Phase shift interferometry phase retrieval system and method fusing physical a priori and temporal information

Abstract

The present application relates to the technical field of optical detection, and more particularly to a phase shift interference phase recovery system and method fusing physical priori and timing information, which calculates a plurality of physical priori information of a sequence of collected phase shift interference images; through a long short-term memory network, timing prediction and fusion are performed on the physical priori features to obtain timing fusion features; after the physical priori features and the timing fusion features are spliced, multi-level feature extraction and step-by-step decoding are performed to obtain phase features of different scales; each scale of the phase features is recovered into a two-dimensional phase representation, and the two-dimensional phase representation is recovered into a corresponding phase map. The present application can effectively combine the advantages of robust object demodulation and deep learning, realize high-precision phase recovery on a plurality of frames of phase shift interference images, and has good engineering application prospect.

Description

Technical Field

[0001] This invention belongs to the field of optical detection technology, and in particular relates to a phase-shifting interference phase recovery system and method that integrates physical prior information and temporal information. Background Technology

[0002] Phase-shift interferometry is a key technology in optical surface inspection, wavefront detection, precision manufacturing quality control, and high-resolution imaging. Its basic idea is to acquire interferometric images at multiple known phase-shift positions, establish a mapping relationship between phase and light intensity through intensity changes, and then obtain the phase distribution to be measured through phase demodulation. This type of method has advantages such as non-contact operation, high sensitivity, and high resolution, and has been widely used in precision optics, semiconductor inspection, micrometrology, and industrial online inspection.

[0003] Existing phase-shifting interferometric phase retrieval methods mostly employ analytical or iterative demodulation strategies, such as window function-weighted phase retrieval methods, weighted polynomial-based phase retrieval methods, and least-squares fitting-based phase estimation methods. These methods achieve good results under ideal imaging conditions, stable phase shifts, and high signal-to-noise ratios. However, in practical applications, they are often affected by the following factors: First, traditional analytical methods are sensitive to outliers due to light source fluctuations, sensor noise, non-uniform modulation, local occlusion, or low-reflection areas. Second, temporal correlations exist between multiple frames, making it difficult for traditional pixel-by-pixel analytical methods to effectively utilize cross-frame redundancy information. Third, while data-driven deep learning methods have strong fitting capabilities, they often lack physical constraints, leading to unstable results, insufficient generalization, or weak interpretability.

[0004] Therefore, how to construct a phase retrieval method that can both inherit physical tolerancing priors and make full use of multi-frame temporal information and spatial context features has become a key issue in improving the accuracy and robustness of phase-shift interferometry. Summary of the Invention

[0005] In view of this, the present invention aims to provide a phase-shifting interferometric phase recovery system and method that integrates physical priors and temporal information. By deeply fusing the initial phase obtained from robust physical demodulation and various quality-related features with a bidirectional temporal deep network, high-precision and robust phase-shifting interferometric phase recovery is achieved under a unified framework. It takes into account physical interpretability, recovery accuracy and engineering practicality, and solves the problems of insufficient accuracy and robustness of traditional phase-shifting demodulation algorithms under the influence of turbulence, noise interference, local low-level conditions, outliers, insufficient utilization of temporal information, and lack of physical constraints in pure deep learning models.

[0006] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A phase-shifting interferometric phase retrieval system integrating physical priors and temporal information includes: a physical prior module, which calculates various physical priors from the acquired phase-shifting interferometric image sequence to form physical prior features; a temporal fusion module, which performs temporal prediction and fusion of the physical prior features through a long short-term memory network to obtain temporal fusion features; an information fusion module, which concatenates the physical prior features and temporal fusion features, performs multi-level feature extraction and step-by-step decoding to obtain phase features at different scales; and a phase retrieval module, which recovers the phase features at each scale into a two-dimensional phase representation, and then recovers the two-dimensional phase representation into the corresponding phase map, wherein the phase map corresponding to the phase feature with the largest scale is the finally recovered phase map.

[0007] Furthermore, in the physics prior module: an intensity observation model is established for each frame in the phase-shifting interferometric image sequence, as follows: I t =a+ccos(θ t )+ssin(θ t ); Among them, I t Let θ represent the phase-shifted interferometric image of frame t, a represent the average intensity of the phase-shifted interferometric image sequence, c and s represent the cosine and sine components, respectively. t Let represent the phase shift angle of the phase-shifted interferometric image in frame t; Calculate the difference between the true frame image in the phase-shifting interferometric image sequence and its corresponding current fitted value, and based on the difference, calculate the Huber weight of each frame image in the phase-shifting interferometric image sequence using the following formula: ; Where, ω t Let r represent the Huber weights of the t-th frame image. t δ represents the difference between the real frame image in frame t and the corresponding current fitted value, and δ represents the supervision threshold. Transform the intensity observation model into a matrix equation: (A T WA)β=(A T WI); in, β=[a,c,s] T I = [I1, I2, ..., I t ]; The matrix equation is solved iteratively using the least squares method to obtain the average intensity, cosine component, and sine component. After the iteration is completed, the standard deviation plot of the difference during the iteration process is calculated. The initial phase map, modulation map, average intensity map, and quality map of the phase-shifted interferometric image sequence are calculated based on the obtained average intensity, cosine component, and sine component; the obtained initial phase map, modulation map, average intensity map, quality map, and standard deviation map are combined to form physical prior features.

[0008] Furthermore, the initial phase diagram, modulation diagram, and quality diagram are obtained using the following formula: ; ; quality = mod / (resid) std +10 -3 ); in, The initial phase map is represented by mod, the modulation map by quality, and the resid map by resid. std Represents a standard deviation plot.

[0009] Furthermore, the regression function obtained through iterative solution is: ; The iteration stops when the overall L2 change of the matrix β parameter between two consecutive iterations is less than 10. -6 .

[0010] Furthermore, in the temporal fusion module: each frame of the phase-shifted interferometric image sequence is convolved and projected, and the resulting features are fed into the forward ConvLSTM unit and the backward ConvLSTM unit to obtain forward temporal features and backward temporal features. The forward and backward features at the same time are concatenated to form bidirectional temporal features. The temporal attention pooling module is used to adaptively weight and fuse the bidirectional temporal features at each time step, while retaining the features at the last time step, the temporal average features, and the temporal maximum response features to form the temporal fusion features.

[0011] Furthermore, in the information fusion module: physical prior features are concatenated with temporal fusion features, and the concatenated features are fed into the U-Net network. The encoding branch of the U-Net network performs multi-level encoding on the concatenated features, and the decoding branch of the U-Net network decodes the features from the encoding branch step by step to obtain phase features at different scales.

[0012] Furthermore, the phase recovery module includes an output head corresponding to the phase feature scale; each output head maps the phase feature of the corresponding scale to a two-channel phase representation feature, one channel being a cosine component and the other channel being a sine component; after normalizing the phase representation feature, the phase is obtained through the arctangent function.

[0013] A phase-shifting interferometric phase retrieval method integrating physical priors and temporal information, characterized by comprising: S1: Preprocess the acquired multiple sets of phase-shifting interferometric image sequences and corresponding real phase maps to obtain the training set; S2: Construct a phase-shifting interferometric phase recovery system that integrates physical priors and temporal information as provided in this invention; S3: Use the training set built in step S1 to train the system built in step S2 to obtain the phase retrieval model; S4: Input the phase-shifting interferometric image sequence to be tested into the phase recovery model obtained in step S3, and output the final phase map.

[0014] Furthermore, in step S3, the system is trained using the following joint loss function: L total =λ1L ph +λ2L sc +λ3L grad +λ4L ms +λ5L smooth +λ6L edge ; Among them, L total L represents the joint loss function. ph L represents phase loss. sc L represents the sine and cosine consistency loss. grad L represents the gradient loss. ms L represents multi-scale loss. smooth L represents the smoothing loss, used to suppress ineffective high-frequency oscillations. edge λ1~λ6 represent the edge consistency loss, and λ1~λ6 represent the loss weights; The phase loss is: ; Among them, L Huber Represents the Huber sub-loss of the fundamental phase, η i This represents the Huber sub-loss weight corresponding to the phase map at the i-th scale before unifying the scale. This represents the phase diagram at the i-th scale before scaling. Represents the true phase diagram; The sine and cosine consistency loss is: ; Where Ω represents the non-zero region in the true phase diagram, and |Ω| represents the total number of elements in the non-zero region. This represents the phase diagram that the system finally recovers. This represents the corresponding true phase diagram; The gradient loss is: ; in, and These represent the calculation of the first-order gradient in the horizontal and vertical directions, respectively. The smoothing loss is: ; The edge consistency loss is: ; in, This represents the calculation of the second-order Laplace derivative; The multi-scale loss is: ; in, This represents the phase map after downsampling at the j-th mesoscale from the phase map finally recovered by the system. This represents the phase map after downsampling the true phase map at the j-th mesoscale, γ. j This represents the corresponding multi-scale loss weight.

[0015] Furthermore, the basic phase Huber sub-loss is: ; Where Huber represents the circumferential phase Huber loss, which is: ; Where ε represents the phase diagram Compared with the true phase diagram The phase difference between them, δ represents the supervision threshold.

[0016] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention creates a phase-shift interferometric phase retrieval system and method that integrates physical priors and temporal information: It explicitly introduces the weighted least-squares robust demodulation results into a deep network, combining physical interpretability with learning adaptability; through bidirectional temporal modeling and temporal attention aggregation, it can fully utilize the dynamic correlation between multiple phase-shifted images; through multi-scale deep supervision and composite loss synergistic optimization, it can simultaneously improve the global phase structure recovery capability and the local edge detail preservation capability. This invention maintains high stability and recovery accuracy even under turbulent interference, low-frequency conditions, and the presence of outliers. Attached Figure Description

[0017] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1A schematic diagram of the phase-shifting interferometric phase recovery system that integrates physical prior and temporal information, as described in an embodiment of the present invention; Figure 2 A schematic flowchart of the phase-shifting interferometric phase recovery method that integrates physical priors and temporal information, as described in an embodiment of the present invention; Figure 3 The comparison results are shown in the embodiments of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0019] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] like Figure 1 As shown in the embodiment of the present invention, the phase-shifting interferometric phase retrieval system that integrates physical priors and temporal information is as follows: Figure 1 As shown, the system includes a physical prior module, a temporal fusion module, an information fusion module, and a phase retrieval module. The physical prior module calculates various physical prior information from the acquired phase-shifting interferometry image sequence, forming physical prior features. The temporal fusion module performs temporal prediction and fusion of the physical prior features using a Long Short-Term Memory (LSTM) network to obtain temporal fusion features. The information fusion module concatenates the physical prior features and temporal fusion features, then performs multi-level feature extraction and step-by-step decoding to obtain phase features at different scales. The phase retrieval module reconstructs the phase features at each scale into a two-dimensional phase representation, and then reconstructs the two-dimensional phase representation into the corresponding phase map. The phase map corresponding to the phase feature with the largest scale is the finally recovered phase map.

[0021] In some embodiments, the data processing procedure of the physical prior module includes: To improve the physical consistency of the subsequent network, robust physical detuning is first performed on each sample. The intensity observation model is first established for each frame in the phase-shifting interferometric image sequence using the following formula: I t =a+ccos(θ t )+ssin(θ t ); Among them, I t Let θ represent the phase-shifted interferometric image of frame t, a represent the average intensity of the phase-shifted interferometric image sequence, c and s represent the cosine and sine components, respectively. tThe phase shift angle θ represents the phase shift angle of the t-th frame of the phase-shifted interferometric image. In this embodiment of the invention, the phase shift angle θ... t Uniformly distributed between 0 and 2π; For the above observation model, this invention employs a weighted least squares method with Huber weights for iterative solution. Specifically, the difference between the true frame image in the phase-shifting interferometric image sequence and its corresponding current fitted value is calculated, and based on the difference, the Huber weight of each frame image in the phase-shifting interferometric image sequence is calculated using the following formula: ; Where, ω t Let r represent the Huber weights of the t-th frame image. t δ represents the difference between the real frame image in frame t and the corresponding current fitted value, and δ represents the supervision threshold, which is specifically set to 0.06 in this embodiment of the invention; Transform the intensity observation model into a matrix equation: (A T WA)β=(A T WI); in, β=[a,c,s] T I = [I1, I2, ..., I t ]; The matrix equation is solved iteratively using the least squares method to obtain the average intensity, cosine component and sine component. After the iteration is completed, the standard deviation map of the difference during the iteration is calculated pixel by pixel along the time dimension. The initial phase map, modulation map, average intensity map, and quality map of the phase-shifted interferometric image sequence are calculated based on the obtained average intensity, cosine component, and sine component. The obtained initial phase map, modulation map, average intensity map, quality map, and standard deviation map are used to form physical prior features, where the standard deviation map is used to characterize the stability of pixels between different phase shift frames.

[0022] In some embodiments, the regression function obtained through iterative solution is: ; The iteration stops when the overall L2 change of the matrix β parameter between two consecutive iterations is less than 10. -6 In some other embodiments, the condition for stopping the iteration may also be that the number of iterations reaches a preset maximum number of iterations.

[0023] In some embodiments, the initial phase map, modulation map, and quality map are obtained using the following formula: ; ; quality = mod / (resid) std +10 -3 ); in, The initial phase map is represented by mod, the modulation map by quality, and the resid map by resid. std This represents a standard deviation plot. As you can understand, a mean intensity plot represents the mean intensity.

[0024] In some embodiments, the data processing of the temporal fusion module includes: performing convolutional projection on each frame of the phase-shifting interferometric image sequence, and feeding the obtained features into the forward ConvLSTM unit and the backward ConvLSTM unit to obtain forward temporal features and backward temporal features; concatenating the forward and backward features at the same time to form bidirectional temporal features; and using a temporal attention pooling module to adaptively weight and fuse the bidirectional temporal features at each time, while retaining the features at the last time, the temporal average features, and the temporal maximum response features to form temporal fusion features. In this embodiment of the invention, the ConvLSTM unit is an existing long short-term network (Shi X, Chen Z, Wang H, et al. Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting[J]. MIT Press, 2015. DOI:10.1007 / 978-3-319-21233-3_6.), and the temporal attention pooling module is also an existing processing module (Yang Z, Yang D, Dyer C, et al. Hierarchical Attention Networks for Document Classification[J]. 2016. DOI:10.18653 / v1 / N16-1174).

[0025] In some embodiments, the data processing of the information fusion module includes: concatenating physical prior features with temporal fusion features, the concatenated features entering the U-Net network, the encoding branch of the U-Net network performing multi-level encoding on the concatenated features, and the decoding branch of the U-Net network performing step-by-step decoding on the features from the encoding branch to obtain phase features at different scales.

[0026] In this embodiment of the invention, in the encoding branch of the U-Net network: the concatenated features are compressed to a basic channel count of 40, and multi-scale features are extracted step-by-step through multiple levels of residual convolutional blocks, including three downsampling operations, with the channel count progressively expanding from 40 to 80, 160, and 320. Each residual convolutional block employs group normalization, SiLU activation, optional Dropout, and a channel attention enhancement unit SEBlock to improve training stability and channel expressive power. At the junction of the encoding and decoding branches of the U-Net network, a multi-receptive field fusion module is used for feature transition. The input features are first transformed by residual convolutional blocks, and then dilated convolutions with dilation rates of 2 and 4 are used in parallel to extract contextual features at different scales. Finally, the ordinary convolutional branch and the two dilated convolutional branches are concatenated in the channel dimension and fused through residual blocks, thereby enhancing the network's ability to model complex phase structures and mid-to-long-range dependencies. In the decoding branch of the U-Net network: spatial resolution is gradually restored by three-level upsampling and residual convolutional blocks, and high-resolution details in the encoding branch are introduced through gated skip connections to obtain the phase features of each decoding level. In this embodiment of the invention, the gated skip connections are existing technology (Oktay O, Schlemper J, Folgoc LL, et al. Attention U-Net: Learning Where to Look for the Pancreas[J].2018.DOI:10.48550 / arXiv.1804.03999).

[0027] In some embodiments, the phase recovery module includes an output head corresponding to the phase feature scale; Each output head maps the phase features of the corresponding scale to a two-channel phase representation feature, one channel being a cosine component and the other a sine component. After normalizing the phase representation features, the phase is obtained through the arctangent function. In this embodiment of the invention, three scale phase maps are output: a fine-scale phase map, a medium-scale phase map, and a coarse-scale phase map. The phase feature with the largest scale is processed by the corresponding output head to obtain the fine-scale phase map. Similarly, the phase features with medium and smallest scales are processed by the corresponding output heads to obtain the medium-scale phase map and the coarse-scale phase map, respectively. The fine-scale phase map is the final recovered phase map.

[0028] This invention also provides a phase-shifting interferometric phase recovery method that integrates physical prior information and temporal information, combined with... Figure 1 and Figure 2 ,include: S1: Preprocess the acquired multiple sets of phase-shifting interferometric image sequences and corresponding real phase maps to obtain the training set.

[0029] In this embodiment of the invention, each set of phase-shifting interferometric image sequences includes 16 frames of phase-shifting interferometric images. The acquisition process of each set of phase-shifting interferometric image sequences is based on the method provided in the existing paper (Tang JU, Ji WU, Zhang J, et al. Highly robust spatiotemporal wavefront prediction with a mixed graph neural network in adaptive optics[J]. Photonics Research (English), 2023(11).), including: A turbulence physical model is constructed, which is based on the Kolmogorov / von Kármán turbulence theory. On this basis, a multi-layer phase screen and angular spectrum propagation are used to simulate the air refractive index fluctuations in the long optical path. At the same time, the Taylor frozen flow hypothesis is combined to introduce the AR(1) time series model to reproduce the dynamic airflow disturbances related to the frame and obtain the turbulence physical model. A standard phase-shifting interference optical path is constructed in the turbulence physics model to generate an ideal original interference light intensity distribution with no interference and regular fringes. Various systematic errors, such as phase shift step size deviation, Gaussian / Poisson imaging noise, motion vibration, image blurring and random bad frames, are introduced into the ideal original interference light intensity distribution to fit the actual measurement degradation effect and obtain the generation model of each frame of phase shift interference image; Multiple simulations were performed on the generative model to obtain multiple sets of phase-shifted interferometric image sequences, each consisting of 16 frames of phase-shifted interferometric images.

[0030] Furthermore, the data preprocessing process in this embodiment of the invention includes: uniformly adjusting the size of all frame phase-shifting interferometric images to 256×256 pixels; for phase-shifting interferometric images, performing random horizontal flipping, random vertical flipping, and random transposition to improve the model's generalization ability to spatial distribution changes; for the true phase map, performing zero-mean normalization on the phase values ​​of non-zero regions in the true phase map to reduce the impact of global bias on training.

[0031] S2: Construct a phase-shifting interference phase recovery system that integrates physical priors and temporal information as provided in this invention.

[0032] S3: Use the training set built in step S1 to train the system built in step S2 to obtain the phase retrieval model.

[0033] In some embodiments, the system is trained using the following joint loss function: L total =λ1L ph +λ2L sc +λ3L grad +λ4Lms +λ5L smooth +λ6L edge ; Among them, L total L represents the joint loss function. ph L represents phase loss. sc L represents the sine and cosine consistency loss. grad L represents the gradient loss. ms L represents multi-scale loss. smooth L represents the smoothing loss, used to suppress ineffective high-frequency oscillations. edge λ represents the edge consistency loss, and λ1~λ6 represent the loss weights.

[0034] The phase loss is: ; Among them, L Huber Represents the Huber sub-loss of the fundamental phase, η i This represents the Huber sub-loss weight corresponding to the phase map at the i-th scale before unifying the scale. This represents the phase diagram at the i-th scale before scaling. This represents the true phase diagram.

[0035] In this embodiment of the invention, phase maps of three scales are output, and the corresponding phase loss is as follows: ; In the above formula, The diagrams represent the fine-scale phase map, the medium-scale phase map, and the coarse-scale phase map, respectively, with η1~η3 representing the corresponding Huber loss weights. It is understood that loss calculation can only be performed when all phase maps are scaled to the same size as the true phase map. Therefore, in this embodiment of the invention, bilinear interpolation upsampling is used to unify the scale of all phase maps to the scale of the true phase map, with η1~η3 being 1, 0.4, and 0.3 respectively.

[0036] The sine and cosine consistency loss is: ; Where Ω represents the non-zero region in the true phase diagram, and |Ω| represents the total number of elements in the non-zero region. This represents the phase diagram that the system finally recovers. This represents the corresponding true phase diagram; The gradient loss is: ; in, and These represent the calculation of the first-order gradient in the horizontal and vertical directions, respectively. The smoothing loss is: ; It should be noted that the purpose of smoothing loss is to prevent the predicted slope surface from being covered with fine burrs and random noise, and to make the surface smooth. Therefore, smoothing loss does not require the truth value to be involved.

[0037] The edge consistency loss is: ; in, This represents the calculation of the second-order Laplace derivative.

[0038] The multi-scale loss is: ; in, This represents the phase map after downsampling at the j-th mesoscale from the phase map finally recovered by the system. This represents the phase map after downsampling the true phase map at the j-th mesoscale, γ. j This represents the corresponding multi-scale loss weight. In this embodiment of the invention, the phase map finally recovered by the system and its corresponding true phase map are simultaneously downsampled by 1 / 2 and 1 / 4, and the corresponding multi-scale loss is: ; In the above formula, The figures, in sequence, represent the phase map finally recovered by the system, the corresponding phase map after 1 / 2 downsampling, and the corresponding phase map after 1 / 4 downsampling. The numbers represent the true phase map, the true phase map after 1 / 2 downsampling, and the true phase map after 1 / 4 downsampling, respectively, with γ1~γ3 being 1, 0.6, and 0.3, respectively.

[0039] In some embodiments, the basic phase Huber sub-loss is: ; Where Huber represents the circumferential phase Huber loss, which is: ; Where ε represents the phase diagram Compared with the true phase diagram The phase difference between them, δ represents the supervision threshold. In this embodiment of the invention, the phase map is... Compared with the true phase diagram The phase difference between the two phases is wrapped in the interval [-π, π] before the circular phase Huber loss is calculated, thus avoiding the spurious large error caused by the 2π periodicity. The basic phase Huber sub-loss is then expressed as: ; Here, wrap represents the function wrapping.

[0040] In this embodiment of the invention, phase maps of three scales were obtained. The supervision threshold corresponding to the smallest scale phase map was 0.24, the supervision threshold corresponding to the medium scale phase map was 0.20, and the supervision threshold corresponding to the largest scale phase map (i.e. the phase map finally recovered) was 0.18.

[0041] Furthermore, the training hyperparameters in this embodiment of the invention include: updating the network parameters using the AdamW optimizer, with an initial learning rate preferably of 1.5 × 10⁻⁶. 4 The optimal minimum learning rate is 5×10. 7 The preferred weight decay is 8×10. 5 A preheating-cosine annealing learning rate strategy is adopted, with a preferred number of preheating rounds of 5. A gradient pruning strategy is used to limit the gradient norm to within 1.0, and mixed precision training is employed to improve computational efficiency. To further enhance stability during the validation phase, this embodiment introduces an exponential moving average model to smoothly update the main model parameters during training, with a preferred decay coefficient of 0.9992.

[0042] S4: Input the phase-shifting interferometric image sequence to be tested into the phase recovery model obtained in step S3, and output the final phase map.

[0043] To verify the effectiveness of the system and method provided by this invention, comparative experiments were also conducted in the embodiments of this invention, and the comparison results are as follows: Figure 3 As shown, specifically, using the same test data, the method provided by this invention and the existing window function weighted phase shift demodulation method (corresponding to) are compared. Figure 3 de Groot), weighted polynomial phase-shift demodulation method (corresponding to Figure 3 Kimi Hibino), and Huber's robust weighted least squares method (corresponding to Figure 3 A comparative experiment was conducted using WLS+Huber (a method from the original text), with root mean square error (RMSE) and mean absolute error (MAE) as evaluation indicators. Furthermore, to analyze the adaptability of the system and method provided by this invention under different degradation conditions, the test data were grouped and statistically analyzed according to the sample perturbation intensity parameter, dividing the test data into a weak perturbation group, a medium perturbation group, and a strong perturbation group, and comparing the recovery errors of different methods under different perturbations. Figure 3As can be seen, this invention achieves the lowest RMSE under weak, medium, and strong turbulence intensities, and maintains high recovery accuracy even as turbulence intensity increases. This is because this invention employs a physical prior construction method based on weighted least squares Huber fitting, combined with joint optimization strategies such as bidirectional temporal feature extraction and multi-scale deep supervision. This allows the model to fully utilize the physical and temporal information of the interferometric image, effectively suppressing the influence of noise and outliers on phase recovery, and improving the accuracy, stability, and robustness of phase prediction under complex turbulence conditions.

[0044] The method of this invention is applicable not only to simulations or offline datasets, but also to online measurement systems. By simply integrating the image acquisition module with the inference module, rapid phase reconstruction of the sample under test can be achieved. For application scenarios with different resolutions, frame rates, or noise levels, the input size, basic channel count, temporal hidden dimension, loss weights, and training epochs can be adjusted accordingly without departing from the core concept of this invention.

[0045] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0046] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A phase-shifting interferometric phase retrieval system integrating physical prior information and temporal information, characterized in that, include: The physical prior module calculates various physical prior information of the acquired phase-shifting interferometric image sequence to form physical prior features; The temporal fusion module uses a long short-term memory network to perform temporal prediction and fusion of physical prior features to obtain temporal fusion features. The information fusion module concatenates physical prior features with temporal fusion features, performs multi-level feature extraction and step-by-step decoding, and obtains phase features at different scales. The phase recovery module restores the phase features at each scale into a two-dimensional phase representation, and then restores the two-dimensional phase representation into the corresponding phase map. The phase map corresponding to the phase feature with the largest scale is the finally restored phase map.

2. The phase-shifting interferometric phase retrieval system integrating physical prior and temporal information according to claim 1, characterized in that, In the physics prior module: An intensity observation model is established for each frame in the phase-shifting interferometric image sequence, as follows: I t =a+ccos(θ t )+ssin(θ t ); Among them, I t Let θ represent the phase-shifted interferometric image of the t-th frame, a represent the average intensity of the phase-shifted interferometric image sequence, c and s represent the cosine and sine components, respectively. t Let represent the phase shift angle of the phase-shifted interferometric image in frame t; Calculate the difference between the true frame image in the phase-shifting interferometric image sequence and its corresponding current fitted value, and based on the difference, calculate the Huber weight of each frame image in the phase-shifting interferometric image sequence using the following formula: ； Where, ω t Let r represent the Huber weights of the t-th frame image. t δ represents the difference between the real frame image in frame t and the corresponding current fitted value, and δ represents the supervision threshold. Transform the intensity observation model into a matrix equation: (AM T WA)β=(A T WI) ( Among them, ,β=[a,c,s] T ,I=[I1,I2,...,I t ]; The matrix equation is solved iteratively using the least squares method to obtain the average intensity, cosine component, and sine component. After the iteration is completed, the standard deviation plot of the difference during the iteration process is calculated. The initial phase map, modulation map, average intensity map, and quality map of the phase-shifted interferometric image sequence are calculated based on the obtained average intensity, cosine component, and sine component. The obtained initial phase map, modulation map, average intensity map, quality map, and standard deviation map are used to form physical prior features.

3. The phase-shifting interferometric phase retrieval system integrating physical priors and temporal information according to claim 2, characterized in that, The initial phase map, modulation map, and quality map are obtained using the following formula: ； ； quality=mod / (resid std +10 -3 ); in, The initial phase map is represented by mod, the modulation map by quality, and the resid map by resid. std Represents a standard deviation plot.

4. The phase-shifting interferometric phase retrieval system integrating physical prior and temporal information according to claim 2, characterized in that, The regression function obtained through iterative solution is: ； The iteration stops when the overall L2 change of the matrix β parameter between two consecutive iterations is less than 10. -6 .

5. The phase-shifting interferometric phase retrieval system integrating physical prior and temporal information according to claim 1, characterized in that, In the time-series fusion module: Convolution projection is performed on each frame of the phase-shifting interferometric image sequence. The resulting features are fed into the forward ConvLSTM unit and the backward ConvLSTM unit to obtain forward and backward temporal features. The forward and backward features at the same time are then concatenated to form bidirectional temporal features. A temporal attention pooling module is used to adaptively weight and fuse the bidirectional temporal features at each time step, while retaining the features of the last time step, the temporal average features, and the temporal maximum response features to form temporal fusion features.

6. The phase-shifting interferometric phase retrieval system integrating physical prior and temporal information according to claim 1, characterized in that, In the information fusion module: Physical prior features are concatenated with temporal fusion features. The concatenated features are then fed into the U-Net network. The encoding branch of the U-Net network encodes the concatenated features at multiple levels, and the decoding branch of the U-Net network decodes the features from the encoding branch level by level to obtain phase features at different scales.

7. The phase-shifting interferometric phase retrieval system integrating physical prior and temporal information according to claim 1, characterized in that, The phase recovery module includes an output head corresponding to the phase feature scale; each output head maps the phase feature of the corresponding scale to a two-channel phase representation feature, one channel being a cosine component and the other channel being a sine component; after normalizing the phase representation feature, the phase is obtained through the arctangent function.

8. A phase-shifting interferometric phase retrieval method integrating physical prior information and temporal information, characterized in that, include: S1: Preprocess the acquired multiple sets of phase-shifting interferometric image sequences and corresponding real phase maps to obtain the training set; S2: Construct a phase-shifting interferometric phase recovery system that integrates physical prior information and temporal information as described in any one of claims 1 to 7; S3: Use the training set built in step S1 to train the system built in step S2 to obtain the phase retrieval model; S4: Input the phase-shifting interferometric image sequence to be tested into the phase recovery model obtained in step S3, and output the final phase map.

9. The phase-shifting interferometric phase recovery method according to claim 8, characterized in that, In step S3, the system is trained using the following joint loss function: L total =λ1L ph +λ2L sc +λ3L grad +λ4L ms +λ5L smooth +λ6L edge ; Among them, L total L represents the joint loss function. ph L represents phase loss. sc L represents the sine and cosine consistency loss. grad L represents the gradient loss. ms L represents multi-scale loss. smooth L represents the smoothing loss, used to suppress ineffective high-frequency oscillations. edge λ1~λ6 represent the edge consistency loss, and λ1~λ6 represent the loss weights; The phase loss is: ； Among them, L Huber Represents the Huber sub-loss of the fundamental phase, η i This represents the Huber sub-loss weight corresponding to the phase map at the i-th scale before unifying the scale. This represents the phase diagram at the i-th scale before scaling. Represents the true phase diagram; The sine and cosine consistency loss is: ； Where Ω represents the non-zero region in the true phase diagram, and |Ω| represents the total number of elements in the non-zero region. This represents the phase diagram that the system finally recovers. This represents the corresponding true phase diagram; The gradient loss is: ； in, and These represent the calculation of the first-order gradient in the horizontal and vertical directions, respectively. The smoothing loss is: ； The edge consistency loss is: ； in, This represents the calculation of the second-order Laplace derivative; The multi-scale loss is: ； in, This represents the phase map after downsampling at the j-th mesoscale from the phase map finally recovered by the system. This represents the phase map after downsampling the true phase map at the j-th mesoscale, γ. j This represents the corresponding multi-scale loss weight.

10. The phase-shifting interferometric phase recovery method according to claim 9, characterized in that, The basic phase Huber sub-loss is: ； Where Huber represents the circumferential phase Huber loss, which is: ； Where ε represents the phase diagram Compared with the true phase diagram The phase difference between them, δ represents the supervision threshold.

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