Phase Unwrapping Method Research Articles

Efficient and robust phase unwrapping method based on SFNet

Phase unwrapping is a crucial step in obtaining the final physical information in the field of optical metrology. Although good at dealing with phase with discontinuity and noise, most deep learning-based spatial phase unwrapping methods suffer from the complex model and unsatisfactory performance, partially due to simple noise type for training datasets and limited interpretability. This paper proposes a highly efficient and robust spatial phase unwrapping method based on an improved SegFormer network, SFNet. The SFNet structure uses a hierarchical encoder without positional encoding and a decoder based on a lightweight fully connected multilayer perceptron. The proposed method utilizes the self-attention mechanism of the Transformer to better capture the global relationship of phase changes and reduce errors in the phase unwrapping process. It has a lower parameter count, speeding up the phase unwrapping. The network is trained on a simulated dataset containing various types of noise and phase discontinuity. This paper compares the proposed method with several state-of-the-art deep learning-based and traditional methods in terms of important evaluation indices, such as RMSE and PFS, highlighting its structural stability, robustness to noise, and generalization.

A ternary complementary Gray code phase unwrapping method in fringe projection profilometry

This paper proposes a phase unwrapping method based on ternary Gray code in fringe projection profilometry. This method does not require additional projection images or any prior knowledge. It accurately determines the segmentation thresholds of the ternary Gray code using only the average intensity and intensity modulation calculated from phase-shifting fringes, effectively reducing projection costs and achieving lower codeword errors. Additionally, a segment selection strategy suitable for the ternary Gray code is proposed. By employing the complementary method, three sets of candidate orders with certain codeword shifts can be generated. The wrapped phase is then divided into three segments: upper, middle, and lower segments, and correspondingly matched with the central regions of the three sets of candidate orders, thus enabling the solution of the absolute phase. Through the segment selection strategy, error-prone areas at the edges of orders are effectively avoided, further enhancing the accuracy of measurement results. Compared to the binary Gray code, the ternary complementary Gray code can encode up to 3m−1 orders when the number of Gray code patterns is m; when the required number of encoding orders is K, only ⌈log3K⌉+1 Gray code patterns are needed. Its additional value capacity precisely enables it to encode more orders, thereby increasing the frequency of phase-shifting fringes and further enhancing measurement efficiency. A series of experiments validates the feasibility, robustness, and superiority of this method.

InSAR phase unwrapping method based on neural network and Nesterov accelerated gradient optimization

InSAR phase unwrapping method based on neural network and Nesterov accelerated gradient optimization

Phase denoising and unwrapping method for moiré fringes based on multiresolution analysis

Phase unwrapping for moiré fringes plays a crucial role in moiré tomography, and the precision of its outcomes deeply influences the detection results concerning high-temperature complex flow fields. In this paper, a phase denoising and unwrapping technique grounded in multiresolution analysis (MRA) is presented, and it is effectively applied to extract phase information from moiré fringes for propane-air flame and argon arc plasma flow fields. Firstly, the wrapped phase undergoes a wavelet packet decomposition for overall denoising. Subsequently, MRA is conducted to refine the denoising process and unwrap phase, involving layered wavelet packet decomposition and iterative unwrapping on different levels of approximate components. Following the hierarchical structure of MRA, the results from different levels are systematically combined and summarized. In order to ascertain the feasibility and applicability of this approach, a comparison is conducted between the results obtained from our proposed method and those obtained from three representative traditional methods. And then, the outcomes obtained from various unwrapping methods in scenarios involving noise and discontinuity, as well as the results between diverse wavelet basis functions, different decomposition layers and distinct iterations, are meticulously analyzed and compared. The findings indicate that our proposed method outperforms traditional phase unwrapping techniques in terms of continuity and smoothness, particularly when exposed to severe noise. Unlike the three classic methods, our proposed method maintains consistent results even in the presence of noise, thereby highlighting its advantages in terms of resilience against noise. In a word, this research serves as a crucial reference for the accurate detection of complex high-temperature flow fields by moiré tomography.

Super-resolution based number-theoretical phase unwrapping method applicable to 2D spiral fringe patterns

Spiral interferometry is a technique that accurately measures changes in 3D structures or refractive indices by converting phase changes into spiral fringe patterns. The spiral fringe patterns consist of phase distributions, which are wrapped from 0 to 2π, requiring phase unwrapping techniques. Phase unwrapping transforms a discontinuous phase image from 0 to 2π into a continuous phase image, which can ultimately be reconstructed into 3D information. The 3D reconstructed information is affected by the unwrapped phase information with noise. Among the phase unwrapping methods, the number-theoretical phase unwrapping method used in 1D structured light is a unique approach that unwraps the phase into a step function. Due to its insensitivity to noise, this method is an effective solution for improving phase unwrapping in noisy environments. However, due to the same characteristics, the resolution inevitably decreases. In this paper, we propose a super-resolution based numerical unwrapping method applicable to two-dimensional spiral patterns. Based on multi-wavelength interpolation, this method not only retains the advantage of the number-theoretical phase unwrapping method, which is insensitive to noise, but also compensates for its disadvantage of resolution degradation. The proposed method uses the basic concept of generating sub-step information by multi-wavelength interpolation and performing super-resolution based on this concept. We perform simulations and experiments to verify the validity. As a result of the verification, it is confirmed that the super-resolution effect of the number-theoretical unwrapping in the 2D spiral fringe patterns can be achieved by the proposed method.

Depth_ASPP_UNet++: a novel 2D ESPI phase unwrapping based on convolutional neural network

Phase unwrapping is a key step in optical metrology and physical optics to obtain accurate phase distributions. In practice, phase images obtained from electronic speckle pattern interferometry (ESPI) exhibit diverse and complex morphology, with significant shape variations and non-uniform densities among different individuals. This takes challenges for accurately extracting phase information and unwrapping the phase. With the progress of deep learning technology in optical image processing, real-time performance and accuracy have become concerned issues. In this paper, an ESPI phase unwrapping method based on convolutional neural network UNet++ is proposed. The proposed network combines the depthwise separable convolution (DSC), atrous spatial pyramid pooling (ASPP), defined as Depth_ASPP_UNet++. In this model, the use of DSC improves network computational efficiency and provides better feature representation capability. In addition, ASPP is introduced to pay more attention to the phase information of the phase image, and then obtain better phase unwrapping results. The experimental results show that our proposed method can obtain excellent results, especially with various of variable density, different noise levels, and different speckle sizes.

A complementary binary code based phase unwrapping method

A complementary binary code based phase unwrapping method

Improved two-frequency temporal phase unwrapping method in fringe projection profilometry

Improved two-frequency temporal phase unwrapping method in fringe projection profilometry

Spatial Relation Awareness Module for Phase Unwrapping

Phase unwrapping is a technique used to recover the original phase from the wrapped phase in the range (−π,π]. Various methods have been proposed for phase unwrapping. In particular, methods using convolutional neural networks (CNNs) have been extensively researched because of their high robustness against noise and fast inference speed. However, conventional CNN-based methods discard the local position information and relationships between pixels in the convolution process, resulting in poor phase-unwrapping performance. To obtain better phase unwrapping results, we propose a module that combines a global convolution network, which applies convolutional layers with a kernel size equivalent to that of the feature maps, and CoordConv, which acquires the positional relationships between pixels. We validated the performance of the proposed method by comparing it with a quality-guided path algorithm and deep learning-based phase unwrapping methods and found that the proposed method is highly robust against noise.

A robust phase unwrapping method for phase shifting coding high-frequency color fringe projection profilometry

Phase unwrapping is one of the key problems in fringe projection profilometry (FPP). How to achieve unambiguous fringe step order to perform phase unwrapping with few patterns still face a major challenge. We propose a robust phase unwrapping method by using a pair of encoded color fringe patterns, one is a conventional three-step phase-shifting color fringe pattern with equal phase shifts, another is added an additional phase shift valve t(k) to the former, in which t(k) is related to the order of fringe periods. A single-valued solution function for t(k) is constructed and used to determine the unique fringe order. Besides, multiplexing this pair of fringes can help denoise the extracted wrapped phase to improve the accuracy. The simulation and experimental results proved that the proposed method can achieve unambiguous phase unwrapping for high-frequency fringe patterns. The proposed method is also applicable for isolated objects.

Weakly supervised phase unwrapping for single-camera fringe projection profilometry

Phase unwrapping is essential in fringe projection profilometry (FPP). FPP's primary focus is to simultaneously realize high-speed, high-precision three-dimensional (3D) reconstruction. The dual-frequency hierarchical temporal phase unwrapping method (DF-TPU) technique is one prominent technique for accomplishing this goal. However, phase errors are inevitable and typically limit the DF-TPU approach's maximal period number, reducing reconstruction accuracy. The fully supervised approaches based on deep learning can unwrap dual-frequency phase maps of single-camera FPP systems but require accurate labels of high-frequency absolute phase. This study proposes a novel deep learning phase unwrapping scheme suited to single-camera FPP setups. Without the need for accurate labels corresponding to the high-frequency phase maps, supervisory signals are extracted from the high-frequency phase map, the one-period phase map, and the geometry constraint to guide the training of the phase unwrapping network. This training is a weakly supervised learning, which makes the time-consuming and expertise-demanding precise labeling unnecessary. Data collected in multiple real-world circumstances, such as motion blur, isolated objects, non-uniform reflectivity, and phase discontinuities, are used to validate the effectiveness of this weakly supervised method. Experimental results demonstrate that the proposed method outperforms the fully supervised and conventional DF-TPU methods in terms of depth accuracy and measurement efficiency in terms of fringe pattern number.

Phase Unwrapping using ML methods

Interferometric Synthetic Aperture Radar (InSAR) revolutionizes surface study by measuring precise ground surface changes. Phase unwrapping, a key challenge in InSAR, involves removing ambiguity in measured phase. Deep learning algorithms like Generative Adversarial Networks (GANs) offer a potential solution for simplifying the unwrapping process.This work evaluates GANs for InSAR phase unwrapping, replacing SNAPHU with GANs. GANs achieve significantly faster processing times (2.38 interferograms per minute compared to SNAPHU’s 0.78 interferograms per minute) with minimal quality degradation. A comparison of SBAS results shows that approximately 84% of GANs points are within 3 millimeters of SNAPHU. These results represent a significant advancement in phase unwrapping methods. While this experiment does not declare a definitive winner, it demonstrates that GANs are a viable alternative in certain scenarios and may replace SNAPHU as the preferred unwrapping method.

A novel knowledge-learning coupling method for InSAR phase unwrapping of large surface displacements in coal mining areas

A novel knowledge-learning coupling method for InSAR phase unwrapping of large surface displacements in coal mining areas

A DSSPI phase unwrapping method for improving the detection efficiency of CFRP-reinforced concrete defect

A DSSPI phase unwrapping method for improving the detection efficiency of CFRP-reinforced concrete defect

Electrically tunable lens assisted absolute phase unwrapping for large depth-of-field 3D microscopic structured-light imaging

This paper presents an absolute phase unwrapping method for large depth-of-field (DOF) microscopic structured-light 3D imaging. We calculate the wrapped phase maps and the fringe contrast maps from fringe images captured under various focus settings realized by an electrically tunable lens. From the fringe contrast maps, we extract each in-focus pixel and determine its approximate depth value from the focus settings. The approximate depth map is then used to create an artificial phase map. The geometric-constraint-based phase unwrapping method is adopted to unwrap the phase of all in-focus pixels using the artificial phase map. The unwrapped in-focus phase map is then used to reconstruct 3D coordinates for the entire DOF with the multi-focus pin-hole model. Experimental results demonstrate that our proposed method only requires three phase-shifted fringe patterns to achieve large DOF 3D imaging.

A predictor-corrector phase unwrapping algorithm for temporally undersampled gradient-echo MRI.

To develop a method for unwrapping temporally undersampled and nonlinear gradient recalled echo (GRE) phase. Temporal unwrapping is performed as a sequential one step prediction of the echo phase, followed by a correction to the nearest integer wrap-count. A spatio-temporal extension of the 1D predictor corrector unwrapping (PCU) algorithm improves the prediction accuracy, and thereby maintains spatial continuity. The proposed method is evaluated using numerical phantom, physical phantom, and in vivo brain data at both 3 T and 9.4 T. The unwrapping performance is compared with the state-of-the-art temporal and spatial unwrapping algorithms, and the spatio-temporal iterative virtual-echo based Nyquist sampled (iVENyS) algorithm. Simulation results showed significant reduction in unwrapping errors at higher echoes compared with the state-of-the-art algorithms. Similar to the iVENyS algorithm, the PCU algorithm was able to generate spatially smooth phase images for in vivo data acquired at 3 T and 9.4 T, bypassing the use of additional spatial unwrapping step. A key advantage over iVENyS algorithm is the superior performance of PCU algorithm at higher echoes. PCU algorithm serves as a robust phase unwrapping method for temporally undersampled and nonlinear GRE phase, particularly in the presence of high field gradients.

A new 3D phase unwrapping method by region partitioning and local polynomial modeling in abdominal quantitative susceptibility mapping.

Accurate phase unwrapping is a critical prerequisite for successful applications in phase-related MRI, including quantitative susceptibility mapping (QSM) and susceptibility weighted imaging. However, many existing 3D phase unwrapping algorithms face challenges in the presence of severe noise, rapidly changing phase, and open-end cutline. In this study, we introduce a novel 3D phase unwrapping approach utilizing region partitioning and a local polynomial model. Initially, the method leverages phase partitioning to create initial regions. Noisy voxels connecting areas within these regions are excluded and grouped into residual voxels. The connected regions within the region of interest are then reidentified and categorized into blocks and residual voxels based on voxel count thresholds. Subsequently, the method sequentially performs inter-block and residual voxel phase unwrapping using the local polynomial model. The proposed method was evaluated on simulation and in vivo abdominal QSM data, and was compared with the classical Region-growing, Laplacian_based, Graph-cut, and PRELUDE methods. Simulation experiments, conducted under different signal-to-noise ratios and phase change levels, consistently demonstrate that the proposed method achieves accurate unwrapping results, with mean error ratios not exceeding 0.01%. In contrast, the error ratios of Region-growing (N/A, 84.47%), Laplacian_based (20.65%, N/A), Graph-cut (2.26%, 20.71%), and PRELUDE (4.28%, 10.33%) methods are all substantially higher than those of the proposed method. In vivo abdominal QSM experiments further confirm the effectiveness of the proposed method in unwrapping phase data and successfully reconstructing susceptibility maps, even in scenarios with significant noise, rapidly changing phase, and open-end cutline in a large field of view. The proposed method demonstrates robust and accurate phase unwrapping capabilities, positioning it as a promising option for abdominal QSM applications.

A phase unwrapping method with the sparse prior for diffraction phase microscopy

Phase unwrapping is widely used in interferometry. In the typical least square (LS) method, the noise in the wrapped phase cannot be removed. An improved algorithm based on total variation (TV) imposes L1-norm on the image gradient to improve the sparsity. However, it may lead to over-sparsity, and the unwrapped phase will be compressed if the penalty term is overlarge. In this study, we proposed a sparse prior phase unwrapping (SPUP) algorithm to solve the wrapped phase of interferograms of diffraction phase microscopy (DPM). Since DPM has a unique sample sparsity in the imaging field of high-power objectives, the L0-norm and L1-norm regularizations are introduced into the SPUP process. The results verify the strong denoising ability and high phase fidelity of the proposed SPUP method. Moreover, the uneven background noise and phase shifting of DPM interferograms could be corrected, demonstrating the great potential of the SPUP method in various interferometry measurements.

Branch-cut phase unwrapping method based on deep learning

ObjectiveAs a typical representative of the phase unwrapping algorithm, the branch-cut method has good anti-noise performance in the phase unwrapping process. However, the branch-cut generated by the traditional branch-cut method cannot accurately block error propagation. MethodThis study proposes a branch-cut phase unwrapping method based on deep learning, which transforms the traditional problem of connecting residual points into a semantic segmentation learning problem, to improve the blocking effect of the branch-cut to the error. The article analyzes the performance of modulation and residue maps in representing phase errors and finds that residue maps have a poor perception of error information in shadow areas in the wrapped phase map. Therefore, a new branch-cut connection criterion is proposed that combines modulation maps and sets the bound of shadow and non-shadow areas as part of branch-cut. Positive and negative residual points are connected by curves along the path of poor modulation, and their polarities are accumulated to maintain branch-cut balance. By using the new branch-cut connection criterion to provide learning samples and using the U-Net++ network structure as the deployment network of branch-cut, the network generates a branch-cut for phase unwrapping, which phase unwrapping path bypasses the branch-cut. ResultsThe experimental results show that the deployment of branch-cut using the U-Net++ network structure can achieve the expected training effect, and the branch-cut generated based on the new connection principle can more effectively block the propagation of errors during phase unwrapping.

Three-Dimensional Reconstruction Based on Multiple Views of Structured Light Projectors and Point Cloud Registration Noise Removal for Fusion.

Structured light technology is typical for capturing 3D point cloud data. This paper proposes a 3D reconstruction system to obtain point cloud data of complex objects based on nine-order Gray code and an eight-step structured light projection combined with a phase shift and phase unwrapping method. In this system, two projectors serve as bilateral projectors for structured light, along with a camera and rotating platforms. These components were used to obtain point cloud data from multiple perspectives, which helps avoid the shadow areas caused by a single projection angle and provides complementary point cloud data. The point clusters scanned under each perspective were transformed into the same coordinate system. Furthermore, a distance-based point cloud noise removal algorithm was proposed to optimize platform noise and facilitate point cloud data fusion. The experimental results proved that the system effectively captures 3D point cloud data for complex objects. The dimensional quantitative analysis of an aero engine blade was also performed.