A single-degraded interferogram reconstruction method based on physical perception orthogonal decoupling

Abstract

The application discloses a single-degraded interferogram reconstruction method based on physical perception orthogonal decoupling, and belongs to the technical field of computational optical imaging and precise optical metrology. Under the constraint condition of not depending on preset space carrier frequency prior knowledge, a physical perception orthogonal decoupling network is constructed, a single-degraded interferogram is taken as a relative reference of phase shift space evolution, and a low-frequency background light field, an in-phase component field and an orthogonal component field which are mutually decoupled are output; adaptive stripping and compensation of composite coherent speckle and local illumination distortion are realized by combining a multi-dimensional physical constraint engine; and a standard virtual phase shift interferogram sequence is synthesized based on a pure physical base field, and an absolute wavefront is extracted. The application realizes dynamic analysis with high fidelity, robustness and processing efficiency in a complex physical degradation environment by fusing the spatial topology perception ability of deep learning and the physical law of interference evolution, and avoids the singular truncation of nonlinear phase regression.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary fields of computational optical imaging, precision optical metrology and deep learning, and specifically relates to a method for reconstructing a single degenerate interferogram based on physical perception orthogonal decoupling. Background Technology

[0002] Phase-shifting interferometry, with its high-precision quantization capabilities, plays a crucial role in precision optical metrology. It is a high-precision, non-contact measurement technique that utilizes the principle of interference to measure the surface morphology, wavefront error, or surface quality of optical components. Its core principle is to extract phase information from the object's surface by controlling the phase difference entering the optical path, thereby reconstructing the surface morphology. However, traditional multi-step phase-shifting interferometry is highly sensitive to physical disturbances in the measurement environment, making it difficult to meet the real-time detection requirements of high-speed dynamic evolution processes. Single-frame interferogram analysis, based on spatial carrier waves and fast Fourier transform, provides an important approach to overcoming time-domain limitations and achieving dynamic phase detection by performing frequency domain analysis and filtering on single-frame interferometric fringe patterns.

[0003] However, simultaneously resolving the low-frequency background light field, modulation amplitude envelope, and high-frequency phase field from a single interferometric observation image containing coherent speckle and spatial local illumination distortion is essentially a highly underdetermined physical inverse problem. Furthermore, due to the even-symmetric nature of the cosine function of the interference fringes, the resolution of a single closed interference fringe is prone to sign ambiguity. Theoretically, methods that heavily rely on prior knowledge of the spatial carrier frequency for frequency domain separation have limitations when dealing with complex high-order closed interference wavefronts, making stable reconstruction difficult.

[0004] To address the challenge of phase extraction from single-frame interferograms, traditional physical computation methods have been widely studied and applied. For example, the Windowed Fourier Transform (WFT) can extract phase through local frequency domain filtering, transforming the underdetermined problem of three unknown global fields (background, amplitude, and phase) into an overdetermined problem of estimating a few parameters within a local window. Furthermore, it utilizes analytic signals to avoid sign ambiguity caused by cosine dual functions, thus simultaneously achieving denoising, background suppression, and phase demodulation. However, when processing interferograms accompanied by complex physical noise such as strong coherent speckle, its smoothing effect easily suppresses high-frequency components of the wavefront, resulting in stripe-like clipping distortion in the reconstructed wavefront. The Riesz Transform can calculate the orthogonal signals of the interference fringes in the digital domain through spatial filtering, thereby synthesizing multi-frame phase-shifted sequences from a single frame image—a process that traditionally requires multiple mechanical phase shifts. However, due to the lack of an adaptive filtering mechanism for broadband noise in its differential operator, it easily introduces dense topological singularities into the wrapped phase in complex degenerate scenarios, leading to global distortion of the subsequent unwrapped wavefront. Another method is Regularized Phase Tracker (RPT), which has strong spatial continuity priors. By treating phase extraction as a global optimal problem, it constructs an objective function that includes data fidelity terms and phase prior constraints. Then, under the regularization framework, it directly solves for the phase field that satisfies physical and statistical assumptions, thus bypassing problems such as filtering, unwrapping, and symbol ambiguity in traditional methods. However, this method is prone to getting stuck in local phase cycle slips in steep speckle noise gradients or high-frequency abrupt change regions, resulting in severe step errors. Moreover, its underlying layer relies on high-density local minimization iterations for optimization, which is computationally time-consuming and difficult to meet the real-time requirements of dynamic continuous observation.

[0005] In recent years, the development of artificial intelligence has driven the shift in optical interferometric analysis towards a data-driven paradigm. Early deep learning methods focused on constructing end-to-end implicit mapping regression models from interferometric intensity to phase, such as MSPS-Net based on a multi-stage phase-shifting network and RSAGAN based on a self-attention mechanism. MSPS-Net, based on a multi-stage phase-shifting network, transforms a single interferometric intensity map into another interferometric map with a known phase shift by utilizing global feature learning capabilities, and then resolves the phase information using a classic two-step phase-shifting algorithm. RSAGAN, based on a self-attention mechanism, enhances the generator's understanding of the global fringe pattern of the interferometric map through self-attention, and learns the implicit mapping from a single intensity map to an interferometric map with a specific phase shift through adversarial training. It then combines this with a differentiable two-step phase-shifting formula to achieve dynamic phase recovery without explicit physical parameters. Although these purely data-driven networks effectively improve the fitting ability of fringes under specific distributions, they are constrained by the inherent 2π phase cutoff characteristic of the arctangent function. The existence of this discontinuous step function increases the difficulty of stable fitting in low signal-to-noise ratio environments. To alleviate the limitations of implicit mapping, recent research has attempted to introduce physical equations to fine-tune the network. For example, SIPN, which introduces an interferometric forward physical model for fine-tuning, works by initially training the network parameters using real / simulated data and then introducing the physical principles of optical interferometry to constrain the loss function to achieve secondary optimization of the network. This improves the model's generalization ability while maintaining accuracy. In addition, TECD-PSNet, which constructs a hybrid architecture of convolution and Transformer, differs from traditional methods. Instead of training a large single model from scratch, it selectively updates parameters based on a network pre-trained on large-scale data. It achieves rapid adaptation by leveraging the advantages of Transformer and convolution modules.

[0006] However, existing physics-guided deep learning methods lack mechanisms for explicit orthogonal physical field decoupling of low-frequency background and attenuation envelope, and often fail to apply physical boundary constraints. This leads to inevitable feature crosstalk and physical field coupling when the network attempts to isolate local non-uniform illumination distortion and speckle, resulting in weak fringe leakage or high-frequency background interference remaining in the reconstructed high-frequency phase field. For single-frame closed interferograms in real-world complex physical degradation environments, there is an urgent need for an absolute wavefront restoration method that can reduce the dependence on spatial carrier frequency priors at the theoretical level, effectively decouple physical component fields, and achieve a balance between reconstruction fidelity, robustness, and computational efficiency under complex noise interference. Summary of the Invention

[0007] To address the challenges of nonlinear feature coupling, phase truncation, and sign ambiguity in single-frame closed interferogram analytical tasks, as well as wavefront reconstruction distortion under complex degenerate environments such as strong coherence speckle and non-uniform illumination distortion, this invention provides a single-frame degenerate interferogram reconstruction method based on physically-perceived orthogonal decoupling. This method relies on the orthogonal phasor decomposition paradigm of the interferometric evolution equation to construct a physically-perceived orthogonal decoupling network. It transforms the traditional highly underdetermined and discontinuous phase direct regression problem into a physically constrained, smooth bipolar physical basis field decoupling process. Finally, it achieves global absolute wavefront reconstruction through synthesizing virtual phase shift sequences and analytical calculations.

[0008] The method includes: Step S1: Obtain degraded interferogram data, construct a dataset, and orthogonally partition the dataset; Step S2: Perform orthogonal phasor decoupling mapping on a single degenerate interferogram based on interferometric evolution orthogonal mapping logic; Step S3: Construct a Physically Aware Orthogonal Decoupling Network (POD-Net) to perform forward inference on a single degraded interferogram; Step S4: Based on the multidimensional physics constraint engine, construct the POD-Net parameter optimization objective loss function and the physics degradation adaptive curriculum learning strategy to jointly optimize the forward inference process of POD-Net in Step S3; Step S5: Based on the output of POD-Net, synthesize a four-step virtual phase-shift interferogram sequence with a standard phase-shift step size in the phase-shift dimension, and output the final wavefront reconstruction by solving the least squares global unwrapping algorithm based on discrete cosine transform.

[0009] In step S1, a two-dimensional Gaussian distribution of low-frequency background light intensity is used. and modulation amplitude To simulate non-uniform illumination, a computer simulation model was used to generate the true wavefront aberration and degraded interferogram based on a linear combination of the first 36 order Fringe Zernike polynomials; the spatial resolution of the degraded interferogram was 512×512 pixels. Furthermore, low-frequency background light intensity and modulation amplitude satisfy and Non-negative and anti-saturation boundary conditions; Furthermore, to meet the progressive requirements of physical degradation adaptive curriculum learning, the dataset is constructed through three independent evolutionary stages, with each stage generating several sets of simulation samples; Furthermore, the dataset was divided into a training set, a validation set, and a test set, with a ratio of 7:2:1; the Zernike multinomial coefficient distribution and random noise seed used in the test set were zero-overlapped with those in the training set. The process in step S2 does not rely on preset spatial carrier frequency prior knowledge. It achieves orthogonal phasor decoupling mapping of a single degenerate interferogram based on interferometric evolution orthogonal mapping logic. This process includes: According to the phase-shifting interference principle, the spatial evolution equation of the intensity distribution of the interference fringes captured on the detector plane is expressed as follows: in, For two-dimensional space pixel coordinates, For phase shift, The light intensity distribution of the low-frequency background light field. The modulation amplitude of the interference fringes, Wrap the phase around the target; The spatial evolution equation of interference fringe intensity distribution is orthogonally expanded based on trigonometric identities, and its expression is: in, For in-phase component fields, the expression is: ; For orthogonal component fields, the expression is: Two basis fields with definite physical meanings and mutual orthogonality are defined by orthogonal expansion.

[0010] Using a single degenerate interferogram as a relative benchmark for phase shift spatial evolution, that is, letting This subjectes it to the self-consistent physical constraints of light intensity: By providing self-supervised observation boundaries through self-consistent physical constraints on light intensity, the originally highly underdetermined nonlinear phase regression task is transformed into a well-determined linear decoupling between the low-frequency background light field and the in-phase component field, thereby avoiding the problems of phase truncation and symbol ambiguity. Step S3 achieves the separation of the low-frequency background light field, in-phase component field and orthogonal component field in step S2 by constructing the Physically Aware Orthogonal Decoupling Network POD-Net. POD-Net adopts an asymmetric topology architecture of single encoder-three parallel decoder, including a shared encoder, three parallel decoder channels and a multi-dimensional physical constraint engine. The shared encoder includes several cascaded Swin T blocks for dimensionality reduction of the input image and captures long-distance spatial dependence and global carrier frequency distribution patterns. The Swin T block includes a cascaded window multi-head self-attention mechanism, a multilayer perceptron, a sliding window self-attention mechanism, and a patch merging dimensionality reduction module. Furthermore, the dimension of the input degenerate interferogram tensor is... After entering the Swing T block, in order to perceive the distribution pattern of global spatial carrier frequencies under complex spatial constraints, the dimensionality reduction is performed by the tile merging dimensionality reduction module, and then the long-distance spatial dependencies are captured by the alternating window multi-head self-attention mechanism and sliding window self-attention mechanism. Furthermore, the shared encoder sequentially maps and enhances the dimension of its feature channels through cascaded Swin T blocks, ultimately outputting a high-dimensional deep semantic feature matrix; The three parallel decoder channels are, in order, the background light field decoder channel, the in-phase component field decoder channel, and the quadrature component field decoder channel. Each of the three decoder channels includes an independent center block, several ECA-U blocks, and a final block corresponding to the background light field decoder, the in-phase component field decoder, and the quadrature component field decoder. Furthermore, the independent central block includes a 3×3 convolutional layer, a batch normalization layer, and a ReLU activation function layer connected in sequence, which are used to split the encoded features and reduce feature crosstalk between different physical component fields from the bottom layer. Furthermore, the ECA-U block includes a bilinear upsampling unit, a cross-scale feature stitching unit, dual 3×3 convolutional layers, a global average pooling layer, a dimension reconstruction module, a sigmoid activation function layer, and a channel interaction weighting module. The ECA-U block calculates channel interaction weights through global average pooling and one-dimensional convolution to adaptively recalibrate feature channel mapping, and enhances the spatial high-frequency properties of interference fringes while maintaining local spatial topological coherence. The final block includes a final 3×3 convolutional layer, a final upsampling unit, a Sigmoid activation function, and a Tanh activation function, which are used to map the decoded features to the boundaries of real physical manifolds that conform to the laws of non-negativity of light intensity and bipolar symmetry. Furthermore, in the final block, the features of each branch are mapped to the real physical boundaries via a specific physical activation function; among them, the predicted background light field The magnitude of the output of the Sigmoid activation function is mapped to... The interval is determined to fit the non-negativity of the detector's light intensity; while the predicted in-phase component field... Orthogonal component fields of the prediction All are then output through the Tanh activation function, and are restricted to... Within the bipolar symmetric physical region.

[0011] Ultimately, POD-Net outputs three decoupled physical basis field tensors with the same dimension.

[0012] Step S4 guides the solution space of POD-Net to smoothly converge to the real physical manifold through a multi-dimensional physical constraint engine. Then, a physical degradation-based adaptive curriculum learning strategy is used to avoid data overlap and verify the robustness of POD-Net across the domain shift between simulation and real physical observation.

[0013] The total loss function of POD-Net is composed of a linearly weighted combination of five physical constraints, and its expression is as follows: in, For pixel-level data fidelity loss function, To reconstruct the self-consistent loss function, Let the amplitude envelope conservation loss function be... For the virtual spatiotemporal evolution self-consistent loss function, The polar coordinate phase cosine loss function, These are the hyperparameter weights of the corresponding loss functions.

[0014] Furthermore, pixel-level data fidelity loss function The expression is: By directly constraining POD-Net at the local pixel scale, the basic numerical accuracy of feature decoupling is established; then, the separation physical field is predicted by calculation. Compared with the benchmark theory real field The mean absolute error (L1 norm) between them.

[0015] Furthermore, reconstruct the self-consistent loss function. The expression is: in, The ideal interferometric truth value removes high-frequency probe noise and ensures uniform global illumination. The reconstruction self-consistent loss function reduces the propagation of strong coherent speckle to subsequent phase resolution processes from the physical manifold level through asymmetric denoising constraints. That is, the network's forward inference input is constrained to a degraded observation image containing composite physical noise; therefore, when calculating the reconstruction self-consistent loss, the constrained prediction... and The sum approximates the true value of ideal interference. This enables blind noise reduction and effective removal of speckle impurities from high-frequency detection.

[0016] Furthermore, the amplitude envelope conservation loss function The expression is: in, To suppress the minimal constant value of gradient singularity in the early stage of POD-Net backpropagation, the preferred value is... ; To obtain the true value of the modulation envelope, the prior of interference amplitude envelope conservation is introduced to avoid the attenuation of field-of-view edge fringe contrast caused by non-uniform illumination and vignetting effects of the optical system in a real closed-path interferometer. Furthermore, the amplitude envelope conservation loss function constrains the predicted composite amplitude of the orthogonal double field in local space to approximate the true value of the ideal, attenuated modulation envelope. This compensates for local illuminance distortion caused by non-uniform spatial lighting.

[0017] Furthermore, the virtual spatiotemporal evolution self-consistent loss function The expression is: in, It is a virtual phase-shifting interference sequence. The true-valued interferometric sequence is used; based on the classical phase-shift evolution equation, a virtual phase-shift interferometric sequence with four standard steps is analytically synthesized using the predicted basis field. and compared it with the corresponding truth interference sequence Apply full-field topological constraints to ensure that the physical field decoupled from a single degenerate interferogram has the rationality to evolve spatiotemporally to any phase-shift state; Furthermore, the classical phase shift evolution equation is expressed as follows: in, Let k be the phase shift at step k. .

[0018] Furthermore, the polar coordinate phase cosine loss function The expression is: in, and These are the network prediction field and the ideal true field of the in-phase components, respectively; and These are the network prediction field and the ideal true field, respectively, representing the orthogonal components; Modulation amplitude The predicted value satisfies ; Modulation amplitude The ideal truth value; By mapping the predicted and true physical fields to vectors on the complex plane in polar coordinates, and directly measuring and optimizing the cosine similarity of the phase angle between the predicted and true vectors through dot product normalization, this approach mathematically avoids the need for direct regression supervision of the wrapped phase, which relies on the arctangent function. Discontinuous step faults introduced by truncation characteristics.

[0019] By eliminating the derivative singularity caused by the inverse trigonometric function step by cosine similarity constraint, the dot product reaches its maximum value when the predicted vector and the true vector are completely coincident in phase angle, and the polar coordinate phase cosine loss function tends to zero.

[0020] During the POD-Net parameter training and optimization process, a physics-degradation adaptive curriculum learning strategy is employed to ensure robust convergence under the constraints of the aforementioned loss function and to mitigate the domain offset between the pure numerical simulation space and real physical observation equipment. The physics-degradation adaptive curriculum learning strategy comprises three progressive evolutionary stages: a pre-training stage, a carrier frequency generalization stage, and a degradation fine-tuning stage. Furthermore, the pre-training stage uses a dataset containing only one-dimensional pure spatial carrier frequencies. By introducing a large-span positive single-axis tilt aberration to generate high-density vertical fringes, the training and optimization process of POD-Net is constrained in a smooth constraint environment without sign ambiguity, thus establishing a basic mathematical mapping channel between interference light intensity and orthogonal dual fields. Furthermore, the carrier frequency generalization stage adopts an interferometric dataset with omnidirectional two-dimensional distributed carrier frequencies, enabling POD-Net to fully consider the spatial topology and logic flow of disambiguation in actual physical observations; by gradually releasing the high-frequency Zernike aberration order, the feature encoding space of POD-Net is guided to establish rotation invariance, enabling it to adaptively understand the directional ambiguity of a single closed fringe and improve the reconstruction of the spatial topology. Furthermore, the degradation fine-tuning stage is used to perform parameter transfer to the degradation domain, opening up Zernike aberrations within a preset order range, and employing a boundary noise generation strategy at the input to construct a physical noise domain dataset for fine-tuning training. During the fine-tuning training process, POD-Net is optimized using the loss function constructed above until the total loss function converges smoothly. Furthermore, boundary noise generation strategies include speckle, Poisson statistical fluctuations, and diffraction rings; Furthermore, to mitigate the domain offset between the numerical simulation environment and the real physical observation equipment, the acquisition of the degraded interferograms in the dataset synchronously references the publicly available test benchmark dataset (TECD Dataset) of a real closed optical path interferometer. The image data in this publicly available test benchmark dataset has the characteristics of real non-uniform edge illumination attenuation and environmental coherent speckle interference. Furthermore, when acquiring data from publicly available benchmark datasets, the datasets are also divided into training, validation, and test sets in a 7:2:1 ratio to support cross-domain fine-tuning and evaluation of the network's real generalization performance. Furthermore, the test set and training set in the publicly available benchmark dataset are divided into non-overlapping sample sources to avoid data overlap and verify the robustness of the network across the domain shift between simulation and real physical observation.

[0021] The process of synthesizing the four-step virtual phase-shifting interferogram sequence in step S5 includes: After completing the orthogonal decoupling of the forward physics field and network convergence, POD-Net stops nonlinear deep learning inference and switches to a deterministic classical mathematical analytical process.

[0022] First, the low-frequency background light field based on the predicted output of POD-Net. In-phase component field and orthogonal component fields A four-step virtual phase-shift interferogram sequence with a standard phase-shift step size in the phase-shift dimension is synthesized. The set standard phase-shift amount satisfies... The corresponding virtual sequence composition equation expands to: Subsequently, since the nonlinear optimization process has been isolated by the orthogonal component fields, POD-Net can call the standard four-step phase-shifting equation to extract the target principal value wrapping phase, the expression of which is: The extracted spatially continuous wrapped phase is input into the least squares global unwrapping algorithm based on discrete cosine transform (DCT). Since the DCT algorithm solves the phase Poisson equation globally in the frequency domain, it has excellent integral smoothing characteristics and can effectively resist topological singularities.

[0023] Finally, a morphological edge mask is applied to the unpacked wavefront, and the translation component (Piston) and tilt carrier frequency term (Tilt) of the stripping system are fitted by least-squares plane fitting to finally output the global absolute reconstructed wavefront.

[0024] The beneficial effects of this invention are as follows: This invention provides a degenerate interferogram reconstruction method based on physically perceptual orthogonal decoupling and virtual phase shifting. This method reduces the dependence of traditional single-frame interferometric fringe analysis on prior knowledge of spatial carrier frequencies. Through orthogonal phasor decomposition of the interferometric evolution equation, it reduces the dependence on enveloping inverse trigonometric functions. The unpacking singularity problem caused by phase truncation and ambiguity of closed fringe symbols is addressed. The network architecture employs a shared encoder and a three-parallel attention decoder, maintaining wavefront spatial topological coherence and reducing feature aliasing. Furthermore, the multi-dimensional physical constraint engine constructed in this invention establishes a denoising representation logic that maps noisy image input to a noiseless ideal truth loss check, achieving effective blind denoising representation and adaptive illumination envelope compensation, thus providing a definite physical conservation basis for orthogonal physical field separation. In addition, the three-stage physical degradation adaptive curriculum learning strategy designed in this invention, considering actual spatial constraints, effectively mitigates the domain offset between numerical simulation and real physical observation equipment. In complex composite degradation tests, this method not only smooths out local fringe leakage and high-frequency background interference but also shortens the single-frame network inference processing time and exhibits small errors. It provides a computational optics scheme with high reconstruction fidelity and noise robustness for dynamic transient high-precision optical metrology. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0026] Figure 1 This is a schematic diagram of the overall architecture of the Physically Perceived Orthogonal Decoupling Network (POD-Net) in the degenerate interferogram reconstruction method based on physically perceived orthogonal decoupling and virtual phase shifting provided in Embodiment 1 of the present invention. Figure 2 This is a schematic diagram of the overall process of the end-to-end absolute wavefront analysis framework for a single degenerate interferogram in a degenerate interferogram reconstruction method based on physical perception orthogonal decoupling and virtual phase shifting provided in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the physical phase evolution and degradation simulation process of the physical degradation adaptive interferometric dataset in a degradation interferogram reconstruction method based on physical perception orthogonal decoupling and virtual phase shifting provided in Embodiment 1 of the present invention; Figure 4 This is a visual schematic diagram of the orthogonal decoupling and wavefront reconstruction process in a degraded interferogram reconstruction method based on physical perception orthogonal decoupling and virtual phase shifting provided in Embodiment 1 of the present invention under a complex physical noise environment. Figure 5 This is a qualitative comparison of the reconstructed wavefront and residual obtained by the traditional classical single-frame interferometric wavefront reconstruction algorithm in the degenerate interferogram reconstruction method based on physical perception orthogonal decoupling and virtual phase shift provided in Embodiment 1 of the present invention. Figure 6This diagram illustrates the orthogonal decomposition and full-link wavefront reconstruction process under complex degradation conditions observed by a real closed optical path interferometer in a degradation interferogram reconstruction method based on physical perception orthogonal decoupling and virtual phase shifting, as provided in Embodiment 1 of the present invention. Figure 7 This is a qualitative comparison of the absolute wavefront reconstruction morphology and spatial wavefront error distribution in a degraded interferogram reconstruction method based on physical perception orthogonal decoupling and virtual phase shifting provided in Embodiment 1 of the present invention, and in the prior art, a deep learning algorithm in a real composite degraded interferometric environment. in: Figure 1 (a) in the figure is an asymmetric backbone feature decoupling architecture diagram of a single encoder-three parallel decoder; Figure 1 (b) in the diagram is a schematic diagram of the scope of the multidimensional physical constraint loss engine and its error backpropagation nodes; Figure 1 (c) is a schematic diagram of the structure of the Swin T block in the shared encoder; Figure 1 (d) in the diagram is a schematic diagram of the structure of the ECA-U block in the decoder; Figure 1 (e) in the diagram is a schematic diagram of the structure of an independent central block; Figure 1 (f) in the diagram is a schematic diagram of the final block structure; Figure 3 (a) in the image is the true wavefront aberration map generated based on the Zernike polynomial; Figure 3 (b) in the figure is a one-dimensional clean space carrier interferogram generated during the pre-training phase; Figure 3 (c) in the diagram represents the omnidirectional two-dimensional spatial carrier frequency generalization interferogram generated during the carrier frequency generalization stage. Figure 3 (d) in the figure is a composite physical degradation interferogram of coherent speckle, Poisson speckle fluctuations and diffraction artifacts injected during the degradation fine-tuning stage; Figure 4 (a) in the figure is a schematic diagram of the low-frequency background light field and the orthogonal double field carrying phase polarity information predicted and separated from a single input by POD-Net; Figure 4 (b) in the diagram is a standard four-step virtual phase-shifting interferometry sequence based on analytical orthogonal basis field synthesis; Figure 4 (c) in the figure represents the topologically continuous principal value wrapped phase graph extracted from the virtual sequence; Figure 4 (d) in the figure is the distribution map of the unsinked tilt absolute wavefront and its wavefront residuals predicted by POD-Net; Figure 4 (e) in the figure shows the final absolute wavefront and its wavefront residual distribution after eliminating the translation and tilt components; Figure 5 (a) in the figure is a qualitative comparison of the reconstructed wavefront and residual obtained by different wavefront reconstruction algorithms under the true value of the two-dimensional spatial carrier frequency; Figure 5(a1) is a schematic diagram showing the qualitative comparison of the reconstructed wavefront and residual obtained by the windowed Fourier transform algorithm based on the true value of the two-dimensional space carrier frequency. Figure 5 (a2) is a schematic diagram showing the qualitative comparison of the reconstructed wavefront and residual obtained by the Ritz transform algorithm under the true value of the two-dimensional space carrier frequency; Figure 5 (a3) is a schematic diagram showing the qualitative comparison of the reconstructed wavefront and residual obtained by the regularized phase tracking algorithm under the true value of the two-dimensional spatial carrier frequency; Figure 5 (a4) is a schematic diagram showing the qualitative comparison of the reconstructed wavefront and residual obtained by the POD-Net algorithm provided by this invention under the true value of the two-dimensional spatial carrier frequency. Figure 5 (b) is a schematic diagram showing a qualitative comparison of the reconstructed wavefronts and residuals obtained by different wavefront reconstruction algorithms under the true value of composite physical degradation. Figure 5 (b1) is a schematic diagram showing the qualitative comparison of the reconstructed wavefront and residual obtained by the windowed Fourier transform algorithm under the true value of composite physical degradation; Figure 5 (b2) is a schematic diagram showing the qualitative comparison of the reconstructed wavefront and residual obtained by the Ritz transform algorithm under the true value of composite physical degradation; Figure 5 (b3) is a schematic diagram showing the qualitative comparison of the reconstructed wavefront and residual obtained by the regularized phase tracking algorithm under the true value of composite physical degradation; Figure 5 (b4) is a schematic diagram showing the qualitative comparison of the reconstructed wavefront and residual obtained by the POD-Net algorithm provided by this invention under the true value of composite physical degradation. Figure 6 (a) in the figure is a schematic diagram of the predicted and extracted background light field and the high-contrast orthogonal component field; Figure 6 (b) in the diagram is a schematic diagram of the synthesized virtual phase-shift sequence; Figure 6 (c) in the diagram is a schematic of the extracted principal value wrapped in the phase; Figure 6 (d) in the figure shows the reconstructed morphology of the unslidable and unslidable absolute wavefronts and their corresponding error distribution diagrams. Figure 6 (e) in the figure represents the spatial difference map between the input interferogram and the model-reconstructed zero-degree virtual reference frame; Figure 7 (a) in the figure is a schematic diagram of the absolute wavefront reconstruction morphology under a real composite degenerate interferometric environment; Figure 7 (b) is a schematic diagram of the absolute wavefront reconstruction morphology obtained by cascaded fully convolutional implicit mapping under a real composite degenerate interference environment; Figure 7 (c) is a schematic diagram of the absolute wavefront reconstruction morphology obtained by a spatial self-attention generative adversarial network under a real composite degenerate interference environment; Figure 7 (d) in the figure is a schematic diagram of the absolute wavefront reconstruction morphology obtained by a physically guided non-explicit decoupling network under a real composite degenerate interference environment; Figure 7 (e) in the figure is a schematic diagram of the absolute wavefront reconstruction morphology obtained by a hybrid network of convolution and Transformer under a real composite degenerate interference environment; Figure 7 (f) is a schematic diagram of the absolute wavefront reconstruction morphology obtained by the physical sensing orthogonal decoupling network provided by the present invention under a real composite degenerate interference environment; Figure 7 (a1) is a schematic diagram of qualitative comparison of spatial wavefront error distribution under real composite degenerate interferometry environment; Figure 7 (b1) is a qualitative comparison diagram of the spatial wavefront error distribution obtained by cascaded fully convolutional implicit mapping under real composite degenerate interference environment; Figure 7 (c1) is a qualitative comparison diagram of the spatial wavefront error distribution obtained by a spatial self-attention generative adversarial network under a real composite degenerate interferometry environment. Figure 7 (d1) is a qualitative comparison diagram of the spatial wavefront error distribution obtained by a physically guided non-explicit decoupling network under a real composite degenerate interference environment. Figure 7 (e1) is a qualitative comparison diagram of the spatial wavefront error distribution obtained by a hybrid network of convolution and Transformer under a real composite degenerate interference environment; Figure 7 (f1) is a qualitative comparison diagram of the spatial wavefront error distribution obtained by the physical sensing orthogonal decoupling network provided by the present invention under a real composite degenerate interference environment. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] Example 1 This embodiment provides a degenerate interferogram reconstruction method based on physically-perceived orthogonal decoupling and virtual phase shifting. Based on the orthogonal phasor decomposition paradigm of the interferometric evolution equation, the method constructs a physically-perceived orthogonal decoupling network, transforming the traditional highly underdetermined and discontinuous phase direct regression problem into a smooth bipolar physical basis field decoupling process with physical constraints. Finally, the reconstruction of the global absolute wavefront is achieved through the synthesis of virtual phase shift sequences and analytical calculation processes.

[0029] The process of this method is as follows: Figure 2As shown, normalized data is obtained through three stages of learning in the physical degradation adaptive curriculum. This data is then trained using a POD-Net consisting of a shared encoder, a three-parallel decoder, and a multi-dimensional physical constraint engine to obtain pre-trained physical perception weights. During the testing phase, real interferometric data combined with the pre-trained physical perception weights are used to decouple the low-frequency background light field, in-phase component field, and orthogonal component field. Four interferograms are then synthesized using virtual phase-shift sequences. Principal value wrapped phase maps are obtained through standard four-step phase-shift analysis. Spatially continuous wrapped phase is then obtained based on DCT least-squares global unwrapping. Finally, absolute wavefront reconstruction is obtained through least-squares plane fitting and de-tilting. This method includes: Step S1: Obtain degraded interferogram data, construct a dataset, and orthogonally partition the dataset; Before performing parameter optimization on the neural network, an interferogram dataset for network training and testing is first constructed.

[0030] Low-frequency background light intensity using a two-dimensional Gaussian distribution and modulation amplitude To simulate non-uniform illumination, a computer simulation model was used to generate the true wavefront aberration and degraded interferogram based on a linear combination of the first 36 order Fringe Zernike polynomials; the spatial resolution of the degraded interferogram was 512×512 pixels. Low frequency background light intensity and modulation amplitude satisfy and The dataset is constructed using non-negative and anti-saturation boundary conditions. To meet the progressive requirements of adaptive learning in physics degradation, the dataset is built through three independent evolutionary stages, each generating 10,000 sets of simulation samples. To eliminate the risks of data memory and overfitting during model training, the dataset is divided into training, validation, and test sets in a ratio of 7:2:1. The Zernike multinomial coefficient distribution and random noise seed used in the test set are zero-overlapping with those in the training set. Step S2: Perform orthogonal phasor decoupling mapping on a single degenerate interferogram based on interferometric evolution orthogonal mapping logic; The process in step S2 does not rely on preset spatial carrier frequency prior knowledge. It achieves orthogonal phasor decoupling mapping of a single degenerate interferogram based on interferometric evolution orthogonal mapping logic. This process includes: According to the phase-shifting interference principle, the spatial evolution equation of the intensity distribution of the interference fringes captured on the detector plane is expressed as follows: in, For two-dimensional space pixel coordinates, For phase shift, The light intensity distribution of the low-frequency background light field. The modulation amplitude of the interference fringes, Wrap the phase around the target; The spatial evolution equation of interference fringe intensity distribution is orthogonally expanded based on trigonometric identities, and its expression is: in, For in-phase component fields, the expression is: ; For orthogonal component fields, the expression is: Two basis fields with definite physical meanings and mutual orthogonality are defined by orthogonal expansion.

[0031] Using a single degenerate interferogram as a relative benchmark for phase shift spatial evolution, that is, letting This subjectes it to the self-consistent physical constraints of light intensity: By providing self-supervised observation boundaries through self-consistent physical constraints on light intensity, the originally highly underdetermined nonlinear phase regression task is transformed into a well-determined linear decoupling between the low-frequency background light field and the in-phase component field, thereby avoiding the problems of phase truncation and symbol ambiguity. Step S3: Construct a Physically Aware Orthogonal Decoupling Network (POD-Net) to perform forward inference on a single degraded interferogram; Step S3 achieves the separation of the low-frequency background light field, in-phase component field, and orthogonal component field in step S2 by constructing the Physically Aware Orthogonal Decoupling Network (POD-Net). POD-Net employs an asymmetric topology architecture of a single encoder and three parallel decoders, such as... Figure 1 As shown, it includes a shared encoder, three parallel decoder channels, and a multi-dimensional physical constraint engine; The shared encoder includes four cascaded Swing T blocks for dimensionality reduction of the input image and captures long-range spatial dependencies and global carrier frequency distribution patterns. The Swing T block includes a cascaded window multi-head self-attention mechanism, a multilayer perceptron, a sliding window self-attention mechanism, and a patch merging dimensionality reduction module. Furthermore, the dimension of the input degenerate interferogram tensor is... After entering the Swing T block, in order to perceive the distribution pattern of global spatial carrier frequencies under complex spatial constraints, the dimensionality reduction is performed by the tile merging dimensionality reduction module, and then the long-distance spatial dependencies are captured by the alternating window multi-head self-attention mechanism and sliding window self-attention mechanism. Furthermore, the shared encoder sequentially maps and enhances the dimension of its feature channels through cascaded Swin T blocks, ultimately outputting a high-dimensional deep semantic feature matrix; The three parallel decoder channels are, in order, the background light field decoder channel, the in-phase component field decoder channel, and the quadrature component field decoder channel. Each of the three decoder channels includes an independent center block, three ECA-U blocks, and a final block corresponding to the background light field decoder, the in-phase component field decoder, and the quadrature component field decoder. Furthermore, the independent central block includes a 3×3 convolutional layer, a batch normalization layer, and a ReLU activation function layer connected in sequence, which are used to split the encoded features and reduce feature crosstalk between different physical component fields from the bottom layer. Furthermore, the ECA-U block includes a bilinear upsampling unit, a cross-scale feature stitching unit, dual 3×3 convolutional layers, a global average pooling layer, a dimension reconstruction module, a sigmoid activation function layer, and a channel interaction weighting module. The ECA-U block calculates channel interaction weights through global average pooling and one-dimensional convolution, which are used to adaptively recalibrate the feature channel mapping and enhance the spatial high-frequency properties of the interference fringes while maintaining the local spatial topological coherence. The final block includes a final 3×3 convolutional layer, a final upsampling unit, a Sigmoid activation function, and a Tanh activation function, which are used to map the decoded features to the boundaries of real physical manifolds that conform to the laws of non-negativity of light intensity and bipolar symmetry. Furthermore, in the final block, the features of each branch are mapped to the real physical boundaries via a specific physical activation function; among them, the predicted background light field The magnitude of the output of the Sigmoid activation function is mapped to... The interval is determined to fit the non-negativity of the detector's light intensity; while the predicted in-phase component field... Orthogonal component fields of the prediction All are then output through the Tanh activation function, and are restricted to... Within the bipolar symmetric physical region.

[0032] Ultimately, POD-Net outputs three decoupled physical basis field tensors with the same dimension.

[0033] Step S4: Based on the multidimensional physics constraint engine, construct the POD-Net parameter optimization objective loss function and the physics degradation adaptive curriculum learning strategy to jointly optimize the forward inference process of POD-Net in Step S3; Step S4 guides the solution space of POD-Net to smoothly converge to the real physical manifold through a multi-dimensional physical constraint engine. Then, a physical degradation-based adaptive curriculum learning strategy is used to avoid data overlap and verify the robustness of POD-Net across the domain shift between simulation and real physical observation.

[0034] The total loss function of POD-Net is composed of a linearly weighted combination of five physical constraints, and its expression is as follows: in, For pixel-level data fidelity loss function, To reconstruct the self-consistent loss function, Let the amplitude envelope conservation loss function be... For the virtual spatiotemporal evolution self-consistent loss function, The polar coordinate phase cosine loss function, These are the hyperparameter weights of the corresponding loss functions.

[0035] Pixel-level data fidelity loss function The expression is: By directly constraining POD-Net at the local pixel scale, the basic numerical accuracy of feature decoupling is established; then, the separation physical field is predicted by calculation. Compared with the benchmark theory real field The mean absolute error (L1 norm) between them.

[0036] Reconstruct the self-consistent loss function The expression is: in, The ideal interferometric truth value removes high-frequency probe noise and ensures uniform global illumination. The reconstruction self-consistent loss function reduces the propagation of strong coherent speckle to subsequent phase resolution processes from the physical manifold level through asymmetric denoising constraints. That is, the network's forward inference input is constrained to a degraded observation image containing composite physical noise; therefore, when calculating the reconstruction self-consistent loss, the constrained prediction... and The sum approximates the true value of ideal interference. This enables blind noise reduction and effective removal of speckle impurities from high-frequency detection.

[0037] Amplitude envelope conservation loss function The expression is: in, To suppress the minimal constant value of gradient singularity in the early stage of POD-Net backpropagation, the preferred value is... ; To obtain the true value of the modulation envelope, the prior of interference amplitude envelope conservation is introduced to avoid the attenuation of field-of-view edge fringe contrast caused by non-uniform illumination and vignetting effects of the optical system in a real closed-path interferometer. Furthermore, the amplitude envelope conservation loss function constrains the predicted composite amplitude of the orthogonal double field in local space to approximate the true value of the ideal, attenuated modulation envelope. This compensates for local illuminance distortion caused by non-uniform spatial lighting.

[0038] Virtual spatiotemporal evolution self-consistent loss function The expression is: in, It is a virtual phase-shifting interference sequence. The true-valued interferometric sequence is used; based on the classical phase-shift evolution equation, a virtual phase-shift interferometric sequence with four standard steps is analytically synthesized using the predicted basis field. and compared it with the corresponding truth interference sequence Apply full-field topological constraints to ensure that the physical field decoupled from a single degenerate interferogram has the rationality to evolve spatiotemporally to any phase-shift state; The classical phase shift evolution equation is expressed as follows: in, Let k be the phase shift at step k. .

[0039] Polar phase cosine loss function The expression is: in, and These are the network prediction field and the ideal true field of the in-phase components, respectively; and These are the network prediction field and the ideal true field, respectively, representing the orthogonal components; Modulation amplitude The predicted value satisfies ; Modulation amplitude The ideal truth value; By mapping the predicted and true physical fields to vectors on the complex plane in polar coordinates, and directly measuring and optimizing the cosine similarity of the phase angle between the predicted and true vectors through dot product normalization, this approach mathematically avoids the need for direct regression supervision of the wrapped phase, which relies on the arctangent function. The discontinuous step fault introduced by the truncation characteristic is addressed by eliminating the derivative singularity caused by the inverse trigonometric function step through cosine similarity constraints. When the predicted vector and the true vector completely coincide in phase angle, the dot product reaches its maximum value, and the polar coordinate phase cosine loss function tends to zero.

[0040] The physics-degradation adaptive curriculum learning strategy includes: during the POD-Net parameter training and optimization process, the strategy ensures robust convergence under the constraints of the aforementioned loss function and mitigates the domain offset between the pure numerical simulation space and real physical observation equipment. The physics-degradation adaptive curriculum learning strategy comprises three progressive evolutionary stages: a pre-training stage, a carrier frequency generalization stage, and a degradation fine-tuning stage, such as... Figure 3 As shown; The physical constraint configurations for the three progressive evolution stages are shown in Table 1: Table 1. Course Learning Stages and Physical Constraint Configurations for the Physically Degraded Adaptive Interferometric Dataset The pre-training phase uses a dataset containing only one-dimensional pure spatial carrier frequencies. By introducing a large-span positive single-axis tilt aberration to generate high-density vertical fringes, the training and optimization process of POD-Net is constrained in a smooth constraint environment without sign ambiguity, thus establishing a basic mathematical mapping channel between interference light intensity and orthogonal dual fields. The carrier frequency generalization stage uses an interferometric dataset with omnidirectional two-dimensional distributed carrier frequencies, enabling POD-Net to fully consider the spatial topology and logic flow of disambiguation in actual physical observations. By gradually releasing the high-frequency Zernike aberration order, the feature encoding space of POD-Net is guided to establish rotation invariance, enabling it to adaptively understand the directional ambiguity of a single closed fringe and improve the reconstruction of the spatial topology. The degradation fine-tuning phase is used to perform parameter transfer to the degradation domain, opening up Zernike aberrations within a preset order range, and employing a boundary noise generation strategy at the input to construct a physical noise domain dataset for fine-tuning training. During the fine-tuning training process, POD-Net is optimized using the loss function constructed above until the total loss function converges smoothly; the boundary noise generation strategies include speckle, Poisson statistical fluctuations, and diffraction rings; To mitigate the domain offset between the numerical simulation environment and real physical observation equipment, the acquisition of degraded interferograms in the dataset synchronously references the publicly available test benchmark dataset (TECD Dataset) of a real closed optical path interferometer. The image data in this publicly available test benchmark dataset has the characteristics of real non-uniform edge illumination attenuation and environmental coherent speckle interference. When acquiring data from the publicly available test benchmark dataset, the dataset is also divided into training, validation, and test sets in a 7:2:1 ratio to support cross-domain fine-tuning of the network and evaluation of real generalization performance. The test set and training set in the publicly available test benchmark dataset are divided according to non-overlapping sample sources to avoid data overlap and verify the robustness of the network across the domain offset between simulation and real physical observation.

[0041] Step S5: Based on the output of POD-Net, synthesize a four-step virtual phase-shift interferogram sequence with a standard phase-shift step size in the phase-shift dimension, and output the final wavefront reconstruction by solving the least squares global unwrapping algorithm based on discrete cosine transform. After completing the orthogonal decoupling of the forward physics field and network convergence, POD-Net stops nonlinear deep learning inference and transitions to a deterministic classical mathematical analytical process: First, the low-frequency background light field based on the network prediction output. In-phase component field and orthogonal component fields A four-step virtual phase-shift interferogram sequence with a standard phase-shift step size in the phase-shift dimension is synthesized. The set standard phase-shift amount satisfies... The corresponding virtual sequence composition equation expands to: Subsequently, since the nonlinear optimization process has been isolated by the orthogonal component fields, POD-Net can call the standard four-step phase-shifting equation to extract the target principal value wrapping phase, the expression of which is: The extracted spatially continuous wrapped phase is input into the least squares global unwrapping algorithm based on discrete cosine transform (DCT). Since the DCT algorithm solves the phase Poisson equation globally in the frequency domain, it has excellent integral smoothing characteristics and can effectively resist topological singularities.

[0042] Finally, a morphological edge mask is applied to the unpacked wavefront, and the translation component (Piston) and tilt carrier frequency term (Tilt) of the stripping system are fitted by least-squares plane fitting to finally output the global absolute reconstructed wavefront.

[0043] A visual diagram illustrating the orthogonal decoupling and wavefront reconstruction process under complex physical noise conditions is shown below. Figure 4 As shown, POD-Net first predicts and separates the low-frequency background light field and the orthogonal double field carrying phase polarity information from a single input. Then, it synthesizes a standard four-step virtual phase-shifting interferometry sequence based on the analytical orthogonal basis field. Next, it extracts the topological continuous principal value wrapped phase map from the virtual sequence. POD-Net predicts the unsinked tilted absolute wavefront and its wavefront residual. After eliminating the translation and tilt components, the final absolute wavefront and its wavefront residual distribution map are obtained.

[0044] In the complex degradation environment of observations using a real closed optical path interferometer, the orthogonal decomposition and full-link wavefront reconstruction processes are as follows: Figure 6As shown, the network proposed in this invention can effectively separate low-frequency background light from orthogonal component fields, not only visually suppressing high-frequency speckle impurities in the original input, but also adaptively compensating for non-uniform edge illumination attenuation; the final reconstructed de-tilted absolute wavefront has morphological consistency with the true value (the root mean square error of the wavefront residual is 0.00143λ), which shows that the method of this invention still has excellent orthogonal decoupling accuracy and noise robustness in real and complex physical degradation environments.

[0045] The effectiveness of the method provided in this invention was verified by testing the numerical convergence stability under different physical degradation phases. The test results are shown in Table 2. Table 2. Component decoupling and wavefront quantitative evaluation results of POD-Net under different physical degradation phases. As shown in Table 2, the method provided by this invention maintains a predicted peak signal-to-noise ratio (PSNR) of over 60 dB for the orthogonal base field under the test conditions listed in Table 2, across the evolution from one-dimensional clean carrier frequencies to two-dimensional omnidirectional carrier frequencies and even complex physical noise. Even under the pressure of local jumps in the inverse trigonometric function caused by strong speckle dark regions, the wrapped-phase PSNR drops to 34.65 dB. Relying on the topological fidelity of orthogonal decomposition and the global integration of the back-end DCT, the final untilted absolute wavefront root mean square (RMS) error still converges smoothly to [the specified value]. This demonstrates that the method exhibits noise robustness under the stated test conditions.

[0046] Furthermore, compared with the prior art, the outstanding substantive features and significant progress (beneficial effects) of the embodiments of the present invention are specifically reflected in the following experimental and data verifications: The method provided by this invention was compared with conventional methods in the prior art under a combined noise environment, and the results are as follows: Figure 5The results are shown in Table 3. The windowed Fourier transform is described in “Kemao Q. Windowed Fourier transform for fringe pattern analysis[J]. Applied Optics, 2004, 43(13): 2695-2702.”, the Riesz transform in “Tounsi Y, Kumar M, Siari A, et al. Digital four-step phase-shifting technique from a single fringe pattern using Riesz transform[J]. Optics Letters, 2019, 44(14): 3434-3437.”, and the regularized phase tracking in “Servin M, Marroquin JL, Cuevas F J. Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms[J]. Journal of the Optical Society of America A, 2001, 18(3): 689-695.”. Table 3. Quantitative Comparison Results of Single-Amplitude Degraded Interferometric Wavefront Reconstruction Algorithms under Complex Physical Noise Environment As shown in Table 3, under combined noise conditions, traditional windowed Fourier transform (WFT), Riesz transform, and regularized phase tracking (RPT) generally suffer from a degradation of wavefront RMS error due to a lack of high-frequency noise immunity mechanisms or limitations imposed by carrier frequency priors. to The processing time for a single frame is as high as 36.65 to 44.05 seconds due to the high-density grid scanning and iterative optimization. The method of this invention not only reduces the wavefront RMS error under the conditions listed in Table 3, but also achieves an average processing time of 26 milliseconds per frame through forward inference using a lightweight orthogonal matrix, which is beneficial to improving the engineering feasibility of dynamic detection.

[0047] The results of the controlled variable ablation experiment of the core physics constraints and training strategy are shown in Table 4: Table 4. Quantitative Results of Ablation Experiments on Control Variables for Core Physics Constraints and Training Strategies As shown in Table 4, the baseline model V1, which relies solely on L1 loss, struggles to extract the effective physical field under strong speckle conditions. This is further supported by the amplitude envelope conservation loss function in this invention. (Provides adaptive envelope compensation), polar coordinate phase cosine loss function The successive introduction of techniques such as (avoiding truncated gradient singularity), efficient channel attention (ECA) (maintaining high-frequency topological response), and adaptive curriculum learning improved the quality of the synthesized sequence from 20.35dB to 59.15dB and reduced the wavefront RMS error, establishing the close coupling relationship between the various technical features of this scheme and the necessity of joint optimization.

[0048] Figure 7The invention presents a qualitative comparison of the absolute wavefront reconstruction morphology and spatial wavefront error distribution between the method provided in this invention and traditional methods under real composite degraded interferometry environments. Table 5 shows the results of the cross-domain generalization ability and reconstruction comparison experiments of real observation scenarios. MSPS-Net is referenced from "Zhao Y, Hu K, Liu F. One-shot phaseretrieval method for interferometry using a multi-stage phase-shifting network[J]. IEEE Photonics Technology Letters, 2022, 35(10): 577-580."; RSAGAN is referenced from "Wu B, Zhang Q, Liu T, et al. RSAGAN: Rapid self-attention generative adversarial nets for single-shot phase-shifting interferometry[J]. Optics and Lasers in Engineering, 2023, 168: 107672."; SIPN is referenced from "Shi R, Zhang T, Shao Y, et al. Single-frame interferogram phase retrieval using a phase-shifting generative adversarial network with physics-based fine-tuning[J]. AppliedOptics, 2024, 63(22): 5856-5866."; TECD-PSNet reference "Hu K, Sun D, ​​Zhao Y.Enhanced single-frame interferometry via hybrid conv-transformer architecture for ultra-precise phase retrieval[J]. Optics Express, 2024, 32(17): 30226-30241."; Table 5. Comparison of Cross-Domain Quantization Results of Different Deep Learning Models under Real-World Composite Degradation Environments As shown in Table 5, when the test benchmark is transferred to the real closed optical path public interference set (TECD Dataset) with edge illumination attenuation and unknown environmental interference, existing deep learning networks based on pure convolutional implicit mapping (MSPS-Net) or non-explicit physical constraints (SIPN) inevitably exhibit feature aliasing and stripe leakage (RMS error distribution in the range of 0.5%). The method of this invention, through effective decoupling of the underlying orthogonal physical field, still stabilizes the global average RMS error at a certain level under real-domain offset. This demonstrates that the method of the present invention possesses high physical interpretability and robustness against noise in degraded environments in the field of dynamic high-precision optical metrology.

[0049] Some steps in the embodiments of the present invention can be implemented using software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk.

[0050] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for reconstructing a single degenerate interferogram based on physical perception orthogonal decoupling, characterized in that, The method described above performs orthogonal phasor decoupling mapping on a single degenerate interferogram based on interferometric evolution orthogonal mapping logic. It achieves forward inference of the single degenerate interferogram by constructing a physically-aware orthogonal decoupling network, and jointly optimizes the physically-aware orthogonal decoupling network through a multi-dimensional physical constraint engine and a physical degradation adaptive curriculum learning strategy. Under the constraint of not relying on the preset spatial carrier frequency prior knowledge, it directly outputs the mutually decoupled background light field, in-phase component field and orthogonal component field from the single degenerate interferogram. Then, based on the output field synthesis standard step size of the virtual phase-shifted interferogram sequence, the wrapped phase is extracted by the analytical algorithm and unwrapped to obtain the reconstructed absolute wavefront.

2. The method according to claim 1, characterized in that, The method includes: Step S1: Obtain degraded interferogram data, construct a dataset, and orthogonally partition the dataset; Step S2: Perform orthogonal phasor decoupling mapping on a single degenerate interferogram based on interferometric evolution orthogonal mapping logic; Step S3: Construct a Physically Aware Orthogonal Decoupling Network (POD-Net) to perform forward inference on a single degraded interferogram; Step S4: Based on the multidimensional physics constraint engine, construct the POD-Net parameter optimization objective loss function and the physics degradation adaptive curriculum learning strategy to jointly optimize the forward inference process of POD-Net in Step S3; Step S5: Based on the output of POD-Net, synthesize a four-step virtual phase-shift interferogram sequence with standard phase-shift step size, and output the final wavefront reconstruction by solving the least squares global unwrapping algorithm based on discrete cosine transform.

3. The method according to claim 2, characterized in that, The physical perception orthogonal decoupling network constructed in step S3 adopts an asymmetric topology architecture of single encoder-three parallel decoder, including a shared encoder, three parallel decoder channels, and a multidimensional physical constraint engine. The shared encoder includes several cascaded Swin T blocks for dimensionality reduction of the input image and captures long-distance spatial dependencies and global carrier frequency distribution patterns. The Swin T block includes a cascaded window multi-head self-attention mechanism, a multilayer perceptron, a sliding window self-attention mechanism, and a patch merging dimensionality reduction module. The three parallel decoder channels include a background light field decoder channel, an in-phase component field decoder channel, and an orthogonal component field decoder channel. Each of the three decoder channels includes an independent center block, several ECA-U blocks, and a final block corresponding to the background light field decoder, the in-phase component field decoder, and the orthogonal component field decoder.

4. The method according to claim 3, characterized in that, The independent central block includes a 3×3 convolutional layer, a batch normalization layer and a ReLU activation function layer connected in sequence, which are used to split the encoded features and reduce feature crosstalk between different physical component fields from the bottom layer. The ECA-U block includes a bilinear upsampling unit, a cross-scale feature stitching unit, a dual 3×3 convolutional layer, a global average pooling layer, a dimension reconstruction module, a sigmoid activation function layer, and a channel interaction weighting module. The ECA-U block calculates channel interaction weights through global average pooling and one-dimensional convolution, which are used to adaptively recalibrate the feature channel mapping and enhance the spatial high-frequency properties of the interference fringes while maintaining the local spatial topological coherence. The final block includes a final 3×3 convolutional layer, a final upsampling unit, a Sigmoid activation function, and a Tanh activation function, which are used to map the decoded features to the boundaries of real physical manifolds that conform to the laws of non-negativity of light intensity and bipolar symmetry, respectively; the Sigmoid activation function is used to output the prediction of the background light field, and the Tanh activation function is used to output the prediction of the in-phase component field and the orthogonal component field.

5. The method according to claim 4, characterized in that, The process of constructing the target loss function for POD-Net parameters based on the multidimensional physical constraint engine in step S4 includes: The total loss function of POD-Net is composed of a linearly weighted combination of five physical constraints, and its expression is as follows: in, For pixel-level data fidelity loss function, To reconstruct the self-consistent loss function, Let the amplitude envelope conservation loss function be... For the virtual spatiotemporal evolution self-consistent loss function, The polar coordinate phase cosine loss function, These are the hyperparameter weights of the corresponding loss function; The pixel-level data fidelity loss function The expression is: The reconstructed self-consistent loss function The expression is: The amplitude envelope conservation loss function The expression is: The virtual spatiotemporal evolution self-consistent loss function The expression is: The polar coordinate phase cosine loss function The expression is: in, These represent the true background light field, in-phase component field, and orthogonal component field of the reference theory, respectively. These represent the predicted separated background light field, in-phase component field, and orthogonal component field, respectively. For the true value of ideal interference, It is a constant value. To modulate the true value of the envelope; It is a virtual phase-shifting interference sequence. It is a true-valued interference sequence; For the ideal truth field of in-phase components, The ideal truth field for orthogonal components; This represents the ideal true value of the modulation amplitude.

6. The method according to claim 5, characterized in that, The physical degradation adaptive curriculum learning strategy in step S4 includes three progressive evolutionary stages, namely the pre-training stage, the carrier frequency generalization stage, and the degradation fine-tuning stage. The pre-training stage uses a dataset containing only one-dimensional pure spatial carrier frequencies. By introducing positive single-axis tilt aberration to generate high-density vertical fringes, the training and optimization process of POD-Net is constrained in a smooth constraint environment without sign ambiguity, thus establishing a basic mathematical mapping channel between interference light intensity and orthogonal double fields. The carrier frequency generalization stage uses an interferometric dataset with omnidirectional two-dimensional distributed carrier frequencies. By releasing the high-frequency Zernike aberration order, POD-Net adaptively understands the directional ambiguity of a single closed fringe and improves the reconstruction of the spatial topology. The degradation fine-tuning stage is used to perform parameter transfer to the degradation domain, open Zernike aberrations within a preset order range, and construct a physical noise domain dataset based on the boundary noise generation strategy for fine-tuning training.

7. The method according to claim 6, characterized in that, Step S2, which involves orthogonal phasor decoupling mapping of a single degenerate interferogram based on interferometric evolution orthogonal mapping logic, includes the following: The expression for the spatial evolution equation of the interference fringe intensity distribution is: in, For two-dimensional space pixel coordinates, For phase shift, The light intensity distribution of the low-frequency background light field. The modulation amplitude of the interference fringes, Wrap the phase around the target; The spatial evolution equation of interference fringe intensity distribution is orthogonally expanded based on trigonometric identities, and its expression is: in, For in-phase component fields, the expression is: ; For orthogonal component fields, the expression is: ; Using a single degenerate interferogram as a relative benchmark for phase-shift spatial evolution, a self-supervised observation boundary is provided through self-consistent physical constraints on light intensity.

8. The method according to claim 7, characterized in that, The process of synthesizing a four-step virtual phase-shift interferogram sequence with a standard phase-shift step size based on the output of POD-Net in step S5 includes: Low-frequency background light field based on POD-Net prediction output In-phase component field and orthogonal component fields A four-step virtual phase-shift interferogram sequence with a standard phase-shift step size is synthesized, wherein the standard phase shift of the four-step virtual phase-shift interferogram sequence satisfies The corresponding virtual sequence composition equation expands to: POD-Net uses the standard four-step phase-shifting equation to extract the target principal value wrapping phase, and its expression is: The extracted spatially continuous wrapped phase is input into a least-squares global unwrapping algorithm based on discrete cosine transform; a morphological edge mask is applied to the unwrapped wavefront, and the translation components and tilt carrier frequency terms of the system are stripped by least-squares plane fitting, finally outputting the globally absolute reconstructed wavefront.

9. The method according to claim 8, characterized in that, In step S1, degraded interferogram data are obtained from the simulated interferometric dataset and the real public dataset to construct a dataset. The dataset is divided into the training set, the validation set and the test set in a ratio of 7:2:

1. In the simulated interference dataset, the interference coefficient distribution and random noise seed of the test set are set to be non-overlapping with those of the training set to avoid data overlap; The real public dataset contains real information on non-uniform edge illumination attenuation and environmentally coherent speckle composite degradation.

10. The method according to any one of claims 1-9, characterized in that, The method is used for precision optical metrology or dynamic interference wavefront restoration under complex degradation environments.

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