An interference microscopic phase distortion elimination method based on PACU Next3+ network

Abstract

The present application relates to the field of optical interferometry, and aims at the phase distortion problem in off-axis interferometric quantitative phase imaging, and provides an interferometric microscopic phase distortion elimination method based on PACUNeXt3+ network. The method comprises the following steps: 1. using Zernike polynomials and test target pictures to simulate and generate a data set; 2. establishing and training a PACUNeXt3+ neural network model; 3. inputting the interference graph I or of the sample to be measured into the trained neural network, and outputting the background interference graph I' r corresponding to the sample without sample information; 4. using the two interference graphs I or and I' r to reconstruct the sample phase distribution φ o (x, y) without phase distortion. The present application has high precision and speed, can eliminate the secondary or high-order phase distortion in interferometric quantitative phase imaging, and has great application prospect in the field of phase imaging.

Description

Technical Field

[0001] This invention relates to the field of optical interferometry technology, and proposes a method for eliminating phase distortion in interferometric microscopy based on PACUNeXt3+ networks. Background Technology

[0002] Interferometric microscopy is an extension of optical measurement techniques into the field of microscopy. It utilizes the principles of light wave interference and microscopic magnification to achieve non-contact measurement of the morphology of minute objects, offering advantages such as high resolution, non-destructive operation, and good stability. However, phase distortion is introduced during quantitative phase imaging in interferometric microscopy due to various factors. Phase distortion refers to the difference between the reconstructed phase distribution obtained from numerical reconstruction of the interferogram and the true phase distribution of the sample. First-order phase distortion occurs because the reference light in the numerical simulation cannot accurately reproduce the actual reference light, resulting in a bias. Second-order phase distortion is caused by wavefront bending of the object light wave due to magnification by the microscope objective during imaging. Higher-order phase distortion is caused by lens manufacturing errors or other factors. These distortions severely affect the accurate reconstruction of the three-dimensional information of the measured object. Therefore, eliminating phase distortion in interferometric microscopy, improving the accuracy of three-dimensional phase distribution reconstruction, and achieving precise measurement of the measured object have become key research issues.

[0003] One common method for eliminating phase distortion is the background subtraction method. This method requires recording two interferograms: first, recording the interferogram I containing the sample. or Then the sample is removed, and an interferogram without the sample (containing the phase distortion of the background) is recorded. r Then put from I or The reconstructed phase minus the phase from I r The reconstructed phase distribution yields the final measurement result after phase distortion removal. A drawback of this method is the need for secondary recording, which limits its application in certain situations.

[0004] Domestic and international scholars have proposed three types of solutions for eliminating phase distortion from an interferogram: traditional numerical fitting methods, physical compensation methods, and deep learning-based methods. Traditional polynomial fitting methods require a large number of blank areas (excluding the sample) in the field of view being measured, and they are not effective in handling high-order phase distortions. Physical compensation methods increase the complexity of the experimental setup and require careful adjustment of optical components for alignment.

[0005] Deep learning-based methods for eliminating phase distortion can start from a single interferogram and eliminate first-, second-, and even higher-order phase distortions, demonstrating high flexibility. Two representative methods have been proposed so far:

[0006] 1. A phase aberration compensation method for digital holographic microscopy based on UNet network (Thanh T, et al. Automatic phase aberration compensation for digital holographic microscopy based on deep learning background detection[J]. Optics Express, 2017, 25(13): 15043-15057.). In this method, the phase distribution containing distortion information is first reconstructed, then the background phase is identified and segmented using the UNet network, and then the Zernike polynomial is fitted to the background to calculate its conjugate phase. Finally, the sample phase distribution with distortion information removed is obtained. The disadvantage of this method is that the reconstructed phase needs to be segmented into the background. Since the phase distribution containing distortion has many aberrations and the edge features of the measured object are weak, it is difficult to accurately segment the measured object. Insufficient segmentation accuracy directly affects the final phase reconstruction accuracy.

[0007] 2. A phase distortion elimination method for digital holographic microscopy based on image inpainting using a two-stage generative adversarial network (SJMa, et al. Quantitative phase imaging in digital holographic microscopy based on image inpainting using a two-stage generative adversarial network[J]. OpticsExpress, 2021, 29(16):24928-24946.). In this technique, morphological image processing techniques such as edge detection are used to remove interference fringes in the sample region of the interferogram, and then a reference interferogram without sample information is generated to obtain the true phase distribution of the sample. The disadvantages of this method are: the sample region in the interferogram needs to be marked, and the training of the GAN network requires a large number of iterations, which is too time-consuming. Summary of the Invention

[0008] This invention proposes a method for eliminating phase distortion in interferometric microscopy based on a PACUNeXt3+ network, to address the problem of phase distortion in interferometric microscopy. The method involves placing sample I... or The interferogram is input into the PACUNeXt3+ network, and the output is the interferogram I′ without the sample. r Then, a two-step subtraction method is used to obtain the phase distribution of the object after phase distortion removal.

[0009] To achieve the objectives of this invention, the present invention provides an interferometric microscopic phase distortion elimination method based on PACUNeXt3+ networks, comprising the following steps:

[0010] Step 1: Use Zernike polynomials and test target images to simulate and generate a dataset, including the sample interferogram I. or Interference pattern without sample I r :

[0011] Step 2: Build and train the PACUNeXt3+ neural network model:

[0012] (2.1) Construct the PACUNeXt3+ neural network model:

[0013] The encoder consists of 4 ResBlock-residual convolutional blocks X Ei (i = 1, 2, 3, 4), 4 Res-UNeXt modules Y Ei The decoder consists of (i = 1, 2, 3, 4) and 3 downsampling layers (MaxPool2d); the decoder consists of 3 ResBlock-residual convolutional blocks X Di (i = 1, 2, 3), 3 Res-UNeXt modules Y Di The network consists of (i=1,2,3) and 3 upsampling layers (Upsample(2)+Conv2d(3*3)). Full-scale deep supervision is used to calculate the loss of the decoder output of each layer, and at the same time, salient features of different scales are fused to form the final output of the network.

[0014] (2.2) Using the normalized dataset I or and I r Train the PACUNeXt3+ neural network until the loss function converges to complete the training and obtain the network weight values.

[0015] Step 3: Normalize the acquired interferogram containing the sample to obtain I. or Inputting a pre-trained PACUNeXt3+ neural network model, the output is the corresponding background interferogram I′ that does not contain sample information. r ;

[0016] Step 4: Using two interferograms I or and I′ r The phase distribution is reconstructed using the background subtraction method: First, the sample-wrapped phase distribution after removing phase distortion is obtained. Then, the unwrapping algorithm is used to obtain the final unwrapped phase distribution φ′. o (x,y).

[0017] Furthermore, in step 2 (2.1) above, in the network encoder part, the input image first passes through the first layer residual convolution block X. E1 and Res-UNeXt module Y E1 Then, a downsampling operation is performed, and the result is input into the next residual convolutional block X. E2 and Res-UNeXt module Y E2 ; and so on, finally inputting into the underlying residual convolutional block X E4 and Res-UNeXt module Y E4 .

[0018] Furthermore, in step 2 (2.1) above, in the network decoder part, each residual convolutional block X Di The structure of (i = 1, 2, 3) is the same as that of X in the encoder. Ei Similarly, each Res-UNeXt module Y Di The structure of (i = 1, 2, 3) is the same as that of Y in the encoder. Ei Similarly, the decoder as a whole employs a full-size skip connection approach. The final output of the network consists of the decoder residual convolutional block X. D1 X D2 X D3 and encoder Res-UNeXt module Y E4 The outputs are concatenated after passing through the deep supervision module.

[0019] Furthermore, for each of the above residual convolutional blocks X Ei / Di (i = 1, 2, 3, 4) all contain two convolutional layers and one efficient channel attention module (ECA-Net). X Ei / Di The input is first subjected to a first convolution (Conv2d) operation, then passed through a normalization layer (BatchNorm2d) and an activation layer (ReLU); then a second convolution (Conv2d) operation is performed, followed by another normalization layer (BatchNorm2d), and finally through an efficient channel attention module (ECA-Net). The output of ECA-Net and the residual convolutional block X are then processed. Ei / Di The inputs are added through skip connections and then output after passing through an activation layer (ReLU).

[0020] Furthermore, each of the above Res-UNeXt modules Y Ei / DiIn the encoding stage (i = 1, 2, 3, 4), the signal first goes through 5-i convolutional layers (Conv2d+BN+ReLU), then through two tokenized multilayer perceptron modules (Tok-MLP). In the decoding stage, the signal first goes through two Tok-MLP modules, then through 4-i convolutional layers (Conv2d+BN+ReLU). The output of the last convolutional layer (Conv2d+BN+ReLU) and the output of the first convolutional layer (Conv2d+BN+ReLU) in the encoding stage are added together through a skip connection and then output.

[0021] Furthermore, each of the above-mentioned deep supervision modules Sup i For each (i = 1, 2, 3, 4), the input is first convolved (Conv2d), and then the feature map resolution is restored to the level of the input image through upsampling before output.

[0022] Compared with the prior art, the advantages of the present invention are:

[0023] 1. Interferograms containing samples do not require any preprocessing and can be directly input into a trained network to output interferograms without samples. The method of this invention is highly accurate and fast, and can eliminate secondary or higher-order phase distortions in quantitative phase imaging of interferometric microscopy, and has great application prospects in the field of phase imaging.

[0024] 2. The PACUNeXt3+ network of this invention uses ResBlock-residual convolutional blocks and Res-UNeXt modules instead of the sequential convolutional blocks used in the original UNet3+ network, effectively reducing information feature loss and solving the "network degradation" problem. The ResBlock-residual convolutional block introduces an efficient channel attention mechanism (ECA-Net), which can enhance channel features without increasing model complexity, thereby improving the accuracy of the output image. The Res-UNeXt module uses a tokenized multilayer perceptron module (Tok-MLP), which reduces feature parameters and computational complexity by shifting the multilayer perceptron. By tagging feature information, the network can focus more on modeling and learning salient features, thereby enhancing the model's ability to reconstruct the background interferogram from the sample interferogram. Attached Figure Description

[0025] Figure 1 This is a diagram of the neural network structure of the present invention.

[0026] Figure 2 This is a structural diagram of other modules in the neural network of this invention.

[0027] in:

[0028] Figure 2 (a) ResBlock structure diagram;

[0029] Figure 2 (b) Structure diagram of the efficient channel attention mechanism (ECA-Net);

[0030] Figure 2 (c) The first Res-UNeXt module structure diagram;

[0031] Figure 2 (d) Schematic diagram of the Tok-MLP (Tok-MLP) module;

[0032] Figure 2 (e) Shifted MLP architecture diagram;

[0033] Figure 2 (f) Structure diagram of the deep supervision module (Supervision).

[0034] Figure 3 For a simulated interferogram I or (256×256 pixels) Comparison results of phase reconstruction using PACUNeXt3+ neural network and UNet3+ neural network respectively.

[0035] in:

[0036] Figure 3 (a) Normalized sample interferogram I or (x,y);

[0037] Figure 3 (b) Normalized background interferogram I r (x,y);

[0038] Figure 3 (c), from I or The phase distribution of the sample obtained by direct reconstruction (including distortion);

[0039] Figure 3 (d), from I or and I r The reconstructed sample reference phase distribution;

[0040] Figure 3 (e) Normalized background interferogram I′ from the PACUNeXt3+ neural network output r (x,y);

[0041] Figure 3 (f), from I or and I′ r The reconstructed sample phase distribution φ′ o(x,y);

[0042] Figure 3 (g) Normalized background interferogram I″ of the original UNet3+ neural network output r (x,y);

[0043] Figure 3 (h), from I or and I″ r The reconstructed sample phase distribution φ″ o (x,y);

[0044] Figure 3 (i), along Figure 3 Comparison of phase values ​​in the direction of the cutoff line in (d), 3(f), and 3(h).

[0045] Figure 4 For a real interferogram I or The results of phase reconstruction using PACUNeXt3+ neural network and UNet3+ neural network are compared.

[0046] in:

[0047] Figure 4 (a) Normalized sample interferogram I or (x,y);

[0048] Figure 4 (b) Normalized background interferogram I r (x,y);

[0049] Figure 4 (c), from I or The phase distribution of the sample obtained by direct reconstruction (including distortion);

[0050] Figure 4 (d), from I or and I r The reconstructed sample reference phase distribution;

[0051] Figure 4 (e) Normalized background interferogram I′ from the PACUNeXt3+ neural network output r (x,y);

[0052] Figure 4 (f), from I or and I′ r The reconstructed sample phase distribution φ′ o (x,y);

[0053] Figure 4 (g) Normalized background interferogram I″ of the original UNet3+ neural network output r(x,y);

[0054] Figure 4 (h), from I or and I″ r The reconstructed sample phase distribution φ″ o (x,y);

[0055] Figure 4 (i), along Figure 4 Comparison of phase values ​​in the direction of the cutoff line in (d), 4(f), and 4(h). Detailed implementation method:

[0056] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0057] This method includes the following steps: 1. Generating a dataset using Zernike polynomials and test target images; 2. Establishing and training the PACUNeXt3+ neural network model; 3. Converting the interferogram containing the test sample into an image. or The input to the trained neural network is the corresponding background interferogram I′ that does not contain sample information. r 4. Using two interferograms I or and I′ r The reconstructed sample phase distribution φ′ with phase distortion removed was obtained. o (x,y).

[0058] Example 1: This invention provides a method for eliminating phase distortion in interferometric microscopy based on a PACUNeXt3+ (Phase Aberration Compensation UNeXt3+) network, specifically including the following steps:

[0059] Step 1: Data Preparation

[0060] (1.1) First, the distortion phase distribution φ is simulated using an n (45 ≥ n ≥ 4) Zernike polynomial. r As shown in the formula below:

[0061]

[0062] Among them, Z i c i These represent the i-th Zernike polynomial and its coefficients, respectively. To obtain the off-axis interferogram, the weighting coefficients of the second and third Zernike terms dominate, producing a distorted phase distribution φ. r .

[0063] (1.2) Simulate and generate samples such as a phase-type USAF-1951 resolution test target, a phase-type NBS 1963A resolution target, and a phase-type Ronche grating. Obtain the true phase distribution φ of the simulated sample by cropping fixed-size regions from different positions of the samples. o .

[0064] (1.3) Generate an interferogram I containing the sample. or Interference map I with background without sample information r The formula for generating the formula is as follows:

[0065] I or (x,y)=A 2 (x,y)+B 2 (x,y)+2A(x,y)B(x,y)cos(φ r +φ o )+n1(x,y), (2)

[0066] I r (x,y)=A 2 (x,y)+B 2 (x,y)+2A(x,y)B(x,y)cos(φ r )+n2(x,y) (3)

[0067] Where n1(x,y) and n2(x,y) are the noise distributions of the interferogram; A(x,y) and B(x,y) are the amplitude distributions of the object beam and the reference beam, respectively. or and I r After normalization, it is used as actual training data, I or Used as network input, I r Used as output labels for the network.

[0068] (1.4) Simulate the generation of datasets, including training and test sets.

[0069] Step 2: Build and train the PACUNeXt3+ neural network model:

[0070] (2.1) Design the PACUNeXt3+ neural network. The network structure diagram is as follows: Figure 1 As shown.

[0071] like Figure 1 The diagram shows the PACUNeXt3+ network architecture. The network adopts the full-size skip connections and full-scale depth supervision of UNet3+. The network consists of an encoder (X... E1 →Y E4 ) and decoder (Y D3 →X D1 It consists of two parts.

[0072] The encoder consists of 4 ResBlock-residual convolutional blocks X Ei (i = 1, 2, 3, 4), 4 Res-UNeXt modules Y Ei The encoder consists of (i = 1, 2, 3, 4) and 3 downsampling layers (MaxPool2d), performing feature selection and feature learning; the decoder consists of 3 ResBlock-residual convolutional blocks X Di (i = 1, 2, 3), 3 Res-UNeXt modules Y Di The network consists of (i=1,2,3) and 3 upsampling layers (Upsample(2)+Conv2d(3*3)). The decoder captures salient feature information at different scales through full-size skip connection. The ResBlock-residual convolutional block uses an efficient channel attention module (ECA-Net) to enhance channel features without increasing model complexity. The Res-UNeXt module introduces a tokenized multilayer perceptron (Tok-MLP) to enable the network to model and learn salient features in the input image. The network uses full-scale deep supervision to calculate the loss of each decoder output and fuses salient features at different scales to form the final output of the network.

[0073] In the network encoder section, the input image first passes through the first residual convolutional block X. E1 and Res-UNeXt module Y E1 Then, a downsampling operation is performed, and the result is input into the next residual convolutional block X. E2 and Res-UNeXt module Y E2 ; and so on, finally inputting into the underlying residual convolutional block X E4 and Res-UNeXt module Y E4 .

[0074] In the network decoder part, each residual convolutional block X Di The structure of (i = 1, 2, 3) is the same as that of X in the encoder. Ei Same (e.g.) Figure 2 (a) shows that each Res-UNeXt module Y Di The structure of (i = 1, 2, 3) is the same as that of Y in the encoder. Ei Similarly, the decoder as a whole adopts a full-size skip connection method. The following uses Y as an example. D3 and X D3 Taking Y as an example, let's illustrate this. E4 The output is upsampled and convolved (Conv2d); the Y... E3Perform a (Conv2d) convolution operation on the output of Y; E2 Y E1 The outputs are then subjected to downsampling (MaxPool2d) and (Conv2d) convolution operations, respectively; the outputs of the above layers are concatenated by a concatenation layer along the channel dimension, and then enter the Res-UNeXt module Y. D3 Then enter the residual convolution block X D3 The output is then processed. Other layer structures follow the same pattern, with each Y in the decoder... Di The inputs (i = 1, 2, 3) are obtained by combining low-level features after upsampling and convolution (Conv2d), features from the same layer after convolution (Conv2d), and high-level features after downsampling (MaxPool2d) and convolution (Conv2d), and then concatenating them by the channel dimension through a concatenation layer (Concat). Furthermore, the input feature maps of each layer in the decoder are first processed by the Res-UNeXt module Y. Di Then, after passing through the residual convolution block X Di The final output of the network is the decoder residual convolution block X. D1 X D2 X D3 and encoder Res-UNeXt module Y E4 The outputs are concatenated after passing through the deep supervision module.

[0075] ResBlock - Residual Convolutional Block Structure as follows Figure 2 As shown in (a), it contains two convolutional layers and an efficient channel attention module (ECA-Net), with each residual convolutional block X Ei / Di For each input (i = 1, 2, 3, 4), the input first undergoes a first convolution (Conv2d) operation, then passes through a normalization layer (BatchNorm2d) and an activation layer (ReLU); then a second convolution (Conv2d) operation is performed, followed by another normalization layer (BatchNorm2d), and finally through an efficient channel attention module (ECA-Net). The output of ECA-Net and the residual convolutional block X... Ei / Di The inputs are summed through skip connections and then passed through a ReLU activation layer before outputting. The efficient channel attention module (ECA-Net) enhances channel features without increasing model complexity, thereby improving phase reconstruction accuracy. Its structure is as follows: Figure 2As shown in (b), ECA-Net first performs spatial feature compression on the input feature map of size H*W*C (H is the image height, W is the image width, and C is the image depth), and then uses global average pooling (GAP) in the spatial dimension to obtain a 1*1*C feature map. Next, channel feature learning is performed on the compressed feature map through convolution (Conv1d) to learn the importance of different channels. At this point, the output dimension is still 1*1*C. Finally, the channel attention features are obtained through an activation function (Sigmoid). Figure 1 The *1*C is multiplied channel-wise with the original input feature map H*W*C to achieve channel attention integration, and finally outputs a feature map H*W*C with channel attention.

[0076] The first Res-UNeXt module Y E1 / D1 Structure such as Figure 2 As shown in (c), the overall structure of the other modules is similar. Each Res-UNeXt module Y... Ei / Di The encoding stage for (i = 1, 2, 3, 4) first goes through 5-i convolutional layers (Conv2d + BN + ReLU), then through two tokenized multilayer perceptron modules (Tok-MLP). During the first convolutional layer, the feature map size changes from H*W*C. in (H is the image height, W is the image width, C) in The number of input channels becomes H*W*C. out (C out (Number of output channels), from the second convolutional layer to the bottom Tok-MLP, the feature map size ranges from H*W*C. out Change to H / 2 (6-i) *W / 2 (6-i) *C mid (C mid The number of channels in the intermediate layers decreases by a factor of 2 with each subsequent layer. In the decoding stage, the system first passes through two Tok-MLP layers, followed by 4-i convolutional layers (Conv2d+BN+ReLU). The input to each layer is obtained by concatenating the output of the previous layer and the output of the encoding stage in the same layer along the channel dimension, followed by upsampling. The feature map size starts from H / 2. (6-i) *W / 2 (6-i) *C mid Transform into H*W*C outThe feature map is magnified layer by layer. The output of the last convolutional layer (Conv2d+BN+ReLU) and the output of the first convolutional layer (Conv2d+BN+ReLU) in the encoding stage are added together through a skip connection before outputting the final result. The Tok-MLP module allows the network to focus more on modeling and learning salient features (sample regions) in the input sample interferogram, thereby enhancing its ability to reconstruct the background interferogram. Its structure is as follows: Figure 2 As shown in (d), Tok-MLP first performs feature learning on the input feature map through a Shifted MLP Width layer, then passes the features through a Depthwise Separable Convolution (DWConv), followed by an activation layer (GeLU) and then feeds it into a Shifted MLP Height layer for feature learning. LayerNorm is then used for layer normalization. Finally, the output salient information feature map is added to the Tok-MLP input feature map via a SkipConnection before outputting the final result. The Shifted MLP reduces feature parameters and computational complexity while still being able to label and model salient feature information. Its structure is as follows: Figure 2 As shown in (e), the Shifted MLP first performs shift and tokenization operations on the input feature map to obtain a tokenized feature map, which is then fed into the multilayer perceptron (MLP) for feature modeling.

[0077] Full-scale deep supervision can compute the loss of each decoder layer's output while fusing salient features from different scales. Its structure is as follows: Figure 2 As shown in (f), each deep supervision module Sup i For each (i = 1, 2, 3, 4), the input is first convolved (Conv2d), and then the feature map resolution is restored to the level of the input image through upsampling before output.

[0078] (2.2) Using dataset I from step 1 or and dataset I r The PACUNeXt3+ neural network was trained. Specifically, the normalized interferogram I containing the samples was trained. or As input to the network, the normalized background interference pattern I, which does not contain sample information. r As the output label of the network, it is related to the interference pattern I′ output by the network. r Calculate the loss function value until the loss function converges to complete the training and obtain the network weight values.

[0079] Step 3: Normalize the interferogram containing the sample obtained in the experiment to obtain I. or Inputting a pre-trained PACUNeXt3+ neural network model, the output is the corresponding background interferogram I′ that does not contain sample information. r ;

[0080] Step 4: Using two interferograms I or and I′ r The phase distribution is reconstructed using the background subtraction method: First, the sample-wrapped phase distribution after removing phase distortion is obtained. Then, the unwrapping algorithm is used to obtain the final unwrapped phase distribution φ′. o (x,y).

[0081] Comparative Example 1. An interferometric microscopy phase distortion elimination method based on PACUNeXt3+ network. Under the same experimental dataset, experimental conditions and parameters, the phase reconstruction results of PACUNeXt3+ network and the original UNet3+ network are compared to verify the advantage of PACUNeXt3+ network in phase reconstruction accuracy. The method includes the following steps:

[0082] Step 1: Data Preparation

[0083] (1.1) First, the distortion phase distribution φ is simulated using a 9th-order Zernike polynomial. r As shown in the formula below:

[0084]

[0085] Among them, Z i c i Let represent the i-th order Zernike polynomial and its coefficients, respectively. To obtain the off-axis interferogram, the weighting coefficients of the 2nd and 3rd Zernike terms are located between [75, 125]. The coefficient of the 4th Zernike term is set between [-4, 4], and the other 6 Zernike coefficients are located between [-0.05, 0.05], resulting in a distorted phase distribution φ of size 256 × 256. r .

[0086] (1.2) Simulated samples such as the phase-type USAF-1951 resolution test target, the phase-type NBS 1963A resolution target, and the phase-type Ronchi grating were generated. Regions of size 256×256 were cropped from different positions in the samples to obtain the true phase distribution φ of the simulated samples. o .

[0087] (1.3) Generate an interferogram I containing the sample. or Interference map I with background without sample information r The formula for generating the formula is as follows:

[0088] I or (x,y)=A 2 (x,y)+B 2 (x,y)+2A(x,y)B(x,y)cos(φ r +φ o )+n1(x,y) (5)

[0089] I r (x,y)=A 2 (x,y)+B 2 (x,y)+2A(x,y)B(x,y)cos(φ r )+n2(x,y) (6)

[0090] Where n1(x,y) and n2(x,y) are the noise distributions of the interferogram, and n1(x,y) and n2(x,y) are assumed to be Gaussian white noise; A(x,y) and B(x,y) are the amplitude distributions of the object beam and the reference beam, respectively, and it is assumed that A(x,y) and B(x,y) are Gaussian distributions. or and I r After normalization, it is used as actual training data, I or For network input, I r Used as output labels for the network.

[0091] (1.4) Simulate the generation of 15,400 data pairs (I or and I r After that, it is divided into training set data pairs (12400) and test set data pairs (3000).

[0092] Step 2: Construct the PACUNeXt3+ neural network model; use the dataset obtained in Step 1 (I or and I r The PACUNeXt3+ network and the original UNet3+ network were trained respectively.

[0093] (2.1) The PACUNeXt3+ neural network is designed as described in Example 1, and the network structure diagram is as follows. Figure 1 As shown.

[0094] (2.2) Using the dataset (I) from step 1 or and I r The PACUNeXt3+ network and the original UNet3+ network were trained separately. Specifically, the normalized interferogram I containing the samples was used. or Two networks are input separately, and the normalized background interference pattern (I) without sample information is generated. r As the output label of the network, it is related to the interferogram I′ output by the network. rCalculate the loss function value until the loss function converges to complete the training and obtain the network weight values.

[0095] Step 3: Normalize the interferogram containing the sample to obtain I. or ( Figure 3 (a)), the background interferogram without sample information is normalized to obtain I. r ( Figure 3 (b)). I or The input is a pre-trained PACUNeXt3+ neural network, and the output is a background interferogram I′ that does not contain sample information. r ( Figure 3 (e)); then put I or Input the original UNet3+ neural network and output a background interferogram I″ that does not contain sample information. r ( Figure 3 (g)).

[0096] To compare the background interferograms output by the two networks, we... Figure 3 The rectangular area at the same location in (e) and 3(g) has been magnified, and it can be seen that I″ r ( Figure 3 (g) contains discontinuities, while the I′ output of the PACUNeXt3+ neural network... r ( Figure 3 (e) shows smooth stripes. Therefore, the quality of the background interferogram output by the PACUNeXt3+ neural network is higher than that of the UNet3+ neural network output.

[0097] Step 4: First, use the Fourier transform method to start from I or Direct reconstruction yields the unencapsulated phase distribution of the sample containing phase distortion. Figure 3 (c)); then from I or and I r Starting from this point, the encapsulation phase distribution of the sample was reconstructed using the Fourier transform method and the background subtraction method. The specific formula is as follows:

[0098]

[0099] In the above formula, FT represents Fourier transform, and IFT represents inverse Fourier transform. d The numerical reference light in off-axis interferometry reconstruction is represented by ξ, η, which represents the filter window in the frequency domain, taking a value of 1 within the selected region and 0 elsewhere. Its function is to filter out the +1 order spectrum, where ξ and η represent the coordinates in the spectral domain. Angular represents the mathematical operation of taking the phase of a complex number. This yields the enclosed phase. Then, the unwrapped phase distribution φ can be obtained through unwrapping operations. o (x,y), φo (x,y) serves as the reference phase distribution, see Figure 3 (d)

[0100] Using two interferograms I or and I′ r The phase distribution φ′ of the sample, reconstructed by the PACUNeXt3+ neural network and free from phase distortion, is finally obtained using the two-step subtraction method. o (x,y), the result is as follows Figure 3 As shown in (f); using two interferograms I or and I″ r Using the same method, the phase distribution φ″ of the sample reconstructed from the original UNet3+ neural network and with phase distortion removed was obtained. o (x,y)( Figure 3 (h)).

[0101] Figure 3 (i) is along Figure 3 Comparison of phase values ​​in the transect direction (row 130, columns 65-125) of (d), 3(f) and 3(h). Figure 3 (d) is from the simulated interferogram I or And simulated background interferogram I r The reconstructed phase distribution is used here as a reference phase for comparison. From Figure 3 (i) It can be seen that, along the cutoff direction, the maximum deviation between the sample's reference phase and the phase value reconstructed using the PACUNeXt3+ neural network is 0.14 rad; while the maximum deviation between the sample's reference phase and the phase value reconstructed using the UNet3+ neural network is 0.56 rad. To quantitatively measure the accuracy of the reconstructed sample phase distribution, Figure 3 The structural similarity index (SSIM) between (f) and 3(d) is 0.9718, while Figure 3 (h) and Figure 3 The Structural Similarity (SSIM) index between (d) is 0.8537. The data shows that, compared to the original UNet3+ network, under the same experimental conditions and parameters, the PACUNeXt3+ network can more accurately obtain the background interferogram of the removed sample. Therefore, using this network can yield a sample phase distribution with higher reconstruction accuracy.

[0102] Comparative Example 2. For the trained network, in specific implementation, it is only necessary to start from step 3 of the present invention. In this embodiment, starting from an experimentally acquired interferogram containing significant noise, the reconstruction results using the PACUNeXt3+ neural network constructed in Example 1 of the present invention and the UNet3+ neural network are compared respectively. The specific steps are as follows:

[0103] Step 1: Normalize an interferogram containing the sample acquired in the dry microscope to obtain I. or ,like Figure 4 As shown in (a). In the same apparatus, the background interference pattern obtained after removing the sample, after normalization, yields I. r ,like Figure 4 As shown in (b).

[0104] Put I or The input is a pre-trained PACUNeXt3+ neural network, and the output is a background interferogram I′ that does not contain sample information. r ( Figure 4 (e)); then put I or Input the original UNet3+ neural network model, output a background interferogram I″ that does not contain sample information. r ( Figure 4 (g)).

[0105] Step 2: First, use the Fourier transform method to start from I or Direct reconstruction yields the phase distribution of the sample containing phase distortion. Figure 4 (c)); The reference unencapsulated phase φ of the sample was then reconstructed using Fourier analysis and background subtraction. o (x,y) see Figure 4 As shown in (d).

[0106] Using two interferograms I or and I′ r Based on Fourier analysis and background subtraction, the phase distribution φ′ of the sample, reconstructed by the PACUNeXt3+ neural network and free of phase distortion, was finally obtained. o (x,y)( Figure 4 (f)); using two interferograms I or and I″ r Using the same method, the phase distribution φ″ of the sample reconstructed from the original UNet3+ neural network and with phase distortion removed was obtained. o (x,y)( Figure 4 (h)).

[0107] Figure 4 (d) The reference phase distribution for the sample. Along Figure 4 (d) Figure 4 (f) and Figure 4 (h) The phase distribution along the transect direction (row 15, columns 60-100) is as follows: Figure 4 As shown in (i). From Figure 4 As can be seen in (i), along the cutoff direction, the maximum error between the phase reconstructed using the PACUNeXt3+ network and the reference phase value of the sample is 0.35 rad; while the maximum error between the phase reconstructed using the UNet3+ network and the reference phase value of the sample is 1.33 rad. Figure 4 (f) and Figure 4 The structural similarity index (SSIM) between (d) and (d) is 0.9385, while Figure 4 (h) and Figure 4 The structural similarity index (SSIM) between (d) is 0.8055. The data indicates that, compared to the original UNet3+ network, the PACUNeXt3+ network performs better and achieves higher reconstruction accuracy for phase reconstruction of experimentally acquired interferograms.

[0108] The above description is merely an 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 method for eliminating phase distortion in interferometric microscopy based on PACUNeXt3+ networks, characterized in that... It includes the following steps: Step 1: Use Zernike polynomials and test target images to simulate and generate a dataset, including the sample interferogram I. or Interference pattern without sample I r : Step 2: Build and train the PACUNeXt3+ neural network model: (2.1) Construct the PACUNeXt3+ neural network model: The encoder consists of 4 ResBlock-residual convolutional blocks X Ei i = 1, 2, 3, 4, 4 Res-UNeXt modules Y Ei The decoder consists of three downsampling layers, i = 1, 2, 3, 4, and three MaxPool2d layers; the decoder is composed of three ResBlock-residual convolutional blocks X. Dj j = 1, 2, 3, 3 Res-UNeXt modules Y Dj The network consists of 1, 2, 3 and 3 upsampling layers (Upsample + Conv2d). Full-scale depth supervision is used to calculate the loss of each decoder output layer, and salient features at different scales are fused to form the final output of the network. ( 2.2) Using normalized dataset I or and I r Train the PACUNeXt3+ neural network until the loss function converges to complete the training and obtain the network weight values. Step 3: Normalize the acquired interferogram containing the sample to obtain I. or Inputting a pre-trained PACUNeXt3+ neural network model, the output is the corresponding background interferogram I′ that does not contain sample information. r ; Step 4: Using two interferograms I or and I′ r The phase distribution is reconstructed using the background subtraction method: First, the sample-wrapped phase distribution φ after removing phase distortion is obtained. o， Then, the unwrapping algorithm is used to obtain the final unwrapped phase distribution φ′. o (x,y).

2. The method for eliminating phase distortion in interferometric microscopy based on PACUNeXt3+ network according to claim 1, characterized in that... In step 2 (2.1), in the network encoder section, the input image first passes through the first residual convolutional block X. E1 and Res-UNeXt module Y E1 Then, a downsampling operation is performed, and the result is input into the next residual convolutional block X. E2 and Res-UNeXt module Y E2 ; and so on, finally inputting into the underlying residual convolutional block X E4 and Res-UNeXt module Y E4 .

3. A method for eliminating phase distortion in interferometric microscopy based on a PACUNeXt3+ network according to claim 1 or 2, characterized in that... In step 2(2.1), in the network decoder section, each residual convolutional block X Dj The structure of j=1,2,3 is the same as that of X in the encoder. Ei Similarly, each Res-UNeXt module Y Dj The structure for j=1,2,3 is the same as that of Y in the encoder. Ei Similarly, the decoder as a whole adopts a full-size skip connection method; the final output of the network is generated by the decoder residual convolution block X. D1 X D2 X D3 and encoder Res-UNeXt module Y E4 The outputs are concatenated after passing through the deep supervision module.

4. The method for eliminating phase distortion in interferometric microscopy based on PACUNeXt3+ network according to claim 3, characterized in that... In step 2 (2.1), each ResBlock-residual convolutional block contains two convolutional layers and an efficient channel attention module ECA-Net, X Dj The input is first subjected to a first Conv2D convolution, then passed through a normalization layer (BatchNorm2d) and an activation layer (ReLU); a second Conv2D convolution is then performed, followed by another normalization layer (BatchNorm2d), and finally passed through an efficient channel attention module (ECA-Net). The output of ECA-Net is then passed to the residual convolutional block X. Dj The inputs are added through a Skip Connection and then output after passing through a ReLU activation layer.

5. The method for eliminating phase distortion in interferometric microscopy based on PACUNeXt3+ network according to claim 4, characterized in that... In step 2 (2.1), the encoding stage of each Res-UNeXt module first goes through 5-i convolutional layers Conv2d+BN+ReLU, and then through two tokenized multilayer perceptron modules Tok-MLP; in the decoding stage, it first goes through two Tok-MLP, and then through 4-j convolutional layers Conv2d+BN+ReLU. The output of the last convolutional layer Conv2d+BN+ReLU and the output of the first convolutional layer Conv2d+BN+ReLU in the encoding stage are added together through a Skip Connection and then output.

6. The method for eliminating phase distortion in interferometric microscopy based on PACUNeXt3+ network according to claim 5, characterized in that... In step 2 (2.1), in the network decoder section, each deep supervision module Sup i For i = 1, 2, 3, 4, the input is first subjected to a Conv2d convolution operation, and then the feature map resolution is restored to the level of the input image by upsampling before output.

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