A two-frame interferogram phase demodulation method based on model-driven deep learning

Abstract

The application discloses a two-frame interferogram phase demodulation method based on model-driven deep learning, which utilizes a physical model of an interferogram to construct a model-driven deep learning training mode; a deep learning network is constructed and trained, two frames of arbitrary phase-shifted interferograms are input, and a wavefront phase, a background intensity, a modulation intensity and a phase shift amount are output; after the training is completed, the wavefront phase output can be obtained by inputting two frames of arbitrary phase-shifted interferograms into the network, and accurate interferogram phase demodulation is realized. Compared with a previous data-driven deep learning demodulation method, the application fully utilizes physical information and has high accuracy, robustness and interpretability.

Description

Technical Field

[0001] This invention relates to the fields of optical measurement and wavefront detection, and in particular to a two-frame interferogram phase demodulation method based on model-driven deep learning. 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:

[0003]

[0004] Where (x, y) are the coordinates of the interference plane, I i (x,y) represents the i-th recorded interferogram, A(x,y) represents the background intensity, and B(x,y) represents the modulation intensity. For the wavefront to be measured, δ i Let be the phase shift corresponding to the i-th interferogram.

[0005] Traditional interferometric phase demodulation methods primarily rely on phase-shifting interferometry, such as four-step or five-step phase-shifting methods. These methods obtain the wrapped phase by performing subtraction and arctangent calculations on the interferogram, and then use unwrapping techniques to reconstruct the true wavefront phase information. However, this technique typically requires high-precision phase shifters, resulting in high equipment costs and complex operation. Furthermore, phase-shifting interferometry is generally suitable for static or quasi-static scenarios because the measurement information changes during phase shifts in dynamic environments, making it unsuitable for dynamic objects or rapidly changing scenes. To address this challenge, researchers have recently proposed phase demodulation methods based on single-frame or two-frame interferograms. These methods reduce the required number of phase shift steps, enabling more accurate phase demodulation in dynamic environments and effectively balancing measurement accuracy and computational efficiency. Compared to single-frame interferogram methods, two-frame interferogram methods not only avoid symbol ambiguity but also obtain more effective information, thus improving accuracy. They are highly practical and represent a method that balances the number of phase shift steps with accuracy. Therefore, phase demodulation methods based on two-frame interferograms have become an important direction in phase demodulation research.

[0006] Despite this, existing two-frame interferogram phase demodulation methods still have certain limitations. For example, classical non-deep learning methods (such as self-adjustment methods, regularized optical flow methods, and Gram-Schmidt orthogonalization methods) show significant performance degradation and limited accuracy when there is strong noise, complex interference fringes, or changes in the measurement environment. Furthermore, these methods typically require complex preprocessing operations on the interferogram, such as filtering, which increases computational complexity. In recent years, with the rapid development of deep learning technology, deep learning-based two-frame interferogram phase demodulation methods have gradually emerged. These methods, trained on a large number of interferogram and phase data pairs, leverage the powerful nonlinear fitting capabilities of deep learning to effectively demodulate the phase of the interferogram. Deep learning models can adaptively learn complex interference fringe patterns and, to some extent, cope with dynamically changing measurement data.

[0007] However, deep learning methods still rely heavily on labeled data, and the training process requires massive amounts of sample data, which makes model training and generalization difficult. Especially when the interference fringe pattern differs significantly from the training dataset, the model's generalization ability and accuracy can be significantly affected. Furthermore, it does not fully utilize the physical model of the interferogram, resulting in poor interpretability. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention proposes a two-frame interferogram phase demodulation method based on model-driven deep learning. The specific technical solution is as follows:

[0009] A two-frame interferogram phase demodulation method based on model-driven deep learning includes the following steps:

[0010] S1: Construct the true wavefront phase using random Zernike coefficients;

[0011] S2: Using the true value of the wavefront phase, generate random phase-shifted two-frame interferogram data pairs to establish a training dataset;

[0012] S3: Establish a U-shaped deep learning interferogram phase demodulation network, including a downsampling part and an upsampling part. The input of the deep learning interferogram phase demodulation network is a pair of randomly phase-shifted interferogram data, and the output is the predicted demodulation phase, phase shift, background intensity, and modulation intensity.

[0013] S4: Using the training dataset established in S2, train the deep learning interferogram phase demodulation network using a model-driven, self-supervised training method, and update the network parameters using gradient descent.

[0014] S5: Input the two frames of random phase-shifted interferograms of the phase to be measured into the trained deep learning interferogram phase demodulation network to obtain the high-precision demodulated phase output.

[0015] Further, step S1 is specifically expressed as follows:

[0016]

[0017] a = [a1, a2, ..., a j ]

[0018] Where (x,y) are the coordinates of the interferogram within the unit circle, and a j Z is the Zernike coefficient. j (x,y) is a Zernike polynomial, and a is a vector consisting of all Zernike coefficients, which can uniquely represent the wavefront.

[0019] Further, step S2 includes the following sub-steps:

[0020] (2.1) Randomly generate background intensity A(x,y), modulation intensity B(x,y), and phase shift δ, where δ ranges from (0,2π):

[0021]

[0022]

[0023] Where A0 represents the background peak intensity, x0 and y0 represent the offset of the light spot in the x and y directions, d represents the beam width, and B0 represents the modulation peak intensity;

[0024] (2.2) Based on A(x,y), B(x,y) and δ, generate two frames of random interferograms:

[0025]

[0026] Where I1(x,y) represents the light intensity of the first frame of the interferogram, and I2(x,y) represents the light intensity of the second frame of the interferogram after the δ phase shift.

[0027] Furthermore, both the downsampling and upsampling parts of the deep learning interferogram phase demodulation network include a 3×3 convolutional module for adjusting the input and output dimensions, and four basic blocks for extracting and mapping information.

[0028] The corresponding base blocks of the downsampling and upsampling parts are connected by jump connections to promote information flow and enhance information flow.

[0029] Each base block comprises two parts. The first part consists of five layers: an LN layer, a 1×1 convolutional layer, a 3×3 convolutional layer, a ReLU activation function, and a 3×3 convolutional layer. The second part consists of four layers: an LN layer, a 1×1 convolutional layer, a ReLU activation function, and a 3×3 convolutional layer. Residual connections are performed within each base block. That is, the input and output of the first part are added element-wise to obtain the input of the second part. The input and output of the second part are added element-wise to obtain the output of the entire base block.

[0030] The deep learning interferogram phase demodulation network has two input channels and four output channels. The first three channels directly output the image, which represents the predicted demodulated phase, background intensity, and modulation intensity, respectively. The fourth channel outputs the predicted phase shift. The predicted phase shift is obtained by averaging the output values ​​of the fourth channel.

[0031] Furthermore, step S4 specifically includes the following sub-steps:

[0032] (4.1) Based on the predicted demodulation phase Background intensity Modulation intensity The first frame of the predicted interferogram is generated by fitting the data. Based on the predicted demodulation phase Background intensity Modulation intensity Phase shift The second frame interferogram of the prediction is generated by fitting.

[0033]

[0034] (4.2) Construct a self-supervised loss function Loss using the predicted light intensity and the input light intensity.

[0035]

[0036] (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 network;

[0037] (4.4) Repeat steps (4.1) to (4.4) until training is complete, and obtain the final deep learning interferogram phase demodulation network.

[0038] The beneficial effects of this invention are as follows:

[0039] The two-frame interferogram phase demodulation method based on model-driven deep learning of the present invention differs from traditional data-driven training. In this method, a model-driven training approach is adopted, incorporating the deep learning network as part of the physical process of interference. The loss function is constructed through self-supervised model driving, and the deep learning model plays a role in accelerating iterative convergence. This avoids the problems of poor generalization and limited accuracy of data-driven methods, and can achieve accurate interferogram demodulation with an error of less than 0.001λ. It is suitable for high-precision and high-dynamic optical interferometry detection and has high robustness. Attached Figure Description

[0040] Figure 1 This is a flowchart of the two-frame interferogram phase demodulation method based on model-driven deep learning according to the present invention.

[0041] Figure 2 This is a diagram of the network structure.

[0042] Figure 3 This is a schematic diagram of the model-driven training and testing process.

[0043] Figure 4 The diagram shows the demodulation results of the interferogram, where (a) is the first frame of the input interferogram, (b) is the second frame of the input interferogram, (c) is the true phase value, and (d) is the demodulated phase output by the network. Detailed Implementation

[0044] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0045] like Figure 1 As shown, a two-frame interferogram phase demodulation method based on model-driven deep learning includes the following steps:

[0046] S1: Using random Zernike coefficients, the true value of the wavefront phase is constructed, which can be expressed as:

[0047]

[0048] a = [a1, a2, ..., a j ]

[0049] Where (x,y) are the coordinates of the interferogram within the unit circle, and a j Z is the Zernike coefficient. j (x,y) is a Zernike polynomial, and a is a vector consisting of all Zernike coefficients, which can uniquely represent the wavefront.

[0050] S2: Using the true wavefront phase value, generate random phase-shifted two-frame interferogram data pairs to establish a training dataset; S2 specifically includes the following sub-steps:

[0051] (2.1) Randomly generate background intensity A(x,y), modulation intensity B(x,y), and phase shift δ, where δ ranges from (0, 2π). Since interference light intensity generally follows a Gaussian distribution, both background intensity A(x,y) and modulation intensity B(x,y) conform to a Gaussian distribution, expressed as:

[0052]

[0053] Where A0 represents the background peak intensity, x0 and y0 represent the offset of the light spot in the x and y directions, d represents the beam width, and B0 represents the modulation peak intensity;

[0054] (2.2) Based on A(x,y), B(x,y), and δ, two random interferograms are generated. We assume the phase shift of the first frame is 0. If it is not actually 0, it is equivalent to adding a constant term to the phase, which does not affect the measurement results. The expression for the light intensity I1(x,y) of the first frame interferogram is:

[0055]

[0056] Correspondingly, the expression for the light intensity I2(x,y) of the second frame interferogram after the δ phase shift is:

[0057]

[0058] Therefore, the training set consists of two randomly phase-shifted interferograms, where the first interferogram is I1(x,y) and the second interferogram is I2(x,y). Since our training set does not contain individual wavefront ground truth labels, there are no paired inputs and labels for supervision. Thus, our training is essentially a model-driven process, rather than a data-driven one.

[0059] S3: As Figure 2 As shown, a U-shaped deep learning interferogram phase demodulation network is established. The input is two frames of randomly phase-shifted interferograms I1(x,y) and I2(x,y), and the output is the predicted background intensity. Predicted modulation intensity Predicted phase Predicted phase shift The image restoration neural network has a U-shaped structure, including a downsampling part and an upsampling part. Both the downsampling and upsampling parts include a 3×3 convolutional module for adjusting the input and output dimensions, and four basic blocks for extracting and mapping information. The corresponding basic blocks in the downsampling and upsampling parts facilitate information flow and enhance information transmission through skip connections. Each basic block consists of two parts: the first part has five layers, namely an LN layer, a 1×1 convolutional layer, a 3×3 convolutional layer, a ReLU activation function, and another 3×3 convolutional layer; the second part has four layers, namely an LN layer, a 1×1 convolutional layer, a ReLU activation function, and another 3×3 convolutional layer. Residual connections are performed within each basic block, meaning the input and output of the first part are summed element-wise to serve as the input of the second part; the input of the second part and the output of the second part are summed element-wise to serve as the output of the entire basic block.

[0060] The network takes two input channels and outputs four output channels, where the fourth channel outputs the predicted phase shift, which should be a constant. Therefore, the first three channels directly output the image as the prediction result, while the output value of the fourth channel is averaged to obtain the predicted phase shift.

[0061] S4: Using the training dataset established in S2, a deep learning interferogram phase demodulation network is trained using a model-driven, self-supervised training method, and the network parameters are updated using gradient descent; for example... Figure 3 As shown, S4 specifically includes the following sub-steps:

[0062] (4.1) Based on the predicted demodulation phase Background intensity Modulation intensity The first frame of the predicted interferogram is generated by fitting the data. Based on the predicted demodulation phase Background intensity Modulation intensity Phase shift The second frame interferogram of the prediction is generated by fitting.

[0063]

[0064] (4.2) Construct a self-supervised loss function Loss using the predicted light intensity and the input light intensity.

[0065]

[0066] (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 network;

[0067] (4.4) Repeat steps (4.1) to (4.4) until training is complete, and obtain the final deep learning interferogram phase demodulation network.

[0068] S5: As Figure 3 As shown, for the two-frame interferogram I of the actual random phase shift to be measured r1 (x,y) and I r2 Given (x, y), input it into the trained network. Then we only need to obtain the predicted phase. It can achieve precise phase demodulation of interferograms.

[0069] The following is a specific embodiment of the method of the present invention to illustrate the technical effects of the present invention.

[0070] S1: Generate 5000 random wavefronts using the first 36 random Zernike polynomials.

[0071] S2: Using 5000 random wavefronts, with A0 ranging from [0.5, 0.6], B0 from [0.3, 0.4], x0 and y0 from [-0.2, 0.2], and d from [0.9, 1.1], the simulated first frame interferogram I1(x, y) and the simulated second frame interferogram I2(x, y) are calculated respectively, thus obtaining two frames of interferogram data for 5000 pairs of random phase shifts.

[0072] S3: Construct a U-shaped deep learning network.

[0073] S4: Use a model-driven approach to train, calculate the self-supervised loss function, and perform gradient descent training 300 times. The model converges, and training is complete.

[0074] S5: Input the two random phase-shifted interferograms of unknown phase into the deep learning network to obtain the demodulated phase of the output.

[0075] like Figure 4 The diagram shows the results of this embodiment. (a) is the first frame of the input interferogram, (b) is the second frame of the input interferogram, (c) is the phase demodulation result of the interferogram, and (d) is the true phase value. The root mean square error between the final obtained phase demodulation result and the true value is below 0.001λ, which shows that the present invention can achieve accurate phase demodulation of two frames of arbitrary phase-shifted interferograms.

[0076] 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 two-frame interferogram phase demodulation method based on model-driven deep learning, characterized in that, Includes the following steps: S1: Construct the true wavefront phase using random Zernike coefficients; S2: Using the true value of the wavefront phase, generate random phase-shifted two-frame interferogram data pairs to establish a training dataset; S3: Establish a U-shaped deep learning interferogram phase demodulation network, including a downsampling part and an upsampling part. The input of the deep learning interferogram phase demodulation network is a pair of randomly phase-shifted interferogram data, and the output is the predicted demodulation phase, phase shift, background intensity, and modulation intensity. S4: Using the training dataset established in S2, train the deep learning interferogram phase demodulation network using a model-driven, self-supervised training method, and update the network parameters using gradient descent. S5: Input the two frames of random phase-shifted interferograms of the phase to be measured into the trained deep learning interferogram phase demodulation network to obtain the high-precision demodulated phase output. The downsampling and upsampling parts of the deep learning interferogram phase demodulation network each include a 3×3 convolutional module for adjusting the input and output dimensions, and four basic blocks for extracting and mapping information. The corresponding base blocks of the downsampling and upsampling parts are connected by jump connections to promote information flow and enhance information flow. Each base block comprises two parts. The first part consists of five layers: an LN layer, a 1×1 convolutional layer, a 3×3 convolutional layer, a ReLU activation function, and a 3×3 convolutional layer. The second part consists of four layers: an LN layer, a 1×1 convolutional layer, a ReLU activation function, and a 3×3 convolutional layer. Residual connections are performed within each base block. That is, the input and output of the first part are added element-wise to obtain the input of the second part. The input and output of the second part are added element-wise to obtain the output of the entire base block. The deep learning interferogram phase demodulation network has two input channels and four output channels. The first three channels directly output the image, which represents the predicted demodulated phase, background intensity, and modulation intensity, respectively. The fourth channel outputs the predicted phase shift. The predicted phase shift is obtained by averaging the output values ​​of the fourth channel.

2. The two-frame interferogram phase demodulation method based on model-driven deep learning according to claim 1, characterized in that, Step S1 is specifically represented as follows: a=[a1,a2,…,a j ] Where (x,y) are the coordinates of the interferogram within the unit circle, and a j Z is the Zernike coefficient. j (x,y) is a Zernike polynomial, and a is a vector consisting of all Zernike coefficients, which can uniquely represent the wavefront.

3. The two-frame interferogram phase demodulation method based on model-driven deep learning according to claim 1, characterized in that, Step S2 includes the following sub-steps: (2.1) Randomly generate background intensity A(x,y), modulation intensity B(x,y), and phase shift δ, where δ ranges from (0,2π): Where A0 represents the background peak intensity, x0 and y0 represent the offset of the light spot in the x and y directions, d represents the beam width, and B0 represents the modulation peak intensity; (2.2) Based on A(x,y), B(x,y) and δ, generate two frames of random interferograms: Where I1(x,y) represents the light intensity of the first frame of the interferogram, and I2(x,y) represents the light intensity of the second frame of the interferogram after the δ phase shift.

4. The two-frame interferogram phase demodulation method based on model-driven deep learning according to claim 1, characterized in that, Step S4 specifically includes the following sub-steps: (4.1) Based on the predicted demodulation phase Background intensity Modulation intensity The first frame of the predicted interferogram is generated by fitting the data. Based on the predicted demodulation phase Background intensity Modulation intensity Phase shift The second frame interferogram of the prediction is generated by fitting. (4.2) Construct a self-supervised loss function Loss using the predicted light intensity and the input light intensity. (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 network; (4.4) Repeat steps (4.1) to (4.4) until training is complete, and obtain the final deep learning interferogram phase demodulation network.

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