An automatic interferogram registration and phase unpacking method based on deep neural networks

Abstract

This invention discloses an automatic interferogram registration and phase unpacking method based on a deep neural network. Specifically, the method involves: generating a true phase and a wrapped phase through simulation, adding noise; generating an interferogram from the wrapped phase, and simulating system jitter present in actual acquisition by translating and rotating the interferogram to generate a dataset; setting up a deep neural network model and optimization algorithm, and training the deep neural network using a hybrid loss function and the generated dataset; determining whether the phase recovery effect meets the requirements based on evaluation metrics, and proceeding to the next step if it does not; otherwise, modifying the network structure, adjusting the values ​​of parameters such as the optimization function, learning rate, and loss function, and retraining; and using the actually acquired interferogram as input to the deep neural network model to calculate the predicted true phase. The method proposed in this invention eliminates the need for interferogram registration, reduces computation time, has good noise resistance, and improves the accuracy of phase unpacking.

Description

Technical Field

[0001] This invention relates to the field of phase-shifting interferometry, and in particular to an automatic interferogram registration and phase unpacking method based on deep neural networks. Background Technology

[0002] Phase-shifting laser interferometers typically generate a modulated phase by tuning the laser wavelength or by using a piezoelectric ceramic plate (PZT) to drive a reference mirror. The image acquisition system then uses a photodetector (such as a CCD) to acquire interferograms with different phase shifts. The commonly used phase-shifting interferometry method employs a four-step phase-shifting method. The processing of the acquired interferograms generally includes two steps: phase calculation and phase unpacking.

[0003] During phase calculation, external interference and jitter in the acquisition system can cause rotational shifts in interferograms with different phase shifts, making accurate registration difficult. This leads to phase recovery errors in the calculated enclosed phase. Designing a highly stable interferometric system is extremely costly and highly dependent on environmental stability. To address these issues, some researchers have proposed a series of methods, such as ensuring similar grayscale distributions in the four interferograms and using mutual coherence operations to determine the positional matching relationship between the interferograms; obtaining the fundamental frequency energy and phase information of each sub-image through circular carrier frequency processing; and correcting positional matching and phase shift errors through the phase difference between the sub-images. However, these methods are computationally complex and difficult to apply in dynamic measurement systems.

[0004] In the phase unpacking process of calculating the true phase from the wrapped phase, commonly used unpacking algorithms, such as path tracing algorithms, will exhibit unpacking errors when the noise level is high. When the system is undersampled, the difference between two adjacent points in the acquired data will exceed π, leading to unpacking errors. In addition, commonly used minimum norm methods, such as the preprocessing conjugate gradient algorithm, have very complex iterative processes and consume a lot of time. In summary, existing phase calculation and phase unpacking processes suffer from poor phase recovery accuracy and long computation time. Summary of the Invention

[0005] The purpose of this invention is to provide a fast and accurate method for automatic interferogram registration and phase unpacking based on deep neural networks.

[0006] The technical solution for achieving the objective of this invention is: an automatic interferogram registration and phase unpacking method based on deep neural networks, comprising the following steps:

[0007] Step S1: Generate a two-dimensional real phase through simulation, calculate the two-dimensional wrapping phase, and add noise;

[0008] Step S2: Calculate the corresponding light intensity interferogram based on the two-dimensional package phase, and simulate the system jitter that exists in the actual acquisition by randomly translating and rotating the image to generate a dataset;

[0009] Step S3: Set the deep neural network model structure, parameters, and optimization algorithm, and train the deep neural network model using the hybrid loss function and the dataset generated in step 2;

[0010] Step S4: Based on evaluation metrics such as structural similarity and peak signal-to-noise ratio, determine whether the phase recovery effect meets the requirements. If it does, proceed to the modulation step S5; otherwise, change the network structure, modify the values ​​of parameters such as the optimization function, learning rate, and loss function, and go to step S3 for retraining.

[0011] Step S5: Use the light intensity interferogram collected by the real system as the input to the trained deep neural network model, and calculate the predicted true phase.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) It can directly calculate the true phase from the interferogram without registering the interferograms of different phase shifts and then calculating the wrapped phase and the true phase, which reduces the calculation time and can be used in dynamic measurements; (2) It has strong anti-noise ability. Commonly used phase unpacking algorithms, such as the minimum path algorithm, will have unpacking errors when the noise level is high. The present invention improves the network's generalization ability to remove different levels of noise by adding different types and levels of noise to the wrapped phase during the dataset generation stage, thereby improving the accuracy of phase unpacking. Attached Figure Description

[0013] Figure 1 This is a flowchart of the interferogram automatic registration and phase unpacking method based on deep neural networks according to the present invention.

[0014] Figure 2 This is a three-dimensional histogram of the initial matrix generated by this invention.

[0015] Figure 3 It is a surface plot of the true phase generated by this invention.

[0016] Figure 4 It is a two-dimensional planar diagram of the real phase generated by this invention and the wrapped phase with added noise.

[0017] Figure 5 It is an interference pattern of light intensity that has been transformed by translation and rotation and cropped in the central region.

[0018] Figure 6 This is a diagram of the convolutional neural network structure used.

[0019] Figure 7 This is a structural diagram of the residual block used.

[0020] Figure 8 It is the true phase map output by the network computation. Detailed Implementation

[0021] The purpose of this invention is to provide an automatic interferogram registration and phase unpacking method based on deep neural networks, which solves the problems of poor noise resistance, inaccurate phase recovery due to phase translation and rotation caused by system jitter, and long calculation time of traditional light intensity interferometry recovery algorithms.

[0022] Combination Figure 1 This invention discloses an automatic interferogram registration and phase unpacking method based on a deep neural network, comprising the following steps:

[0023] Step S1: Generate a two-dimensional real phase through simulation, calculate the two-dimensional wrapping phase, and add noise;

[0024] Step S2: Calculate the corresponding light intensity interferogram based on the two-dimensional package phase, and simulate the system jitter that exists in the actual acquisition by randomly translating and rotating the image to generate a dataset;

[0025] Step S3: Set the deep neural network model structure, parameters, and optimization algorithm, and train the deep neural network model using the hybrid loss function and the dataset generated in step 2;

[0026] Step S4: Based on evaluation metrics such as structural similarity and peak signal-to-noise ratio, determine whether the phase recovery effect meets the requirements. If it does, proceed to the modulation step S5; otherwise, change the network structure, modify the values ​​of parameters such as the optimization function, learning rate, and loss function, and go to step S3 for retraining.

[0027] Step S5: Use the light intensity interferogram collected by the real system as the input to the trained deep neural network model, and calculate the predicted true phase.

[0028] As a specific example, in step S1, a two-dimensional true phase is generated through simulation, and a two-dimensional wrapping phase is calculated, with noise added, as follows:

[0029] S11. Randomly generate a matrix of size within a specific interval. The values ​​of the matrix are within the set interval and satisfy either a Gaussian distribution or a uniform distribution. Randomly select an interpolation algorithm to expand the initial matrix as the true phase ω.

[0030] S12, According to the formula Calculate the package phase And randomly select one from salt-and-pepper noise and Gaussian noise to add to the wrapping phase.

[0031] As a specific example, in S12, one of salt-and-pepper noise or Gaussian noise is randomly selected and added to the wrapping phase. Specifically as follows:

[0032] The function `angle` calculates the phase angle of a complex number. Its value is in the range [-π, π]. First, the phase angle is enclosed in a variable. Divide by π, then randomly select one of salt-and-pepper noise or Gaussian noise to add to the wrapped phase. The salt-and-pepper noise density is a random number between 0.01 and 0.2, and the Gaussian noise standard deviation is a random number between 0.01 and 0.20. After adding the noise, multiply the phase by π to restore its numerical range.

[0033] As a specific example, in step S2, the corresponding light intensity interferogram is generated based on the two-dimensional wrapping phase calculation, as follows:

[0034] S21. Randomly generate a matrix whose size is within a set range, and whose values ​​are within the set range and are uniformly distributed; select an interpolation algorithm to expand the initial matrix as the background light intensity A.

[0035] S22. Randomly generate a matrix whose size is within a set interval, and whose values ​​are within the set interval and satisfy uniform distribution; select an interpolation algorithm to expand the initial matrix as the contrast term V;

[0036] S23. Using a four-step phase shifting method, for the wrapped phase that has already had noise added. Generate intensity interferograms of four different phase shifts.

[0037]

[0038]

[0039]

[0040]

[0041] S24. The generated light intensity interferogram Randomly rotate -10° to 10°, randomly translate -20 to 20 pixels vertically and horizontally, and crop a 256×256 portion from the central region as the final intensity interferogram. At the same time, the true phase is also cropped from the central region in a 256×256 size as the final intensity interferogram.

[0042] As a specific example, step S3 describes setting the deep neural network model structure, parameters, and optimization algorithm, where the Adam algorithm is used for optimization, and the network model structure is as follows:

[0043] The deep neural network model structure is based on the residual block U-Net, with the light intensity interferogram as the network input and the output corresponding to the true phase;

[0044] The deep neural network model includes an encoder, a bottleneck layer, and a decoder. The encoder has four layers, each consisting of two consecutive residual blocks. The output of each layer serves as the input to the next layer and the corresponding decoder layer. The bottleneck layer contains two consecutive residual blocks. The decoder has the same number of layers as the encoder, and each layer contains an upsampling layer and two consecutive residual blocks for feature decoding. The feature map output from the last layer of the decoder is convolved with a 1×1 layer to output the true phase.

[0045] As a specific example, step S3 describes training a deep neural network model using a hybrid loss function and the dataset generated in step 2, where the hybrid loss function L... mix The formula for (x,y) is as follows:

[0046] L mix (x,y)=α1L l1 (x,y)+α2L MS-SSIM (x,y)

[0047] Where α1 and α2 are hyperparameters, α1 is set to 0.14 and α2 is set to 0.86;

[0048] Mean absolute error loss L l1 The formula for (x,y) is:

[0049]

[0050] Where 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.

[0051] Multi-scale structural similarity loss L MS-SSIM The formula for (x,y) is:

[0052]

[0053] Among them, c j s j These represent the calculation of the contrast term and structure term after performing j consecutive low-pass filtering on the original image and downsampling with a sampling interval of 2, respectively, where M represents the total number of consecutive low-pass filtering operations.

[0054] The formula for the brightness term l(x,y) is:

[0055]

[0056] The formula for the contrast term c(x,y) is:

[0057]

[0058] The formula for the structure term s(x,y) is:

[0059]

[0060] Where, μ x ,μ y Let σ represent the mean of x and y, respectively. x ,σ y σ represents the standard deviation of x and y, respectively. xy Let C1, C2, and C3 represent the covariances of x and y, where C1, C2, and C3 are constant values ​​that satisfy:

[0061] C1 = (K1L) 2

[0062] C2 = (K2L) 2

[0063] C3 = C2 / 2

[0064] Where K1 = 0.01, K2 = 0.03, L = 2 B -1, B = 8.

[0065] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0066] Example

[0067] Combination Figure 1 This embodiment uses a method for automatic registration and phase unpacking of light intensity interferograms based on deep neural networks, which includes the following steps:

[0068] Step S1: Generate a random matrix of a specific size, generate the true phase using an interpolation algorithm, generate the wrapping phase from the true phase, and add a certain amount of noise to the wrapping phase;

[0069] Furthermore, the steps are as follows:

[0070] S11. Randomly generate a square matrix (size between 2×2 and 25×25, numerical range 2-30), with a distribution type of either uniform or Gaussian distribution, such as... Figure 2 As shown, a method is randomly selected from nearest neighbor interpolation, quadratic interpolation, and bicubic interpolation to expand the matrix to 320×320 as the true phase. Figure 3 It is a surface plot of the true phase.

[0071] S12, According to the formula Calculate the wrapper phase, where ω is the true phase. It's about wrapping the phase. The function `angle` calculates the phase angle of a complex number, with values ​​in the range [-π, π]. First, wrap the phase... Divide by π, then randomly select one from salt-and-pepper noise and Gaussian noise to add to the wrapped phase. 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 the noise, multiply the phase by π to restore its original value range. Figure 4 The left image shows the true phase, while the right image shows the wrapped phase with added noise.

[0072] Step S2: Wrap the phase to generate an intensity interferogram. After the intensity interferogram is randomly translated and rotated, the central region is selected as the final interference phase.

[0073] Furthermore, the steps are as follows:

[0074] S21. Randomly generate a square matrix (size between 2×2 and 5×5, value range between 0 and 1) and satisfy uniform distribution; expand the initial matrix into a 320×320 matrix through a linear interpolation algorithm, and then linearly map the value range to 0.7-1 as the background light intensity A.

[0075] S22. Randomly generate a square matrix (size between 2×2 and 5×5, value range between 0 and 1) and satisfy uniform distribution; expand the initial matrix into a 320×320 matrix through a linear interpolation algorithm, and then linearly map the value range to 0.7-1 as the contrast term V.

[0076] S23. Using a four-step phase shifting method, for the wrapped phase that has already had noise added. Generate four intensity interferograms with different phase shifts:

[0077]

[0078]

[0079]

[0080]

[0081] S24. The generated light intensity interferogram and The image is randomly rotated from -10° to 10°, and then randomly shifted vertically and horizontally by -20 to 20 pixels. A 256×256 pixel portion is then cropped from the central region of all intensity interferograms to obtain the final intensity interferogram. Simultaneously, a 256×256 pixel portion from the central region is also cropped to obtain the final true phase. Figure 5 It is a cropped image of four interferograms from the central region.

[0082] Step S3: Adjust the deep neural network structure, optimize the algorithm and loss function, and train using the generated dataset.

[0083] The convolutional neural network mechanism is as follows: Figure 6 As shown, the neural network consists of a four-layer encoder, a bottleneck layer, and a four-layer decoder. Each layer of the encoder comprises two consecutive residual blocks. The output of each encoder layer serves as the input to the next encoder layer, and simultaneously, through skip connections, serves as the input to the decoder at the same level. Each decoder layer receives the output of the previous layer, upsamples it using a PixelShuffle operation, concatenates it with the output of the corresponding encoder layer, passes it through two consecutive residual blocks, and then uses it as the input to the next layer. The output feature map of the last decoder layer is then subjected to a 1x1 convolution to obtain the final output. The structure of the residual blocks is as follows. Figure 7 As shown, it 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 stride of the first 3×3 convolution is 2 and the padding is 1. Otherwise, the stride is 1. At the same time, the first 3×3 convolution realizes the change of the number of channels of the feature map. The stride of the last three 3×3 convolution layers is always 1, and the number of input channels and the number of output channels remain unchanged.

[0084] The formula for the hybrid loss function used is as follows:

[0085] L mix (x,y)=α1L l1 (x,y)+α2L MS-SSIM (x,y)

[0086] The formula for the mean absolute error loss is:

[0087]

[0088] Where 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.

[0089] The formula for multi-scale structural similarity loss is:

[0090]

[0091] The formula for the brightness term is:

[0092]

[0093] Contrast formula:

[0094]

[0095] Structure term formula:

[0096]

[0097] Where μ x ,μ y Let σ represent the mean of x and y, respectively. x ,σ y σ represents the standard deviation of x and y, respectively. xy Let C1, C2, and C3 represent the covariances of x and y, where C1, C2, and C3 are constant values ​​that satisfy:

[0098] C1 = (K1L) 2

[0099] C2 = (K2L) 2

[0100] C3 = C2 / 2

[0101] Where K1 = 0.01, K2 = 0.03, L = 2 B -1, where B = 8.

[0102] c j With s j The numbers represent the calculation of contrast and structure after performing j consecutive low-pass filtering and downsampling with a sampling interval of 2 on the original image, respectively. α1 and α2 are hyperparameters, set to 0.14 and 0.86, respectively.

[0103] Step S4: Evaluate the phase retrieval performance using metrics such as structural similarity, root mean square error, and peak signal-to-noise ratio to determine if the requirements are met. If so, proceed to step S5; otherwise, adjust the model structure and parameters, and return to step S3 for retraining. Figure 8 It is the true phase calculated and output by the trained network.

[0104] Step S5: The light intensity interferogram acquired by the real system is used as the network input, and the network calculates the true phase.

[0105] In summary, this invention directly calculates the true phase from the interferogram, eliminating the need for registration of interferograms with different phase shifts and subsequent calculation of the wrapped phase and the true phase. This reduces computation time and allows for use in dynamic measurements. Furthermore, this invention exhibits strong noise resistance. Commonly used phase unpacking algorithms, such as the minimum path algorithm, often fail to unpack when noise levels are high. This invention improves the network's generalization ability to remove different levels of noise by adding different types and levels of noise to the wrapped phase during the dataset generation stage, thereby enhancing the accuracy of phase unpacking.

Claims

1. A method for automatic interferogram registration and phase unpacking based on deep neural networks, characterized in that, Includes the following steps: Step S1: Generate a two-dimensional real phase through simulation, calculate the two-dimensional wrapping phase, and add noise; Step S2: Calculate the corresponding light intensity interferogram based on the two-dimensional package phase, and simulate the system jitter that exists in the actual acquisition by randomly translating and rotating the image to generate a dataset; Step S3: Set the deep neural network model structure, parameters, and optimization algorithm, and train the deep neural network model using the hybrid loss function and the dataset generated in step 2; Step S4: Based on evaluation indicators such as structural similarity and peak signal-to-noise ratio, determine whether the phase recovery effect meets the requirements. If it does, proceed to modulation step S5. If the requirements are not met, the network structure is changed, the values ​​of parameters such as the optimization function, learning rate, and loss function are modified, and the process proceeds to step S3 for retraining. Step S5: Use the light intensity interferogram collected by the real system as the input to the trained deep neural network model, and calculate the predicted true phase. Step S3 describes setting the deep neural network model structure, parameters, and optimization algorithm, where the Adam algorithm is used for optimization. The network model structure is as follows: The deep neural network model structure is based on the residual block U-Net, with the light intensity interferogram as the network input and the output corresponding to the true phase; The deep neural network model includes an encoder, a bottleneck layer, and a decoder. The encoder has four layers, each consisting of two consecutive residual blocks. The output of each layer serves as the input to the next layer and the corresponding encoder layer. The bottleneck layer contains two consecutive residual blocks. The decoder has the same number of layers as the encoder, and each layer contains an upsampling layer and two consecutive residual blocks for feature decoding. The feature map output from the last layer of the decoder is convolved with a 1×1 convolution to output the true phase. Step S3 describes training the deep neural network model using a hybrid loss function and the dataset generated in step 2. The hybrid loss function... The formula is as follows: ； in and For hyperparameters, Set to 0.14, Set to 0.86; Mean Absolute Error Loss The formula is: ； Where 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; Multi-scale structural similarity loss The formula is: ； in, , These represent the calculation of the contrast term and structure term after performing j consecutive low-pass filtering on the original image and downsampling with a sampling interval of 2, respectively, where M represents the total number of consecutive low-pass filtering operations. Brightness item The formula is: ； Contrast item The formula is: ； Structure item The formula is: ； in, represent the means of x and y, respectively. These represent the standard deviations of x and y, respectively. Represents the covariance of x and y. It is a constant value that satisfies: ； ； ； in B=8.

2. The method for automatic interferogram registration and phase unpacking based on deep neural networks according to claim 1, characterized in that, In step S1, a two-dimensional true phase is generated through simulation, and a two-dimensional wrapping phase is calculated, with noise added, as detailed below: S11. Randomly generate a matrix whose size falls within a specific interval. The matrix values ​​are within the set interval and satisfy either a Gaussian distribution or a uniform distribution. Randomly select an interpolation algorithm to expand the initial matrix as the true phase. ; S12, According to the formula Calculate the package phase And randomly select one from salt-and-pepper noise or Gaussian noise to add to the wrapped phase. .

3. The method for automatic interferogram registration and phase unpacking based on deep neural networks according to claim 2, characterized in that, In step S12, one of salt-and-pepper noise or Gaussian noise is randomly selected and added to the wrapping phase. The details are as follows: function This indicates the calculation of the phase angle of a complex number, with values ​​in... First, wrap the phase. Divide by Then, randomly select either salt-and-pepper noise or Gaussian noise and add it to the phase wrapper. The salt-and-pepper noise density is a random number between 0.01 and 0.2, and the Gaussian noise standard deviation is a random number between 0.01 and 0.

20. After adding the noise, multiply the phase by... Restore its numerical range.

4. The method for automatic interferogram registration and phase unpacking based on deep neural networks according to claim 1, characterized in that, In step S2, the corresponding light intensity interferogram is generated based on the two-dimensional wrapping phase calculation, as follows: S21. Randomly generate a matrix whose size is within a set interval, and whose values ​​are within the set interval and satisfy a uniform distribution; select an interpolation algorithm to expand the initial matrix as the background light intensity. ; S22. Randomly generate a matrix whose size is within a set interval, and whose values ​​are within the set interval and satisfy uniform distribution; select an interpolation algorithm to expand the initial matrix as the contrast term V; S23. Using a four-step phase shifting method, for the wrapped phase that has already had noise added. Four intensity interferograms with different phase shifts were generated. , , , : ； ； ； ； S24. The generated light intensity interferogram Randomly rotate -10° to 10°, randomly shift -20 to 20 pixels vertically and horizontally, and then crop a 256×256 portion from the center region of all intensity interferograms as the final intensity interferogram. At the same time, the true phase is also cropped from the center region of a 256×256 portion as the final true phase.

Images