CN117315437A - Phase shift value estimation method and system of phase shift interferogram based on convolutional neural network - Google Patents
Phase shift value estimation method and system of phase shift interferogram based on convolutional neural network Download PDFInfo
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Abstract
The invention relates to the technical field of interference phase shift, in particular to a phase shift value estimation method and a phase shift value estimation system of a phase shift interferogram based on a convolutional neural network, wherein the phase distribution is represented by a Zernike polynomial, and an initial interferogram is generated according to an interference theoretical model; adding a random phase shift value to the initial interference pattern to simulate a phase shift interference pattern, thereby generating a two-frame phase shift interference pattern; constructing a phase shift value estimation framework based on a convolutional neural network; setting a loss function, a learning rate, an optimizer and the like to optimize network parameters, and generating a phase shift value estimation network model; and processing the phase shift interference pattern by adopting the optimized network model to estimate a corresponding phase shift value. Compared with the traditional method, the convolutional neural network method is not required to have complex calculation flow and has better generalization capability, has robustness to high noise, and can accurately extract random phase shift values.
Description
Technical Field
The invention relates to the technical field of interference phase shift, in particular to a phase shift value estimation method and a phase shift value estimation system of a phase shift interferogram based on a convolutional neural network.
Background
In the optical interferometry technology, accurate extraction of phase information is crucial, and a phase shift method is a common and effective phase extraction method in interferometry, and high-precision phase recovery is realized through recorded multi-frame interferograms; the phase extraction method based on the phase shift method comprises a known step length phase shift method, an unknown step length but regular phase shift method, a random step length phase shift method and the like. In the known step phase shift method, accurate phase shifting is critical. The least square method is a known step-length phase shift algorithm, and accurate phase shift values are needed to effectively extract phases; however, due to environmental disturbance and other factors, phase shift errors are easy to generate; in addition, most two-step random phase shift algorithms need to know the phase shift value in advance to recover the phase when extracting the phase; therefore, how to accurately and efficiently estimate the phase shift value is important.
At present, a two-step random phase shift method generally needs to extract a phase shift value process, and the phase shift value extraction method comprises a Kreis algorithm, an extremum interference (EVI) method, a Gram-Schmidt (GS) quadrature normalization method, a phase step length calibration algorithm (PSC) and the like; the Kreis algorithm can be used for phase shift value extraction in the interferogram, which is based on the spectrum analysis of the interferogram; the Kreis algorithm can extract smaller phase shift values, but has poorer noise immunity; the EVI determines a phase shift value through the intensity ratio of an interference extremum in the interference pattern to a corresponding position in another interference pattern; the phase step calibration algorithm (PSC) is a phase step number algorithm for calibrating two interferograms, and is mainly based on calculating the correlation coefficient of the two interferograms; the GS orthogonal normalization method determines an orthogonal normalization interferogram base from two frames of interferograms; because of factors such as noise interference, most methods can realize high-precision phase shift value extraction after interference pattern denoising; furthermore, advanced Iterative Algorithms (AIA) can extract phase shift values and phases from three-frame interferograms, but require iterative computations, resulting in slow computation speeds.
Disclosure of Invention
Aiming at the defects of the prior method, the convolutional neural network method is applied to the extraction of the phase values of the two-frame interferograms; compared with the traditional method, the convolutional neural network method does not need complex calculation flow and has better generalization capability, and has robustness to high noise and accurately predicts the phase shift value under the condition of complex interferograms.
The technical scheme adopted by the invention is as follows: the phase shift value estimation method and system of the phase shift interferogram based on the convolutional neural network comprise the following steps:
step one, using Zernike polynomials to represent phase distribution, and generating an initial interference pattern according to an interference theory model;
step two, adding a random phase shift value to the interference pattern to simulate a phase shift interference pattern, so as to generate a two-frame phase shift interference pattern;
further, the generated interferogram mathematical model is:
wherein k is the number of interferograms; a (x, y) is the background light intensity; b (x, y) is contrast;is the phase to be recovered; d, d k Is the phase shift value; η (eta) k (x, y) is the noise added to the interferogram.
Further, the phase shift value of the initial interferogram is 0, and the phase shift value of the phase shift interferogram is 0 to pi.
Step three, constructing a phase shift value estimation framework based on a convolutional neural network;
furthermore, the initial interferogram and the phase shift interferogram are used as inputs of the convolutional neural network, and the phase shift value is used as an output.
Further, the convolutional neural network includes: a first branch network and a second branch network of the same structure, the first branch network comprising: 3 layers of 3 x 3 convolution, performing feature extraction on the image by using an activation function after each convolution layer, outputting feature images by 1 layer of 1 x 1 convolution layer, and splicing the single-channel feature images of two branch networks into a two-channel feature image; the two-channel feature map is subjected to 1×1 convolution layer information extraction, and feature vectors after flattening layers are transferred to a full connection layer for mapping.
Training a neural network model, and predicting the phase shift value of the interferogram.
Further, two frames of interferograms are input into a neural network frame, and estimated nodes are output through calculation.
Further, the MAE loss function is used for measuring the difference between the estimated phase shift value and the real phase shift value, and an Adam optimizer is used for finding out the weight and the paranoid under the minimum loss function.
Further, the formula of the MAE loss function is:
wherein d i To estimate the phase shift value, d i For the true phase shift value, n is the batch size.
Further, setting iteration times, and executing forward propagation, loss calculation, backward propagation and parameter updating processes; training the whole training data once for each iteration; finally, a trained model is obtained.
Further, the phase shift interferogram phase shift value estimation system based on the convolutional neural network comprises: a memory for storing instructions executable by the processor; and the processor is used for executing the instructions to realize a phase shift interference diagram phase shift value estimation method based on the convolutional neural network.
The invention has the beneficial effects that:
1. the estimation accuracy of the phase shift value is high; the noise immunity is strong; the calculation speed is high; end-to-end processing; the neural network model is utilized to extract the characteristics of the interferograms, so that the complex characteristics in the interferograms are effectively captured, and the estimation accuracy of the phase shift value is improved.
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FIG. 1 is a flow chart of a phase shift value estimation method and system of a phase shift interferogram based on a convolutional neural network;
FIG. 2 is a diagram of a neural network model architecture of the present invention;
FIG. 3 is a schematic diagram of a training phase of the neural network model of the present invention;
FIG. 4 is a schematic diagram of a testing phase of the neural network model of the present invention;
FIGS. 5 (a) and 5 (b) are a first set of test initial and phase shift interferograms, respectively;
FIGS. 6 (a) and 5 (b) are a second set of test initial and phase shift interferograms, respectively;
FIGS. 7 (a) and 5 (b) are a third set of test initial and phase shift interferograms, respectively;
FIGS. 8 (a) and 5 (b) are a fourth set of test initial and phase shift interferograms, respectively;
fig. 9 (a) and fig. 5 (b) are a fifth set of test initial interferograms and phase-shift interferograms, respectively.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples, which are simplified schematic illustrations showing only the basic structure of the invention and thus showing only those constructions that are relevant to the invention.
As shown in fig. 1, a phase shift value estimation method of a phase shift interferogram based on a convolutional neural network comprises the following steps:
generating phase distribution by using a Zernike polynomial, wherein the phase distribution is realized by adopting a simulation mode; generating an interference pattern based on an interference theory model, introducing a random phase shift value (the value range is 0-pi), and simulating phase shift interference patterns with different distributions to enable the phase shift interference patterns to be more in line with actual measurement data; taking the generated two-frame phase shift interferograms and corresponding phase shift values as training data sets, and setting a loss function, a learning rate, an optimizer and the like by establishing a phase shift value estimation model based on a convolutional neural network so as to train the network; in the network training process, calculating a loss function to measure the error between a predicted phase shift value and a real phase shift value, and an optimizer is used for searching the weight and the bias under the minimum loss function to find an optimal model; after training, the model can directly predict the phase shift value for the input two-frame noise phase shift interference diagram.
Step one, generating an interference pattern based on a Zernike polynomial and an interference theoretical model;
specifically, the initial interferogram mathematical model is expressed as follows:
wherein a (x, y) is the background light intensity of the initial interferogram, and let a (x, y) =0.5; b (x, y) is contrast, let b (x, y) =0.3;is a phase generated based on a Zernike polynomial; d, d 1 For the phase shift value (d 1 ＝0)；η 1 (x, y) is noise in the interferogram; k is the number of phase-shifted interferograms (k=1).
And step two, the initial interference pattern is subjected to random phase shift values (the range is 0-pi), so that a phase shift interference pattern is generated.
Specifically, the second frame phase shift interferogram mathematical model is expressed as follows:
wherein a (x, y) is the background light intensity of the phase-shift interferogram, let a (x, y) =0.5; b (x, y) is contrast, let b (x, y) =0.3;is a phase generated based on a Zernike polynomial; d, d 2 Is a random phase shift value (the value range is 0 to pi); η (eta) 2 (x, y) is noise in the interferogram; k is the number of phase-shifted interferograms (k=2).
In the initial interferogram and the phase-shift interferogram, the Zernike polynomials involved can represent optical aberrations, theoretical wave surfaces, and fitted wave surfaces; the process of generating the simulated interferograms involves using Zernike polynomials to model the effects of different aberrations, which are superimposed together to generate a phase profile, thereby forming a two-frame interferogram.
The mathematical model of the phase representation based on the Zernike polynomials is as follows:
in the method, in the process of the invention,is a phase, a i The ith term coefficient is Zernike polynomial; z is Z i (x, y) is the ith term of the Zernike polynomial.
Step three, preparing a data set;
the specific contents are as follows:
the simulated two-frame phase-shift interferograms are divided into a training set and a testing set, and phase shift values of the phase-shift interferograms are used as labels and correspond to the two-frame phase-shift interferograms one by one.
When training data is generated, generating phases by using the first ten terms of the Zernike polynomials, so as to meet the diversity of the training data; random noise with different signal-to-noise ratios (15-60 dB) is added to be as close as possible to the interference pattern of the real acquisition.
It should be noted that the method is suitable for processing two-frame interferograms with phase shift values ranging from 0 to pi.
And step four, constructing a phase shift value estimation framework based on the convolutional neural network.
The input data of the neural network is a random value interference pattern of two frames in a certain range; the two sets of interferograms are input into branches of two multilayer convolution layers, respectively.
The network structure of the first branch comprises 3 layers of convolution layers (3×3), and an activation function is used after each convolution layer for extracting characteristics of the interference pattern; next, a feature map is output by setting 1 layer convolution layer (1×1).
Likewise, the structure of the second branch comprises 3 convolutions (3 x 3), each of which is followed by an activation function for feature extraction of the interferogram. Next, a feature map is output by setting 1 layer convolution layer (1×1).
The two branches respectively output a feature map of 128×128 pixels of a single channel; then, splicing the two feature images together by adopting a splicing method to generate two-channel feature images; and finally, after information extraction is carried out through a convolution layer (1 multiplied by 1), the information is transmitted to a full connection layer for mapping, and finally, a predicted result is output.
The neural network extracts features from the two interferograms through a multi-layer convolution layer and a splicing method, combines the features to obtain a richer feature information diagram, and finally adopts a full-connection layer for mapping to obtain a final estimated result.
And fifthly, training a phase shift value estimation model based on the convolutional neural network.
The specific contents are as follows:
firstly, the training set is input into a neural network framework, data is calculated layer by layer through a convolution layer and an activation function, prediction outputs are generated, the prediction outputs are compared with labels, and an MAE loss function is used for measuring the difference between a predicted value and a true value.
The learning rate was set to 0.0001 and Adam optimization algorithm was used to find the weights and paraphrases that minimize the loss function.
Setting the iteration number to be 70, and executing the following steps in each iteration: firstly, forward propagation is carried out, training data is input into a model, and prediction output is calculated; then, calculating a loss function, and measuring the difference between the predicted value and the true value; then, back propagation is carried out, and the gradient of the loss function to the model parameters is calculated; finally, the weight and bias of the convolutional neural network model are updated according to the gradient information by using an Adam optimization algorithm.
Repeating the execution until the preset iteration times are reached, and training the whole training data set once for each iteration to gradually optimize the performance of the model; finally, after 70 iterative training, a phase shift value estimation model is obtained, which can predict the input data.
The specific flow is as follows:
reading data: the prepared data (interferograms and phase shift values) are loaded.
Model definition: defining a network architecture and defining a weight initialization function.
Loss and optimizer: scripts define a loss function (MAE) and an optimizer (Adam) for the training model. The difference between the estimated phase shift value and the true phase shift value (label) is measured by setting a loss function and calculating the average value of absolute values, and the mathematical model is expressed as follows:
wherein d i To estimate the phase shift value, d i For the true phase shift value, n is the batch size.
Adjusting parameters of the neural network to an optimal state by adopting an Adam optimizer, adjusting a learning rate on a designated round, and updating by using a new learning rate by the optimizer so as to minimize a loss function; MAE loss function and Adam optimizer are key components in the training process of neural network, and model parameters are updated by back propagation and gradient descent method, so that the loss between the estimated value and the standard value is minimized, and the network performance is improved.
Training cycle: the dataset is iterated over a number of rounds. Within each round, the data batch is traversed, performing a training cycle.
And (3) saving a model: after each round is finished, the trained model file is stored in a designated folder.
Testing a model;
using the new simulated data as a test set, inputting the test data set into a neural network model, and outputting a predicted phase shift value; and comparing the estimated phase shift value with the real phase shift value, thereby further evaluating the model.
The specific flow is as follows:
the pre-trained model is loaded and the 70 th model trained is used to load into the test.
Inputting a test data set into the trained neural network model to obtain a phase shift value, and comparing and evaluating a final test result (estimated phase shift value) with an actual value (real phase shift value); in theory, the true phase shift value is similar to the estimated phase shift value and has a very small difference. Evaluating the performance of the network model by calculating the difference value of the two; finally, 5 groups of data are selected from the test result, and the signal to noise ratio is respectively 15dB, 20dB and 30dB; the test interferograms are shown in FIGS. 5-9, and the test results are shown in Table 1.
Table 1 test results
According to the test result, the difference between the real phase shift value and the estimated phase shift value is very small, namely the fitting effect of the neural network model is good, and the test result is in ideal expectation.
With the above-described preferred embodiments according to the present invention as an illustration, the above-described descriptions can be used by persons skilled in the relevant art to make various changes and modifications without departing from the scope of the technical idea of the present invention. The technical scope of the present invention is not limited to the description, but must be determined according to the scope of claims.
Claims (8)
1. The phase shift value estimation method of the phase shift interferogram based on the convolutional neural network is characterized by comprising the following steps of:
step one, using Zernike polynomials to represent phase distribution, and generating an initial interference pattern according to an interference theory model;
step two, adding a random phase shift value to the interference pattern to simulate a phase shift interference pattern, so as to generate a two-frame phase shift interference pattern;
step three, constructing a phase shift value estimation framework based on a convolutional neural network;
training a neural model network, and predicting an interferogram phase shift value;
2. the phase shift interferogram phase shift value estimation method based on the convolutional neural network according to claim 1, wherein the interferogram mathematical model is:
wherein k is the number of interferograms; a (x, y) is the background light intensity; b (x, y) is contrast;is the phase to be recovered; d, d k Is the phase shift value; η (eta) k (x, y) is the noise added to the interferogram.
3. The phase shift value estimation method of a phase shift interferogram based on a convolutional neural network according to claim 1, wherein the phase shift value of the initial interferogram is 0, and the phase shift value of the phase shift interferogram is 0 to pi.
4. The phase shift value estimation method of phase shift interferograms based on convolutional neural network according to claim 1, wherein the initial interferograms and the phase shift interferograms are used as inputs of the convolutional neural network, and the phase shift values are used as outputs.
5. The phase shift interferogram phase shift value estimation method based on the convolutional neural network according to claim 1, wherein the convolutional neural network comprises: a first branch network and a second branch network of the same structure, the first branch network comprising: 3 layers of 3 x 3 convolution, performing feature extraction on the image by using an activation function after each convolution layer, outputting feature images by 1 layer of 1 x 1 convolution layer, and splicing the single-channel feature images of two branch networks into a two-channel feature image; the two-channel feature map is subjected to 1×1 convolution layer information extraction, and feature vectors after flattening layers are transferred to a full connection layer for mapping.
6. The phase shift interferogram phase shift value estimation method based on the convolutional neural network according to claim 1, wherein the loss function of the convolutional neural network adopts an MAE loss function, and the Adam optimizer is used to find the weight and the bias under which the loss function is minimized.
7. The method for estimating phase shift values of phase shift interferograms based on convolutional neural network of claim 6, wherein the MAE loss function is formulated as:
wherein d i To estimate the phase shift value, d i For the true phase shift value, n is the batch size.
8. The phase shift interferogram phase shift value estimation system based on the convolutional neural network is characterized by comprising: a memory for storing instructions executable by the processor; a processor for executing instructions to implement a convolutional neural network-based phase shift interferogram phase shift value estimation method as recited in any one of claims 1-7.
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