Phase shift interferogram phase shift value estimation method and system based on convolutional neural network

Abstract

The present application relates to the technical field of interference phase shift, and especially relates to a phase shift interference image phase shift value estimation method and system based on a convolutional neural network, a Zernike polynomial is used to express a phase distribution, and an initial interference image is generated according to an interference theory model; a random phase shift value is added to the initial interference image to simulate a phase shift interference image, thereby generating two frames of phase shift interference images; a phase shift value estimation framework based on a convolutional neural network is constructed; a loss function, a learning rate, an optimizer and the like are set to optimize network parameters, and a phase shift value estimation network model is generated; and the optimized network model is used to process the phase shift interference images to estimate corresponding phase shift values. The present application applies the convolutional neural network method to extraction of phase shift values of two frames of interference images, and compared with a traditional method, the convolutional neural network method does not need a complex calculation process and has good generalization ability, is robust to high noise, and can accurately extract random phase shift values.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of phase-shifting interferometry, and in particular to a method and system for estimating phase-shifting values of phase-shifting interferograms based on a convolutional neural network. BACKGROUND

[0002] In optical interferometry, the accurate extraction of phase information is crucial. Phase-shifting is a common and effective method for phase extraction in interferometry, which achieves high-precision phase recovery through multiple recorded interferograms. Phase extraction methods based on phase-shifting include known step phase-shifting, unknown step but regular phase-shifting, and random step phase-shifting. In known step phase-shifting, accurate phase shifting is crucial. Least squares is a known step phase-shifting algorithm that requires accurate phase shifting values to effectively extract the phase. However, due to environmental disturbances and other factors, phase shifting errors can easily occur. In addition, most two-step random phase-shifting algorithms require prior knowledge of the phase shifting value to recover the phase when extracting the phase. Therefore, how to accurately and efficiently estimate the phase shifting value is crucial.

[0003] Currently, two-step random phase-shifting methods typically require a phase shifting value extraction process. Phase shifting value extraction methods include Kreis algorithm, extreme value interference (EVI) method, Gram-Schmidt (GS) orthogonal normalization method, and phase step calibration algorithm (PSC). Kreis algorithm can be used to extract phase shifting values in interferograms, which is based on spectral analysis of interferograms. Kreis algorithm can extract smaller phase shifting values, but has poor noise resistance. EVI determines the phase shifting value by comparing the intensity ratio of the interference extreme value in the interferogram to the corresponding position in another interferogram. The phase step calibration algorithm (PSC) is a phase step number algorithm used to calibrate two interferograms, mainly based on calculating the correlation coefficient of the two images. The GS orthogonal normalization method determines the orthogonal normalization interferogram basis from two frames of interferograms. Due to noise interference and other factors, most methods require denoising of the interferogram to achieve high-precision phase shifting value extraction. In addition, the advanced iterative algorithm (AIA) can extract phase shifting values and phases from three frames of interferograms, but requires iterative calculations, resulting in slow calculation speed. SUMMARY

[0004] To address the shortcomings of existing methods, the present application applies a convolutional neural network method to the extraction of phase values from two frames of interferograms. Compared to traditional methods, the convolutional neural network method does not require complex calculation processes and has good generalization ability, robustness to high noise, and accurate prediction of phase shifting values in complex interferogram cases.

[0005] The technical solution adopted by the present application is as follows:

[0006] Step one, the phase distribution is expressed by Zernike polynomial, and the initial interferogram is generated according to the interference theory model;

[0007] Step two, the random phase shift value is added to the interferogram to simulate the phase shift interferogram, so as to generate two frames of phase shift interferogram;

[0008] Further, the mathematical model of the generated interferogram is:

[0009]

[0010] In the formula, k is the frame number of the interferogram; a(x, y) is the background light intensity; b(x, y) is the contrast; is the phase to be recovered; d k is the phase shift value; η k (x, y) is the noise added in the interferogram.

[0011] Further, the phase shift value of the initial interferogram is 0, and the phase shift value of the phase shift interferogram is 0 to π.

[0012] Step three, a phase shift value estimation framework based on convolutional neural network is constructed;

[0013] Further, the initial interferogram and the phase shift interferogram are taken as the input of the convolutional neural network, and the phase shift value is taken as the output.

[0014] Further, the convolutional neural network includes: a first branch network and a second branch network with the same structure, the first branch network includes: 3 layers of 3x3 convolution, an activation function is used after each convolution layer to extract features of the image, and a feature map is output through a 1x1 convolution layer, and the single channel feature maps of the two branch networks are spliced into two channel feature maps; the two channel feature maps are extracted through a 1x1 convolution layer, and then the feature vectors after the flattening layer are transmitted to the full connection layer for mapping.

[0015] Step four, the neural network model is trained to predict the phase shift value of the interferogram.

[0016] Further, the two frames of interferogram are input into the neural network framework, and the estimated node is output through calculation.

[0017] Further, the MAE loss function is used to measure the difference between the estimated phase shift value and the true phase shift value, and the Adam optimizer is used to find the weights and biases under the minimum loss function.

[0018] Further, the formula of the MAE loss function is:

[0019]

[0020] In the formula, d i is the estimated phase shift value, and d` iis the actual phase shift value, and n is the batch size.

[0021] Furthermore, the number of iterations is set, and forward propagation, loss calculation, backpropagation, and parameter update processes are executed; each iteration trains the entire training data once; finally, the trained model is obtained.

[0022] Furthermore, the phase shift value estimation system for phase-shifted interferograms based on convolutional neural networks includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement the phase shift value estimation method for phase-shifted interferograms based on convolutional neural networks.

[0023] The beneficial effects of this invention are:

[0024] 1. High accuracy in estimating phase shift values; strong noise resistance; fast calculation speed; end-to-end processing; utilizes a neural network model for interferogram feature extraction, effectively capturing complex features in the interferogram and improving the accuracy of phase shift value estimation. Attached Figure Description

[0025] Figure 1 This is a flowchart of the phase shift value estimation method and system based on a convolutional neural network for phase shift interferograms according to the present invention.

[0026] Figure 2 This is a diagram of the neural network model structure of the present invention;

[0027] Figure 3 This is a schematic diagram of the training phase of the neural network model of the present invention;

[0028] Figure 4 This is a schematic diagram of the testing phase of the neural network model of the present invention;

[0029] Figure 5 (a) Figure 5 (b) shows the initial interferogram and phase-shifted interferogram of the first test group, respectively;

[0030] Figure 6 (a) Figure 5 (b) shows the initial interferogram and phase-shifted interferogram of the second set of tests, respectively;

[0031] Figure 7 (a) Figure 5 (b) shows the initial interferogram and phase-shifted interferogram for the third set of tests, respectively;

[0032] Figure 8 (a) Figure 5 (b) shows the initial interferogram and phase-shifted interferogram for the fourth test group, respectively;

[0033] Figure 9 (a) Figure 5(b) testing the initial interferogram and the phase-shifted interferogram of the fifth group, respectively. DETAILED DESCRIPTION

[0034] The present application will be further described with reference to the accompanying drawings and examples, which are simplified schematic diagrams illustrating the basic structure of the present application in a schematic manner, and thus only show the components related to the present application.

[0035] As shown in the drawings, Figure 1 A phase shift value estimation method for phase-shifted interferograms based on a convolutional neural network includes the following steps:

[0036] Phase distribution generation is performed by Zernike polynomials, which is realized in a simulation manner; interferograms are generated based on an interference theory model, and random phase shift values (with a value range of 0-π) are introduced to simulate phase-shifted interferograms with different distributions, so that they are more consistent with actual measurement data; the generated two frames of phase-shifted interferograms and the corresponding phase shift values are used as training data sets, a phase shift value estimation model based on a convolutional neural network is established, loss functions, learning rates, and optimizers are set, and the network is trained; in the network training process, the error between the predicted phase shift value and the true phase shift value is measured by calculating the loss function, the optimizer is used to find the weights and biases that minimize the loss function, and the best model is found; after training, the model can directly predict the phase shift value for the input two frames of noisy phase-shifted interferograms.

[0037] Step one, interferogram generation based on Zernike polynomials and an interference theory model;

[0038] Specifically, the mathematical model of the initial interferogram is expressed as follows:

[0039]

[0040] In the formula, a(x, y) is the background light intensity of the initial interferogram, and a(x, y) = 0.5; b(x, y) is the contrast, and b(x, y) = 0.3; is the phase generated based on Zernike polynomials; d1 is the phase shift value (d1 = 0); η1(x, y) is the noise in the interferogram; k is the number of phase-shifted interferogram frames (k = 1).

[0041] Step two, random phase shift values (range of 0-π) are added to the initial interferogram to generate a phase-shifted interferogram.

[0042] Specifically, the mathematical model of the second frame of phase-shifted interferogram is expressed as follows:

[0043]

[0044] In the formula, a(x, y) is the background light intensity of the phase shift interferogram, let a(x, y) = 0.5; b(x, y) is the contrast, let b(x, y) = 0.3; Is the phase generated based on Zernike polynomial; d2 is a random phase shift value (the value range is 0 to π); η2(x, y) is the noise in the interferogram; k is the frame number of the phase shift interferogram (k = 2).

[0045] In the above initial interferogram and phase shift interferogram, the Zernike polynomial involved can represent optical aberration, theoretical wave surface and fitting wave surface; the process of generating the simulation interferogram involves using Zernike polynomial to simulate different aberration effects, superimposing them together to generate a phase distribution, and then forming two frames of interferograms.

[0046] The phase expression mathematical model based on Zernike polynomial is as follows:

[0047]

[0048] In the formula, a(x, y) is the background light intensity of the phase shift interferogram, let a(x, y) = 0.5; b(x, y) is the contrast, let b(x, y) = 0.3; Is the phase, a i Is the coefficient of the i-th term of the Zernike polynomial; Z i (x, y) is the i-th term of the Zernike polynomial.

[0049] Step three, prepare the data set;

[0050] The specific content is as follows:

[0051] The simulated two frames of phase shift interferograms are divided into a training set and a test set, the phase shift value of the phase shift interferogram is taken as a label, and the two frames of phase shift interferograms Figure 1 Correspond.

[0052] When generating the training data, the first ten terms of the Zernike polynomial are used to generate the phase, which satisfies the diversity of the training data; random noise with different signal-to-noise ratios (15-60dB) is added to make the interferogram as close to the real collected interferogram as possible.

[0053] It should be noted that the method of the present application is suitable for processing two frames of interferograms with a phase shift value ranging from 0 to π.

[0054] Step four, construct a phase shift value estimation framework based on a convolutional neural network.

[0055] The input data of the neural network is two frames of random value interferograms within a certain range; the two sets of interferograms are respectively input into the branch of two multilayer convolutional layers.

[0056] The network structure of the first branch includes 3 layers of convolutional layers (3x3), each followed by an activation function for feature extraction from the interferogram. Then, a 1-layer convolutional layer (1x1) is set to output the feature map.

[0057] Similarly, the structure of the second branch includes 3 layers of convolutional layers (3x3), each followed by an activation function for feature extraction from the interferogram. Then, a 1-layer convolutional layer (1x1) is set to output the feature map.

[0058] The two branches output single-channel 128x128 pixel feature maps, respectively. Then, the two feature maps are spliced together using a splicing method to generate a two-channel feature map. Finally, after information extraction by a convolutional layer (1x1), the result is passed to a fully connected layer for mapping, and the final estimated result is output.

[0059] The neural network extracts features from the two interferograms and combines them through multiple layers of convolutional layers and a splicing method to obtain a more rich feature information map. Finally, a fully connected layer is used for mapping to obtain the final estimated result.

[0060] Step five, train the phase shift value estimation model based on the convolutional neural network.

[0061] The specific content is as follows:

[0062] First, input the training set into the neural network framework. The data is calculated layer by layer through convolutional layers and activation functions to generate prediction outputs. These prediction outputs are compared with the labels, and the MAE loss function is used to measure the difference between the predicted values and the true values.

[0063] Set the learning rate to 0.0001 and use the Adam optimization algorithm to find the weights and biases that minimize the loss function.

[0064] Set the number of iterations to 70. In each iteration, perform the following steps: first, forward propagation, input the training data into the model, and calculate the prediction output. Then, calculate the loss function to measure the difference between the predicted values and the true values. Next, perform backpropagation to calculate the gradient of the loss function with respect to the model parameters. Finally, use the Adam optimization algorithm to update the weights and biases of the convolutional neural network model based on the gradient information.

[0065] Repeat the execution until the predetermined number of iterations is reached. Each iteration trains the entire training data set to gradually optimize the performance of the model. After 70 iterations of training, the phase shift value estimation model is obtained, which can predict the input data.

[0066] The specific process is as follows:

[0067] Data reading: load the prepared data (interferogram and phase shift value).

[0068] Model definition: Define the network architecture, define the weight initialization function.

[0069] Loss and optimizer: The script defines the loss function (MAE) and optimizer (Adam) for training the model. By setting the loss function, the average of the absolute value is calculated to measure the difference between the estimated phase shift value and the true phase shift value (label), which is mathematically expressed as follows:

[0070]

[0071] where d i is the estimated phase shift value, d` i is the true phase shift value, and n is the batch size.

[0072] The Adam optimizer is used to adjust the parameters of the neural network to the optimal state, and the learning rate is adjusted on the specified number of rounds. The optimizer uses the new learning rate to update, so as to minimize the loss function; MAE loss function and Adam optimizer are the key components in the training process of neural network, through back propagation and gradient descent method to update the model parameters, so that the loss between the estimated value and the standard value is minimized, thereby improving the network performance.

[0073] Training loop: Iterate the dataset for a certain number of rounds. In each round, iterate through the data batches and perform the training loop.

[0074] Save the model: After each round, save the trained model file to the specified folder.

[0075] Test the model;

[0076] Use the simulated new data as the test set, input the test data set into the neural network model, and output the estimated phase shift value; compare the estimated phase shift value with the true phase shift value, so as to further evaluate the model.

[0077] The specific process is as follows:

[0078] Load the pre-trained model, and use the 70th trained model to load into the test.

[0079] The input test data set in the trained neural network model can obtain the phase shift value, and the final test result (estimated phase shift value) is compared with the actual value (true phase shift value); in theory, the true phase shift value is approximately equal to the estimated phase shift value, and the difference is very small. By calculating the difference between the two, the performance of the network model is evaluated; finally, 5 groups of data are selected in the test results, and the signal-to-noise ratios are 15dB, 15dB, 20dB, 20dB and 30dB; as Figures 5-9 is the test interference diagram, and the test result comparison is shown in Table 1.

[0080] Table 1 test results

[0081]

[0082] According to the test results, the difference between the true phase shift value and the estimated phase shift value is very small, that is, the fitting effect of the neural network model is good, and the test results of the present application are within the ideal expectation.

[0083] Based on the above ideal embodiments according to the present application, through the above description, relevant personnel can make various changes and modifications without deviating from the technical idea of the present application. The technical scope of the present application is not limited to the content of the specification, and the technical scope must be determined according to the scope of claims.

Claims

1. A method for estimating phase shift values ​​in phase-shifted interferograms based on convolutional neural networks, characterized in that, Includes the following steps: Step 1: Represent the phase distribution using Zernike polynomials and generate an initial interferogram based on the interference theory model; Step 2: Add random phase shift values ​​to the interferogram to simulate a phase-shifted interferogram, thereby generating two frames of phase-shifted interferograms; The initial interferogram and the phase-shifted interferogram are used as inputs to the convolutional neural network, and the phase shift value is used as the output. Step 3: Construct a phase shift estimation framework based on convolutional neural networks; The convolutional neural network includes a first branch network and a second branch network with the same structure. The first branch network includes three 3×3 convolutional layers. After each convolutional layer, an activation function is used to extract features from the image, and a feature map is output through a 1×1 convolutional layer. The single-channel feature maps of the two branch networks are concatenated to form a two-channel feature map. The two-channel feature map is then processed by a 1×1 convolutional layer to extract information, and the feature vector after flattening is passed to a fully connected layer for mapping. Step 4: Train the neural model network to predict the phase shift value of the interferogram.

2. The method for estimating the phase shift value of a phase-shifted interferogram based on a convolutional neural network according to claim 1, characterized in that, The mathematical model for interferograms is: In the formula, k The number of interferogram frames; a ( x,y () represents the background light intensity; b ( x , y () represents contrast. ( x , y () represents the phase to be recovered; d k This represents the phase shift value; η k ( x , y () represents noise added to the interferogram.

3. The method for estimating the phase shift value of a phase-shifted interferogram based on a convolutional neural network according to claim 1, characterized in that, The initial phase shift of the interferogram is 0, and the phase shift of the phase-shifted interferogram ranges from 0 to π.

4. The method for estimating the phase shift value of a phase-shifted interferogram based on a convolutional neural network according to claim 1, characterized in that, The loss function of a convolutional neural network adopts MAE The loss function is determined by using the Adam optimizer to find the weights and biases that minimize the loss function.

5. The method for estimating the phase shift value of a phase-shifted interferogram based on a convolutional neural network according to claim 4, characterized in that, MAE The formula for the loss function is: In the formula, d i To estimate the phase shift value, d ` i This is the true phase shift value. n This represents the batch size.

6. A phase shift value estimation system for phase-shifted interferograms based on convolutional neural networks, 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 phase shift value estimation method for phase-shifted interferograms based on any one of claims 1-5.

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