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

Abstract

The invention discloses a two-frame interferogram phase demodulation method based on model-driven deep learning, and the method comprises the steps: constructing a model-driven deep learning training mode through employing a physical model of an interferogram; constructing and training a deep learning network, inputting two frames of interference patterns of any phase shift, and outputting a wavefront phase, background intensity, modulation intensity and phase shift amount; after training is completed, two frames of interferograms of any phase shift are input into the network to obtain an output wavefront phase, and accurate interferogram phase demodulation is realized. Compared with a conventional data-driven deep learning demodulation method, the method provided by the invention makes full use of physical information, and has high accuracy, robustness and interpretability.

Description

Technical Field

[0001] The present invention relates to the field of optical measurement and wavefront detection, and particularly to a two-frame interferogram phase demodulation method based on model-driven deep learning. Background Art

[0002] Optical interferometry is a super-precise measurement method, widely used in fields such as wavefront detection, object topography measurement, and computer-generated holography. Its basic principle is to form interference fringes through the interference of a wavefront to be measured and a reference wavefront. The wavefront to be measured carries the physical information to be measured, and 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 of the interference light intensity is usually:

[0003]

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

[0005] Traditional interferometric phase demodulation methods mainly rely on phase-shifting interferometry techniques, such as four-step or five-step phase-shifting methods. By performing calculations such as subtraction and arctangent on the interferograms, the wrapped phase is obtained, and further, the true wavefront phase information is restored through unwrapping techniques. However, this technique usually requires a high-precision phase shifter, with high equipment costs and complex operations. In addition, the phase-shifting interferometry method is usually applicable to static or quasi-static scenarios because the measured information changes during the phase shift in a dynamic environment. Therefore, it cannot meet the requirements for dynamic objects or rapidly changing scenarios. To address this challenge, in recent years, researchers have proposed some phase demodulation methods based on single-frame or two-frame interferograms. These methods can achieve more precise phase demodulation in a dynamic environment by reducing the required number of phase shift steps and effectively balance measurement accuracy and computational efficiency. Compared with the single-frame interferogram method, the two-frame interferogram method can not only avoid the problem of sign ambiguity but also obtain more effective information to improve accuracy, with strong practicality, and is a method that balances the number of phase shift steps and accuracy. Therefore, the phase demodulation method based on two-frame interferograms has become an important direction in phase demodulation research.

[0006] However, existing two-frame interferogram phase demodulation methods still have certain limitations. For example, classical non-deep learning methods (such as self-adjusting methods, regularized optical flow methods, and Gram-Schmidt orthogonalization methods) experience a significant decline in performance and have limited accuracy when the noise is strong, the interference fringes are complex, or the measurement environment changes. In addition, these methods usually require complex preprocessing operations on the interferogram, such as filtering, which increases the computational complexity. In recent years, with the rapid development of deep learning technology, two-frame interferogram phase demodulation methods based on deep learning have gradually emerged. These methods can effectively demodulate the phase of the interferogram by training on a large number of interferogram-phase data pairs and leveraging the powerful non-linear fitting ability of deep learning. The deep learning model can adaptively learn complex interference fringe patterns and, to a certain extent, handle dynamically changing measurement data.

[0007] However, deep learning methods still rely on a large amount of labeled data, and the training process requires a vast amount of sample data, which makes it difficult to train and promote the model. Especially when there are significant differences between the interference fringe pattern and the training dataset, the generalization ability and accuracy of the model may be significantly affected. Moreover, it does not fully utilize the physical model of the interferogram and has poor interpretability. Summary of the Invention

[0008] Aiming at the deficiencies of the existing technology, the present invention proposes a two-frame interferogram phase demodulation method based on model-driven deep learning. The specific technical solutions are as follows:

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

[0010] S1: Use random Zernike coefficients to construct the true value of the wavefront phase;

[0011] S2: Use the true value of the wavefront phase to generate random phase-shifted two-frame interferogram data pairs and 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 the random phase-shifted two-frame interferogram data pairs, and the output is the predicted demodulated phase, phase shift amount, background intensity, and modulation intensity;

[0013] S4: Use the training dataset established in S2 to 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-frame interferogram with random phase shift of the phase to be measured into the trained deep learning interferogram phase demodulation network to obtain the output high-precision demodulated phase result.

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

[0016]

[0017] a = [a 1 , a 2 ,..., a j

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

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

[0020] (2.1) Randomly generate the background intensity A(x, y), the modulation intensity B(x, y), and the phase shift amount δ, and the range of δ is (0, 2π):

[0021]

[0022]

[0023] where A 0 represents the background peak intensity, x 0 and y 0 represent the offsets of the light spot in the x and y directions, d represents the beam width, and B 0 represents the modulation peak intensity;

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

[0025]

[0026] where I 1 (x, y) represents the light intensity of the first-frame interferogram, and I 2 (x, y) represents the light intensity of the second-frame interferogram with a phase shift of δ.

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

[0028] ​The information flow is promoted and the information stream is enhanced through skip connections between the corresponding basic blocks of the downsampling part and the upsampling part;

[0029] Each of the basic blocks includes two parts. The first part has five layers, which are, in sequence, the LN layer, the 1×1 convolutional layer, the 3×3 convolutional layer, the activation function ReLU, and the 3×3 convolutional layer. The second part has four layers, which are, in sequence, the LN layer, the 1×1 convolutional layer, the activation function ReLU, and the 3×3 convolutional layer. Residual connections are made inside the basic block, that is, after the input and output of the first part are added element-wise, the result is used as the input of the second part. After the input of the second part and the output of the second part are added element-wise, the result is used as the output of the entire basic block;

[0030] The input of the deep learning interferogram phase demodulation network is two channels, and the output is four channels. The first three channels directly output pictures, which are the predicted demodulated phase, background intensity, and modulation intensity respectively. The output of the fourth channel is the predicted phase shift amount. By averaging the output values of the fourth channel, the predicted phase shift amount is obtained.

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

[0032] (4.1) Generate a predicted first-frame interferogram by fitting according to the predicted demodulated phase background intensity modulation intensity Generate a predicted second-frame interferogram by fitting according to the predicted demodulated phase According to the predicted demodulated phase background intensity modulation intensity phase shift amount Generate a predicted second-frame interferogram 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) Use the Adam optimizer with a learning rate of 0.001 to perform gradient descent on the loss function Loss and update the deep learning network;

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

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

[0039] The two-frame interferogram phase demodulation method based on model-driven deep learning of the present invention, different from traditional data-driven training, adopts a model-driven training method in this method. The deep learning network is regarded as a part of the interference physical process, and a loss function is constructed through self-supervised model driving. The deep learning model plays a role in accelerating iterative convergence, thus avoiding the problems of poor generalization and limited accuracy of the data-driven method, and can achieve precise interferogram demodulation with an error less than 0.001λ, which is applicable to high-precision and high-dynamic optical interference detection and has high robustness. Description of the Drawings

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

[0041] Figure 2 It is a structural diagram of the network.

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

[0043] Figure 4 It is a diagram of the interferogram demodulation result. Among them, (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 Embodiment

[0044] The present invention will be described in detail below according to the drawings and preferred embodiments. The purpose and effect of the present invention will become clearer. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

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

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

[0047]

[0048] a = [a 1 , a 2 ,..., a j

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

[0050] ​S2: Generate a pair of interferogram data with random phase shifts using the true wavefront phase, and establish a training dataset. S2 specifically includes the following sub-steps:

[0051] (2.1) Randomly generate the background intensity A(x, y), the modulation intensity B(x, y), and the phase shift amount δ, where the range of δ is (0, 2π). Since the interference light intensity is generally Gaussian-distributed, both the background intensity A(x, y) and the modulation intensity B(x, y) conform to the Gaussian distribution, and the expressions are:

[0052]

[0053] where A 0 represents the background peak intensity, x 0 and y 0 represent the offsets of the light spot in the x and y directions, d represents the beam width, and B 0 represents the modulation peak intensity;

[0054] (2.2) Generate two frames of random interferograms based on A(x, y), B(x, y), and δ. We assume that the phase shift amount of the first frame is 0. If it is actually not 0, it is equivalent to adding a constant term to the phase, which does not affect the measurement result. The expression for the light intensity I 1 (x, y) of the first frame interferogram is

[0055]

[0056] Correspondingly, the expression for the light intensity I 2 (x, y) of the second frame interferogram after a phase shift of δ is

[0057]

[0058] Thus, the training set consists of two frames of interferograms with random phase shifts, where the first frame interferogram is I 1 (x, y), and the second frame interferogram is I 2 (x, y). Here, our training set does not contain separate wavefront true value labels, so there are no paired inputs and labels for supervision. Therefore, our training is essentially a model-driven task rather than a data-driven one.

[0059] S3: As Figure 2 shown, establish a U-shaped deep learning interferogram phase demodulation network. The input is two frames of interferograms with random phase shifts I 1 (x, y) and I 2 (x, y), and the output is the predicted background intensity the predicted modulation intensity the predicted phase the predicted phase shift amount The overall image restoration neural network has a U-shaped structure, including a downsampling part and an upsampling part; both the downsampling part and the upsampling part include a 3×3 convolution module to adjust the dimensions of the input and output, and four basic blocks to extract and map information. The corresponding basic blocks between the downsampling part and the upsampling part are connected by skip connections to promote information flow and enhance the information stream; the basic block includes two parts. The first part has five layers, which are the LN layer, 1×1 convolution layer, 3×3 convolution layer, activation function ReLU, and 3×3 convolution layer in sequence; the second part has four layers, which are the LN layer, 1×1 convolution layer, activation function ReLU, and 3×3 convolution layer in sequence; there is a residual connection inside the basic block, that is, after the input and output of the first part are added element-wise, it is used as the input of the second part; after the input of the second part and the output of the second part are added element-wise, it is used as the output of the entire basic block.

[0060] The input of the network has two channels, and the output has four channels. The output of the fourth channel is the predicted phase shift amount, which should be a constant. Therefore, the first three channels directly output the picture as the prediction result, and the output values of the fourth channel are averaged to obtain the predicted phase shift amount

[0061] S4: Using the training data set established in S2, train the deep learning interferogram phase demodulation network in a self-supervised training manner using the model-driven method, and update the network parameters using gradient descent; as Figure 3 shown, S4 specifically includes the following sub-steps:

[0062] (4.1) According to the predicted demodulated phase background intensity modulation intensity fit and generate the predicted first-frame interferogram According to the predicted demodulated phase background intensity modulation intensity phase shift amount fit and generate the predicted second-frame interferogram

[0063]

[0064] (4.2) Use the predicted light intensity and the input light intensity to construct a self-supervised loss function Loss

[0065]

[0066] (4.3) Use the Adam optimizer with a learning rate of 0.001 to perform gradient descent on the loss function Loss and update the deep learning network;

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

[0068] S5: As Figure 3 shown, for the two-frame interferograms I r1 (x, y) and I r2 (x, y) with random phase shifts to be actually measured, input them into the trained network. At this time, we only need to obtain the predicted phase to achieve accurate phase demodulation of the interferogram.

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

[0070] S1: Use the first 36 random Zernike polynomials to generate 5000 random wavefronts

[0071] S2: For the 5000 random wavefronts, use A 0 in the range of [0.5, 0.6], B 0 in the range of [0.3, 0.4], x 0 and y 0 in the range of [-0.2, 0.2], and d in the range of [0.9, 1.1]. Calculate the simulated first-frame interferogram I 1 (x, y) and the simulated second-frame interferogram I 2 (x, y) respectively, so as to obtain 5000 pairs of two-frame interferogram data with random phase shifts.

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

[0073] S4: Use the model-driven method for training, calculate the self-supervised loss function, and perform gradient descent training 300 times until the model converges and the training is completed.

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

[0075] As Figure 4 shown, it is the result diagram of this embodiment. (a) is the input first-frame interferogram, (b) is the input second-frame interferogram, (c) is the interferogram phase demodulation result, and (d) is the phase true value. The root mean square error between the finally obtained phase demodulation result and the true value is below 0.001λ, and it can be seen that the present invention can achieve accurate phase demodulation of two-frame interferograms with arbitrary phase shifts.

[0076] Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not used 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. Any modifications, equivalent substitutions, etc. made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims

1. A two-frame interferogram phase demodulation method based on model-driven deep learning, characterized in that: The following steps are involved: S1: Use random Zernike coefficients to construct the true value of the wavefront phase; S2: Using the true value of the wavefront phase, generate two-frame interference pattern data pairs with random phase shifts to establish a training data set; S3: Establishing a U-shaped deep learning interferogram phase demodulation network, including a downsampling part and an upsampling part, wherein the input of the deep learning interferogram phase demodulation network is a pair of two randomly phase-shifted interferogram data frames, and the output is a predicted demodulation phase, phase shift amount, background intensity, and modulation intensity; S4: Using the training data set established in S2, the deep learning interferogram phase demodulation network is trained in a self-supervised training mode using a model-driven method, and the network parameters are updated using gradient descent; S5: Input the two-frame interference pattern of the random phase shift of the phase to be measured into the trained deep learning interference pattern phase demodulation network to obtain the output high-precision demodulation phase result.

2. The two-frame interference pattern phase demodulation method based on model-driven deep learning according to claim 1 is characterized in that: The step S1 is specifically expressed as follows: <h2 style=";text-align:left;direction:ltr">a=[a1,a2,...,a<h2 style=";text-align:left;direction:ltr"> j <h2 style=";text-align:left;direction:ltr"> ] Among them, (x, y) is the coordinate of the interference pattern in the unit circle, a j is the Zernike coefficient, Z j (x, y) is the Zernike polynomial, and a is a vector composed of all Zernike coefficients, which can uniquely represent the wave surface.

3. The two-frame interference pattern phase demodulation method based on model-driven deep learning according to claim 1 is characterized in that: The 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 the range of δ is (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, two frames of random interference patterns are generated: Wherein, I1(x, y) represents the intensity of the interference pattern of the first frame, and I2(x, y) represents the intensity of the interference pattern of the second frame after the δ phase shift.

4. The two-frame interference pattern phase demodulation method based on model-driven deep learning according to claim 1, characterized in that: The downsampling and upsampling parts of the deep learning interferogram phase demodulation network each include a 3×3 convolution module for input and output dimension adjustment, and four basic blocks for extracting and mapping information; The corresponding basic blocks of the down-sampling part and the up-sampling part are connected by skip connections to promote information flow and enhance information flow; Each of the basic blocks includes two parts, the first part has five layers, which are LN layer, 1×1 convolution layer, 3×3 convolution layer, activation function ReLU and 3×3 convolution layer in sequence; the second part has four layers, which are LN layer, 1×1 convolution layer, activation function ReLU and 3×3 convolution layer in sequence; residual connection is performed inside the basic block, that is, the input and output of the first part are added at the element level and used as the input of the second part; the input and output of the second part are added at the element level and used as the output of the entire basic block; The input of the deep learning interference pattern phase demodulation network is two channels, and the output is four channels. The first three channels directly output images, which are the predicted demodulation phase, background intensity, and modulation intensity respectively; the output of the fourth channel is the predicted phase shift, and the output values ​​of the fourth channel are averaged to obtain the predicted phase shift.

5. The two-frame interference pattern phase demodulation method based on model-driven deep learning according to claim 1, characterized in that: The step S4 specifically includes the following sub-steps: (4.1) According to the predicted demodulation phase Background intensity Modulation Intensity Fitting generates the predicted first frame interferogram According to the predicted demodulation phase Background intensity Modulation Intensity Phase shift Fitting generates the predicted second frame interferogram (4.2) Use the predicted light intensity and input light intensity to construct the self-supervised loss function Loss (4.3) Use the Adam optimizer with a learning rate of 0.001 to perform gradient descent on the loss function Loss and update the deep learning network; (4.4) Repeat steps (4.1) to (4.4) until the training is completed to obtain the final deep learning interferogram phase demodulation network.

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