Wrapped Phase Map Research Articles

Robust phase unwrapping algorithm for gear interferometry based on mutual information and adaptive spin-inpainting approaches

An enhanced robust phase unwrapping algorithm for gear tooth flank measurement by laser interferometry is proposed. The method integrates wrapped phase mutual information estimation with an adaptive spin-inpainting strategy, resulting in improved quality phase maps to guide the phase unwrapping process. Mutual information estimation is employed to investigate potential phase relationships among interference fringes in the wrapped phase map, forming the foundation for the suppression and recovery of abnormal fringes. The adaptive spin-inpainting method, which adjusts in response to fringe density, plays a crucial role in efficiently addressing the restoration of abnormal fringes and obtaining the optimized quality map. With the enhanced new quality map, the approach yields optimized results, enabling a concurrent assessment of unwrapping process efficiency and quality. Several simulations and experiments were conducted to validate the effectiveness of the proposed method. Comparative analyses against commonly employed methods consistently demonstrate the superior performance of the proposed algorithm.

Fringe-based depth segmentation via minimum-fringe-period-based singular points extraction

In the field of machine vision, depth segmentation plays a crucial role in dividing targets into different regions based on abrupt changes in depth. Phase-shifting depth segmentation is a technique that extracts singular points to form segmentation lines by leveraging the phase-shifting invariance of singular points in different wrapped phase maps. This makes it immune to color, texture, and camera exposure. However, current phase-shifting depth segmentation techniques face challenges in the precision of segmentation. To overcome this issue, this paper proposes a singular points extraction technique by constructing a more comprehensive threshold with the help of the minimum period of the phase map. Taking full advantage of the proposed technique, mean-value points and order singular points are accurately filtered out, and the integrity of segmentation lines in high-curvature regions can be guaranteed. During optimization processing, the precision of segmentation is improved by employing a low-cost morphology-based optimization model. Simulation results demonstrate the segmentation accuracy reaches up to 98.58% even in a noisy condition. Experimental results on different objects indicate that the proposed method exhibits good generalization and robustness.

Three 1-bit speckle-embedded pulse-width modulation patterns for robust absolute 3D measurement

In three-dimensional (3D) shape measurement techniques using structured light, 1-bit pulse-width modulation (PWM) patterns and 1-bit speckle patterns can be projected at high speed. However, when combining PWM and speckle patterns to integrate their advantages, the decoupling problem is insurmountable. In this work, a novel 1-bit speckle-embedded PWM (SPPWM) method was proposed to achieve absolute 3D shape measurement using only three binary patterns. Our method consists of three main steps: First, a sinusoidal pattern reconstruction network was proposed to eliminate the high-order harmonics and speckle patterns in the SPPWM patterns and obtain high-quality sinusoidal patterns. Second, a multi-temporal spatial correlation matching algorithm was proposed to obtain a coarse disparity map from the three SPPWM patterns. Third, the high-accuracy wrapped phase map is used as an additional constraint for refining the coarse disparity map to obtain the final high-accuracy disparity map for absolute 3D measurement without phase unwrapping. Our method combines the advantages of fringe projection profilometry techniques for high-precision wrapped phase retrieval and speckle correlation matching algorithms for robust and unambiguous disparity map calculation. The experimental results demonstrated that our method could realize high-precision absolute 3D shape measurement with an accuracy of 0.057 mm using only three 1-bit SPPWM patterns. Furthermore, different simulation noises were used to demonstrate the robustness of the proposed method.

Object phase-valid region segmentation method for FPP-based three-dimensional measurement

In most existing studies based on fringe projector profilometry (FPP), the whole scenario is reconstructed, or the ideal experimental settings are established to segment the object easily. However, in real industrial scenarios, automated object detection and segmentation are essential to perform object-level measurement. To address the problem, a dual-wavelet feature interaction network (DWFI-Net) is developed in this paper to perform object phase-valid region segmentation, where both the background and shadow are removed. In our work, the modulation and wrapped phase maps are considered as inputs innovatively. The modulation maps provide abundant structures and textures, while the wrapped phase maps complement and enhance shadows and edges. An adaptive wavelet feature interaction (AWFI) module is presented to learn and fuse the features, where discrete wavelet transformation (DWT) is applied to decompose the features. An edge-aware discrete cosine transformation (EDCT) module is developed as a decoder, where the discrete cosine transformation (DCT) is applied to interpret the fused features. Qualitative and quantitative experiments are performed to verify the superiority of our DWFI-Net and its effectiveness on object-level three-dimensional measurement based on FPP.

Deep Learning in the Phase Extraction of Electronic Speckle Pattern Interferometry

Electronic speckle pattern interferometry (ESPI) is widely used in fields such as materials science, biomedical research, surface morphology analysis, and optical component inspection because of its high measurement accuracy, broad frequency range, and ease of measurement. Phase extraction is a critical stage in ESPI. However, conventional phase extraction methods exhibit problems such as low accuracy, slow processing speed, and poor generalization. With the continuous development of deep learning in image processing, the application of deep learning in phase extraction from electronic speckle interferometry images has become a critical topic of research. This paper reviews the principles and characteristics of ESPI and comprehensively analyzes the phase extraction processes for fringe patterns and wrapped phase maps. The application, advantages, and limitations of deep learning techniques in filtering, fringe skeleton line extraction, and phase unwrapping algorithms are discussed based on the representation of measurement results. Finally, this paper provides a perspective on future trends, such as the construction of physical models for electronic speckle interferometry, improvement and optimization of deep learning models, and quantitative evaluation of phase extraction quality, in this field.

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.

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.

Wrapped phase aberration compensation using deep learning in digital holographic microscopy

In digital holographic microscopy (DHM), phase aberration compensation is a general problem for improving the accuracy of quantitative phase measurement. Current phase aberration compensation methods mainly focus on the continuous phase map after performing the phase filtering and unwrapping to the wrapped phase map. However, for the wrapped phase map, when larger phase aberrations make the fringes too dense or make the noise frequency features indistinct, either spatial-domain or frequency-domain based filtering methods might be less effective, resulting in phase unwrapping anomalies and inaccurate aberration compensation. In order to solve this problem, we propose and design a strategy to advance the phase aberration compensation to the wrapped phase map with deep learning. As the phase aberration in DHM can be characterized by the Zernike coefficients, CNN (Convolutional Neural Network) is trained by using massive simulated wrapped phase maps as network inputs and their corresponding Zernike coefficients as labels. Then the trained CNN is used to directly extract the Zernike coefficients and compensate the phase aberration of the wrapped phase before phase filtering and unwrapping. The simulation results of different phase aberrations and noise levels and measurement results of MEMS chip and biological tissue samples show that, compared with current algorithms that perform phase aberration compensation after phase unwrapping, the proposed method can extract the Zernike coefficients more accurately, improve the phase data quality of the consequent phase filtering greatly, and achieve more accurate and reliable sample profile reconstruction. This phase aberration compensation strategy for the wrapped phase will have great potential in the applications of DHM quantitative phase imaging.

Phase Unwrapping Method of Φ-OTDR System Based on Recursive-Branch-Cut Algorithm

Phase unwrapping is a crucial technique in phase-sensitive optical time domain reflectometry (Φ-OTDR) systems. Due to the effects of system under-sampling, I/Q imbalance and environmental noise, the traditional method of unwrapping the phase is prone to wrapping or even distortion. In this work, a two-dimensional phase unwrapping method based on the recursive-branch-cut (RBC) algorithm is proposed and studied to improve the accuracy of the demodulated phase waveform. The data near the vibration location is expanded into a two-dimensional wrapped phase map along the time direction. According to the abnormal phase distribution law, the two-dimensional wrapped phase map is divided into sliding windows of different lengths. Under the constraint of ensuring the global continuity of the phase, the local phase is optimized by selecting an appropriate integration path, and the error is minimized, thereby suppressing the propagation of abnormal noise in the global. The experimental results show that in the range of 1-80 Hz, the method can stably increase the upper limit of the system dynamic range by 3.21 dB. At the same time, the system has a good linear strain response capability, and the strain sensitivity is 22.46rad/με×m and R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> =0.9997. In addition, the method greatly improves the demodulation characteristics without increasing the generality and practicability of the system, which is beneficial to the fully digital realization of the heterodyne detection technology.

Pixel-wise phase unwrapping of fringe projection profilometry based on deep learning

Phase unwrapping is a crucial step in high-precision optical metrology, aimed at retrieving absolute phases from wrapped phases. This paper presents a deep learning-based phase unwrapping method that enhances the conventional three-wavelength heterodyne method and achieves pixel-wise phase unwrapping using a wrapped phase map and two fringe patterns. The proposed method formulates the phase unwrapping task as a semantic segmentation problem that infers an absolute fringe order for each wrapped phase pixel. The verification results demonstrate that the method can accurately measure surfaces with complex topologies. Under low noise conditions, the proposed method achieves performance comparable to the three-wavelength heterodyne method, with similarity rates between the fringe order maps obtained by the two methods of up to 0.99; additionally, the method exhibits superb resistance to severe noise. Moreover, the proposed method is more efficient in terms of fringe pattern efficiency by at least 44.44%.

Single-shot 3D measurement of highly reflective objects with deep learning.

Three-dimensional (3D) measurement methods based on fringe projection profilometry (FPP) have been widely applied in industrial manufacturing. Most FPP methods adopt phase-shifting techniques and require multiple fringe images, thus having limited application in dynamic scenes. Moreover, industrial parts often have highly reflective areas leading to overexposure. In this work, a single-shot high dynamic range 3D measurement method combining FPP with deep learning is proposed. The proposed deep learning model includes two convolutional neural networks: exposure selection network (ExSNet) and fringe analysis network (FrANet). The ExSNet utilizes self-attention mechanism for enhancement of highly reflective areas leading to overexposure problem to achieve high dynamic range in single-shot 3D measurement. The FrANet consists of three modules to predict wrapped phase maps and absolute phase maps. A training strategy directly opting for best measurement accuracy is proposed. Experiments on a FPP system showed that the proposed method predicted accurate optimal exposure time under single-shot condition. A pair of moving standard spheres with overexposure was measured for quantitative evaluation. The proposed method reconstructed standard spheres over a large range of exposure level, where prediction errors for diameter were 73 µm (left) and 64 µm (right) and prediction error for center distance was 49 µm. Ablation study and comparison with other high dynamic range methods were also conducted.

Phase Unwrapping-Free Fringe Projection Profilometry for 3D Shape Measurement

Phase unwrapping is always the necessary procedure in fringe projection profilometry (FPP). This letter presents an efficient phase unwrapping-free FPP method. Both the wrapped phase maps of the measured object and the reference plane are extracted by phase-shifting algorithm. If the depth range of the measured object is within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula> in phase domain, the three-dimensional (3D) shape can be directly reconstructed by converting the wrapped phase difference into absolute phase difference without phase unwrapping process. Simulations and experiments are carried out, and their results demonstrate the effectiveness and robustness of the proposed method.

Simulated wrapped phase optimizes phase retrieval in phase-shifting interferometry.

Phase retrieval is crucial in phase-shifting interferometry and other phase measurement techniques. However, in noisy wrapped phase maps with high steepness, discontinuities arise and cause phase unwrapping errors. To solve this problem, this Letter presents a phase retrieval method based on a simulated wrapped phase. By establishing the correspondence between the simulated and measured interferograms, the difference in wrapped phases between them can be obtained. The difference in wrapped phase map, which has sparse and wide interference fringes, has a higher reliability of phase unwrapping. The proposed method not only possesses high phase retrieval accuracy but it also simplifies the processing of interferograms. Furthermore, the layout of all interferometric systems, the parameters of optical components, and the model of the measured object are known, so the proposed method can be used as a reference for phase retrieval.

Adaptive horizontal scaling method for speckle-assisted fringe projection profilometry.

Phase-shifting method is widely used in fringe projection profilometry to obtain high-precision wrapped phase maps. The wrapped phase map needs to be converted to an absolute phase map to recover 3D information. The speckle pattern based phase unwrapping method requires only one additional auxiliary pattern, showing great potential for fast 3D measurements. In this paper, a speckle assisted four-steps phase-shifting method was proposed for 3D measurements. This method requires five structured light patterns to complete 3D measurements, including four-steps phase-shifting fringe patterns and a speckle pattern which is used to remove phase ambiguity. The main challenge of speckle based phase unwrapping method is to overcome the mismatch problem which often occurs in some very steep surfaces. In order to improve the speckle matching accuracy, an adaptive horizontal scaling method was proposed. A voting strategy based on phase-connected regions was proposed to reduce the computational overhead. The experiments demonstrate its superior performance, and an accuracy of 0.21 mm was achieved.

Single-frequency and accurate phase unwrapping method using deep learning

Phase unwrapping is an important part of fringe projection profilometry(FPP), which greatly affects the efficiency and accuracy of reconstruction. Phase unwrapping methods with deep learning achieve single-frequency phase unwrapping without additional cameras. However, existing methods have low accuracy in the real complex scene, and can not process data whose resolution is greater than the resolution of training data. This paper introduces a neural convolutional network named as VRNet which achieves accurate and single-frequency phase unwrapping without extra cameras. VRNet with encoder-decoder structure gets multi-scale feature maps through feeding the wrapped phase map into the encoder, then fuses the feature maps recursively by using the proposed feature fusion module to accomplish precise prediction. In order to further improve the accuracy of phase unwrapping, this paper presents a phase correction method based on the distribution characteristics of the absolute phase. The method divides the cross-section of the absolute phase map into several curves and identifies a misclassified pixel by comparing its absolute phase value with the value of neighboring curves. In contrast to existing methods, the method is row-independent and does not require segmentation of image. Moreover, this paper accomplishes the prediction of high-resolution data through the phase stitching strategy and fine-tuning the phase correction method. Extensive experiments show that the proposed method is able to achieve high-accuracy and single-frequency phase unwrapping in real scenes which consist of at least one complex object, and is also effective for wrapped phase maps with a resolution larger than the training data.

Fast and accurate 3D face reconstruction based on facial geometry constraints and fringe projection without phase unwrapping

Phase unwrapping is a critical process and a challenging step in fringe projection profilometry. Methods employing additional auxiliary patterns or embedding signals in the projected fringe pattern can successfully address this issue, but most of them suffer from increased number of structured patterns or depressed signal-to-noise ratio (SNR) of fringe images, which are not expected in real-time high-accuracy application such as 3D face reconstruction. In this paper, a 3D face reconstruction method that completely sidesteps the phase unwrapping process is proposed. Phase order lines (POLs) are first extracted from the left and right wrapped phase map of the stereo vision system respectively, and then the left and right POLs are matched by automatically drawing polylines on the face with facial geometry constraints as prior knowledge. Finally, based on the matched POL pairs, fine matching is performed directly employing the wrapped phase to generate a dense disparity map. Compared with the conventional, the processing time of the proposed method is further improved without sacrificing accuracy. Experiments demonstrate the effectiveness and robustness of the method.

Two-dimensional phase unwrapping by a high-resolution deep learning network

Phase measurements are of considerable interest in the field of optical metrology. Retrieving unambiguous phases from a single ambiguous wrapped phase map is a tricky problem. Conventional spatial phase unwrapping approaches are vulnerable to noise, the large variation range of phase surfaces, and phase discontinuity. In this study, the task of phase unwrapping is formulated as a pixel-wise semantic segmentation problem, and a high-resolution deep learning network named the HRNet is employed to infer an integer multiple of 2π for every pixel aiming to remove 2π discontinuities. The effectiveness and superiority of the proposed method are verified on both simulated and real data and through qualitative and quantitative comparisons with two deep learning-based methods and five classical spatial phase unwrapping methods.

Co-phase state detection for segmented mirrors by dual-wavelength optical vortex phase-shifting interferometry.

The application of large-aperture telescopes requires the support of co-phase measurement techniques for segmented mirrors. This paper proposes a novel method to detect the co-phase state of segmented mirrors by applying a dual-wavelength phase-shifting interferometer based on optical vortex. Theory and experiments indicate that the wrapped phase map edges obtained by phase-shifting interference of the vortex beam are distributed in the form of a Fermat spiral. The piston error of the segmented mirrors corresponds to the rotation of the standard Fermat spiral center. In contrast, the tip/tilt error corresponds to the alteration of the center position of the deformed Fermat spiral. The rotation angle and the center position of the spiral are obtained by curve fitting, and the co-phase errors can be inversely solved. The experiments achieved an accuracy of approximately 4.04 nm in the piston and 0.16″ in the tip/tilt. The method avoids using complex lens arrays and devices, has an extended measurement range, high accuracy, and allows the co-phase errors between all sub-mirrors to be obtained in real-time. This study provides a novel and general method for detecting co-phase errors in a segmented primary mirror.

EESANet: edge-enhanced self-attention network for two-dimensional phase unwrapping.

In this paper, we first propose a quantitative indicator to measure the amount of prior information contained in the wrapped phase map. Then, Edge-Enhanced Self-Attention Network is proposed for two-dimensional phase unwrapping. EESANet adopts a symmetrical en-decoder architecture and uses self-designed Serried Residual Blocks as its basic block. We add Atrous Spatial Pyramid Pooling and Positional Self-Attention to the network to obtain the long-distance dependency in phase unwrapping, and we further propose Edge-Enhanced Block to enhance the effective edge features of the wrapped phase map. In addition, weighted cross-entropy loss function is employed to overcome the category imbalance problem. Experiments show that our method has higher precision, stronger robustness and better generalization than the state-of-the-art.

Phase unwrapping algorithm based on phase edge tracking for dynamic measurement.

Phase unwrapping is an essential procedure for fringe projection profilometry (FPP). To improve measurement efficiency and reduce phase unwrapping errors (PUEs) in dynamic measurement, a phase unwrapping algorithm based on phase edge tracking is proposed, which unwraps the current wrapped phase map with the aid of the previously unwrapped one. The phase edges are accurately tracked and their trajectories are used to divide the phase map into several regions, each of which is unwrapped either temporally or spatially according to its properties. It doesn't require extra patterns for phase unwrapping once the initial unwrapped phase map is obtained, thus significantly increasing the frame rate of the 3D result. Meanwhile, it greatly reduces the PUEs caused by noise amplification and motion-induced misalignment of phase edges. Experiments prove that it is capable of retrieving the absolute phase maps of complex dynamic scenes with high unwrapping accuracy and efficiency.