Two-frame interferogram end-to-end phase demodulation method based on course learning

Abstract

The invention discloses a two-frame interferogram end-to-end phase demodulation method based on curriculum learning, and the method comprises the steps: constructing a deep learning interferogram phase demodulation network, and at the first stage, training the network through employing a simple wavefront containing a small number of Zernike polynomial coefficients and interferogram data of uniformly distributed background items and modulation items; in the second stage, training is carried out by using complex wavefront containing more Zernike coefficients in combination with interferogram data of uniformly distributed background items and modulation items, then the background items and the modulation items are replaced with Gaussian distribution, and training in the third stage is carried out; and finally, on the basis of the third stage, noise is added for further training. According to the invention, starting from an interferogram model, a training path from easy to difficult is designed, and end-to-end phase demodulation of two frames of interferograms is realized. Compared with a direct training method, the method has higher accuracy and robustness.

Description

Technical Field

[0001] The present invention relates to the fields of optical measurement and wavefront detection, and in particular to a two-frame interferogram end-to-end phase demodulation method based on curriculum learning. Background Art

[0002] Optical interferometry is an ultra-high-precision measurement method widely used in wavefront detection, object topography measurement, and computational holography. Its basic principle is to form interference fringes through the interference between the wavefront to be measured and the reference wavefront. The wavefront to be measured carries information about the physical quantity to be measured, while the interferogram is the fringe image recorded by a camera or detector. By phase demodulating these interferograms, the physical quantity can be accurately obtained. The expression for the interference light intensity is usually:

[0003]

[0004] Where (x, y) is the interference plane coordinate, I i (x,y) is the i-th interference pattern recorded, A(x,y) is the background intensity, B(x,y) is the modulation intensity, is the wavefront to be measured, δ i is the phase shift corresponding to the i-th interference pattern.

[0005] Traditional interferometric phase demodulation methods usually use phase-shifting interferometry (such as four-step or five-step phase-shifting methods) to extract the wrapped phase by performing operations such as subtraction and inverse tangent on the interference pattern, and further restore the true wavefront information through unwrapping technology. However, phase-shifting interferometry relies on high-precision phase shifters, which are complex to operate and costly. It is only applicable to static or quasi-static scenes and performs poorly in dynamic environments. To meet this challenge, a phase demodulation method based on two-frame interferograms has been proposed in recent years to solve the phase demodulation problem in dynamic environments. Compared with single-frame interferograms, the two-frame interferogram phase demodulation method can provide higher accuracy and effectively avoid the sign ambiguity problem. Therefore, the two-frame interferogram method balances measurement accuracy and computational efficiency to a certain extent and has become an important research direction.

[0006] Despite this, traditional two-frame interferogram phase demodulation methods still have certain limitations. Classic non-deep learning methods, such as self-adjustment methods, regularized optical flow methods, and Gram-Schmidt orthogonalization methods, can achieve phase demodulation with a certain degree of accuracy, but their performance degrades significantly when there is strong noise interference, complex interference fringes, or changes in the measurement environment. In addition, these methods often require preprocessing of the interferogram (such as filtering operations), and the resulting phase is wrapped in the interval [-π, π] and is not continuously distributed, so an additional unwrapping step is required, which increases the computational complexity.

[0007] In recent years, with the rapid development of deep learning technology, deep learning-based two-frame interferogram phase demodulation methods have emerged. Existing deep learning methods mainly fall into three paths: the first is to take advantage of the fact that the similarity between interferograms is greater than the similarity between the interferogram and the wavefront, input two interferogram frames, output an interferogram with a specific phase shift, then use traditional methods to demodulate multiple interferograms and finally unwrap them; the second is to input two interferogram frames, output the wrapped phase, and finally unwrap them; the third is to input two interferogram frames and directly output the unwrapped phase, which is called end-to-end phase demodulation. However, the biggest problem with direct training through traditional deep learning is that the mapping relationship between the phase to be measured and the input interferogram is relatively complex, causing traditional deep learning to easily fall into local optimal points, making it difficult to learn the optimal mapping, which in turn affects demodulation accuracy and generalization ability. Summary of the Invention

[0008] In response to the shortcomings of the existing technology, the present invention proposes a two-frame interferogram end-to-end phase demodulation method based on curriculum learning based on the existing curriculum learning method. For interferogram demodulation, this method arranges a set of effective curriculum learning paths from easy to difficult, gradually expanding the coefficients of Zernike polynomials, the complexity of background and modulation, and noise, so that the deep learning network can more effectively avoid falling into local optimal values ​​and learn the mapping of interferogram to wavefront phase.

[0009] The purpose of the present invention is achieved through the following technical solutions:

[0010] A two-frame interferogram end-to-end phase demodulation method based on curriculum learning, comprising the following steps:

[0011] Step 1: construct the phase true value of the first wavefront and the phase true value of the second wavefront using randomly generated Zernike polynomials, wherein the number of terms of the Zernike polynomial of the first wavefront is less than the number of terms of the Zernike polynomial of the second wavefront;

[0012] Step 2: Generate four sets of two-frame interferogram data pairs from random cameras based on the true phase value to build a data set; the four sets of two-frame interferogram data pairs have different levels of complexity;

[0013] Step 3: Establish a deep learning interferogram phase demodulation network. The input of the network is two frames of randomly phase-shifted interferograms, and the output is the phase obtained by end-to-end demodulation. The deep learning interferogram phase demodulation network includes an encoder, an intermediate demodulation block, a decoder and four connection blocks. The encoder includes a 3×3 convolution block 1, a demodulation block 1, a demodulation block 2, a demodulation block 3 and a demodulation block 4, and the decoder includes a demodulation block 5, a demodulation block 6, a demodulation block 7, a demodulation block 8 and a 3×3 convolution block 2. The demodulation blocks of the encoder and the demodulation blocks of the decoder correspond one to one and are used to extract and map information. The demodulation blocks of the encoder and the corresponding demodulation blocks of the decoder are connected by a connection block to extract multi-scale information. The intermediate demodulation block is used to connect the output of the encoder and the input of the decoder for integrating information flow. The 3×3 convolution block 1 and the 3×3 convolution block 1 are used for input and output dimension adjustment.

[0014] Step 4: Using the course learning method, the deep learning interferogram phase demodulation network is trained in sequence from simple to complex using the dataset constructed in step 2.

[0015] Step 5: Input the two-frame random phase-shifted interferogram to be tested into the deep learning interferogram phase demodulation network trained in the course, and the model outputs the wavefront phase directly demodulated end-to-end.

[0016] Furthermore, the step 1 includes the following sub-steps:

[0017] S1.1: Generate 15 random Zernike coefficients a and 36 random Zernike coefficients b respectively:

[0018] a=[a1,a2,...,a 15 ]

[0019] b=[b1,b2,...,b 36 ]

[0020] S1.2: Generate the true phase value of the first wavefront using 15 random Zernike coefficients a This is a simple wavefront; the true phase value of the second wavefront is generated using 36 random Zernike coefficients b. This is a complex wavefront:

[0021]

[0022] Among them, (x, y) is the rectangular coordinate, Z j (x,y) is a Zernike polynomial.

[0023] Furthermore, in step 2, four sets of two-frame interference pattern data pairs are generated in order from simple to complex, specifically:

[0024] The true phase value of the first wavefront containing only 15 random Zernike coefficients a is used and uniformly distributed background terms and modulation terms, generating the first set of two-frame interference pattern data pairs I 1-1 (x,y),I 2-1 (x,y);

[0025] The phase truth value of the second wavefront is generated using 36 random Zernike coefficients b. and uniformly distributed background terms and modulation terms to generate a second set of two-frame interference pattern data pairs I 1-2 (x,y),I 2-2 (x,y);

[0026] The phase truth value of the second wavefront is generated using 36 random Zernike coefficients b. and Gaussian distribution background term and modulation term, generate the third set of two-frame interference pattern data pair I 1-3 (x,y) and I 2-3 (x,y);

[0027] On the basis of the third set of two-frame interferogram data pairs, random noise is added to generate the fourth set of two-frame interferogram data pairs I 1-4 (x,y) and I 2-4 (x,y).

[0028] Furthermore, each demodulation block of the encoder and decoder has the same structure, consisting of two parts. The first part has five layers, namely, an LN layer, a 1×1 convolutional layer, a ReLU activation function, a 3×3 convolutional layer, and a ReLU activation function; the second part has three layers, namely, an LN layer, a 1×1 convolutional layer, and a ReLU activation function. Residual connections are implemented within the demodulation blocks, meaning that the input and output of the first part are element-wise added together and then used as the input of the second part; the input and output of the second part are element-wise added together and then used as the output of the entire demodulation block.

[0029] Furthermore, each of the connection blocks first enters an LN layer, and the information obtained is divided into two parts. The first part inputs a 1×1 convolution layer, an activation function ReLU, and a 1×1 convolution layer to extract small spatial scale information; the second part inputs a 1×1 convolution layer, an activation function ReLU, and a 5×5 convolution layer to extract large spatial scale information; then the two parts are spliced ​​and input into the activation function ReLU and a 3×3 convolution layer in sequence.

[0030] Furthermore, the connections between the various layers of the deep learning interferogram phase demodulation network are specifically as follows:

[0031] The input of the 3×3 convolution block 1 of the encoder is two frames of interference images, the output of the 3×3 convolution block 1 is used as the input of the demodulation block 1, the output of the demodulation block 1 is also used as the input of the connection block 1 and the demodulation block 2, the output of the demodulation block 2 is also used as the input of the connection block 2 and the demodulation block 3, the output of the demodulation block 3 is also used as the input of the connection block 3 and the demodulation block 4, the output of the demodulation block 4 is also used as the input of the connection block 4 and the intermediate demodulation block, the output of the intermediate demodulation block and the output of the connection block 4 are used as the input of the demodulation block 5, the output of the demodulation block 5 and the output of the connection block 3 are used as the input of the demodulation block 6, the output of the demodulation block 6 and the output of the connection block 2 are used as the input of the demodulation block 7, the output of the demodulation block 7 and the output of the connection block 1 are used as the input of the demodulation block 8, the output of the demodulation block 8 is used as the input of the 3×3 convolution block 2, and the output of the 3×3 convolution block 2 is the phase obtained by end-to-end demodulation, that is, the predicted phase.

[0032] Furthermore, the step 4 specifically includes the following sub-steps:

[0033] S4.1: Use the first two-frame interferogram data pair I constructed in step 2 1-1 (x,y),I 2-1 (x,y) is used as the input of the deep learning interferogram phase demodulation network, and the output is the predicted value The loss function is L1 loss, and the parameters of the deep learning interferogram phase demodulation network are updated by gradient descent method;

[0034] S4.2: Use the second set of two-frame interferogram data constructed in step 2 to 1-2 (x,y),I 2-2 (x,y) is used as the input of the deep learning interferogram phase demodulation network updated in S4.1, and the output is the predicted value The loss function is L1 loss, and the parameters of the deep learning interferogram phase demodulation network are updated again by the gradient descent method;

[0035] S4.3: Use the third set of two-frame interferogram data constructed in step 2 to obtain 1-3 (x,y) and I 2-3 (x,y) is used as the input of the deep learning interferogram phase demodulation network updated in S4.2, and the output is the predicted value The loss function is the root mean square loss, and the parameters of the deep learning interferogram phase demodulation network are updated again by the gradient descent method;

[0036] S4.4: Use the fourth set of two-frame interferogram data constructed in step 2 to obtain 1-4 (x,y) and I 2-4 (x,y) is the input of the deep learning interferogram phase demodulation network updated in S4.3, and the output is the predicted value The loss function is the root mean square loss, and the parameters of the deep learning interferogram phase demodulation network are updated again by the gradient descent method to obtain the final deep learning interferogram phase demodulation network.

[0037] The beneficial effects of the present invention are as follows:

[0038] (1) Different from traditional direct training, the two-frame interferogram end-to-end phase demodulation method based on curriculum learning of the present invention adopts a curriculum learning training method, gradually expanding the coefficients of the Zernike polynomials, the complexity of the background and modulation, and the noise in the constructed dataset. Through the easy-to-difficult training strategy, the human learning process is imitated, so that the deep learning network can more effectively learn the mapping relationship from the interferogram to the end-to-end demodulation phase, thereby avoiding falling into the local minimum and improving the demodulation accuracy.

[0039] (2) The present invention combines course learning and deep learning methods, first training simple samples and then gradually introducing more complex interference patterns to help the model gradually master the demodulation task, so that the model can gradually accumulate knowledge and improve the demodulation accuracy when processing more complex phase demodulation tasks, and finally achieve end-to-end efficient demodulation, thereby significantly improving the performance of two-frame interference pattern phase demodulation, especially in dynamic and noisy environments, and improving the accuracy and robustness of phase demodulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of the end-to-end phase demodulation method of two-frame interference images based on curriculum learning of the present invention.

[0041] Figure 2 A structural diagram of the network.

[0042] Figure 3 Schematic diagram of the training process based on curriculum learning.

[0043] Figure 4 Figure 2 is the interferogram demodulation result diagram, where (a) is the first frame of the input interferogram to be measured, (b) is the second frame of the input interferogram to be measured after random phase shift, (c) is the true phase value, and (d) is the end-to-end demodulated phase output by the network. DETAILED DESCRIPTION

[0044] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments, and the purpose and effects of the present invention will become more apparent. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0045] like Figure 1 As shown, the end-to-end phase demodulation method of two-frame interferograms based on curriculum learning in an embodiment of the present invention includes the following steps:

[0046] Step 1: Use randomly generated Zernike polynomials to construct the phase truth value of the first wavefront and the phase truth value of the second wavefront, respectively, where the number of terms of the Zernike polynomial of the first wavefront is less than the number of terms of the Zernike polynomial of the second wavefront.

[0047] Step 1 includes the following sub-steps:

[0048] S1.1: Generate 15 random Zernike coefficients a and 36 random Zernike coefficients b respectively:

[0049] a=[a1,a2,...,a 15 ]

[0050] b=[b1,b2,...,b 36 ]

[0051] S1.2: Generate the true phase value of the first wavefront using 15 random Zernike coefficients a This is a simple wavefront; the true phase value of the second wavefront is generated using 36 random Zernike coefficients b. This is a complex wavefront:

[0052]

[0053] Among them, (x, y) is the rectangular coordinate, Z j (x,y) is a Zernike polynomial.

[0054] Step 2: Generate four sets of two-frame interferogram data pairs from random cameras based on the true phase value to build a data set; the four sets of two-frame interferogram data pairs have different levels of complexity;

[0055] The general expression for the interference pattern is:

[0056]

[0057] Among them, I(x,y) is the interference pattern, A(x,y) is the modulation term of the interference pattern, and B(x,y) is the background term of the interference pattern. is the true phase value of the wavefront, δ is the phase shift, and n(x,y) is the noise.

[0058] in:

[0059] The true phase value of the first wavefront containing only 15 random Zernike coefficients a is used And the uniformly distributed background term and modulation term generate the first set of two-frame interferogram data pairs:

[0060]

[0061] Among them, A1 and B1 are randomly generated constants.

[0062] The phase truth value of the second wavefront is generated using 36 random Zernike coefficients b. And the uniformly distributed background term and modulation term generate the second set of two-frame interferogram data pairs:

[0063]

[0064] The phase truth value of the second wavefront is generated using 36 random Zernike coefficients b. And Gaussian distribution background and modulation terms, generate the third set of two-frame interference pattern data pairs:

[0065]

[0066] Among them, A2(x,y) and B2(x,y) are two wavefronts of Gaussian distribution, and the expression is:

[0067]

[0068] Where A0 and B0 represent the peak intensity, x0 and y0 represent the offset of the focus point, and d represents the beam width.

[0069] Based on the third set of two-frame interferogram data pairs, random noise is added to generate the fourth set of two-frame interferogram data pairs:

[0070]

[0071] Among them, n1(x,y) and n2(x,y) are random noises.

[0072] Step 3: Establish a deep learning interferogram phase demodulation network. The input of the network is two frames of random phase-shifted interferograms, and the output is the phase obtained by end-to-end demodulation. Figure 2 As shown in the figure, the deep learning interferogram phase demodulation network consists of an encoder, an intermediate demodulation block, a decoder, and four connection blocks. Both the downsampling and upsampling sections include a 3×3 convolutional module for resizing the input and output dimensions, and four demodulation blocks for extracting and mapping information. The corresponding demodulation blocks in the downsampling and upsampling sections are connected by connection blocks to extract multi-scale information, enabling the downsampled high-resolution information to be better combined with the upsampled low-resolution information.

[0073] Specifically, if Figure 2As shown, the encoder includes 3×3 convolution block 1, demodulation block 1, demodulation block 2, demodulation block 3, and demodulation block 4, and the decoder includes demodulation block 5, demodulation block 6, demodulation block 7, demodulation block 8, and 3×3 convolution block 2. These demodulation blocks are all used to extract and map information. The demodulation blocks of the encoder and the demodulation blocks of the decoder correspond one to one, and are connected in the middle through connection blocks. That is, demodulation block 1 is connected to demodulation block 8 through connection block 1, demodulation block 2 is connected to demodulation block 7 through connection block 2, demodulation block 3 is connected to demodulation block 6 through connection block 3, and demodulation block 4 is connected to demodulation block 5 through connection block 3; the input of the encoder's 3×3 convolution block 1 is two frames of interference patterns, the output of the 3×3 convolution block 1 is the input of demodulation block 1, the output of demodulation block 1 is simultaneously the input of connection block 1 and demodulation block 2, the output of demodulation block 2 is simultaneously the input of connection block 2 and demodulation block 3, and the output of demodulation block 3 is simultaneously the input of connection block 3 and demodulation block 3. The output of demodulation block four is used as the input of connection block four and the intermediate demodulation block at the same time. The output of the intermediate demodulation block and the output of connection block four are used as the input of demodulation block five. The output of demodulation block five and the output of connection block three are used as the input of demodulation block six. The output of demodulation block six and the output of connection block two are used as the input of demodulation block seven. The output of demodulation block seven and the output of connection block one are used as the input of demodulation block eight. The output of demodulation block eight is used as the input of 3×3 convolution block two. The output of 3×3 convolution block two is the phase obtained by end-to-end demodulation, that is, the predicted phase.

[0074] Each demodulation block in the encoder and decoder has the same structure, consisting of two parts. The first part has five layers: an LN layer, a 1×1 convolutional layer, a ReLU activation function, a 3×3 convolutional layer, and a ReLU activation function. The second part has three layers: an LN layer, a 1×1 convolutional layer, and a ReLU activation function. Residual connections are implemented within the demodulation blocks. The input and output of the first part are element-wise added together and then used as the input of the second part. The input and output of the second part are element-wise added together and then used as the output of the entire demodulation block.

[0075] Each connected block first enters a LN layer. The resulting information is divided into two parts. The first part is fed into a 1×1 convolutional layer, a ReLU activation function, and a 1×1 convolutional layer to extract small-scale information. The second part is fed into a 1×1 convolutional layer, a ReLU activation function, and a 5×5 convolutional layer to extract large-scale information. The two parts are then concatenated and fed into a ReLU activation function and a 3×3 convolutional layer.

[0076] Step 4: Using the course learning method, the deep learning interferogram phase demodulation network is trained in sequence from simple to complex using the dataset constructed in step 2.

[0077] like Figure 3 As shown, step four specifically includes the following sub-steps:

[0078] S4.1: Use the first two-frame interferogram data pair I constructed in step 2 1-1 (x,y),I 2-1 (x,y) is used as the input of the deep learning interferogram phase demodulation network, and the output is the predicted value The loss function is The Adam optimizer, L1 loss, and learning rate of 0.001 are used to perform gradient descent training on the loss function Loss1 for 50 rounds. During the training, the parameters of the deep learning interferogram phase demodulation network are updated by the gradient descent method.

[0079] S4.2: Use the second set of two-frame interferogram data constructed in step 2 to 1-2 (x,y),I 2-2 (x,y) is used as the input of the deep learning interferogram phase demodulation network updated in S4.1, and the output is the predicted value The loss function is The Adam optimizer, L1 loss, and learning rate of 0.001 are used to perform gradient descent training on the loss function Loss2 for 50 rounds. During the training, the parameters of the deep learning interferogram phase demodulation network are updated by the gradient descent method.

[0080] S4.3: Use the third set of two-frame interferogram data constructed in step 2 to obtain 1-3 (x,y) and I 2-3 (x,y) is used as the input of the deep learning interferogram phase demodulation network updated in S4.2, and the output is the predicted value The loss function is The Adam optimizer, root mean square (MSE) loss, and learning rate of 0.0001 were used to perform gradient descent training on the loss function Loss3 for 50 rounds. The deep learning network parameters were updated by gradient descent during training.

[0081] S4.4: Use the fourth set of two-frame interferogram data constructed in step 2 to obtain 1-4 (x,y) and I 2-4 (x,y) is the input of the deep learning interferogram phase demodulation network updated in S4.3, and the output is the predicted value The loss function is The Adam optimizer, root mean square (MSE) loss, and learning rate of 0.0001 are used to perform gradient descent training on the loss function Loss4 for 50 rounds. During the training, the deep learning network parameters are updated by the gradient descent method. After the training is completed, the final deep learning interferogram phase demodulation network is obtained.

[0082] Step 5: Input the two-frame random phase-shifted interferogram to be tested into the deep learning interferogram phase demodulation network trained in the course, and the model outputs the wavefront phase directly demodulated end-to-end.

[0083] A specific embodiment of the method of the present invention is given below to illustrate the technical effects of the present invention.

[0084] S1: Generate 2000 random first wavefronts using the first 15 random Zernike polynomial coefficients a Generate 2000 random second wavefronts using random 36-term Zernike polynomial coefficients b

[0085] S2: Using 2000 random first wave Using the range of A1 to [0.4, 0.6], the range of B1 to [0.2, 0.4], and the range of δ to [0.1rad, 3rad], we can get the two-frame interference pattern I in the first step of the course. 1-1 (x,y) and I 2-1 (x,y); using 2000 random second wave Using the range of A1 to [0.4, 0.6], the range of B1 to [0.3, 0.4], and the range of δ to [0.1rad, 3rad], we can get the two-frame interference pattern I in the second step of the course. 1-2 (x,y) and I 2-2 (x,y); using 2000 random second wave Using the range of A0 to [0.4, 0.6], the range of B0 to [0.3, 0.4], the range of x0 and y0 to [-0.2, 0.2], the range of d to [0.9, 1.1], and the range of δ to [0.1rad, 3rad], we can get the two-frame interference pattern I in the third step of the course. 1-3 (x,y) and I 2-3 (x, y); finally, add Gaussian noise n1(x, y) and n2(x, y) with a signal-to-noise ratio range of [10dB, 40dB] to obtain the two-frame interference pattern I in the fourth step of the course learning. 1-4 (x,y) and I 2-4 (x,y).

[0086] S3: Build a deep learning interferogram phase demodulation network, input two frames of interferograms with random phase shifts, and output end-to-end demodulated phase.

[0087] S4: Using the constructed dataset, the deep learning model is trained in a course-based learning manner from easy to difficult, with 50 rounds of training for each step, and a total of 200 rounds to complete the training.

[0088] S5: Input the two-frame interferogram of random phase shift to be tested into the model trained by course learning, and the model outputs the wavefront phase of direct end-to-end demodulation.

[0089] like Figure 4 As shown in the figure, it is the result of this embodiment. (a) is the first frame of the input interferogram to be measured, (b) is the second frame of the input interferogram to be measured after random phase shift, (c) is the true phase value, and (d) is the end-to-end demodulated phase output by the network. The root mean square error between the final wavefront phase and the true value is less than 0.0005λ, which shows that the present invention can achieve accurate end-to-end phase demodulation of two interferogram frames.

[0090] Those skilled in the art will understand that the foregoing descriptions are merely preferred embodiments 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 will still be able to modify the technical solutions described in the foregoing examples or substitute equivalents for some of the technical features therein. Any modifications, equivalent substitutions, etc. made within the spirit and principles of the invention shall be included within the scope of protection of the invention.

Claims

1. A two-frame interferogram end-to-end phase demodulation method based on curriculum learning, characterized in that: The following steps are involved: Step 1: construct the phase true value of the first wavefront and the phase true value of the second wavefront using randomly generated Zernike polynomials, wherein the number of terms of the Zernike polynomial of the first wavefront is less than the number of terms of the Zernike polynomial of the second wavefront; Step 2: Generate four sets of two-frame interferogram data pairs from random cameras based on the true phase value to build a data set; the four sets of two-frame interferogram data pairs have different levels of complexity; Step 3: Establish a deep learning interferogram phase demodulation network. The input of the network is two frames of randomly phase-shifted interferograms, and the output is the phase obtained by end-to-end demodulation. The deep learning interferogram phase demodulation network includes an encoder, an intermediate demodulation block, a decoder and four connection blocks. The encoder includes a 3×3 convolution block 1, a demodulation block 1, a demodulation block 2, a demodulation block 3 and a demodulation block 4, and the decoder includes a demodulation block 5, a demodulation block 6, a demodulation block 7, a demodulation block 8 and a 3×3 convolution block 2. The demodulation blocks of the encoder and the demodulation blocks of the decoder correspond one to one and are used to extract and map information. The demodulation blocks of the encoder and the corresponding demodulation blocks of the decoder are connected by a connection block to extract multi-scale information. The intermediate demodulation block is used to connect the output of the encoder and the input of the decoder for integrating information flow. The 3×3 convolution block 1 and the 3×3 convolution block 1 are used for input and output dimension adjustment. Step 4: Using the course learning method, the deep learning interferogram phase demodulation network is trained in sequence from simple to complex using the dataset constructed in step 2. Step 5: Input the two-frame random phase-shifted interferogram to be tested into the deep learning interferogram phase demodulation network trained in the course, and the model outputs the wavefront phase directly demodulated end-to-end.

2. The two-frame interferogram end-to-end phase demodulation method based on curriculum learning according to claim 1 is characterized in that The step one has the following sub-steps: S1.1: Generate 15 random Zernike coefficients a and 36 random Zernike coefficients b respectively: <h2 style=";text-align:left;direction:ltr">a=[a1,a2,...,a<h2 style=";text-align:left;direction:ltr"> 15 <h2 style=";text-align:left;direction:ltr"> ] b=[b1,b2,...,b 36 ] S1.2: Generate the true phase value of the first wavefront using 15 random Zernike coefficients a This is a simple wavefront; the true phase value of the second wavefront is generated using 36 random Zernike coefficients b. This is a complex wavefront: Among them, (x, y) is the rectangular coordinate, Z j (x,y) is a Zernike polynomial.

3. The two-frame interferogram end-to-end phase demodulation method based on curriculum learning according to claim 1 is characterized in that In step 2, four sets of two-frame interference pattern data pairs are generated in order from simple to complex, specifically: The true phase value of the first wavefront containing only 15 random Zernike coefficients a is used and uniformly distributed background terms and modulation terms, generating the first set of two-frame interference pattern data pairs I 1-1 (x,y),I 2-1 (x,y); The phase truth value of the second wavefront is generated using 36 random Zernike coefficients b. and uniformly distributed background terms and modulation terms to generate a second set of two-frame interference pattern data pairs I 1-2 (x,y),I 2-2 (x,y); The phase truth value of the second wavefront is generated using 36 random Zernike coefficients b. and Gaussian distribution background term and modulation term, generate the third set of two-frame interference pattern data pair I 1-3 (x,y) and I 2-3 (x,y); On the basis of the third set of two-frame interferogram data pairs, random noise is added to generate the fourth set of two-frame interferogram data pairs I 1-4 (x,y) and I 2-4 (x,y).

4. The two-frame interferogram end-to-end phase demodulation method based on curriculum learning according to claim 3 is characterized in that Each demodulation block in the encoder and decoder has the same structure, consisting of two parts. The first part has five layers, consisting of an LN layer, a 1×1 convolutional layer, a ReLU activation function, a 3×3 convolutional layer, and a ReLU activation function. The second part has three layers, consisting of an LN layer, a 1×1 convolutional layer, and a ReLU activation function. Residual connections are implemented within the demodulation blocks, meaning that the input and output of the first part are element-wise added together and then used as the input of the second part. The input and output of the second part are element-wise added together and then used as the output of the entire demodulation block.

5. The two-frame interferogram end-to-end phase demodulation method based on curriculum learning according to claim 4 is characterized in that Each connection block first enters an LN layer, and the information obtained is divided into two parts. The first part inputs a 1×1 convolution layer, an activation function ReLU, and a 1×1 convolution layer to extract small spatial scale information; the second part inputs a 1×1 convolution layer, an activation function ReLU, and a 5×5 convolution layer to extract large spatial scale information; then the two parts are spliced ​​and input into the activation function ReLU and a 3×3 convolution layer in sequence.

6. The two-frame interferogram end-to-end phase demodulation method based on curriculum learning according to claim 5 is characterized in that The connections between the various layers of the deep learning interferogram phase demodulation network are specifically as follows: The input of the 3×3 convolution block 1 of the encoder is two frames of interference images, the output of the 3×3 convolution block 1 is used as the input of the demodulation block 1, the output of the demodulation block 1 is also used as the input of the connection block 1 and the demodulation block 2, the output of the demodulation block 2 is also used as the input of the connection block 2 and the demodulation block 3, the output of the demodulation block 3 is also used as the input of the connection block 3 and the demodulation block 4, the output of the demodulation block 4 is also used as the input of the connection block 4 and the intermediate demodulation block, the output of the intermediate demodulation block and the output of the connection block 4 are used as the input of the demodulation block 5, the output of the demodulation block 5 and the output of the connection block 3 are used as the input of the demodulation block 6, the output of the demodulation block 6 and the output of the connection block 2 are used as the input of the demodulation block 7, the output of the demodulation block 7 and the output of the connection block 1 are used as the input of the demodulation block 8, the output of the demodulation block 8 is used as the input of the 3×3 convolution block 2, and the output of the 3×3 convolution block 2 is the phase obtained by end-to-end demodulation, that is, the predicted phase.

7. The two-frame interferogram end-to-end phase demodulation method based on curriculum learning according to claim 6 is characterized in that: The step 4 specifically includes the following sub-steps: S4.1: Use the first two-frame interferogram data pair I constructed in step 2 1-1 (x,y),I 2-1 (x,y) is used as the input of the deep learning interferogram phase demodulation network, and the output is the predicted value The loss function is L1 loss, and the parameters of the deep learning interferogram phase demodulation network are updated by gradient descent method; S4.2: Use the second set of two-frame interferogram data constructed in step 2 to 1-2 (x,y),I 2-2 (x,y) is the input of the deep learning interferogram phase demodulation network updated in S4.1, and the output is the predicted value The loss function is L1 loss, and the parameters of the deep learning interferogram phase demodulation network are updated again by the gradient descent method; S4.3: Use the third set of two-frame interferogram data constructed in step 2 to obtain 1-3 (x,y) and I 2-3 (x,y) is used as the input of the deep learning interferogram phase demodulation network updated in S4.2, and the output is the predicted value The loss function is the root mean square loss, and the parameters of the deep learning interferogram phase demodulation network are updated again by the gradient descent method; S4.4: Use the fourth set of two-frame interferogram data constructed in step 2 to obtain 1-4 (x,y) and I 2-4 (x,y) is the input of the deep learning interferogram phase demodulation network updated in S4.3, and the output is the predicted value The loss function is the root mean square loss, and the parameters of the deep learning interferogram phase demodulation network are updated again by the gradient descent method to obtain the final deep learning interferogram phase demodulation network.

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