A deep learning-based single-frame dual-wavelength interference phase demodulation method

Abstract

The application discloses a single-frame dual-wavelength interference phase demodulation method based on deep learning and belongs to the technical field of photoelectric measurement. The application is based on a Dual-wavelength network (D-Net) and a Phasenetwork (P-Net), only needs a frame of dual-wavelength interference graph, can obtain two single-wavelength interference graphs through a well-trained D-Net network, takes the two obtained interference graphs as inputs of the P-Net, can obtain two wrapped phases respectively, and can obtain dual-wavelength phases through unwrapping operation of the two wrapped phases. Finally, the surface of a measured optical element is obtained from the phase distribution. The application generates a data set for network training by constructing an interference graph generation model. A proper optimizer and a loss function are adopted, a learning rate decay strategy is introduced, an Adam optimization algorithm is used to update network parameter weights in a training process, training and testing are alternately performed to prevent network overfitting and guarantee the generalization ability of the network. The application can be used for expanding the detection range of optical interference, improving detection precision and simplifying detection operation.

Description

Technical Field

[0001] This invention relates to a single-frame dual-wavelength phase demodulation method based on deep learning, and more particularly to a wide-range, high-precision, and easy-to-operate measurement method, belonging to the field of optoelectronic measurement technology. Background Technology

[0002] Phase-shifting interferometry (PSI) offers advantages such as high accuracy, high speed, and non-contact operation, making it a mature technique for quantitative phase imaging and morphological measurement. However, in single-wavelength PSI, the quantitative phase calculated using the arctan function is typically confined to the range of (-π, π) because the optical path difference is greater than the detection wavelength and cannot be definitively determined. To address this issue, various phase unwrapping algorithms have been employed to achieve continuous phase information. However, these algorithms are complex, time-consuming, and ineffective. Another key method for eliminating phase discontinuities is dual-wavelength PSI. This method involves subtraction between two confined phases within a single wavelength, yielding a composite wavelength longer than either wavelength alone. This not only expands the measurement range of the phase target but also improves the accuracy of phase imaging.

[0003] In recent years, different types of dual-wavelength PSI techniques have been proposed for two-phase demodulation. In 2014, W. Zhang, X. Lu, L. Fei, H. Zhao, H. Wang, and L. Zhong proposed a synchronous phase-shifting dual-wavelength PSI to extract the wrapped phase of each wavelength, but it requires five interferograms with a special 2π phase shift and an additional two-step approximation algorithm. In 2016, X. Xu, Y. Wang, Y. Ji, Y. Xu, M. Xie, and H. Han proposed a two-step phase demodulation algorithm that can extract the phase from five dual-wavelength interferograms with high accuracy and high speed. Although it still requires a special 2π phase shift, it does not require an additional computational algorithm. Both of the above methods are efficient, but they rely on a special 2π phase shift to demodulate the phase of a single wavelength. To avoid using special phase shifts, in 2018, X.Xu, Y.Wang, Y.Ji, Y.Xu, M.Xie, and H.Han proposed a two-wavelength iterative method based on the least squares algorithm to retrieve the wrap-around phase of a single wavelength for two-wavelength interferograms with random phase shifts.

[0004] With the improvement of computing power, deep learning (DL) has become a rapidly developing technology due to its ability to extract image features using convolutional neural networks (CNNs). In recent years, deep learning has been widely used in semantic segmentation, phase retrieval, optical image reconstruction, phase aberration compensation, and phase unwrapping. In 2020, to address the problem of how to effectively recover the phase of each wavelength using the fewest possible wavelength interferograms, Xiaoqing Xu, Ming Xie, Ying Ji, and Yawei Wang proposed a novel deep learning-based dual-wavelength interferogram demodulation method. This method requires only three randomly phase-shifted dual-wavelength interferograms. Through a deep neural network, three interferograms with arbitrary phase shifts at each wavelength can be obtained. Using these interferograms, the wrapper phase of each individual wavelength is extracted using an iterative phase retrieval algorithm, and then the phase at different synthetic beat wave wavelengths is calculated.

[0005] The purpose of dual-wavelength interferometry is to expand the measurement range. Dual-wavelength measurement requires acquiring two single-wavelength fringe patterns to obtain the surface profile of the component under test. Traditionally, there are two methods for acquiring these two single-wavelength fringe patterns: 1. Changing the light source. After obtaining the surface profile measured by one light source, it is necessary to change to another light source to measure the surface profile again. This process inevitably introduces vibrations and measurement errors. 2. Introducing a beam splitter into the optical path. This requires a high-precision beam splitter, increasing the complexity of the optical system and potentially leading to incomplete beam splitting. Furthermore, when acquiring multiple frames of interferograms of the surface profile under test, the phase shifter used can introduce environmental disturbances, making the operation complex.

[0006] In summary, existing dual-wavelength interferogram demodulation methods inevitably introduce environmental disturbances during phase shifting and are complex to operate. How to effectively recover the wavelength phase using the fewest possible wavelength interferograms remains a challenge. Summary of the Invention

[0007] Existing dual-wavelength interferometric phase detection methods require multiple frames of interferograms and rely on complex hardware and cumbersome iterative processes, making it difficult to simultaneously guarantee large-scale and high-precision detection. The main objective of this invention is to provide a deep learning-based single-frame dual-wavelength interferogram phase demodulation method. By constructing a dual-wavelength interferometric system, only a single frame of dual-wavelength interferogram is needed. Through a well-trained neural network, the optical surface profile of the sample under test can be obtained. This invention does not require high-precision components such as phase shifters and beam splitters, and it eliminates the need for preprocessing operations such as normalization and noise reduction of the dual-wavelength interferogram. It boasts advantages such as simple optical path, large measurement range, high accuracy, and high efficiency.

[0008] The objective of this invention is achieved through the following technical solution.

[0009] This invention discloses a single-frame dual-wavelength interferogram phase demodulation method based on deep learning, comprising the following steps:

[0010] Step 1: Construct a dual-wavelength interferometric system model and obtain the dataset. In phase fitting, the first 11 terms of the Zernike polynomial play a major role, generating a random wavefront distribution. Two parallel light sources with wavelengths of 632.8 nm and 533 nm are emitted, and the beams are split and enter the reference and measurement optical paths respectively. The light wave in the measured optical path, carrying phase difference information, interferes with the beam in the reference optical path, and the dual-wavelength interference fringe pattern is acquired by a CCD. The wavefront of the dual-wavelength interferometric measurement is generated by the Zernike polynomial, but because the wavelengths of the two parallel light sources are different, the two light sources carry different phases. Based on the characteristic that the two light sources carry different phases, deep learning methods are used to obtain two single-wavelength interferograms, thereby achieving beam splitting. Then, based on the mapping relationship between the interferogram and the phase, a neural network is constructed in the subsequent step 2 to obtain the wrapped phase of the two single wavelengths, thus realizing the function of obtaining the wrapped phase from a single frame of the interferogram, and finally obtaining the dual-wavelength interference fringe pattern.

[0011] Step 2: Construct a neural network. Based on the U-Net network, build a Dual-wavelength network (D-Net) and a Phase network (P-Net) to demodulate the dual-wavelength interferogram. The D-Net mainly consists of two parts: an encoder and a decoder. The encoder includes four modules, each containing a Batch Normalization (BN) layer, an activation function, two convolutions, and a pooling layer with a stride of 2. After processing by each module, the pixel count of the feature map gradually decreases. The decoder is symmetrical to the encoder and also includes four modules. Each module includes an upsampling operation with a stride of 2, which is then concatenated with the encoder. The output is then passed through a module consisting of a BN layer, an activation function, and two convolutions, and another module consisting of a BN layer, an activation function, a convolution, and a Clamp function. The Clamp function controls the output within [0,1], which is beneficial for neural network convergence and improves network accuracy, directly outputting the predicted two single-wavelength interferograms.

[0012] Like the D-Net network, P-Net is divided into two parts: an encoder and a decoder. The encoder consists of four modules. Each module includes a Batch Normalization (BN) layer, an activation function, a convolution, a resblock module, and a pooling layer with a stride of 2. The decoder is symmetrical to the encoder and also consists of four modules. Each module includes an upsampling operation with a stride of 2, which is then concatenated with the encoder for feature mapping. The decoder is then passed through a module consisting of a BN layer, an activation function, a convolution, and a resblock module, and outputs a two-wavelength wrapper phase through a convolution and a Clamp function. The resblock module increases both the network's depth and gradient propagation capability, enabling the network to extract higher-level and abstract features. The resblock module is used to bias the two Conv2D layers. Analysis shows that bias is necessary for regression problems, and enabling bias improves the network's results. U-Net and the resblock module extensively use cascading operations to ensure gradient propagation, improve the network's prediction accuracy and efficiency, and shorten the training time. Placing a Clamp function at the end of the network restricts the network output to [0,1], which helps the network converge and improves the network accuracy.

[0013] The network needs to perform the following functions: analyze the dual-wavelength interference fringe pattern obtained from the CCD, output two single-wavelength interference fringe patterns through the D-Net network, and then output two single-wavelength wrapping phases through the P-Net network. Therefore, a deep network is required to achieve high accuracy. However, as the number of network layers increases, the number of model parameters and computational cost will increase significantly. Therefore, when building the network, it is necessary not only to improve the prediction accuracy but also to minimize the computational cost and improve the convergence speed. Based on the above analysis, the D-Net structure is as follows:

[0014] The first part is the encoder module: BN layer + activation function + convolutional layer C1 + convolutional layer C2 + pooling layer P1;

[0015] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0016] • Activation functions are used to incorporate nonlinear factors, thereby increasing the expressive power of the model;

[0017] • Convolutional layers C1 and C2 are used for feature extraction;

[0018] • Pooling layer P1 uses max pooling to reduce the size of the parameter matrix;

[0019] The second part is the decoder module: upsampling P2 + concatenation + BN layer + convolutional layer C3 + convolutional layer C4 + activation function;

[0020] • Upsample P2 to increase the size of the parameter matrix;

[0021] • By splicing and fusing feature information, information from deep and shallow layers can be combined;

[0022] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0023] • Activation function: Incorporating nonlinear factors increases the model's expressive power;

[0024] • Convolutional layers C3 and C4 are used for feature extraction;

[0025] Part 3: BN layer + activation function + convolutional layer C5 + Clamp function;

[0026] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0027] • Activation function: Incorporating nonlinear factors increases the model's expressive power;

[0028] • Convolutional layer C5 is used for feature extraction;

[0029] The Clamp function sets the network output range to (0, 1), improving the network's accuracy and making it easier to converge.

[0030] The P-Net architecture is designed as follows:

[0031] The first part is the encoder module: BN layer + activation function + convolutional layer C1 + resblock module + pooling layer P1;

[0032] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0033] • Activation functions are used to incorporate nonlinear factors, thereby increasing the expressive power of the model;

[0034] • Convolutional layer C1 is used for feature extraction;

[0035] The resblock module enhances the gradient propagation capability of the network while increasing its depth.

[0036] • Pooling layer P1 uses max pooling to reduce the size of the parameter matrix;

[0037] The second part is the decoder module: upsampling P2 + concatenation + BN layer + activation function + convolutional layer C2 + resblock module;

[0038] • Upsample P2 to increase the size of the parameter matrix;

[0039] • By splicing and fusing feature information, information from deep and shallow layers can be combined;

[0040] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0041] • Activation function: Incorporating nonlinear factors increases the model's expressive power;

[0042] • Convolutional layer C2 performs feature extraction;

[0043] The resblock module enhances the gradient propagation capability of the network while increasing its depth.

[0044] Part 3, C3+Clamp function for convolutional layers;

[0045] • Convolutional layer C3 performs feature extraction;

[0046] The Clamp function sets the network output range to (0, 1), improving the network's accuracy and making it easier to converge.

[0047] Step 3: Train the neural network using the simulation dataset. Using the dual-wavelength interference fringe pattern obtained in Step 1 as the dataset, and its corresponding single-wavelength interference fringes as the network's output parameters, iteratively train the D-Net network. After multiple iterations, the D-Net network learns the mapping relationship between the dual-wavelength interference fringe pattern and the two single-wavelength interference fringe patterns. Training ends when the loss value drops to a preset value, resulting in a fully trained D-Net network. Next, using the two single-wavelength interference fringe patterns obtained in Step 1 as the dataset, and their corresponding wrapping phases as the output parameters, iteratively train the P-Net network. After multiple iterations, the P-Net network learns the mapping relationship between the single-wavelength interference fringe pattern and the wrapping phase. Training ends when the loss value drops to a preset value, resulting in a fully trained P-Net network.

[0048] The Adam optimization algorithm is used to update network parameter weights during training. Alternating between testing and training can prevent overfitting and ensure the network's generalization ability.

[0049] Step 4: Input an interferogram of the surface of the object to be tested into the network trained in Step 3. The network will execute data transmission and obtain two single-wavelength enclosed phases simultaneously. Then, use the unwrapping algorithm to unwrap them to obtain continuous dual-wavelength phases, realize the surface shape detection of the actual system, expand the surface shape detection range, improve the detection accuracy, and simplify the detection operation process.

[0050] For a trained network, the corresponding phase can be obtained directly from the dual-wavelength interferogram without the need for additional hardware, which significantly improves the measurement range and simplifies the operation process.

[0051] Beneficial effects:

[0052] 1. The deep learning-based single-frame dual-wavelength interferogram phase demodulation method disclosed in this invention only requires obtaining the corresponding dataset to train the convolutional neural network, which can realize the phase demodulation of the dual-wavelength interferogram. Compared with the existing dual-wavelength phase demodulation methods, it can overcome the difficulties of demodulation using a single-frame dual-wavelength interferogram.

[0053] 2. The deep learning-based single-frame dual-wavelength interferogram phase demodulation method disclosed in this invention utilizes the acquired dual-wavelength interferogram as a dataset and its corresponding single-wavelength interferogram as the network's output parameters to iteratively train a D-Net network. After multiple iterations, the D-Net network learns the mapping relationship between the dual-wavelength interferogram and the two single-wavelength interferograms. Training ends when the loss value drops to a preset value, resulting in a well-trained D-Net network. Then, using the acquired two single-wavelength interferograms as a dataset and their corresponding wrapping phase as the output parameters, a P-Net network is iteratively trained. After multiple iterations, the P-Net network learns the mapping relationship between the single-wavelength interferogram and the wrapping phase. Training ends when the loss value drops to a preset value, resulting in a well-trained P-Net network. During training, the Adam optimization algorithm is used to update the network parameter weights. Alternating between testing and training prevents overfitting and ensures the network's generalization ability.

[0054] 3. The deep learning-based single-frame dual-wavelength interferogram phase demodulation method disclosed in this invention uses an interferogram of the surface of the object under test, input into a trained network. The network executes data transmission and can simultaneously obtain two single-wavelength enclosed phases. Then, an unpacking algorithm is used to unpack them to obtain continuous dual-wavelength phases, realizing surface shape detection in practical systems, expanding the surface shape detection range, improving detection accuracy, and simplifying the detection operation process. This invention directly inputs the dual-wavelength image acquired on the CCD into the network without relying on additional hardware devices or requiring image preprocessing, greatly reducing the complexity of the optical system. By outputting a dual-wavelength phase map from the acquired single-frame dual-wavelength interferogram, the residual error PV (Peak-to-Veally) value is calculated to be 0.1696 rad, and the RMS (Root-Mean-Square) value is 0.0320 rad, significantly improving detection accuracy and simplifying the operation process.

[0055] 4. The single-frame interferogram phase demodulation method based on deep learning disclosed in this invention avoids the difficulty of collecting large datasets in actual systems through system simulation, expands data sources, and improves data generalization. Attached Figure Description

[0056] Figure 1 Schematic diagram of the optical path on the surface of the optical element under test;

[0057] Figure 2 This is a dual-wavelength interferogram acquired by the detector;

[0058] Figure 3 Predict the interference fringe pattern corresponding to λ1 for the D-Net network;

[0059] Figure 4 Predict the interference fringe pattern corresponding to λ2 for the D-Net network;

[0060] Figure 5 Predict the package phase corresponding to λ1 for the P-Net network;

[0061] Figure 6 Predict the package phase corresponding to λ2 for the P-Net network;

[0062] Figure 7 The phase distribution of the two-wavelength interferogram;

[0063] Figure 8 Here is a diagram of the D-Net network structure;

[0064] Figure 9 This is a diagram of the P-Net network structure.

[0065] Figure 10 The training curve of the loss function for D-Net is shown below, where: Figure 10 (a) is the training curve of the loss function corresponding to λ1. Figure 10 (b) is the training curve of the loss function corresponding to λ2;

[0066] Figure 11 The training curve of the loss function for P-Net is shown, where: Figure 11 (a) is the training curve of the loss function corresponding to λ1. Figure 11 (b) is the training curve of the loss function corresponding to λ2;

[0067] Figure 12 For the 1000 validation frames generated in the simulation, calculate the point-to-point error between the predicted phase and the ideal phase, where... Figure 12 (a) is the PV value. Figure 12 (b) is the RMS value.

[0068] Figure 13 This is a flowchart of the single-frame dual-wavelength interferometric phase demodulation method based on deep learning disclosed in this invention.

[0069] Among them, Laser1 is a helium-neon laser with a wavelength of 632.8nm, Laser2 is a diode solid-state laser with a wavelength of 533nm, CL1 and CL2 are beam expanders and collimators, BS1 and BS2 are beam splitters, M1 is a reference mirror, M2 is the mirror under test, and CCD is a detector. Detailed Implementation

[0070] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The technical problems solved by the present invention and its beneficial effects are also described. It should be noted that the described embodiments are only intended to facilitate understanding of the present invention and do not constitute any limitation thereof.

[0071] like Figure 13 As shown in the figure, this embodiment discloses a single-frame dual-wavelength interferometric phase demodulation method based on deep learning for recovering the surface of the optical element under test. The optical path principle diagram for measuring the surface of the optical element under test is shown in the figure. Figure 1 As shown.

[0072] This example uses a dual-source interference system to describe the invention in detail. Laser1 is a helium-neon laser with a wavelength of 632.8 nm, and Laser2 is a diode solid-state laser with a wavelength of 533 nm.

[0073] Step 1: Establish a simulation system for the optical path of the optical element under test. Laser1 and Laser2 are separated into two beams by beam expanders and collimators BS1 and BS2, respectively. One beam illuminates the reference mirror M1, and the other beam illuminates the mirror surface M2 under test. Finally, the light is collected by a CCD detector. Figure 2 This is a dual-wavelength interferogram acquired by the detector.

[0074] Step Two Figure 8 This example uses the main structure diagram of a Dual-wavelength network (D-Net). Building a neural network, D-Net mainly consists of two parts: an encoder and a decoder. The encoder comprises four program blocks. The decoder is symmetrical to the encoder and also includes four program blocks. The last module is the Clamp function, which controls the network output within (0,1). The network input is a dual-wavelength interferogram, as shown... Figure 2 As shown, the shape size is (128, 128, 1). The network output is an interferogram of two single wavelengths, as shown... Figure 3 , Figure 4 As shown. The D-Net design in this example is as follows:

[0075] The first part is the encoder's program block: BN layer + activation function + convolutional layer C1 + convolutional layer C2 + pooling layer P1;

[0076] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0077] • Activation functions are used to incorporate nonlinear factors, thereby increasing the expressive power of the model;

[0078] • Convolutional layers C1 and C2 are used for feature extraction;

[0079] • Pooling layer P1 uses max pooling to reduce the size of the parameter matrix;

[0080] The second part is the decoder's program blocks: upsampling P2 + concatenation + BN layer + activation function + convolutional layer C3 + convolutional layer C4;

[0081] • Upsample P2 to increase the size of the parameter matrix;

[0082] • By splicing and fusing feature information, information from deep and shallow layers can be combined;

[0083] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0084] • Activation function: Incorporating nonlinear factors increases the model's expressive power;

[0085] • Convolutional layers C3 and C4 are used for feature extraction;

[0086] Part 3: BN layer + activation function + convolutional layer C5 + Clamp function;

[0087] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0088] • Activation function: Incorporating nonlinear factors increases the model's expressive power;

[0089] • Convolutional layer C5 is used for feature extraction;

[0090] The Clamp function sets the network output range to (0, 1), improving the network's accuracy and making it easier to converge.

[0091] Step 3 Figure 9 The main structure diagram of the Phase network (P-Net) used in this example is shown. The neural network is built as follows: P-Net is similar to D-Net, consisting of two parts: an encoder and a decoder. The encoder includes four program blocks. The decoder is symmetrical to the encoder and also includes four program blocks. The last module is the Clamp function, which controls the network output within (0,1). The network input consists of two single-wavelength interferograms with a shape size of (128, 128, 1). The network output consists of two single-wavelength wrap-around phases, as shown... Figure 5 , Figure 6 As shown. The P-Net design in this example is as follows:

[0092] The P-Net architecture is designed as follows:

[0093] The first part is the encoder's program block: BN layer + activation function + convolutional layer C1 + resblock module + pooling layer P1;

[0094] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0095] • Activation functions are used to incorporate nonlinear factors, thereby increasing the expressive power of the model;

[0096] • Convolutional layer C1 is used for feature extraction;

[0097] The resblock module enhances the gradient propagation capability of the network while increasing its depth.

[0098] • Pooling layer P1 uses max pooling to reduce the size of the parameter matrix;

[0099] The second part is the decoder's program blocks: upsampling P2 + concatenation + BN layer + activation function + convolutional layer C2 + resblock module;

[0100] • Upsample P2 to increase the size of the parameter matrix;

[0101] • By splicing and fusing feature information, information from deep and shallow layers can be combined;

[0102] • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed;

[0103] • Activation function: Incorporating nonlinear factors increases the model's expressive power;

[0104] • Convolutional layer C2 performs feature extraction;

[0105] The resblock module enhances the gradient propagation capability of the network while increasing its depth.

[0106] Part 3, C3+Clamp function for convolutional layers;

[0107] • Convolutional layer C3 performs feature extraction;

[0108] The Clamp function sets the network output range to (0, 1), improving the network's accuracy and making it easier to converge.

[0109] Step 4: From Step 1, 6000 dual-wavelength interferograms are obtained. 3000 are used as the training set for the D-Net network, 2000 as the validation set, and 1000 as the test set. This dataset is used to train the network. To train the R-Net network, 9000 single-wavelength interferograms are generated from Step 1. 5000 are used as the training set for the R-Net network, 3000 as the validation set, and 1000 as the test set.

[0110] The loss function used during training is Mean Squared Error (MSE), and the Adam algorithm is chosen as the optimization function. When training the D-Net network, the learning rate is 0.01, decaying at a rate of 0.1 every 30 epochs, with 100 epochs and a batch size of 10. When training the R-Net network, the learning rate is 0.0001, decaying at a rate of 0.1 every 60 epochs, with 120 epochs and a batch size of 10. The decrease in the loss function curve during training is shown below. Figure 10 , Figure 11 As shown in the figure. After training, the prediction accuracy of the neural network was tested using a test set of 1000 images. The histogram of the training results is shown in the figure. Figure 12 As shown, the left graph represents the PV value, and the right graph represents the RMS value. The average RMS value is 0.074 rad, and the average PV value is 0.507 rad.

[0111] Step 5: After step 4, the neural network has acquired excellent predictive capabilities. When recovering the optical surface information of the sample under test, it can follow the following... Figure 13 The following steps are performed according to the flowchart shown: (1) Obtain a dual-wavelength interferogram of the surface of the optical element to be tested according to step one; (2) Input the image into the neural network for prediction; (3) Perform unwrapping operation on the two wrapped phases to obtain the surface shape, realize the surface shape detection of the actual system, expand the surface shape detection range, improve the detection accuracy, and simplify the detection operation process.

[0112] For a trained network, the corresponding phase can be obtained directly from the dual-wavelength interferogram without the need for additional hardware, which significantly improves the measurement range and simplifies the operation process.

[0113] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A single-frame dual-wavelength interferometric phase demodulation method based on deep learning, characterized in that: Includes the following steps: Step 1: Construct a dual-wavelength interferometric system model and obtain the dataset. In phase fitting, the first 11 terms of the Zernike polynomial play a major role, generating a random wavefront distribution. Two parallel light sources with wavelengths of 632.8 nm and 533 nm are emitted, and the beams are split and enter the reference and measurement optical paths respectively. The light wave in the measured optical path, carrying phase difference information, interferes with the beam in the reference optical path, and the dual-wavelength interferogram is acquired by a CCD. The wavefront of the dual-wavelength interferometric measurement is generated by the Zernike polynomial, but because the wavelengths of the two parallel light sources are different, the two light sources carry different phases. Based on the characteristic that the two light sources carry different phases, deep learning is used to obtain two single-wavelength interferograms, thereby achieving beam splitting. Then, based on the mapping relationship between the interferogram and the phase, a neural network is constructed in the subsequent step 2 to obtain the wrapping phase of the two single wavelengths, thus realizing the function of obtaining the wrapping phase from a single frame interferogram, and finally obtaining the dual-wavelength interferometric fringe pattern. Step 2: Build a neural network. Based on the U-Net network, construct a Dual-wavelength network (D-Net) and a Phase network (P-Net) to demodulate the dual-wavelength interferogram. The D-Net mainly consists of two parts: an encoder and a decoder. The encoder includes four modules, each of which includes a BatchNormalization (BN) layer, an activation function, two convolutions, and a pooling layer with a stride of 2. After processing by each module, the pixel count of the feature map gradually decreases. The decoder is symmetrical to the encoder and also includes four modules. Each module includes an upsampling operation with a stride of 2, which is then concatenated with the encoder. The output is then passed through a module consisting of a BN layer, an activation function, and two convolutions, and another module consisting of a BN layer, an activation function, a convolution, and a Clamp function. By introducing the Clamp function, the output is controlled within [0,1], which is beneficial for the convergence of the neural network and improves the accuracy of the network. The output directly predicts the two single-wavelength interferograms. Like the D-Net network, P-Net is also divided into two parts: an encoder and a decoder. The encoder consists of four modules: each module includes a BN layer, an activation function, a convolution, a resblock module, and a pooling layer with a stride of 2. The decoder is symmetrical to the encoder and also includes four modules. Each module includes an upsampling operation with a stride of 2. Then, it is concatenated with the encoder for feature mapping. Then, it is passed through a module consisting of a BN layer, an activation function, a convolution, and a resblock module. Through a convolution and a Clamp function, it outputs the wrap-around phase of two wavelengths. The purpose of adding the resblock module is not only to increase the network depth but also to enhance its gradient propagation capability, enabling the network to extract higher-level and abstract features. In the network, the bias of the two Conv2D layers in the resblock module is enabled. Analysis results show that bias is necessary for regression problems, and enabling bias leads to better network results. U-net and the resblock module extensively use cascading operations to ensure gradient propagation, improve the network's prediction accuracy and efficiency, and shorten the training time. Placing a Clamp function at the end of the network to restrict the network output to [0,1] facilitates network convergence and improves network accuracy. The network analyzes the dual-wavelength interference fringe pattern obtained from the CCD and outputs two single-wavelength interference fringe patterns through the D-Net network, and then outputs two single-wavelength wrapping phases through the P-Net network. Therefore, a deep network is required to achieve high accuracy. However, as the number of network layers increases, the number of model parameters and computational cost will increase significantly. Therefore, when building the network, it is necessary not only to improve the prediction accuracy of the network, but also to minimize the network's computational cost and improve the network's convergence speed. Step 3: Train the neural network using the simulation dataset. Using the dual-wavelength interference fringe pattern obtained in Step 1 as the dataset, and its corresponding single-wavelength interference fringes as the network's output parameters, iteratively train the D-Net network. After multiple iterations, the D-Net network learns the mapping relationship between the dual-wavelength interference fringe pattern and the two single-wavelength interference fringe patterns. Training ends when the loss value drops to a preset value, resulting in a fully trained D-Net network. Next, using the two single-wavelength interference fringe patterns obtained in Step 1 as the dataset, and their corresponding wrapping phases as the output parameters, iteratively train the P-Net network. After multiple iterations, the P-Net network learns the mapping relationship between the single-wavelength interference fringe pattern and the wrapping phase. Training ends when the loss value drops to a preset value, resulting in a fully trained P-Net network. During training, the Adam optimization algorithm is used to update the network parameter weights; alternating between testing and training can prevent overfitting and ensure the network's generalization ability. Step 4: Input an interferogram of the surface of the object to be tested into the network trained in Step 3. The network can simultaneously obtain two single-wavelength wrapped phases by performing data transmission. Then, the unwrapping algorithm is used to unwrap them to obtain continuous dual-wavelength phases, realizing the surface shape detection of the actual system and expanding the surface shape detection range.

2. The single-frame dual-wavelength interferometric phase demodulation method based on deep learning as described in claim 1, characterized in that: The D-Net structure is as follows: The first part is the encoder module: BN layer + activation function + convolutional layer C1 + convolutional layer C2 + pooling layer P1; • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed; • Activation functions are used to incorporate nonlinear factors, thereby increasing the expressive power of the model; • Convolutional layers C1 and C2 are used for feature extraction; • Pooling layer P1 uses max pooling to reduce the size of the parameter matrix; The second part is the decoder module: upsampling P2 + concatenation + BN layer + convolutional layer C3 + convolutional layer C4 + activation function; • Upsample P2 to increase the size of the parameter matrix; • By splicing and fusing feature information, information from deep and shallow layers can be combined; • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed; • Activation function: Incorporating nonlinear factors increases the model's expressive power; • Convolutional layers C3 and C4 are used for feature extraction; Part 3: BN layer + activation function + convolutional layer C5 + Clamp function; • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed; • Activation function: Incorporating nonlinear factors increases the model's expressive power; • Convolutional layer C5 is used for feature extraction; The Clamp function sets the network output range to (0, 1), improving network accuracy and facilitating convergence. The P-Net structure is as follows: The first part is the encoder module: BN layer + activation function + convolutional layer C1 + resblock module + pooling layer P1; • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed; • Activation functions are used to incorporate nonlinear factors, thereby increasing the expressive power of the model; • Convolutional layer C1 is used for feature extraction; The resblock module enhances the gradient propagation capability of the network while increasing its depth. • Pooling layer P1 uses max pooling to reduce the size of the parameter matrix; The second part is the decoder module: upsampling P2 + concatenation + BN layer + activation function + convolutional layer C2 + resblock module; • Upsample P2 to increase the size of the parameter matrix; • By splicing and fusing feature information, information from deep and shallow layers can be combined; • Batch Normalization (BN) layers solve the gradient vanishing problem and improve network convergence speed; • Activation function: Incorporating nonlinear factors increases the model's expressive power; • Convolutional layer C2 performs feature extraction; The resblock module enhances the gradient propagation capability of the network while increasing its depth. Part 3, C3+Clamp function for convolutional layers; • Convolutional layer C3 performs feature extraction; The Clamp function sets the network output range to (0, 1), improving the network's accuracy and making it easier to converge.

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