A high-precision phase demodulation method based on a phaseUnet++ network

Abstract

The present application relates to the technical field of optical interferometry, and particularly relates to a high-precision phase demodulation method based on a PhaseUnet++ network.The method comprises the following steps:1. Zernike polynomials are used to generate training data and test data for network training;2. a neural network PhaseUnet++ is established and trained;3. normalized cosine interferograms I cos and auxiliary diagrams I sac are input into the trained network, and normalized sinusoidal interferograms I sin are output;4. the wrapped phase distribution is obtained by using an arctangent function, and the unwrapped phase distribution φ(x,y) is obtained by using a phase unwrapping algorithm.The present application has high precision, can process interferograms of different sizes, has strong noise resistance, can realize phase measurement of dynamic samples, has high reconstruction result precision, simple steps, wide application range, and great application prospect in the field of optical interferometry research.

Description

Technical Field

[0001] This invention relates to the technical field of optical interferometry, mainly to the field of optical phase measurement technology, and specifically to a high-precision phase demodulation method based on the PhaseUnet++ network. Background Technology

[0002] In optical interferometry of spherical and aspherical surfaces, the test beam is reflected by the surface under test and interferes with the reference beam, forming an interferogram on the detector. To obtain the surface morphology of the object under test, phase demodulation of the interferogram is required. Interferogram demodulation is a key issue in optical interferometry, and its accuracy directly determines the final measurement accuracy of the interferometric device.

[0003] Traditional phase demodulation methods typically involve two main steps: 1. Obtaining the wrapped phase distribution from the interferogram; 2. Using a phase unwrapping algorithm to remove the wrapping from the wrapped phase distribution to obtain the unwrapped phase distribution. For interferograms containing closed fringes, obtaining the wrapped phase distribution usually requires recording n (n>=2) phase-shifted interferograms. Examples include a four-step phase-shifting algorithm using time-shifting interferometry or a four-step phase-shifting algorithm using spatial parallel phase-shifting. In time-shifting interferometry, the sample must be stationary, requiring the recording of multiple phase-shifted interferograms that change over time; therefore, it cannot be used for measuring dynamically changing samples (Daniel Malacara, Optical shop testing, 2007, John Wiley & Sons, Inc.). In spatial parallel phase-shift interferometry, CCD / CMOS photosensitive chips need to be spatially reused, which leads to problems such as reduced spatial resolution or reduced field of view (Li.J, et al. Optics Express, 26(4), 2018: 4392-4400. doi:10.1364 / OE.26.004392).

[0004] Demodulating the enclosed / unenclosed phase distribution from an interferogram containing closed fringes not only makes full use of the spatial bandwidth product of CCD / CMOS (thus having the advantage of high spatial resolution), but also enables real-time measurement of dynamically changing samples.

[0005] Deep learning-based data processing methods possess powerful data fitting capabilities, thus attracting increasing attention in areas such as interferogram processing. Currently, two representative deep learning-based methods have been proposed for demodulating single interferograms containing closed fringes:

[0006] 1. A phase demodulation method for closed interferograms based on Unet network (Yuan.S, et al. Optics Express, 29(2), 2021:2538-2554, doi:10.1364 / OE.413385). This technique is based on the traditional Unet network, with the main body of the network being a four-layer U-shaped network structure, and the processing of each layer is implemented through DenseBlock. This neural network can obtain the wrapped phase distribution from a single interferogram, and then use a phase unwrapping algorithm to obtain the unwrapped phase distribution. The input and output of the network are the normalized interferogram and the normalized wrapped phase, respectively. However, this method has the following disadvantages: 1) It can only input interferograms of a fixed size with a resolution of 256×256. 2) It has a large demodulation error (greater than 1.0 rad) for interferograms with sparse fringes.

[0007] 2. Demodulation method based on hypercolumn convolutional neural network (HCNN) (Zhao.Zh, et al. Optics Express, 29(11), 2021:16406-16421, doi:10.1364 / OE.410723). This technique is based on hypercolumn convolutional neural network (HCNN). Using a trained neural network, the unwrapped phase distribution can be directly output from a single interferogram. However, this method has the following drawback: there is an obvious abrupt phase error (>1 rad) in the unwrapped phase distribution directly output by the network. In order to obtain the correct phase distribution, it is necessary to perform complex error correction on the phase distribution directly output by the network. The specific process includes determining the error region and performing polynomial fitting on the phase distribution of the error region before the final unwrapped phase distribution can be obtained.

[0008] In conclusion, with the further development of science and technology, optimizing the demodulation method of a single interferogram containing closed fringes has become a research focus for those skilled in the art. Summary of the Invention

[0009] The purpose of this invention is to provide a high-precision phase demodulation method based on the PhaseUnet++ network, so as to solve the shortcomings of existing technologies, such as large demodulation error for sparse closed fringe interferograms, fixed input interferogram resolution, and small applicability.

[0010] To achieve the objectives of this invention, the proposed technical solution is: a high-precision phase demodulation method based on the PhaseUnet++ network, comprising the following steps:

[0011] Step 1: First, use Zernike polynomials to generate the unwrapped phase distribution φ, then generate the corresponding training data pairs, and finally generate the corresponding training data, test data, and validation data.

[0012] Step 2: Construction and training of the convolutional neural network:

[0013] (2.1) Design a PhaseUnet++ neural network, including: Residual connection block ResBlock, Conv2D convolutional layer, BatchNorm2d normalization layer, ReLU activation layer, MaxPool2d pooling layer, ConvTranspose2d deconvolutional layer, Concat connection layer, Dropout layer and clamp layer;

[0014] (2.2) Using dataset (I) cos I sac and II sin The PhaseUnet++ neural network is trained until the loss function stops decreasing and remains stable, at which point the training is complete and the weight values ​​of each layer of the network are obtained.

[0015] Step 3: Normalize the cosine interferogram obtained from the actual measurement to obtain I. cos , put I cos And auxiliary diagram I sac Input the trained neural network PhaseUnet++, output a normalized sinusoidal interferogram I sin .

[0016] Step 4: Calculate the package phase distribution using the arctangent formula. Subsequently, phase unwrapping was performed using traditional unwrapping techniques, ultimately yielding the unwrapped phase distribution φ(x,y).

[0017] Furthermore, in step (2.1) above, each ResBlock convolutional block X i.j (i,j=0,1,2,…) involves convolving the input, then passing it through a normalization layer BatchNorm2d and an activation layer ReLU, followed by another convolution, then through another normalization layer BatchNorm2d, and finally adding it to the input through a Concat layer. The output is then passed through an activation layer ReLU.

[0018] Furthermore, in step (2.1) above, the input I cos and I sac The graphs are obtained by passing X through a ResBlock block. cos and X sac Then X is obtained through the concat layer. 0.0 ; X 0.0 As input to the network, X 0.0 X is obtained through the MaxPool2d layer. 1.0 X 1.0After upsampling through the ConvTranspose2d layer and X 0.0 X is obtained by concatenating the layers along the channel dimension using the concat layer. 0.1 The structure of other layers follows the same pattern.

[0019] Furthermore, in the network described above, the input to each ResBlock convolutional block is obtained by concatenating the outputs of all preceding ResBlock convolutional blocks and the output of the bottom-left ResBlock convolutional block in the same layer through a concat layer along the channel dimension.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0021] 1. This invention utilizes cosine interference pattern I cos And auxiliary diagram I sac As input, a sinusoidal interferogram I is obtained by training a neural network. sin Then, the wrapped phase distribution is calculated, and finally, the unwrapped phase distribution is obtained by unwrapping the phase. By establishing a neural network, the problem of phase demodulation of closed fringe interferograms is solved. The measurement process uses a normalized interferogram to realize phase measurement of dynamic samples, and the reconstruction results are highly accurate and the steps are simple.

[0022] 2. This invention and the use of a single image I cos This network can achieve higher reconstruction accuracy compared to the network used as input.

[0023] 3. This invention is applicable to interferograms of different resolutions and sizes, and is equally suitable for dense or sparse interferograms. The trained network can perform phase demodulation on interferograms of different sizes. The size of the interferogram is not limited to a fixed size; for example, 256×256, 512×512, and 832×832 are all possible. It has a wide range of applications and great potential for application in the field of optical interferometry research. Attached image description:

[0024] Figure 1 This is a structural diagram of the neural network of the present invention.

[0025] Figure 2 This is a normalized cosine interferogram I of the present invention. cos A schematic diagram of phase demodulation (resolution 256×256).

[0026] in:

[0027] Figure 2 (a) The true unwrapped phase distribution;

[0028] Figure 2(b) Normalized cosine interferogram I cos ;

[0029] Figure 2 (c) Auxiliary input diagram I sac ;

[0030] Figure 2 (d) The normalized sine stripe I of the network output sin ;

[0031] Figure 2 (e) Wrapping phase distribution

[0032] Figure 2 (f), the reconstructed unwrapped phase distribution φ(x,y);

[0033] Figure 2 (g) Error distribution between the reconstructed unwrapped phase and the true phase distribution;

[0034] Figure 2 (h) is a cross-sectional view of the error distribution along the white line in Figure (g).

[0035] Figure 3 This is a schematic diagram of phase demodulation for the sparse normalized cosine interferogram (resolution 256×256) and the dense normalized cosine interferogram (resolution 256×256) of the present invention.

[0036] in:

[0037] Figure 3 (a) Normalized cosine interference pattern with sparse fringes I cos1 ;

[0038] Figure 3 (b) Normalized cosine interference pattern with dense fringes I cos2 ;

[0039] Figure 3 (c), I cos1 The corresponding auxiliary input is Figure I. sac1 ;

[0040] Figure 3 (d), I cos2 The corresponding auxiliary input is Figure I. sac2 ;

[0041] Figure 3 (e), I cos1 ( Figure 3 (a)) corresponds to the true unwrapped phase distribution;

[0042] Figure 3 (f), I cos2 ( Figure 3 (b) corresponds to the true unwrapped phase distribution;

[0043] Figure 3 (g), from I cos1 and I sac1 The reconstructed unwrapped phase distribution φ1(x,y);

[0044] Figure 3 (h), from I cos2 and I sac2 The reconstructed unwrapped phase distribution φ2(x,y);

[0045] Figure 3 (i), sparse stripes ( Figure 3 (a) and 3(c)) Error distribution between the reconstructed phase distribution and the true phase;

[0046] Figure 3 (j), dense stripes ( Figure 3 (b) and (d)) Error distribution between the reconstructed phase distribution and the true phase.

[0047] Figure 4 Normalized cosine interferograms of different resolution sizes according to the present invention I cos A schematic diagram of phase demodulation (in order: 384×384, 512×512, 640×640, 832×832).

[0048] in:

[0049] Figure 4 (a) Normalized cosine interferogram I cos1 (Resolution size is 384×384);

[0050] Figure 4 (b) Normalized cosine interferogram I cos2 (Resolution size is 512×512);

[0051] Figure 4 (c) Normalized cosine interferogram I cos3 (Resolution size is 640×640);

[0052] Figure 4 (d) Normalized cosine interferogram I cos4 (Resolution size is 832×832);

[0053] Figure 4 (e), I cos1 Corresponding auxiliary input diagram I sac1 ;

[0054] Figure 4 (f), Icos2 Corresponding auxiliary input diagram I sac2 ;

[0055] Figure 4 (g), I cos3 Corresponding auxiliary input diagram I sac3 ;

[0056] Figure 4 (h), I cos4 Corresponding auxiliary input diagram I sac4 ;

[0057] Figure 4 (i), I cos1 The corresponding true unwrapped phase distribution (384×384);

[0058] Figure 4 (j), I cos2 The corresponding true unwrapped phase distribution (512×512);

[0059] Figure 4 (k), I cos3 The corresponding true unwrapped phase distribution (640×640);

[0060] Figure 4 (l), I cos4 The corresponding true unwrapped phase distribution (832×832);

[0061] Figure 4 (m), the reconstructed unwrapped phase distribution φ1(x,y)(384×384);

[0062] Figure 4 (n), the reconstructed unwrapped phase distribution φ2(x,y)(512×512);

[0063] Figure 4 (o), the reconstructed unwrapped phase distribution φ3(x,y)(640×640);

[0064] Figure 4 (p), the reconstructed unwrapped phase distribution φ4(x,y)(832×832);

[0065] Figure 4 (q), Error map between the reconstructed unwrapped phase φ1(x,y)(384×384) and the true phase;

[0066] Figure 4 (r), Error map between the reconstructed unwrapped phase φ2(x,y)(512×512) and the true phase;

[0067] Figure 4(s), Error map between the reconstructed unwrapped phase φ3(x,y)(640×640) and the true phase;

[0068] Figure 4 (t), Error plot between the reconstructed unwrapped phase φ4(x,y)(832×832) and the true phase.

[0069] Figure 5 Figure I is a single image of the present invention. cos The neural network as input and I cos I sac Comparison of phase demodulation results of the neural network as input.

[0070] in:

[0071] Figure 5 (a) Normalized cosine interferogram I cos (Resolution 256×256);

[0072] Figure 5 (b) Auxiliary input diagram I sac (Resolution 256×256);

[0073] Figure 5 (c), I cos Corresponding true unwrapped phase distribution

[0074] Figure 5 (d), I cos The unwrapped phase distribution φ1(x,y) is reconstructed as input;

[0075] Figure 5 (e), I cos and I sac Simultaneously, the unwrapped phase distribution φ2(x,y) is used as input for reconstruction;

[0076] Figure 5 (f), the error distribution between φ1(x,y) and the true phase distribution;

[0077] Figure 5 (g), the error distribution between φ2(x,y) and the true phase distribution. Detailed implementation method:

[0078] The present invention will now be described in detail with reference to detailed embodiments and accompanying drawings.

[0079] This method includes the following steps: 1. Using Zernike polynomials to generate training and testing data for network training; 2. Building and training the neural network PhaseUnet++; 3. Converting the normalized cosine interferogram I... cos And auxiliary diagram Isac The trained network is input, and the normalized sinusoidal interferogram I is output. sin 4. Obtain the wrap-around phase distribution using the arctangent function. The unwrapped phase distribution φ(x,y) is obtained using a phase unwrapping algorithm. This technique is not only highly accurate, but also capable of handling interferograms of different sizes and has strong noise resistance.

[0080] This invention provides a high-precision phase demodulation method based on the PhaseUnet++ network, which specifically includes the following steps:

[0081] Step 1: Data preparation. Use Zernike polynomials to generate data for network training. The specific steps are as follows;

[0082] Step 1: Generate an unwrapped phase map using the first n (45 ≥ n ≥ 4) Zernike polynomials (Mahajan VN, et.al., J. Opt. Soc. Am. A, 2007, 24(9): 2994-3016, doi: 10.1364 / JOSAA.24.002994), as shown in the following formula:

[0083]

[0084] Where φ(x,y) is the unwrapped phase distribution; Z i c i These represent the i-th order Zernike polynomial and its coefficients. The Zernike coefficients c2 and c3 of the 2nd and 3rd terms are random numbers between [-25, 25]; the coefficient of the 4th term is a random number between

[125] , and the other Zernike coefficients are random numbers between [-0.5, 0.5]. By setting the range of Zernike coefficients, an unwrapped phase distribution φ with an radian range of 10–120 rad is generated, with an image size of 256 × 256 pixels.

[0085] Step 2: After generating the unwrapped graph, generate the corresponding training data pairs using the following method:

[0086]

[0087] Among them: I cos This is the normalized cosine interferogram. sac As an auxiliary diagram, by I cos It is obtained by taking the inverse cosine and then performing a sine transformation. II sin The true value of the normalized sine fringes is used as the label for the output.

[0088] Step 3: Generate 40,000 data pairs with a resolution of 256×256 (I cos Isac II sin After that, the sklearn module is used to generate the corresponding training data, test data, and validation data in an 8:1:1 ratio. The training set contains 32,000 images, the test set contains 4,000 images, and the validation set contains 4,000 images.

[0089] Step 2: Design the PhaseUnet++ network and train it using the data obtained in Step 1. The specific steps are as follows:

[0090] Step 1: Design the PhaseUnet++ neural network

[0091] Design the phase demodulation network PhaseUnet++, the network structure diagram is as follows. Figure 1 As shown, the PhaseUnet++ network features downsampling and upsampling. Through dense network connections, it retains more dimensional feature information, allowing subsequent network layers to freely choose between shallow and deep features. Furthermore, the use of skip connections in the convolutional layers effectively reduces the gradient vanishing problem, making training easier. In this embodiment, the PhaseUnet++ neural network includes: a Conv2D convolutional layer, a BatchNorm2d normalization layer, a ReLU activation layer, a ResBlock residual connection block, a MaxPool2d pooling layer, a ConvTranspose2d deconvolutional layer, and a Concat connection layer.

[0092] For the input I cos and I sac The graphs are obtained by passing X through the ResBlock layer. cos and X sac Then X is obtained through the concat layer. 0.0 X 0.0 As input to the network, X 0.0 X is obtained through the MaxPool2d layer. 1.0 X 1.0 After upsampling through the ConvTranspose2d layer and X 0.0 X is obtained by concatenating the layers along the channel dimension using the concat layer. 0.1 The structure of other layers follows the same pattern (see...). Figure 1 (As shown). In the network, the input of each ResBlock convolutional block is obtained by concatenating the outputs of all preceding ResBlock convolutional blocks and the output of the bottom-left ResBlock convolutional block in the same layer through a concat layer along the channel dimension, which can capture features from different layers.

[0093] For each ResBlock convolutional block X i.j(i,j=0,1,2,…) involves convolving the input, then passing it through a normalization layer BatchNorm2d and an activation layer ReLU, followed by another convolution, then through another normalization layer BatchNorm2d, and finally adding it to the input through a Concat layer. The output is then passed through an activation layer ReLU.

[0094] Step 2: Train the PhaseUnet++ neural network using the training data from Step 1. Specifically, train the normalized cosine interferogram I. cos And auxiliary diagram I sac As input to the network; I cos Sine interference pattern II after 90-degree phase shift sin As the output label of the network, it is related to the network's output I. sin Calculate the loss function value until the loss function stops decreasing and remains stable, then the training is complete and the weight values ​​of each layer of the network are obtained.

[0095] Step 3: Normalize the cosine interferogram obtained from the actual measurement to obtain I. cos , put I cos And auxiliary diagram I sac Input a trained neural network, output a normalized sinusoidal interferogram I sin .

[0096] Step 4: Using cosine interferometry I cos Sine Interference Diagram I sin The calculation yields the package phase distribution The specific implementation is as follows:

[0097]

[0098] in, It is a wrap-around phase distribution, I sin (x,y) is the normalized sine interferogram, I cos (x,y) is the normalized cosine interferogram. After calculating the wrapped phase distribution, the phase is unwrapped using a traditional unwrapping algorithm, and finally the unwrapped phase distribution φ(x,y) is obtained.

[0099] Example 1. A phase demodulation method based on deep learning, comprising the following steps:

[0100] Step 1: Data preparation, using Zernike polynomials to generate data for network training;

[0101] Step 1: Generate an unwrapped phase map using the first 10 orders of the Zernike polynomial, as shown in the following formula;

[0102]

[0103] Where φ(x, y) is the unwrapped phase distribution; Z i c i These represent the i-th order Zernike polynomial and its coefficients. The Zernike coefficients c2 and c3 of the 2nd and 3rd terms are random numbers between [-25, 25]; the coefficient of the 4th term is a random number between

[125] , and the other Zernike coefficients are random numbers between [-0.5, 0.5]. By setting the range of Zernike coefficients, an unwrapped phase distribution φ(x, y) with an radian range of 10–120 rad is generated, with an image size of 256 × 256 pixels. Figure 2 (a) shows a distribution map of the unwrapped phase φ.

[0104] The normalized cosine interferogram I will then be calculated using φ. cos ( Figure 2 (b) The formula is shown below:

[0105] I cos (x,y)=cos(φ(x,y))

[0106] Step 2: Normalize the cosine fringes (for non-normalized fringes) to obtain I. cos Then, another input image I is obtained using the following formula. sac ( Figure 2 (c)):

[0107] I sac (x,y)=sin(acos(I cos (x,y)))

[0108] Step 2: Design the PhaseUnet++ network and train it using the data obtained in Step 1.

[0109] Step 1: Design the PhaseUnet++ neural network. cos I sac As input, II sin The neural network is trained using the output labels. The PhaseUnet++ neural network includes: Conv2D convolutional layer, BatchNorm2d normalization layer, ReLU activation layer, ResBlock residual connection block, MaxPool2d pooling layer, ConvTranspose2d deconvolutional layer, and Concat connection layer;

[0110] For the input I cos and I sac The graphs are obtained by passing X through the ResBlock layer. cos and X sac Then X is obtained through the concat layer. 0.0X 0.0 As input to the network, X 0.0 X is obtained through the MaxPool2d layer. 1.0 X 1.0 After upsampling through the ConvTranspose2d layer and X 0.0 X is obtained by concatenating the layers along the channel dimension using the concat layer. 0.1 The structure of other layers follows the same pattern (see...). Figure 1 (As shown). In the network, the input to each ResBlock convolutional block is obtained by concatenating the outputs of all preceding ResBlock convolutional blocks and the output of the bottom-left ResBlock convolutional block in the same layer through a concat layer along the channel dimension.

[0111] For each ResBlock convolutional block X i.j (i,j=0,1,2,…) involves convolving the input, then passing it through a normalization layer BatchNorm2d and an activation layer ReLU, followed by another convolution, then through another normalization layer BatchNorm2d, and finally adding it to the input through a Concat layer. The output is then passed through an activation layer ReLU.

[0112] Step 2: Train the PhaseUnet++ neural network using the training data. Training is complete when the loss function stops decreasing and remains stable, yielding the weight values ​​for each layer of the network.

[0113] Step 3: Normalize the cosine interferogram obtained from the actual measurement to obtain I. cos , put I cos And auxiliary diagram I sac Input a trained neural network, output a normalized sinusoidal interferogram I sin ( Figure 2 (d)).

[0114] Step 4: Through cosine interference pattern I cos Sine Interference Diagram I sin The calculation yields the package phase distribution ( Figure 2 (e)). The specific implementation is as follows:

[0115]

[0116] in, To enclose the phase distribution, I sin (x,y) is the normalized sine interferogram, I cos (x, y) represents the normalized cosine interferogram. A traditional unwrapping algorithm is used to... Phase unwrapping is performed, and the unwrapped phase distribution map φ(x,y) is finally obtained. Figure 2 (f)).

[0117] Figure 2 (g) shows the difference between the reconstructed unwrapped phase distribution and the true phase distribution. It can be seen that the maximum reconstruction error is less than 0.05 rad. To quantitatively measure the accuracy of the reconstructed unwrapped phase distribution, the root mean square error (RMSE) between the reconstructed phase distribution and the true value was calculated, and the result is 0.0013 rad, indicating that the reconstruction result has high accuracy. To visually display the error distribution, we provide the values ​​along... Figure 2 (g) Cross-sectional view along the white line, as shown Figure 2 As shown in (h).

[0118] Example 2: Steps 1 and 2 are the same as in Example 1, resulting in a trained neural network. Therefore, in practical implementation, it is only necessary to start from step three of the method of this invention. This example verifies its effectiveness by inputting interferograms of different densities; the specific steps are as follows.

[0119] Step 3: Input the normalized cosine interferograms with sparse and dense fringes into the trained PhaseUnet++ network, respectively. Figure 3 (a) and (c) are cosine interference patterns with sparse fringes, respectively. cos1 and its auxiliary diagram I sac1 , Figure 3 (b) and (d) are cosine interference patterns with denser fringes, respectively. cos2 and its auxiliary diagram I sac2 . Figure 3 (a) and (c) Input the PhaseUnet++ network and output the normalized sine stripe I. sin1 ; Figure 3 (b) Input the PhaseUnet++ network into 3(d) and output the corresponding normalized sine stripe I. sin2 .

[0120] Step 4: Calculate the package phase distribution. The specific implementation is as follows:

[0121]

[0122] in, (i = 1, 2) represents the corresponding package phase distribution, I sini (x,y) represents the corresponding sinusoidal interferogram, I cosi (x, y) represents the corresponding cosine interferogram, with subscripts i = 1 and 2 indicating sparse and dense fringes, respectively. A traditional phase unwrapping algorithm is used to... Unwrapping is performed, and the unwrapped phase distribution φ is finally obtained. i (x,y), respectively as Figure 3 (g) Figure 3 As shown in (h).

[0123] Figure 3 (e) Figure 3 (f) represent the sparseness of the stripes ( Figure 3 (a)), dense stripes ( Figure 3 (b) shows the true unwrapped phase distribution corresponding to the interferogram. Figure 3 (i) Figure 3 (j) represents the error distribution between the reconstructed phase distribution and the true value. Figure 3 (i) has a root mean square error (RMSE) of 0.0018 rad. Figure 3 The RMSE of (j) is 0.0022 rad. The results show that the phase distribution can be reconstructed with high accuracy in both sparse and dense interferograms.

[0124] Example 3: Steps 1 and 2 are the same as in Example 1, resulting in a trained neural network. Therefore, in practical implementation, it is only necessary to start from step three above. This example verifies its effectiveness by inputting interferograms of different sizes (384×384, 512×512, 640×640, and 832×832). The neural network outputs images with the same resolution as the input images, regardless of the input image size.

[0125] Step 3: Convert the normalized cosine interferograms I at different resolutions respectively. cos1 (384×384)( Figure 4 a) and its corresponding auxiliary diagram I sac1 ( Figure 4 .e) ; Normalized cosine interferogram I cos2 (512×512)( Figure 4 .b) and its corresponding auxiliary diagram I sac2 ( Figure 4 .f); Normalized cosine interferogram I cos3 (640×640)( Figure 4 .c) and its corresponding auxiliary diagram I sac3 ( Figure 4 .g); Normalized cosine interferogram I cos4 (832×832)( Figure 4 .d) and its corresponding auxiliary diagram I sac4 ( Figure 4 Enter the PhaseUnet++ network in .h) respectively.

[0126] The PhaseUnet++ network outputs normalized sinusoidal interferograms of corresponding sizes (384×384, 512×512, 640×640, and 832×832), respectively. sin1 I sin2 I sin3 and I sin4 .

[0127] Step 4: From the cosine interference diagram I respectively cosi (i = 1, 2, 3, 4) and the corresponding sinusoidal interferogram I sini (i = 1, 2, 3, 4) yields the package phase distribution. The specific implementation is as follows:

[0128]

[0129] in, This represents the corresponding package phase distribution.

[0130] After calculating the package phase distribution, the traditional unpacking algorithm is used to... Perform phase unwrapping to obtain the final unwrapped phase distribution φ. i (x, y). The result is as follows: Figure 4 As shown in (m), 4(n), 4(o), and 4(p), the image sizes are 384×384, 512×512, 640×640, and 832×832, respectively.

[0131] To compare the accuracy of the reconstruction results, Figure 4 (i), 4(j), 4(k), and 4(l) respectively demonstrate Figure 4 The true unwrapped phase distributions corresponding to (a), 4(b), 4(c), and 4(d) Figure 4 Figures (q), (r), (s), and (t) show the error distribution of the reconstruction results, with root mean square errors (RMSE) of 0.0028 rad, 0.0035 rad, 0.0037 rad, and 0.0071 rad, respectively. The results indicate that this network can obtain accurate reconstruction results for interferograms of different resolutions.

[0132] Comparative Example. Input only a single cosine interferogram I cos Phase Unet++1 network and normalized cosine interferogram I cos Auxiliary Figure I sac Simultaneously, the reconstruction accuracy of PhaseUnet++2, used as input, was compared. The results show that I cos I sac Meanwhile, the PhaseUnet++2 network, used as input, yields better reconstruction results with higher accuracy. The specific steps are as follows:

[0133] Step 1: Data preparation, using Zernike polynomials to generate data for network training;

[0134] Step 1: Generate an unwrapped phase distribution map using the first 10 orders of the Zernike polynomial, as shown in the following formula:

[0135]

[0136] Where φ(x,y) is the unwrapped phase distribution; Z i c i These represent the i-th order Zernike polynomial and its coefficients. The Zernike coefficients c2 and c3 of the 2nd and 3rd terms are random numbers between [-25, 25]; the coefficient of the 4th term is a random number between

[125] , and the other Zernike coefficients are random numbers between [-0.5, 0.5]. By setting the range of Zernike coefficients, an unwrapped phase distribution φ with an radian range of 10–120 rad is generated, with an image size of 256 × 256 pixels.

[0137] Step 2: After generating the unwrapped phase φ, the corresponding training data is generated using the following method:

[0138]

[0139] Step 3: After generating 40,000 data pairs with a resolution of 256×256, use the sklearn module to generate corresponding training, test, and validation data in an 8:1:1 ratio. The training set contains 32,000 images, the test set contains 4,000 images, and the validation set contains 4,000 images.

[0140] Step 2: Training the Neural Network Phase Unet++1: Directly apply the normalized cosine interferogram I cos Normalized sine stripes II sin The labels are used as input and output labels respectively for training.

[0141] Training the neural network Phase Unet++2: Normalizing the cosine interferogram I cos And auxiliary diagram I sac Simultaneously, as input, the normalized sine stripe II sin Used as output labels for training.

[0142] The only difference between PhaseUnet++1 and PhaseUnet++2 is the dimension of the input layer convolutional kernels; all other network parameters are exactly the same.

[0143] Step 3: Transform the normalized cosine interferogram I cos ( Figure 5(a) Input the trained neural network PhaseUnet++1 and output the normalized sinusoidal interferogram I. sin1 The phase distribution of the package is obtained based on the arctangent function. This leads to the unwrapped phase distribution φ1(x,y), Figure 5 As shown in (d));

[0144] Using the same interferogram I cos ( Figure 5 (a) and auxiliary diagram I sac ( Figure 5 (b) Simultaneously input PhaseUnet++2, and the output is the normalized sine interferogram I. sin2 The phase distribution of the package is obtained based on the arctangent function. This leads to the unwrapped phase distribution φ2(x,y), such as Figure 5 As shown in (e);

[0145] To compare the accuracy of the reconstruction results, Figure 5 (c) shows the actual unwrapped phase distribution. Figure 5 (f) and (g) show the error distributions of the reconstruction results using Phase Unet++1 and Phase Unet++2, respectively, with root mean square errors (RMSE) of 0.0031 rad and 0.0018 rad, respectively. The results indicate that using Phase Unet++1 and Phase Unet++2... cos and I sac The PhaseUnet++2 network, used as input, has higher reconstruction accuracy.

[0146] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A high-precision phase demodulation method based on PhaseUnet++ network, characterized in that: Includes the following steps Step 1: First, use Zernike polynomials to generate the unwrapped phase distribution Φ(x,y), then generate the corresponding training data pairs, and finally generate the corresponding training data, test data, and validation data. The training data pairs are: Among them: I cos Normalized cosine interferogram; I sac As an auxiliary diagram, by I cos I. Obtained by taking the inverse cosine and then performing a sine transformation; sin The true value of the normalized sine fringes is used as the label for the output; Step 2: Construction and training of the convolutional neural network: (2.1) Design a PhaseUnet++ neural network, including: Residual connection block ResBlock, Conv2D convolutional layer, BatchNorm2d normalization layer, ReLU activation layer, MaxPool2d pooling layer, ConvTranspose2d deconvolutional layer, Concat connection layer, Dropout layer and clamp layer; Each ResBlock convolutional block X i.j (i,j=0,1,2,…) all involve convolving the input, then passing it through a normalization layer BatchNorm2d and an activation layer ReLU, then convolving it again, passing it through a normalization layer BatchNorm2d, adding it to the input through a Concat layer, and finally passing it through an activation layer ReLU before outputting the result. Input I cos and I sac The graphs are obtained by passing X through a ResBlock block. cos and X sac Then X is obtained through the concat layer. 0.0 X 0.0 As input to the network; X 0.0 X is obtained through the MaxPool2d layer. 1.0 X 1.0 After upsampling through the ConvTranspose2d layer and X 0.0 X is obtained by concatenating the layers along the channel dimension using the concat layer. 0.1 The structure of other layers follows the same pattern; The input to each ResBlock convolutional block is obtained by concatenating the outputs of all preceding ResBlock convolutional blocks and the output of the bottom-left ResBlock convolutional block in the same layer through a concat layer along the channel dimension. (2.2) Using dataset I cos I sac and II sin The PhaseUnet++ neural network is trained until the loss function stops decreasing and remains stable, and the training is completed, and the weight values ​​of each layer of the network are obtained. Step 3: Normalize the cosine interferogram obtained from the actual measurement to obtain I. cos1 , put I cos1 And auxiliary diagram I sac1 Input the trained neural network PhaseUnet++, output a normalized sinusoidal interferogram I sin1 ; Step 4: Calculate the package phase distribution using the arctangent formula. Subsequently, phase unwrapping was performed using traditional unwrapping techniques, ultimately yielding the unwrapped phase distribution Φ1(x, y).

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