CN115205349A - A Deep Neural Network-Based Interferogram Automatic Registration and Phase Unpacking Method - Google Patents

Abstract

The invention discloses a method for automatic registration and phase unpacking of an interferogram based on a deep neural network. The method comprises the following steps: generating a real phase and a wrapping phase through simulation and adding noise; generating an interferogram from the wrapping phase; Generate a data set by simulating the system jitter existing in the actual acquisition; set the deep neural network model and optimization algorithm, use the hybrid loss function and the generated data set to train the deep neural network; judge whether the phase recovery effect meets the requirements according to the evaluation index , if it is satisfied, go to the next step; if it is not satisfied, change the network structure, modify the values of parameters such as optimization function, learning rate and loss function, and retrain; use the actually collected interferogram as the input of the deep neural network model, and calculate The predicted true phase. The method proposed by the invention does not need to register the interferogram, reduces the calculation time, has good anti-noise capability, and improves the accuracy of phase unpacking.

Description

A Deep Neural Network-Based Interferogram Automatic Registration and Phase Unpacking Method

technical field

The invention relates to the technical field of phase-shifting interference, in particular to an interferogram automatic registration and phase unpacking method based on a deep neural network.

Background technique

Phase-shifting laser interferometers generally generate modulation phases by tuning the laser wavelength or pushing the reference mirror through a piezoelectric ceramic sheet (PZT), and then the image acquisition system uses photodetectors (such as CCDs) to collect interferograms with different phase-shifting amounts. The phase-shifting interferometry adopts a four-step phase-shifting method, and the processing of the collected interferogram generally includes two steps of phase calculation and phase unpacking.

During the phase calculation process, due to external interference, jitter and other factors in the acquisition system, the interferograms with different phasors have rotational offset and other phenomena, which are difficult to accurately register, resulting in phase recovery errors in the calculated package phase. Designing a very stable interferometric system requires a very high cost and is highly dependent on environmental stability. In order to solve the above problems, some scholars have proposed a series of methods, such as making the four interferograms have similar grayscale distribution, using mutual interference operation to determine the position matching relationship between the interferograms; obtaining the The fundamental frequency energy and phase information can be used to correct the position matching error and phasor error through the phase difference between the sub-images. However, these methods are complicated in calculation process and difficult to apply in dynamic measurement systems.

In the phase unpacking process in which the real phase is calculated from the wrapped phase, the commonly used unpacking algorithms such as the path tracing algorithm will have unpacking errors when the noise level is large. When the system is under-sampled, the difference between two adjacent points in the collected data The value will exceed π, which will make the unpacking error. In addition, the commonly used minimum norm method, such as the preprocessing conjugate gradient algorithm, the iterative process is very complicated and takes a long time. In conclusion, there are problems of poor phase recovery accuracy and long calculation time in the existing phase calculation and phase unpacking process.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a fast and accurate method for automatic registration and phase unpacking of interferogram based on deep neural network.

The technical solution for realizing the object of the present invention is: a deep neural network-based interferogram automatic registration and phase unpacking method, comprising the following steps:

Step S1, generating a two-dimensional real phase through simulation, and calculating a two-dimensional wrapping phase, adding noise;

Step S2, generating a corresponding light intensity interferogram according to the two-dimensional wrapping phase calculation, and simulating the system jitter existing in the actual acquisition by randomly translating and rotating the image to generate a data set;

Step S3, setting the deep neural network model structure, parameters, and optimization algorithm, and using the hybrid loss function and the data set generated in step 2 to train the deep neural network model;

Step S4, according to evaluation indicators such as structural similarity, peak signal-to-noise ratio, etc., determine whether the phase recovery effect meets the requirements, and if so, enter the modulation step S5; if not, change the network structure, and modify parameters such as the optimization function, the learning rate, and the loss function. , and go to step S3 to retrain;

Step S5, the light intensity interferogram collected by the real system is used as the input of the deep neural network model after training, and the predicted real phase is obtained through calculation.

Compared with the prior art, the present invention has the following significant advantages: (1) the real phase is directly calculated from the interferogram, and it is not necessary to register the interferograms of different phasors to calculate the wrapped phase and the real phase, which reduces the need for calculation (2) Strong anti-noise ability, commonly used phase unpacking algorithms such as the minimum path algorithm, when the noise level is large, the phenomenon of unpacking errors will occur. Adding different types and different levels of noise to the wrapped phase improves the generalization ability of the network to remove different levels of noise and improves the accuracy of phase unpacking.

Description of drawings

FIG. 1 is a flow chart of the method for automatic registration and phase unpacking of interferograms based on deep neural network according to the present invention.

FIG. 2 is a three-dimensional histogram of the initial matrix generated by the present invention.

Figure 3 is a surface plot of the true phase generated by the present invention.

Figure 4 is a two-dimensional plan view of the real phase and the noise-added wrapped phase generated by the present invention.

Figure 5 is the light intensity interferogram after translation and rotation transformation and cropping the central region.

Figure 6 is a diagram of the structure of the convolutional neural network used.

FIG. 7 is a structural diagram of the residual block used.

Figure 8 is the true phase plot of the network computation output.

Detailed ways

The purpose of the present invention is to provide an interferogram automatic registration and phase unpacking method based on a deep neural network, which solves the problem that the traditional light intensity interference recovery algorithm has poor anti-noise ability, and the existence of system jitter causes phase translation and rotation, which makes the recovery phase inaccurate and calculation. long time etc.

1, a deep neural network-based interferogram automatic registration and phase unpacking method of the present invention includes the following steps:

Step S1, generating a two-dimensional real phase through simulation, and calculating a two-dimensional wrapping phase, adding noise;

Step S2, generating a corresponding light intensity interferogram according to the two-dimensional wrapping phase calculation, and simulating the system jitter existing in the actual acquisition by randomly translating and rotating the image to generate a data set;

Step S3, setting the deep neural network model structure, parameters, and optimization algorithm, and using the hybrid loss function and the data set generated in step 2 to train the deep neural network model;

Step S4, according to evaluation indicators such as structural similarity, peak signal-to-noise ratio, etc., determine whether the phase recovery effect meets the requirements, and if so, enter the modulation step S5; if not, change the network structure, and modify the parameters of the optimization function, learning rate and loss function. , and go to step S3 to retrain;

Step S5, the light intensity interferogram collected by the real system is used as the input of the deep neural network model after training, and the predicted real phase is obtained through calculation.

As a specific example, in step S1, the two-dimensional real phase is generated by simulation, and the two-dimensional wrapped phase is calculated, and noise is added, as follows:

S11. Randomly generate a matrix with a size within a specific interval, the value of the matrix is within the set interval, and satisfies one of Gaussian distribution or uniform distribution; randomly select an interpolation algorithm, and expand the initial matrix as the real phase ω;

计算包裹相位

并随机从椒盐噪声、高斯噪声中选择一种添加至包裹相位

S12. According to the formula

Calculate wrap phase

And randomly select one of salt and pepper noise and Gaussian noise to add to the wrapped phase

具体如下：As a specific example, in S12, randomly select one of salt and pepper noise and Gaussian noise to add to the wrapped phase

details as follows:

除以π，再从椒盐噪声、高斯噪声中随机选择其一添加至包裹相位，其中椒盐噪声密度为0.01～0.2之间的随机数，高斯噪声标准差为0.01～0.20之间的随机数，添加噪声完成后，再将相位乘以π恢复其数值范围。The function angle represents the calculation of the phase angle of the complex number. The function value is in [-π,π]. First wrap the phase

Divide by π, and then randomly select one of the salt and pepper noise and Gaussian noise to add to the wrapping phase, where the salt and pepper noise density is a random number between 0.01 and 0.2, and the standard deviation of the Gaussian noise is a random number between 0.01 and 0.20. After the noise is complete, multiply the phase by π to restore its range of values.

As a specific example, in step S2, a corresponding light intensity interferogram is generated according to the two-dimensional wrapping phase calculation, as follows:

S21. Randomly generate a matrix whose size is within the set interval, and the value of the matrix is within the set interval and satisfies a uniform distribution; select an interpolation algorithm, and expand the initial matrix as the background light intensity A;

S22. Randomly generate a matrix whose size is within the set interval, and the value of the matrix is within the set interval and satisfies a uniform distribution; select an interpolation algorithm, and expand the initial matrix as the contrast term V;

生成四个不同移相相位的光强干涉图

S23, adopt the four-step phase shift method, for the package phase to which noise has been added

Generate light intensity interferograms with four different phase-shifted phases

随机旋转-10°至10°，随机纵向和横向循环平移-20到20个像素，从中心区域截取大小为256×256的部分作为最终的光强干涉图，同时真实相位也截取中心区域大小为256×256的部分作为最终的光强干涉图。S24, to the generated light intensity interferogram

Random rotation -10° to 10°, random vertical and horizontal circular translation - 20 to 20 pixels, intercepting a 256×256 part from the central area as the final light intensity interferogram, while the real phase also intercepts the central area with a size of The 256×256 section serves as the final light intensity interferogram.

As a specific example, the deep neural network model structure, parameters, and optimization algorithm are set as described in step S3, wherein the optimization algorithm adopts Adam algorithm, and the network model structure is as follows:

The structure of the deep neural network model is based on the U-Net of the residual block, the light intensity interferogram is used as the input of the network, and the output corresponds to the real phase;

The deep neural network model includes an encoder, a bottleneck layer, and a decoder; the encoder has 4 layers, each layer is composed of 2 consecutive residual blocks, and the output of each layer is used as the input of the next layer and the input of the corresponding decoder layer ; The bottleneck layer contains 2 consecutive residual blocks; the number of layers of the decoder and the encoder is the same, each layer contains an upsampling layer and 2 consecutive residual blocks for feature decoding; the output of the last layer of the decoder The feature map of is 1×1 convoluted to output the true phase.

As a specific example, the mixed loss function and the data set generated in step 2 are used to train the deep neural network model as described in step S3, and the formula of the mixed loss function L ^mix (x, y) is as follows:

L ^mix (x,y)=α ₁ L ^l1 (x,y)+α ₂ L ^MS-SSIM (x,y)

where α ₁ and α ₂ are hyperparameters, α ₁ is set to 0.14, and α ₂ is set to 0.86;

The formula for the mean absolute error loss L ^l1 (x, y) is:

Among them, x represents the actual true phase, y represents the predicted true phase output by the deep neural network model network, and N represents the number of matrix elements of the true phase;

The multi-scale structural similarity loss L ^MS-SSIM (x, y) formula is:

Among them, c _j and s _j respectively represent the contrast item and the structure item after performing j consecutive low-pass filtering on the original image and down-sampling with a sampling interval of 2, and M represents the total number of consecutive low-pass filtering;

The formula for the luminance term l(x,y) is:

The formula for the contrast term c(x,y) is:

The formula for the structure item s(x,y) is:

Among them, μ _x , μ _y represent the mean of x and y, respectively, σ _x , σ _y represent the standard deviation of x and y, respectively, σ _xy represents the covariance of x and y, C ₁ , C ₂ , C ₃ are constant values ,Satisfy:

C ₁ =(K ₁ L) ²

C ₂ =(K ₂ L) ²

C ₃ =C ₂ /2

Wherein K ₁ =0.01, K ₂ =0.03, L=2 ^B -1, B=8.

The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

Example

With reference to FIG. 1, the present embodiment of the deep neural network-based light intensity interferogram automatic registration and phase unpacking method includes the following steps:

Step S1, generating a random matrix of a specific size, generating a real phase through an interpolation algorithm, generating a wrapped phase from the real phase, and adding a certain noise to the wrapped phase;

Further, the method steps are as follows:

S11. Randomly generate a square matrix (the size is between 2×2 and 25×25, the value range is 2-30), the distribution type is one of uniform distribution or Gaussian distribution, as shown in Figure 2, and then randomly interpolate from the nearest neighbor , quadratic interpolation, bicubic interpolation, choose a method to expand the matrix to 320×320, as the real phase, Figure 3 is the surface map of the real phase.

计算包裹相位，其中ω是真实相位，

是包裹相位，函数angle表示计算复数的相位角，值在[-π,π]中，先将包裹相位

除以π，再随机从椒盐噪声，高斯噪声中随机选择其一添加至包裹相位，其中椒盐噪声密度为0.01至0.2之间的随机数，高斯噪声标准差在0.01至0.20，添加噪声完成后，再将相位乘以π恢复其原始数值范围，图4中左图是真实相位，右图是添加了噪声的包裹相位。S12. According to the formula

Calculate the wrapped phase, where ω is the true phase,

is the wrapping phase, the function angle represents calculating the phase angle of the complex number, the value is in [-π,π], first wrap the phase

Divide by π, and then randomly select one of the salt and pepper noise and Gaussian noise to add to the wrapped phase, where the salt and pepper noise density is a random number between 0.01 and 0.2, and the standard deviation of the Gaussian noise is between 0.01 and 0.20. After adding noise, The phase is then multiplied by π to restore its original value range. The left image in Figure 4 is the true phase, and the right image is the wrapped phase with noise added.

Step S2, wrapping the phase to generate a light intensity interferogram, and after the light intensity interferogram is randomly translated and rotated, the central area is intercepted as the final interference phase;

Further, the method steps are as follows:

S21. Randomly generate a square matrix (the size is between 2×2 and 5×5, and the value range is 0-1), and it satisfies the uniform distribution; through the linear interpolation algorithm, the initial matrix is expanded into a 320×320 matrix, and then Linearly map the numerical range to 0.7-1 as the background light intensity A;

S22. Randomly generate a square matrix (the size is between 2×2 and 5×5, and the value range is 0-1), and satisfy the uniform distribution; through the linear interpolation algorithm, the initial matrix is expanded into a 320×320 matrix, and then Linearly map the numerical range to 0.7-1 as the contrast term V;

生成四个不同移相相位的光强干涉图：S23, adopt the four-step phase shift method, for the package phase to which noise has been added

Generate light intensity interferograms with four different phase-shifted phases:

和

随机旋转-10°至10°，并随机纵向和横向循环平移-20到20个像素，再从所有光强干涉图的中心区域截取大小为256×256的部分作为最终的光强干涉图，同时真实相位也截取中心区域大小为256×256的部分作为最后的真实相位，图5是截取了中心区域的四幅干涉图。S24, to the generated light intensity interferogram

and

Randomly rotate -10° to 10°, and randomly rotate longitudinally and laterally by -20 to 20 pixels, and then intercept a 256×256 part from the central area of all light intensity interferograms as the final light intensity interferogram. The real phase also intercepts the part of the central area with a size of 256×256 as the final real phase. Figure 5 shows four interferograms intercepted from the central area.

Step S3, adjust the structure of the deep neural network, optimize the algorithm, and the loss function, and use the generated data set for training.

The mechanism of the convolutional neural network is shown in Figure 6. The neural network includes a four-layer encoder, a bottleneck layer, and a four-layer decoder. Each layer of the encoder consists of two consecutive residual blocks, each The output of the encoder of one layer is used as the input of the encoder of the next layer, and at the same time, it is used as the input of the decoder of the same layer through skip connection. After the output is spliced, after two consecutive residual blocks are used as the input of the next layer, the output feature map of the last layer of the decoder is subjected to 1x1 convolution to obtain the final output. The structure of the residual block is shown in Figure 7, which contains four 3×3 convolutions and one 1×1 convolution. When the height and width of the output feature map of the residual block are halved, the first 3×3 convolution The step size of the convolution is 2, the padding is 1, otherwise the step size is 1, and the first 3×3 convolution realizes the change of the number of channels of the feature map, and the step size of the last three 3×3 convolution layers is always 1. The number of input channels and output channels remain unchanged.

The mixed loss function formula used is as follows:

L ^mix (x,y)=α ₁ L ^l1 (x,y)+α ₂ L ^MS-SSIM (x,y)

where the mean absolute error loss formula is:

Among them, x represents the actual true phase, y represents the predicted true phase output by the network, and N represents the number of matrix elements of the true phase.

The multi-scale structural similarity loss formula is:

The formula for the luminance term is:

Contrast term formula:

Structure item formula:

where μ _x , μ _y represent the mean of x and y, σ _x , σ _y represent the standard deviation of x and y, respectively, σ _xy represent the covariance of x and y, C ₁ , C ₂ , C ₃ are constant values, Satisfy:

C ₁ =(K ₁ L) ²

C ₂ =(K ₂ L) ²

C ₃ =C ₂ /2

where K ₁ =0.01, K ₂ =0.03, L=2 ^B -1, where B=8.

c _j and s _j respectively represent the contrast and structure of the original image after j consecutive low-pass filtering and down-sampling with a sampling interval of 2. α ₁ and α ₂ are hyperparameters, which are set to 0.14 and 0.86.

Step S4, judge whether the phase recovery effect meets the requirements by evaluating indicators such as structural similarity, root mean square error, and peak signal-to-noise ratio, and if so, modulate step S5; otherwise, adjust the model structure and parameters, and go to step S3 Retraining, Figure 8 is the true phase of the network computed output after training.

Step S5, the light intensity interferogram collected by the real system is used as the network input, and the real phase is obtained through the network calculation.

To sum up, the present invention directly calculates the real phase from the interferogram, and does not need to register the interferograms of different phasors to calculate the wrapped phase and the real phase, which reduces the calculation time and can be used in dynamic measurement. In addition, the present invention has strong anti-noise capability. Commonly used phase unpacking algorithms such as the minimum path algorithm may cause unpacking errors when the noise level is relatively large. The present invention adds different types and different types of packing phases to the packing phase during the data set generation stage. The level of noise improves the generalization ability of the network to remove different levels of noise, and improves the accuracy of phase unpacking.

Claims (6)

1. a kind of interferogram automatic registration and phase unpacking method based on deep neural network, is characterized in that, comprises the following steps: Step S1, generating a two-dimensional real phase through simulation, and calculating a two-dimensional wrapping phase, adding noise; Step S2, generating a corresponding light intensity interferogram according to the two-dimensional wrapping phase calculation, and simulating the system jitter existing in the actual acquisition by randomly translating and rotating the image to generate a data set; Step S3, setting the deep neural network model structure, parameters, and optimization algorithm, and using the hybrid loss function and the data set generated in step 2 to train the deep neural network model; Step S4, according to the evaluation indicators such as structural similarity and peak signal-to-noise ratio, determine whether the phase recovery effect meets the requirements, and if so, enter the modulation step S5; if not, change the network structure, and modify the parameters of the optimization function, learning rate and loss function. , and go to step S3 to retrain; Step S5, the light intensity interferogram collected by the real system is used as the input of the deep neural network model after training, and the predicted real phase is obtained through calculation. 2. the interferogram automatic registration and phase unpacking method based on deep neural network according to claim 1, is characterized in that, in step S1, generate two-dimensional real phase by simulation, and calculate two-dimensional wrapping phase, add noise ,details as follows: S11. Randomly generate a matrix with a size within a specific interval, the value of the matrix is within the set interval, and satisfies one of Gaussian distribution or uniform distribution; randomly select an interpolation algorithm, and expand the initial matrix as the real phase ω; S12. According to the formula

Calculate wrap phase

And randomly select one of salt and pepper noise and Gaussian noise to add to the wrapped phase

3. the interferogram automatic registration and phase unpacking method based on deep neural network according to claim 2, it is characterized in that, in described S12, randomly select one from salt and pepper noise, Gaussian noise and add to the packing phase

details as follows: The function angle means to calculate the phase angle of the complex number, the value is in [-π,π], first wrap the phase

Divide by π, and then randomly select one of the salt and pepper noise and Gaussian noise to add to the wrapping phase, where the salt and pepper noise density is a random number between 0.01 and 0.2, and the standard deviation of the Gaussian noise is a random number between 0.01 and 0.20. After the noise is complete, multiply the phase by π to restore its range of values. 4. the interferogram automatic registration and phase unpacking method based on deep neural network according to claim 1, is characterized in that, in step S2, according to two-dimensional wrapping phase calculation to generate corresponding light intensity interferogram, specifically as follows: S21. Randomly generate a matrix whose size is within the set interval, and the value of the matrix is within the set interval and satisfies a uniform distribution; select an interpolation algorithm, and expand the initial matrix as the background light intensity A; S22. Randomly generate a matrix whose size is within the set interval, and the value of the matrix is within the set interval and satisfies a uniform distribution; select an interpolation algorithm, and expand the initial matrix as the contrast term V; S23, adopt the four-step phase shift method, for the package phase to which noise has been added

Generate light intensity interferograms with four different phase-shifted phases

S24, to the generated light intensity interferogram

Random rotation -10° to 10°, random vertical and horizontal circular translation -20 to 20 pixels, and then intercept a 256 × 256 part from the central area of all light intensity interferograms as the final light intensity interferogram, and at the same time real The phase also intercepts the central area with a size of 256×256 as the final real phase. 5. the interferogram automatic registration and phase unpacking method based on deep neural network according to claim 1, is characterized in that, described in step S3, sets deep neural network model structure, parameter, optimization algorithm, wherein optimization algorithm adopts Adam algorithm, the network model structure is as follows: The structure of the deep neural network model is based on the U-Net of the residual block, the light intensity interferogram is used as the input of the network, and the output corresponds to the real phase; The deep neural network model includes an encoder, a bottleneck layer, and a decoder; the encoder has 4 layers, each layer is composed of 2 consecutive residual blocks, and the output of each layer is used as the input of the next layer and the input of the corresponding encoder layer ; The bottleneck layer contains 2 consecutive residual blocks; the number of layers of the decoder and the encoder is the same, each layer contains an upsampling layer and 2 consecutive residual blocks for feature decoding; the output of the last layer of the decoder The feature map of is 1×1 convoluted to output the true phase. 6. The interferogram automatic registration and phase unpacking method based on deep neural network according to claim 1, is characterized in that, described in step S3, uses the data set that hybrid loss function and step 2 generate to deep neural network model For training, the formula of the mixed loss function L ^mix (x, y) is as follows: L ^mix (x,y)=α ₁ L ^l1 (x,y)+α ₂ L ^MS-SSIM (x,y) where α ₁ and α ₂ are hyperparameters, α ₁ is set to 0.14, and α ₂ is set to 0.86; The formula for the mean absolute error loss L ^l1 (x, y) is:

Among them, x represents the actual true phase, y represents the predicted true phase output by the deep neural network model, and N represents the number of matrix elements of the true phase; The multi-scale structural similarity loss L ^MS-SSIM (x, y) formula is:

Among them, c _j and s _j respectively represent the contrast item and the structure item after performing j consecutive low-pass filtering on the original image and down-sampling with a sampling interval of 2, and M represents the total number of consecutive low-pass filtering; The formula for the luminance term l(x, y) is:

The formula for the contrast term c(x, y) is:

The formula for the structural item s(x, y) is:

Among them, μ _x , μ _y represent the mean of x and y, σ _x , σ _y represent the standard deviation of x and y, respectively, σ _xy represent the covariance of x and y, C ₁ , C ₂ , C ₃ are constant values ,Satisfy: C ₁ =(K ₁ L) ² C ₂ =(K ₂ L) ² C ₃ =C ₂ /2 where K ₁ =0.01, K ₂ =0.03, L=2 ^B -1, B=8.

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