Tilt phase shift interferogram phase demodulation method based on tilt perception and self-guiding network
By using a U-shaped structure based on tilt sensing and self-guided networks, combined with self-supervised training of physical models, the problem of tilt phase shift error in optical interferometry is solved, achieving efficient and accurate phase demodulation and improving the stability and generalization ability of the network.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2025-12-19
- Publication Date
- 2026-04-21
AI Technical Summary
Existing optical interferometry techniques have limited measurement accuracy when dealing with tilt phase shift errors caused by environmental vibrations or imperfections in phase shifters. In particular, large-aperture interferometers are easily affected by tilt effects. Traditional methods are sensitive to initial guesses and are prone to getting trapped in local optima. Deep learning methods lack effective constraints and generalization capabilities for tilt parameters.
A U-shaped structure based on tilt perception and self-guided network is adopted. Tilting features are adaptively extracted through deep learning network and combined with self-supervised training of physical model to achieve end-to-end phase demodulation. The tilt guidance module is used to predict the initial tilt parameters and fuse them with the features, thus avoiding the limitations of traditional methods.
It achieves efficient and accurate phase demodulation of complex tilted phase-shifting interferograms, improves the extraction accuracy of tilt parameters and the generalization ability of the network, and avoids the local optima problem of traditional methods without the need for training with a large amount of labeled data.
Smart Images
Figure CN121898623A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of optical measurement and wavefront detection, and in particular to a method for phase demodulation of tilt phase-shift interferograms based on tilt sensing and self-guided networks. Background Technology
[0002] Optical interferometry is an ultra-precise measurement technique widely used in wavefront detection, object topography measurement, and computational holography. Its basic principle is the formation of interference fringes through the interference of a wavefront to be measured with a reference wavefront. The wavefront to be measured carries the physical information to be measured, while the interferogram is the fringe image recorded by a camera or detector. By demodulating the phase of these interferograms, precise physical quantities can be obtained. The expression for the intensity of the interfering light is typically: Where (x,y) are the coordinates of the interference plane, I m (x,y) represents the m-th recorded interferogram, A(x,y) represents the background intensity, B(x,y) represents the modulation intensity, φ(x,y) represents the wavefront to be measured, and δ m Let be the tilt phase shift corresponding to the m-th interferogram.
[0003] In actual measurements, due to environmental vibrations or imperfections in the phase shifter, the phase shift term δ is often a spatial variable containing a random piston and a tilt gradient. Where, represents the k-th xm Tilt gradient in the x-direction of the frame, k ym d represents the gradient along the y-direction. m This represents the random piston in the m-th frame.
[0004] This spatially varying tilt phase shift error is one of the main factors affecting the accuracy of interferometry, and interferometers with large apertures are particularly susceptible to these tilt effects. This uncontrolled variation, especially tilt translation, severely impairs measurement accuracy and introduces significant errors into the calculated phase map. Therefore, developing robust phase extraction methods capable of handling arbitrary unknown phase shifts (including piston and tilt components) is crucial for reliable interferometry under practical conditions. Early iterative methods used first-order Taylor series expansions to linearize the problem, but their applicability was limited to small tilt errors. Subsequent iterative methods utilized nonlinear least squares techniques, model-based fitting, or partitioning the interferogram to estimate local phase shifts and then fitting a global tilt plane. While these methods can handle larger tilts than earlier methods, these iterative techniques may have some drawbacks, such as sensitivity to initial guesses, potential convergence to local optima, errors from approximations, sensitivity to non-uniform backgrounds and modulation, significant computational costs, and a tendency to get trapped in local optima. In recent years, deep learning methods have demonstrated the potential for rapid phase recovery. However, existing methods either lack an intrinsic model of the physical model of tilt phase shift, resulting in limited generalization ability; or require a large amount of labeled data for supervised training; or employ a two-stage (prediction + optimization) approach, failing to achieve fully end-to-end processing. In particular, existing deep learning networks typically use general convolutional structures, making it difficult to explicitly and accurately extract and utilize tilt information from multi-frame data. They also lack effective constraints on the physical continuity of tilt parameters, limiting their performance and stability.
[0005] Therefore, developing a new deep learning method that can deeply integrate physical models, achieve end-to-end processing, does not rely on external labels, and specifically performs structured perception, decoupling, and optimization of tilt parameters has significant theoretical and applied value. Summary of the Invention
[0006] To address the shortcomings of existing technologies, this invention proposes a tilt phase-shift interferogram phase demodulation method based on tilt sensing and a self-guided network.
[0007] The specific technical solution is as follows: A tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided networks includes the following steps: S1: Construct the true wavefront phase using random Zernike coefficients; S2: Using the true wavefront phase value, generate a multi-frame sequence of random tilt phase-shift interferograms to establish a training dataset; the random tilt phase-shift interferograms are obtained through random pistons and tilt gradients. S3: Establish a U-shaped deep learning interferogram phase demodulation network, including: a downsampling module, a tilt feature extraction module, a tilt guidance module, and an upsampling module. The network input is a multi-frame sequence of tilt phase-shifted interferograms. The downsampling module and the tilt feature extraction module adaptively extract and decouple tilt-related features based on the inter-frame variation information of the interferograms. The tilt guidance module predicts the initial tilt phase-shift parameters based on the tilt-related features. The upsampling module performs upsampling based on the initial tilt phase-shift parameters and the tilt-related features, and finally outputs multiple decoupled physical quantities, including: the predicted wrapping phase, background intensity, modulation intensity, and the predicted tilt phase-shift parameters of each frame of input tilt phase-shifted interferograms. S4: Using the training dataset, train the deep learning interferogram phase demodulation network using a physical model-driven self-supervised training method, and update the network parameters using gradient descent; S5: Input the multi-frame random tilt phase shift interferogram of the phase to be measured into the trained deep learning interferogram phase demodulation network to obtain the wrapped phase, and then use the unwrapping algorithm to obtain the demodulated phase result.
[0008] Furthermore, S2 is specifically implemented through the following sub-steps: (2.1) Randomly generate background intensity A(x,y) and modulation intensity B(x,y) that conform to a Gaussian distribution; (2.2) Randomly generate the piston and the tilt gradients in the x and y directions, and generate multiple tilt phase shifts δ accordingly. m m=1,2,3,…,M, where M is the total number of frames of the generated interferogram; (2.3) Based on background intensity A(x,y), modulation intensity B(x,y) and tilt phase shift δ m Generate multiple frames of random tilted phase-shift interferograms I m (x,y); Each wavefront phase true value corresponds to a sequence of multiple frames of random tilted phase-shift interferograms, which are denoted as a group. The training dataset is built by combining the groups.
[0009] Further, in step (2.1), the expressions for background intensity A(x,y) and modulation intensity B(x,y) are as follows: In the formula, A0 represents the background peak intensity, B0 represents the modulation peak intensity, x0 represents the beam offset in the x direction, y0 represents the beam offset in the y direction, and D represents the beam width.
[0010] Furthermore, in step (2.2), the tilt phase shift δ m The expression is as follows: In the formula, δ represents the tilt phase shift of the m-th frame, and k xm Let k represent the tilt gradient in the x-direction of the m-th frame. ym d represents the tilt gradient in the y-direction of the m-th frame. m This represents the random piston in the m-th frame.
[0011] Furthermore, in step (2.3), the generated multi-frame random tilt phase-shift interferogram I m The expression for (x,y) is as follows: In the formula, I m (x,y) represents the light intensity of the m-th frame of the interferogram; φ(x,y) is the true value of the wavefront phase.
[0012] Furthermore, both the downsampling module and the upsampling module include a 3×3 convolution module for adjusting the input and output dimensions, and several basic modules for extracting and mapping information, with the same number of basic modules for upsampling and downsampling; the corresponding basic modules of the downsampling part and the upsampling part promote information flow and enhance information flow through skip connections; the tilt feature extraction module is integrated between the downsampling module and the upsampling module.
[0013] Furthermore, the basic module comprises two parts. The first part consists of six layers, namely an LN layer, a 1×1 convolutional layer, a 3×3 convolutional layer, a BN layer, an activation function ReLU, and a 3×3 convolutional layer. The second part consists of five layers, namely an LN layer, a 1×1 convolutional layer, a BN layer, an activation function ReLU, and a 3×3 convolutional layer. The basic module performs residual connections internally. That is, the input and output of the first part are added element-wise and used as the input of the second part; the input of the second part and the output of the second part are added element-wise and used as the output of the entire basic module.
[0014] Furthermore, the internal structure of the tilt feature extraction module includes: a pairwise frame difference unit, used to calculate the difference features of the input feature map in the channel dimension and output the difference feature map to explicitly extract the temporal change information caused by the tilt phase shift; An orientation-sensitive convolutional group contains multiple orientation-selective convolutional kernels that act on the difference feature map to match the tilt effect in any direction in order to extract gradient and edge information in different directions; A spatial attention unit is used to weight inter-frame variation features, highlight areas with significant tilt effects, focus on the most significant changes in the difference feature map, and enhance sensitivity to tilt information.
[0015] Furthermore, step S4 specifically includes the following sub-steps: (4.1) Input the training dataset into the deep learning interferogram phase demodulation network to obtain the predicted package phase. Background intensity Modulation intensity Tilt phase shift parameters Based on this, a multi-frame interferogram is generated through fitting: In the formula, This represents the predicted light intensity of the m-th frame of the interferogram. The tilt phase shift of the predicted m-th frame interferogram; (4.2) Using the predicted light intensity and input light intensity of the interferogram, as well as the initial tilt phase shift parameter and the predicted tilt phase shift parameter, a self-supervised loss function Loss is constructed, as shown in the following expression: In the formula, P tilt P is the initial tilt phase shift parameter. final To predict tilt phase shift parameters; (4.3) Using the Adam optimizer with a learning rate of 0.001, gradient descent is applied to the loss function Loss to update the deep learning interferogram phase demodulation network; (4.4) Repeat steps (4.1) to (4.4) until the loss function reaches the threshold or the maximum number of training iterations is reached. Training ends and the trained deep learning interferogram phase demodulation network is obtained.
[0016] The beneficial effects of this invention are: (1) The method of this invention combines the rapid prediction capability of deep learning with the precise constraints of physical models. Through end-to-end network design, it achieves efficient and accurate phase demodulation of complex tilt phase-shift interferograms containing random pistons and tilt gradients. The innovative tilt feature extraction module inside the network can directly and adaptively extract and decouple tilt-related features from inter-frame changes, which significantly improves the sensitivity and extraction accuracy of tilt parameters. The tilt guidance module predicts the initial tilt parameters as strong guidance information, and the guidance information is fused with the tilt-related features and then fed into the backbone network, which effectively avoids the problem of traditional iterative methods being sensitive to initial values and easily getting trapped in local optima.
[0017] (2) The present invention adopts a model-driven self-supervised training method, which uses physical reconstruction loss to strongly constrain the network output. Training can be completed without a large amount of labeled ground truth data, and it has strong generalization ability and practicality. Attached Figure Description
[0018] Figure 1This is a flowchart of the tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network in an embodiment of the present invention.
[0019] Figure 2 This is a schematic diagram of the structure of the deep learning interferogram phase demodulation network in an embodiment of the present invention.
[0020] Figure 3 This is a schematic diagram of the training stage of the deep learning interferogram phase demodulation network in an embodiment of the present invention.
[0021] Figure 4 This is a schematic diagram of the testing phase of the deep learning interferogram phase demodulation network in an embodiment of the present invention.
[0022] Figure 5 This is a schematic diagram of the phase demodulation effect in an embodiment of the present invention, wherein (a) is a schematic diagram of the true phase value, (b) is a schematic diagram of the demodulated phase, and (c) is a schematic diagram of the root mean square error between the true phase value and the phase demodulation result. Detailed Implementation
[0023] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
[0024] like Figure 1 As shown, a phase demodulation method for tilt phase-shift interferograms based on tilt sensing and self-guided networks specifically includes the following steps: S1: Using random Zernike coefficients, construct several true values for the wavefront phase, expressed as follows: In the formula, φ(x,y) is the true value of the wavefront phase, and (x,y) are the coordinates of the interference plane. a 1~ a j Z represents the random Zernike coefficients. j (x,y) is a Zernike polynomial. j Let Zernike terms be the number of terms. a It is a vector consisting of all Zernike coefficients, used to uniquely represent the wavefront.
[0025] S2: Using the ground truth wavefront phase values, generate a sequence of multiple frames of random tilted phase-shift interferograms. Each ground truth wavefront phase value corresponds to a sequence of multiple frames of random tilted phase-shift interferograms, which are denoted as a group. Combine these groups to build a training dataset. S2 specifically includes the following sub-steps: (2.1) Randomly generate background intensity A(x,y) and modulation intensity B(x,y); since the interference light intensity is generally Gaussian distributed, both background intensity A(x,y) and modulation intensity B(x,y) conform to Gaussian distribution, and their expressions are: In the formula, A0 represents the background peak intensity, x0 represents the offset of the light spot in the x direction, y0 represents the offset of the light spot in the y direction, D represents the beam width, and B0 represents the modulation peak intensity.
[0026] (2.2) In actual measurements, due to environmental vibrations or imperfections in the phase shifter, the tilt phase shift δ is often a spatial variable that includes a random piston and a tilt gradient, expressed as follows: In the formula, δ represents the tilted phase shift, and k x k represents the slope gradient in the x-direction. y Let represent the gradient along the y-direction, and d represent the random piston.
[0027] The following are the multiple tilt phase shifts generated accordingly: ... In the formula, δ1 represents the tilt phase shift of the first frame, and k x1 k represents the tilt gradient in the x-direction of the first frame. y1 d1 represents the tilt gradient in the y-direction of the first frame, and d1 represents the random piston in the first frame; δ M k represents the tilt phase shift of the Mth frame. xM Let k represent the tilt gradient in the x-direction of the M-th frame. yM Let d represent the tilt gradient in the y-direction of the M-th frame. M This represents the random piston in the Mth frame; M is the total number of frames in the generated interferogram, M≥3.
[0028] (2.3) Based on A(x,y), B(x,y) and δ, generate multi-frame random tilt phase-shift interferograms, as shown in the following expression: ... In the formula, I1(x,y) represents the light intensity of the interferogram with a tilt phase shift of δ1 (i.e., the light intensity of the first frame of the interferogram), and I2(x,y) represents the light intensity of the interferogram with a tilt phase shift of δ2 (i.e., the light intensity of the second frame of the interferogram).M (x,y) represents the tilted phase shift of δ M The light intensity of the interferogram (i.e., the light intensity of the Mth frame interferogram).
[0029] Each wavefront phase corresponds to a sequence of multiple random tilted interferograms, denoted as a group. These groups are then combined to obtain the training dataset. This training dataset does not contain individual wavefront ground truth labels, and therefore lacks paired inputs and labels for supervision. Thus, the training in this invention is essentially a model-driven process, rather than a data-driven one.
[0030] S3: Construct a U-shaped deep learning interferogram phase demodulation network, such as... Figure 2 As shown, the network includes: a downsampling module (i.e., encoder), a tilt feature extraction module, a tilt guidance module, an upsampling module (i.e., decoder), and a multi-head output module. The network input is a multi-frame tilt phase-shift interferogram; the downsampling module and the tilt feature extraction module adaptively extract and decouple tilt-related features based on the inter-frame variation information of the interferogram; the tilt guidance module predicts the initial tilt phase-shift parameters based on the tilt-related features; the upsampling module upsamples the initial tilt phase-shift parameters and the tilt-related features, and finally outputs multiple decoupled physical quantities through the multi-head output module, including: the predicted wrap phase, background intensity, modulation intensity, and the predicted tilt phase-shift parameters of each frame of the input tilt phase-shift interferogram.
[0031] Specifically, both the encoder and decoder include a 3×3 convolutional module for adjusting the input and output dimensions, and several basic modules for extracting and mapping information. The number of basic modules for upsampling and downsampling is the same. Skip connections are used between the corresponding basic modules of the downsampling and upsampling parts to facilitate and enhance information flow. The tilt feature extraction module is integrated between the encoder and decoder.
[0032] Each basic module consists of two parts. The first part has six layers: an LN layer, a 1×1 convolutional layer, a 3×3 convolutional layer, a BN layer, a ReLU activation function, and a 3×3 convolutional layer. The second part has five layers: an LN layer, a 1×1 convolutional layer, a BN layer, a ReLU activation function, and a 3×3 convolutional layer. Residual connections are used within the basic module; that is, the input and output of the first part are element-wise summed and used as the input of the second part; the input and output of the second part are element-wise summed and used as the output of the entire basic module.
[0033] After multi-frame tilt phase-shift interferograms are input into the encoder, they are first adjusted in dimension by a 3×3 convolution module, then downsampled by a 2×2 module, and finally the frame difference is calculated before being input into the tilt feature extraction module. The internal structure of the tilt feature extraction module includes: a pairwise frame difference unit, used to calculate the difference features of the input feature map in the channel (frame) dimension and output the difference feature map to explicitly extract the temporal change information caused by tilt phase shift; a direction-sensitive convolution group, containing convolution kernels with multiple direction selectivity, which acts on the difference feature map to match the tilt effect in any direction to extract gradient and edge information in different directions; and a spatial attention unit, used to weight the inter-frame change features, highlight the regions with significant tilt effects, and further focus on the most significant changes in the difference feature map to enhance the sensitivity to tilt information.
[0034] Based on the extracted tilt-related features, the tilt guidance module predicts a set of initial tilt phase shift parameters P. tilt =(k xp ,k yp ,d p ), where k xp k represents the initial slope gradient in the x-direction. yp d represents the initial slope gradient in the y-direction. p The initial piston term is represented; after fusing it with tilt-related features (via channel concatenation), it is upsampled 2×2 by a base module, then dimensionally adjusted by a 3×3 convolution module, and finally output through a multi-head output module with multiple parallel output heads to simultaneously output the final decoupled physical quantities: the predicted wrap phase. Background intensity Modulation intensity And the predicted tilt phase shift parameter P of each frame of the input tilt phase shift interferogram. final =(k xf ,k yf ,d f ), where k xf k represents the predicted slope gradient in the x-direction. yf d represents the predicted slope gradient in the y-direction. f This indicates the predicted piston term.
[0035] S4: Using the training dataset established in S2, train the deep learning interferogram phase demodulation network constructed in S3 using a self-supervised training method driven by a physical model, and update the network parameters using gradient descent. For example... Figure 3 As shown, S4 specifically includes the following sub-steps: (4.1) Input the training dataset into the deep learning interferogram phase demodulation network to obtain the predicted package phase. Background intensity Modulation intensity The tilt phase shift parameters are used to fit and generate the predicted M-frame interferogram. ... (4.2) Using the predicted interferogram intensity and the input intensity (i.e., the actual intensity), as well as the initial tilt phase shift parameter and the predicted tilt phase shift parameter, a self-supervised loss function Loss is constructed: (4.3) Using the Adam optimizer with a learning rate of 0.001, gradient descent is applied to the loss function Loss to update the deep learning interferogram phase demodulation network.
[0036] (4.4) Repeat steps (4.1) to (4.4) until the loss function reaches the threshold or the maximum number of training iterations is reached. Training is then complete, and the trained deep learning interferogram phase demodulation network is obtained.
[0037] S5: As Figure 4 As shown, a multi-frame random tilt phase-shift interferogram of the phase to be measured is input into a trained deep learning interferogram phase demodulation network to obtain the wrapped phase, and then the unwrapping algorithm is used to obtain the output demodulated phase result.
[0038] The following is a specific embodiment of the method of the present invention to illustrate the technical effects of the present invention.
[0039] S1: Generate 6000 random wavefronts φ(x,y) using the first 36 random Zernike coefficients.
[0040] S2: Set the total number of interferogram frames M=5, use the range of A0 as [0.3, 0.5], the range of B0 as [0.4, 0.5], the ranges of x0 and y0 as [-0.3, 0.3], and the range of D as [0.8, 1.0]; randomly generate 5 sets of tilt phase shift parameters, and the tilt gradient k x1 ~k x5 k y1 ~k y5 The range of all values is [-0.1, 0.1], and the range of piston terms d1~d5 is [0, 2π]. For 6000 random wavefronts, 6000 sets of random tilt phase-shift interferogram sequences {I1, I2, ..., I5} with 5 frames per set are generated accordingly.
[0041] S3: Construct a deep learning interferogram phase demodulation network.
[0042] S4: Train the deep learning interferogram phase demodulation network using a physical model-driven self-supervised training method, calculate the self-supervised loss function, and perform gradient descent training 500 times (i.e., set the maximum number of training times to 500). The model converges, and training is complete.
[0043] S5: Input a new set of 5 randomly tilted phase-shift interferograms to be tested into the deep learning interferogram phase demodulation network trained in S4 to obtain the wrapped phase, and then use the unwrapping algorithm to obtain the output demodulated phase result.
[0044] like Figure 5 As shown, it is a result diagram of this embodiment. Figure 5 (a) is the true value of the phase. Figure 5 (b) shows the phase demodulation result of the interferogram. Figure 5 (c) shows the root mean square error (RMSE). The final RMSE of the phase demodulation result is 0.000351λ, which is below 0.001λ. This indicates that the demodulated phase output by the network is highly consistent with the true value, verifying that the method of this invention can achieve efficient and accurate phase demodulation of multi-frame random tilt phase shift interferograms.
[0045] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.
Claims
1. A method for phase demodulation of tilt phase-shift interferograms based on tilt sensing and self-guided networks, characterized in that, Includes the following steps: S1: Construct the true wavefront phase using random Zernike coefficients; S2: Using the true wavefront phase value, generate a multi-frame sequence of random tilt phase-shift interferograms to establish a training dataset; the random tilt phase-shift interferograms are obtained through random pistons and tilt gradients. S3: Establish a U-shaped deep learning interferogram phase demodulation network, including: a downsampling module, a tilt feature extraction module, a tilt guidance module, and an upsampling module. The network input is a multi-frame sequence of tilt phase-shifted interferograms. The downsampling module and the tilt feature extraction module adaptively extract and decouple tilt-related features based on the inter-frame variation information of the interferograms. The tilt guidance module predicts the initial tilt phase-shift parameters based on the tilt-related features. The upsampling module performs upsampling based on the initial tilt phase-shift parameters and the tilt-related features, and finally outputs multiple decoupled physical quantities, including: the predicted wrapping phase, background intensity, modulation intensity, and the predicted tilt phase-shift parameters of each frame of input tilt phase-shifted interferograms. S4: Using the training dataset, train the deep learning interferogram phase demodulation network using a physical model-driven self-supervised training method, and update the network parameters using gradient descent; S5: Input the multi-frame random tilt phase shift interferogram of the phase to be measured into the trained deep learning interferogram phase demodulation network to obtain the wrapped phase, and then use the unwrapping algorithm to obtain the demodulated phase result.
2. The tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network according to claim 1, characterized in that, S2 is specifically implemented through the following sub-steps: (2.1) Randomly generate background intensity A(x,y) and modulation intensity B(x,y) that conform to a Gaussian distribution; (2.2) Randomly generate the piston and the tilt gradients in the x and y directions, and generate multiple tilt phase shifts δ accordingly. m m=1,2,3,…,M, where M is the total number of frames of the generated interferogram; (2.3) Based on background intensity A(x,y), modulation intensity B(x,y) and tilt phase shift δ m Generate multiple frames of random tilted phase-shift interferograms I m (x,y); Each wavefront phase true value corresponds to a sequence of multiple frames of random tilted phase-shift interferograms, which are denoted as a group. The training dataset is built by combining the groups.
3. The tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network according to claim 2, characterized in that, In step (2.1), the expressions for background intensity A(x,y) and modulation intensity B(x,y) are as follows: In the formula, A0 represents the background peak intensity, B0 represents the modulation peak intensity, x0 represents the beam offset in the x direction, y0 represents the beam offset in the y direction, and D represents the beam width.
4. The tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network according to claim 2, characterized in that, In step (2.2), the tilt phase shift δ m The expression is as follows: In the formula, δ represents the tilt phase shift of the m-th frame, and k xm Let k represent the tilt gradient in the x-direction of the m-th frame. ym d represents the tilt gradient in the y-direction of the m-th frame. m This represents the random piston in the m-th frame.
5. The tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network according to claim 2, characterized in that, In step (2.3), the generated multi-frame random tilt phase-shift interferogram I m The expression for (x,y) is as follows: In the formula, I m (x,y) represents the light intensity of the m-th frame of the interferogram; φ(x,y) is the true value of the wavefront phase.
6. The tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network according to claim 1, characterized in that, Both the downsampling module and the upsampling module include a 3×3 convolution module for adjusting the input and output dimensions, and several basic modules for extracting and mapping information. The number of basic modules for upsampling and downsampling is the same. The corresponding basic modules of the downsampling part and the upsampling part promote information flow and enhance information flow through skip connections. The tilt feature extraction module is integrated between the downsampling module and the upsampling module.
7. The tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network according to claim 6, characterized in that, The basic module consists of two parts. The first part has six layers, namely, an LN layer, a 1×1 convolutional layer, a 3×3 convolutional layer, a BN layer, an activation function ReLU, and a 3×3 convolutional layer. The second part has five layers, namely, an LN layer, a 1×1 convolutional layer, a BN layer, an activation function ReLU, and a 3×3 convolutional layer. The basic module performs residual connections internally. That is, the input and output of the first part are added element-wise and used as the input of the second part; the input of the second part and the output of the second part are added element-wise and used as the output of the entire basic module.
8. The tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network according to claim 1, characterized in that, The internal structure of the tilt feature extraction module includes: a pairwise frame difference unit, used to calculate the difference features of the input feature map in the channel dimension and output the difference feature map to explicitly extract the temporal change information caused by the tilt phase shift; An orientation-sensitive convolutional group contains multiple orientation-selective convolutional kernels that act on the difference feature map to match the tilt effect in any direction in order to extract gradient and edge information in different directions; A spatial attention unit is used to weight inter-frame variation features, highlight areas with significant tilt effects, focus on the most significant changes in the difference feature map, and enhance sensitivity to tilt information.
9. The tilt phase-shift interferogram phase demodulation method based on tilt sensing and self-guided network according to claim 2, characterized in that, S4 specifically includes the following sub-steps: (4.1) Input the training dataset into the deep learning interferogram phase demodulation network to obtain the predicted package phase. Background intensity Modulation intensity Tilt phase shift parameters Based on this, a multi-frame interferogram is generated through fitting: In the formula, This represents the predicted light intensity of the m-th frame of the interferogram. The tilt phase shift of the predicted m-th frame interferogram; (4.2) Using the predicted light intensity and input light intensity of the interferogram, as well as the initial tilt phase shift parameter and the predicted tilt phase shift parameter, a self-supervised loss function Loss is constructed, as shown in the following expression: In the formula, P tilt P is the initial tilt phase shift parameter. final To predict tilt phase shift parameters; (4.3) Using the Adam optimizer with a learning rate of 0.001, gradient descent is applied to the loss function Loss to update the deep learning interferogram phase demodulation network; (4.4) Repeat steps (4.1) to (4.4) until the loss function reaches the threshold or the maximum number of training iterations is reached. Training ends and the trained deep learning interferogram phase demodulation network is obtained.