface phase-shifting interferogram and the actual phase-shifting interferogram.

[0015] Furthermore, the mathematical model of the loss function is expressed as follows: In the formula, To predict multi-surface phase-shift interferograms, The image represents a real multi-surface phase-shifting interferogram, where n is the number of training samples.

[0016] Furthermore, in step five, a weighted 36-step phase-shift recovery algorithm is used to perform phase recovery on the multi-surface interferogram generated by the convolutional neural network to verify its effectiveness.

[0017] The beneficial effect of this invention is that it applies the convolutional neural network method to the prediction of multi-surface phase-shift interferograms. Compared to actually acquiring multiple frames (36 frames in this invention as an example) of phase-shift interferograms, the convolutional neural network method only needs to acquire 6 frames of phase-shift interferograms, significantly reducing the required wavelength tuning range and increasing the measurement range of the device under test. Furthermore, a weighted 36-step phase-shift recovery algorithm is used to perform phase recovery on the multi-surface interferograms generated by the convolutional neural network to verify its effectiveness.

[0018] This invention offers high prediction accuracy for multi-surface phase-shifting interferograms; strong noise resistance; end-to-end processing; and the use of a neural network model for interferogram feature extraction, which effectively captures complex features in multi-surface interferograms and improves the prediction accuracy of multi-surface phase-shifting interferograms.

[0019] The multi-surface phase-shift interferogram prediction method proposed in this invention predicts the subsequent 5N / 6 frames of multi-surface phase-shift interferograms using the first N / 6 frames of interferograms. Therefore, the accuracy of the training data is crucial. Simultaneously, there is a one-to-one correspondence between the input data (the first N / 6 frames of multi-surface phase-shift interferograms) and the label (true value) data (the subsequent 5N / 6 frames of multi-surface phase-shift interferograms) to ensure that the model can correctly learn the relationship between the input and output multi-surface phase-shift interferograms during training. Attached Figure Description

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Figure 1 This is a flowchart of the neural network-based multi-surface phase-shifting interferogram prediction method of the present invention. Figure 2 This is a structural diagram of the neural network model of the present invention.

[0022] Figure 3 This is a schematic diagram of the training phase of the neural network model of the present invention.

[0023] Figure 4 (a) is the input data for testing the first group of convolutional neural network models. Figure 4 (b) is the label data for testing the first group of convolutional neural network models. Figure 4(c) is the output data of the first group of convolutional neural network model tests.

[0024] Figure 5 (a) The front surface wrapping phase map obtained by using the weighted 36-step phase recovery algorithm on the test data of the first group of convolutional neural network models.

[0025] Figure 5 (b) is the front surface phase information cloud map obtained after using the weighted 36-step phase recovery algorithm on the test data of the first group of convolutional neural network models.

[0026] Figure 5 (c) is the thickness-wrapped phase map obtained after using the weighted 36-step phase recovery algorithm on the test data of the first group of convolutional neural network models.

[0027] Figure 5 (d) is the thickness phase information cloud map obtained after using the weighted 36-step phase recovery algorithm on the test data of the first group of convolutional neural network models.

[0028] Figure 5 (e) is the back surface wrapping phase map obtained after using the weighted 36-step phase recovery algorithm on the test data of the first group of convolutional neural network models.

[0029] Figure 5 (f) is the back surface phase information cloud map obtained after using the weighted 36-step phase recovery algorithm on the test data of the first group of convolutional neural network models.

[0030] Figure 6 (a) is the input data for testing the second group of convolutional neural network models.

[0031] Figure 6 (b) is the label data for testing the second group of convolutional neural network models.

[0032] Figure 6 (c) is the output data of the second group of convolutional neural network model tests.

[0033] Figure 7 (a) The front surface wrapping phase map obtained by using the weighted 36-step phase recovery algorithm on the test data of the second group of convolutional neural network models.

[0034] Figure 7 (b) is the front surface phase information cloud map obtained by using the weighted 36-step phase recovery algorithm on the test data of the second group of convolutional neural network models.

[0035] Figure 7 (c) is the thickness-wrapped phase map obtained by using the weighted 36-step phase recovery algorithm on the test data of the second group of convolutional neural network models.

[0036] Figure 7 (d) is the thickness phase information cloud map obtained after using the weighted 36-step phase recovery algorithm on the test data of the second group of convolutional neural network models.

[0037] Figure 7 (e) is the back surface wrapping phase map obtained by using the weighted 36-step phase recovery algorithm on the test data of the second group of convolutional neural network models.

[0038] Figure 7 (f) is the back surface phase information cloud map obtained by using the weighted 36-step phase recovery algorithm on the test data of the second group of convolutional neural network models.

[0039] Figure 8 (a) is the input data for testing the third group of convolutional neural network models.

[0040] Figure 8 (b) is the label data for testing the third group of convolutional neural network models.

[0041] Figure 8 (c) is the output data of the third group of convolutional neural network model tests.

[0042] Figure 9 (a) The front surface wrapping phase map obtained by using the weighted 36-step phase recovery algorithm on the test data of the third group of convolutional neural network models.

[0043] Figure 9 (b) is the front surface phase information cloud map obtained by using the weighted 36-step phase recovery algorithm on the test data of the third group of convolutional neural network models.

[0044] Figure 9 (c) is the thickness-wrapped phase map obtained by using the weighted 36-step phase recovery algorithm on the test data of the third group of convolutional neural network models.

[0045] Figure 9 (d) is the thickness phase information cloud map obtained after using the weighted 36-step phase recovery algorithm on the test data of the third group of convolutional neural network models.

[0046] Figure 9 (e) is the back surface wrapping phase map obtained by using the weighted 36-step phase recovery algorithm on the test data of the third group of convolutional neural network models.

[0047] Figure 9 (f) is the back surface phase information cloud map obtained by using the weighted 36-step phase recovery algorithm on the test data of the third group of convolutional neural network models. Detailed Implementation

[0048] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0049] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, features defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0050] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0051] Reference Figure 1-9 A method for predicting multi-surface interferograms based on convolutional neural networks includes the following steps: Step 1: Generate multiple frames of simulated multi-surface interferograms based on Zernike polynomials, wavelength tuning principles, and the theoretical model of superposition of interference light intensity.

[0052] Specifically, the mathematical model for simulating multi-surface phase-shifting interferograms is expressed as follows: In the formula, k is the number of interferogram frames (k=1~36), and k is 1 in the initial interferogram; To make the background light intensity, ; , , The adjustment parameters are respectively the front surface, the back surface, and the thickness, so that... , ; , , These are the front surface phase information, rear surface phase information, and thickness information to be recovered, respectively. ,in, , Represented by Zernike polynomials; , , These represent the phase shift values ​​for the front surface, rear surface, and thickness, respectively. The phase shift value of the front surface is π / 4; This is noise added to the interferogram.

[0053] In the aforementioned multi-surface phase-shifting interferograms, the Zernike polynomials involved can represent optical aberrations, theoretical wavefronts, and fitted wavefronts. The process of generating the simulated interferograms involves using Zernike polynomials to simulate different aberration effects, superimposing them together to generate a phase distribution, and then generating 36 frames of multi-surface phase-shifting interferograms.

[0054] The mathematical model of phase distribution based on Zernike polynomials is expressed as follows:

[0055] In the formula, For the front surface phase distribution, For the rear surface phase distribution, , They are and The coefficient of the i-th term in the Zernike polynomial; Let be the i-th term of the Zernike polynomial, and n be the total number of terms using the Zernike polynomial. In this invention, let n =20.

[0056] Step 2: Prepare the dataset For the simulated multi-surface phase-shifting interferograms, the first one-sixth is taken as input data and the last five-sixths as label data. In this embodiment, the simulated 36 frames of multi-surface phase-shifting interferograms are divided into training set and test set. The first 6 frames of multi-surface phase-shifting interferograms are used as input, and the last 30 frames of multi-surface phase-shifting interferograms are used as label data (true values), and the input and label correspond one-to-one.

[0057] When generating training data, the first twenty terms of the Zernike polynomial are used to generate the phase distribution to satisfy the diversity of training data; random noise with different signal-to-noise ratios (20~100dB) is added to approximate the interferograms collected in the real environment as closely as possible.

[0058] It should be noted that the method of the present invention is applicable to the processing of multi-surface phase shift interferograms with a front surface phase shift value of π / 4.

[0059] Step 3: Construct a multi-surface phase-shifting interferogram prediction framework based on convolutional neural networks.

[0060] The input data for the neural network consists of the first six frames of multi-surface phase-shifting interferograms, each image being 256×256 pixels in size and divided into six channels, which are then input into the convolutional neural network.

[0061] The overall neural network structure can be divided into two parts: downsampling and upsampling.

[0062] In the downsampling section, the network structure consists of five downsampling blocks, from Conv2d_1 to Conv2d_5. Each downsampling block comprises three convolutional layers plus an activation function and one max-pooling layer. In Conv2d_1, the input is a 256×256 6-channel multisurface interferogram. 64 convolutional kernels of size 3×3 are used to extract low-level features, resulting in a 64-channel feature map of size 256×256. Max-pooling is then performed using a filter with a stride of 2 and a size of 2×2, producing a 64-channel feature map of size 128×128. Similarly, subsequent convolutional blocks (Conv2d_2 to Conv2d_5) yield 128, 256, 512, and 512-channel feature maps, with feature map sizes of 128×128, 64×64, 32×32, and 16×16, respectively. The downsampling section is used to gradually reduce the image size and extract features.

[0063] The feature maps generated in the downsampling part are then input into the upsampling part. The network structure of the upsampling part consists of four upsampling blocks, from Conv2d_6 to Conv2d_9. Each upsampling block consists of one upsampling layer and three convolutional layers plus activation functions. In Conv2d_6, the input is a 32×32 512-channel feature map obtained by upsampling the feature map output from Conv2d_5 and concatenating the 32×32 512-channel feature map output from Conv2d_4, resulting in a 32×32 1024-channel feature map. The convolutional layer uses 512 3×3 convolutional kernels to extract depth features, thus producing a 32×32 512-channel feature map. Similarly, in subsequent upsampling blocks (Conv2d_7 to Conv2d_9), 256, 128, and 64-channel feature maps are obtained, with feature map sizes of 64×64, 128×128, and 256×256, respectively. The upsampling part is used to restore the feature image extracted by the downsampling part to the size of the original input image, and is combined with the convolutional layer through the upsampling layer to combine features of different resolutions.

[0064] Finally, an output layer is used to convert the 256×256 64-channel feature map output from the upsampled part into a 256×256 30-channel multi-surface phase-shift interferogram using 30 1×1 convolutional kernels, which serves as the final output of the neural network.

[0065] Overall, the neural network extracts features from the 6-channel input multi-surface interferogram through a downsampling component, resulting in a richer feature map. Then, it utilizes the obtained feature information through skip connections and upsampling to predict the subsequent 30 frames of multi-surface phase-shifting interferograms.

[0066] Step 4: Train a multi-surface phase-shifting interferogram prediction model based on a convolutional neural network The details are as follows: First, the training set (the first 6 frames of multi-surface phase-shifting interferograms) is shuffled and its batch size (the number of data points passed to the program for training at one time) is increased by DataLoader before being input into the neural network framework. The data is then processed layer by layer through downsampling and upsampling to generate predicted outputs. These predicted outputs are compared with the true labeled data, and the MSE loss function is used to measure the difference between the predicted and true values.

[0067] With a learning rate of 0.001, the Adam optimization algorithm is used to find the network weights that minimize the loss function.

[0068] Specifically, the iteration count is set to 100. In each iteration, the following steps are performed: First, forward propagation is performed, inputting the training data into the model and calculating the predicted output. Then, the loss function is calculated to measure the difference between the predicted and true values. Next, backpropagation is performed to calculate the gradient of the loss function with respect to the model parameters. Finally, the Adam optimization algorithm is used to update the weights and biases of the convolutional neural network model based on the gradient information.

[0069] Repeat these steps until the predetermined number of iterations is reached. Each iteration trains the entire training dataset once to gradually optimize the model's performance. Finally, after 100 iterations, a trained model is obtained that can accurately predict the input data.

[0070] The specific process is as follows: S4.1 Data Reading: The prepared data (the first 6 frames of multi-surface phase-shifting interferograms) is loaded using DataLoader and calculated through the network to generate the prediction results. Its main function is to shuffle the data order (random reading) and increase the Batch_size (the number of data points passed to the program for training at one time).

[0071] S4.2 Model Definition: Define the network structure and the weight initialization function.

[0072] S4.3 Loss and Optimizer: The predicted results are compared with the labels (true values), and the mean squared error loss function (MSE) is used to measure the difference between the predicted multi-surface phase-shifting interferogram and the true multi-surface phase-shifting interferogram.

[0073] Define a loss function (MSE) and an optimizer (Adam) for training the model. By setting the loss function, the average of the squared errors is calculated to measure the difference between the predicted multi-surface phase-shifting interferogram and the actual phase-shifting interferogram (label). The mathematical model of the loss function is expressed as follows:

[0074] In the formula, To predict multi-surface phase-shift interferograms, The image represents a real multi-surface phase-shifting interferogram, where n is the number of training samples.

[0075] By calculating the gradient of the loss function with respect to the model parameters, the direction of parameter adjustment is determined. This gradient information is passed back from the output layer to the input layer, updating the parameters layer by layer. The Adam optimization algorithm updates the weights and biases based on the calculated gradient information, causing the loss function to gradually decrease.

[0076] This step uses the Adam optimizer to adjust the neural network parameters to their optimal state. The learning rate is adjusted at specified epochs, and the optimizer is updated using the new learning rate to minimize the loss function. The MSE loss function and the Adam optimizer are crucial components in the neural network training process. They update the model parameters through backpropagation and gradient descent to minimize the loss between the predicted results and the labeled data, thereby improving network performance.

[0077] S4.4 Training Loop: Iterate through the dataset within a certain number of rounds. In this embodiment, the number of iterations is set to 100, executing forward propagation, loss calculation, backpropagation, and parameter update processes. Each iteration trains the entire training data once; that is, within each round, the data batch is traversed, and the training loop is performed.

[0078] S4.5 Saving the Model: After each round, save the trained model file to the specified folder, and save the learning rate and loss value corresponding to each round in an Excel spreadsheet for easy analysis of model performance after training.

[0079] Step 5: Test the model.

[0080] Using re-simulated multi-surface phase-shift interferogram data as the test set, the test data is input into the neural network model, which outputs a predicted multi-surface phase-shift interferogram. The predicted multi-surface phase-shift interferogram is compared with the real multi-surface phase-shift interferogram in Matlab to further evaluate the accuracy of the model.

[0081] The specific process is as follows: S5.1. Configure the GPU device and load the pre-test model. Use the model with the best performance after training (smallest loss value) to load into the test.

[0082] S5.2. Input the trained neural network model into the test dataset to obtain the prediction results. Compare and evaluate the final test results (predicted multi-surface phase-shift interferograms for the last 30 frames) with the label data (real multi-surface phase-shift interferograms for the last 30 frames). Theoretically, the real multi-surface phase-shift interferograms are approximately the same as the predicted multi-surface phase-shift interferograms, with a very small difference.

[0083] S5.3. A weighted 36-step phase-shift recovery algorithm was used to recover the phase of the multi-surface interferogram generated by the convolutional neural network to verify its effectiveness. The performance of the network model was evaluated by calculating the peak-valley (PV) value and root mean square (RMS) value of the recovered phase. Finally, three sets of data (accurate to four decimal places) were selected in the test results. The test input data, label data, prediction output results, and phase recovery results are as follows: Figures 4-9 As shown in Table 1, the test results are compared.

[0084] Table 1 Comparison of Test Results

[0085] Based on the above test results, the error between the real multi-surface phase-shifting interferogram and the predicted multi-surface phase-shifting interferogram is extremely small, that is, the fitting effect of the neural network model is good, and the test results of this invention are within the expected range.

[0086] To address the problem in multi-surface phase-shift interferometry (MSI) that the limited wavelength range of lasers makes it impossible to acquire the required MSI in specific situations, such as when the component thickness is too small or the number of interferogram frames to be acquired is too large, this invention proposes a multi-surface phase-shift interferogram prediction method based on a convolutional neural network (CNN). The method involves designing a CNN framework; training the neural network model and optimizing its parameters using a large dataset; testing the network model; and finally, using the optimized network model to process the first six frames of MSI to predict the subsequent 30 frames, thus achieving accurate prediction of MSI.

[0087] In summary, this invention relates to a method for predicting multi-surface phase-shift interferograms based on convolutional neural networks. The phase distribution of the front and rear surfaces is generated using Zernike polynomials, implemented through simulation. Multi-surface interferograms are simulated based on the wavelength tuning principle and the theory of superposition of interferometric light intensity, and a fixed phase shift value (π / 4) is introduced to simulate multi-surface phase-shift interferograms with different distributions, making them more consistent with actual measurement data. The generated first 6 frames of multi-surface phase-shift interferograms (input) and the next 30 frames (labels) are used as training datasets. A phase shift value estimation model based on a convolutional neural network is established, and the loss function, learning rate, and optimizer are set to train the network. During network training, the error between the predicted multi-surface phase-shift interferogram and the actual multi-surface phase-shift interferogram is measured by calculating the loss function, and the optimizer is used to find the weights and biases that minimize the loss function, thus finding the optimal model. After training, the model can predict the subsequent 30 frames of multi-surface phase-shift interferograms based on the input 6 frames of multi-surface phase-shift interferograms.

[0088] The multi-surface phase-shift interferogram prediction method proposed in this invention predicts the subsequent 5N / 6 frames of multi-surface phase-shift interferograms using the first N / 6 frames of interferograms. Therefore, the accuracy of the training data is crucial. Simultaneously, there is a one-to-one correspondence between the input data (the first N / 6 frames of multi-surface phase-shift interferograms) and the label (true value) data (the subsequent 5N / 6 frames of multi-surface phase-shift interferograms) to ensure that the model can correctly learn the relationship between the input and output multi-surface phase-shift interferograms during training.

[0089] This invention offers high prediction accuracy for multi-surface phase-shifting interferograms; strong noise resistance; end-to-end processing; and the use of a neural network model for interferogram feature extraction, which effectively captures complex features in multi-surface interferograms and improves the prediction accuracy of multi-surface phase-shifting interferograms.

[0090] 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 by the scope of the claims.

Claims

1. A method for predicting multi-surface interferograms based on convolutional neural networks, characterized in that, Includes the following steps, Step 1: Generate N frames of simulated multi-surface interferograms based on Zernike polynomials, wavelength tuning principles, and the theoretical model of superposition of interference light intensity. Step 2: Take the first one-sixth as input data and the last five-sixths as label data, with the input data corresponding to the label data; Step 3: Construct a multi-surface phase-shift interferogram prediction model based on a convolutional neural network. The model includes multiple downsampling blocks, multiple upsampling blocks, and an output layer. Each downsampling block consists of 3 convolutional layers + activation functions and 1 max-pooling layer. Each upsampling block consists of 1 upsampling layer and 3 convolutional layers + activation functions. The downsampling blocks are used to gradually reduce the image size and extract features. The upsampling blocks are used to restore the feature image extracted from the downsampling part to the size of the original input image. The upsampling layers are combined with the convolutional layers to combine features of different resolutions. The output layer uses 5N / 6 1×1 convolutional kernels to convert the 256×256 64-channel feature map output from the upsampling part into a 256×256 5N / 6-channel multi-surface phase-shift interferogram, which is the final output of the neural network. Step 4: Divide the input data into N / 6 channels and input them into a convolutional neural network. Train a multi-surface phase-shifting interferogram prediction model based on the convolutional neural network and iterate to obtain the optimal model. Step 5: Use the optimal model to predict the multi-surface phase-shift interferogram, and use the weighted 36-step phase-shift recovery algorithm to perform phase recovery on the multi-surface interferogram generated by the convolutional neural network to verify its effectiveness.

2. The multi-surface interferogram prediction method based on convolutional neural networks according to claim 1, characterized in that, The training process of the multi-surface phase-shifting interferogram prediction model based on convolutional neural networks includes: S4.1 inputs the training data, namely the first one-sixth frame of multi-surface phase-shifting interferograms, into the neural network framework, and generates the prediction results through network calculation; S4.2 compares the predicted results with the labels and uses the mean squared error loss function to measure the difference between the predicted multi-surface phase-shift interferogram and the actual multi-surface phase-shift interferogram. S4.3 determines the direction of parameter adjustment by calculating the gradient of the loss function with respect to the model parameters. This gradient information is passed from the output layer back to the input layer, updating the parameters layer by layer. The Adam optimization algorithm updates the weights and biases based on the calculated gradient information, so that the loss function gradually decreases. S4.4 Training Loop: Iterates over the dataset in a certain number of rounds. Each iteration trains the entire training dataset once to gradually optimize the model's performance.

3. The multi-surface interferogram prediction method based on convolutional neural networks according to claim 2, characterized in that, In step S4.1, the first one-sixth frame of the multi-surface phase-shifting interferogram is shuffled by DataLoader and the number of data transmitted in a single pass is increased before being input into the neural network framework.

4. The multi-surface interferogram prediction method based on convolutional neural networks according to claim 2, characterized in that, In step S4.3, a loss function is set, and the average of the squared errors is calculated to measure the difference between the predicted multi-surface phase-shift interferogram and the actual phase-shift interferogram.

5. The multi-surface interferogram prediction method based on convolutional neural networks according to claim 4, characterized in that, The mathematical model of the loss function is expressed as follows: In the formula, To predict multi-surface phase-shift interferograms, The image represents a real multi-surface phase-shifting interferogram, where n is the number of training samples.

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