Phase Unwrapping Research Articles

A novel intensity-based phase unwrapping method for highly discontinuous topology

Abstract The research on the spatial phase unwrapping method is primarily concerned with unwrapping the phase of highly discontinuous objects. This study presents a phase unwrapping method that utilizes an illumination attenuation model to effectively unwrap the phase of discontinuous objects. Initially, the attenuation features of light intensity with distance are examined, and using the phase height model in the fringe projection profilometry system, the unwrapped light intensity-phase difference distribution map is computed. Next, the phase mask is utilized to divide the non-continuous area, and the process of phase unwrapping is carried out on each individual section. Ultimately, the phase jump order produced by the light intensity-phase difference is employed to direct the sub-regions in accomplishing the phase fusion and creating the global unwrapped phase map.The method shown in this study accomplishes phase unwrapping in areas with discontinuities without adding complexity to the system or requiring additional projection images. Furthermore, it is also successful for isolated regions with phase jumps. This research verifies the efficacy of the phase unwrapping algorithm in handling phase discontinuity through simulation and experimentation.

Application of the Stacking-InSAR method for analyzing changes in forest canopy height

The brief communication demonstrates the potential for quantitative assessment of forest canopy height dynamics in mature and young pine forests on a plain using the method of weighted summing of time series of unwrapped interferometric phases. The latter were obtained using a modern approach based on cloud computations. By comparing the rates of canopy height growth for the years 2017, 2018, and 2019, it has been confirmed that the growth rate is influenced by the amount of precipitation in May-July of the respective year.

Acoustic imaging of the underground space with sensor arrays by phase unwrapping and synthetic focusing

Acoustic imaging of the underground space with sensor arrays by phase unwrapping and synthetic focusing

Transition of synchronization state during the quasiperiodic route to chaos in coupled friction-induced continuous oscillators

Friction-induced vibration, particularly associated with the squealing problem in disk brake systems, has been a longstanding challenge in the automotive industry. In our research, we employed the synchronization theory to gain insights into the interaction between two coupled cantilever beams attached with tip masses. This proposed model emulates the dynamics of a mountain bike disk brake assembly. The work explores a range of collective behaviors, including synchronized periodic, multi-periodic, quasiperiodic, as well as desynchronized chaotic and quasiperiodic oscillations. Despite numerous studies reported on the synchronization phenomenon in discrete friction-induced oscillatory systems, there appears to be a lack of similar research on continuous systems. This work stands as the first of its kind in exploring the dynamics of synchronization between two coupled continuous systems exhibiting a quasiperiodic route to chaos. A bifurcation study is conducted utilizing the Poincaré points corresponding to the local maxima of oscillation amplitude with respect to the zero-velocity crossing. The results showed the existence of narrow multi-periodic windows during the quasiperiodic route at several locations. Additionally, the existence of multiple quasiperiodic attractors exhibiting different states of synchronization for the same set of parameters is observed. We analyzed the time evolution of the cumulative instantaneous phase difference between the coupled signals and identified distinct states of synchronization possessed by the system. The coupled system undergoes interesting phenomena such as complete phase lock, intermittent phase lock, and phase drifting. Moreover, the transition occurring to the state of synchronization during the quasiperiodic route to chaos is studied employing the phase locking value, the Pearson linear correlation coefficient, and the relative mean frequency. Notably, our findings revealed that while the Pearson correlation can effectively identify both the mode and strength of synchronization, other measures such as phase lock value and relative mean frequency only reflect synchronization strength.

Fast phase distortion identification and automatic distortion compensated reconstruction for digital holographic microscopy using deep learning

Digital holographic microscopy (DHM) is a quantitative phase measurement technique with full-field, contactless, and fast. The technique provides accurate micro-surface morphology of samples. These steps are essential for accurate phase reconstruction, such as holographic focusing, numerical diffraction, phase unwrapping and distortion compensation. Performing these processes manually is time-consuming and is not conducive to the general application of the technology. In order to improve the detection efficiency, this paper proposes a deep learning model that can achieve fast identification of DHM phase distortion and automatic phase distortion compensation reconstruction. The model can be preprocessed for holographic phase to accurately identify the type of phase distortion present in the phase. And adaptively adjust the network weight parameters for phase distortion compensation reconstruction. The experimental results show that the method proposed in this paper achieves fast and accurate identification of multiple phase distortions. The model has high accuracy and strong generalization ability. The reconstructed holographic phase map has PSNR of 35.2743dB and RMSE as low as 10-2 level in the face of complex mixed aberrations. The identification and reconstruction processes took 0.005s and 0.058s, both in milliseconds, respectively. The evaluation indexes SSIM, FSIM and NC can reach above 0.99. It is shown that the method in this paper is not only capable of reconstructing holograms, but also able to effectively retain the detailed features of the original image.

Effect of kinematics on ground reaction force during single-leg jump landing in children: a causal decomposition approach in jumpers and non-jumpers.

The interaction between joint kinematics and kinetics is usually assessed by linear correlation analysis, which does not imply causality. Understanding the causal links between these variables may help develop landing interventions to improve technique and create joint-specific strengthening programs to reduce reaction forces and injury risk. Therefore, the aim of this study was to analyze the causal interaction between lower limb sagittal kinematics and vertical ground reaction force (VGRF) during single-leg jump landing in children who are jumpers (volleyball and gymnastics) and non-jumpers, using the causal empirical decomposition method. Our hypothesis is that children who participate in jumping sports, compared to those who do not, employ a different joint strategy to regulate ground reaction forces during landing, particularly at the ankle level. Two groups were compared: the jumpers group (n = 14) and the non-jumpers (control group, n = 11). The causal interaction between sagittal kinematics and VGRF was assessed using ensemble empirical mode decomposition (EEMD) and time series instantaneous phase dependence in bi-directional causality. The relative causal strength (RCS) between the time series was quantified as the relative ratio of absolute cause strength between kinematics and VGRF. A significant interaction between joint and group was found for RCS (p = 0.035, η 2 p = 0.14). The post-hoc analysis showed the jumpers group had higher ankle-to-VGRF RCS than the control group (p = 0.017, d = 1.03), while in the control group the hip-to-VGRF RCS was higher than the ankle-to-VGRF RCS (p = 0.004, d = 0.91). Based on the causal decomposition approach, our results indicate that practicing jumping sports increases the causal effect of ankle kinematics on ground reaction forces in children. While non-jumper children rely more on the hip to modulate reaction forces, jumper children differ from non-jumpers by their greater use of the ankle joint. These findings could be used to develop specific training programs to improve landing techniques according to practice level, potentially helping to reduce the risk of injury in both athletes and non-athletes.

Excipient Induced Unusual Phase Separation in Bovine Serum Albumin Solution: An Explicit Role Played by Ion-Hydration.

We report an instantaneous room-temperature phase separation of 1 mM bovine serum albumin solution in the presence of (20% acetic acid+0.2 M NaCl), a routinely used food preservative; an opaque liquid-like phase (L) coexists in equilibrium with a granular gel like phase (G). Interestingly, neither 20% acetic acid nor 0.2 M NaCl individually induces such a phase separation. Field emission scanning electron microscopy (FESEM) and high-resolution transmission electron microscopy (HRTEM) imaging show aggregated proteins to be dispersed in the upper phase, while the lower phase is composed of cross-linked fibrils (hydrogels). Mid-IR FTIR, Raman scattering, and circular dichroism (CD) experiments reveal a significant increase in the β-sheet content in BSA, which confirms the formation of amyloids in the presence of the excipient. Both L and G phases undergo distinct visual and microscopic changes upon incubation at 25 and 80 °C. It is evident that the added salt plays a pivotal role in bringing about this otherwise unique phase behavior. We divulge the explicit role of the ion associated hydration using THz-FTIR measurements in the 1.5-16.7 THz (50-550 cm-1) frequency window. Systematic alteration in the ion-induced THz-active mode of water envisions the key role of ions in shaping the various phases. Our study depicts an intriguing observation of severe amyloidosis of BSA upon the addition of a food preservative, even at room temperature, which is expected to add new insight into amyloid research. Considering the increasing number of individuals suffering from several neurodegenerative disorders (Alzheimer's, Parkinson's, type-2 diabetes, obesity, cancer, etc.), this study leads a caution toward critically revisiting the usage of known food preservatives.

Unwrap-Net: A deep neural network-based InSAR phase unwrapping method assisted by airborne LiDAR data

In Interferometric Synthetic Aperture Radar (InSAR) data processing, accurately unwrapping the phase is crucial for measuring elevation or deformation. DCNN models such as PhaseNet and PGNet have improved the efficiency and accuracy of phase unwrapping, but they still face challenges such as incomplete multiscale feature learning, high feature redundancy, and reliance on unrealistic datasets. These limitations compromise their effectiveness in areas with low coherence and high gradient deformation. This study proposed Unwrap-Net, a novel network model featuring an encoder-decoder structure and enhanced multiscale feature learning via ASPP (Atrous Spatial Pyramid Pooling). Unwrap-Net minimizes feature redundancy and boosts learning efficiency using SERB (Residual Convolutional with SE-block). For dataset construction, airborne LiDAR terrain data combined with land cover data from optical images, using the SGS (Sequential Gaussian Simulation) method, are used to synthesize phase data and simulate decorrelation noise. This approach creates a dataset that closely approximates real-world conditions. Additionally, the introduction of a new high-fidelity optimization loss function significantly enhances the model’s resistance to noise. Experimental results show that compared to the SNAPHU and PhaseNet models, the SSIM of the Unwrap-Net model improves by over 13%, and the RMSE is reduced by more than 34% in simulated data experiments. In real data experiments, SSIM improves by over 6%, and RMSE is reduced by more than 49%. This indicates that the unwrapping results of the Unwrap-Net model are more reliable and have stronger generalization capabilities. The related experimental code and dataset will be made available at https://github.com/yangwangyangzi48/UNWRAPNETV1.git.

Binocular composite grayscale fringe projection profilometry based on deep learning for single-shot 3D measurements

The efficiency and precision of 3D shape reconstruction has been a focus in the fringe projection profilometry (FPP). However, achieving high-quality 3D measurement for isolated or overlapping objects from single fringe image is still a challenging task in the field. In this paper, a binocular composite grayscale fringe projection profilometry (BCGFPP) based on deep learning is proposed, in which a two-stage one-to-three network (TONet) is trained to predict the images required for phase unwrapping. The obtained absolute phase map exhibits high precision and eliminates deviation error and periodic ambiguity typically encountered in traditional sinusoidal composite fringe coding scheme. Haar transform principle is employed to form a Haar-like composite fringe pattern (HCFP), which consists of three different frequencies, serving as the input. TONet architecture is designed to predict images required by the tri-frequency four-step phase-shifting method (TFPM). Further, the absolute phase is calculated and the disparity map is obtained by matching the absolute phase of the left and right cameras. Finally, the 3D shape of the object can be restored by the system calibration parameters. Experimental results demonstrate the approach can greatly reduce the number of fringes required and achieve the accuracy of the absolute phase close to the training set.

Monitoring the Subsidence in Wan’an Town of Deyang Based on PS-InSAR Technology (Sichuan, China)

In recent years, land subsidence has become a crucial factor affecting urban safety and sustainable development, especially in Wan’an Town. To accurately monitor and analyze the land subsidence in Wan’an Town, this study uses the PS-InSAR technique combined with an improved DEM for detailed research on land subsidence in Wan’an Town. PS-InSAR, or Permanent Scatterer Interferometric SAR, is suitable for high-precision monitoring of surface deformation. The natural neighbor interpolation method optimizes DEM data, improving its spatial resolution and accuracy. In this study, multiple periods of SAR imagery data of Wan’an Town were collected and preprocessed through radiometric calibration, phase unwrapping, and other steps. Using the PS-InSAR technique, the phase information of permanent scatterers (PS points) on the surface was extracted to establish a deformation model and preliminarily analyze the land subsidence in Wan’an Town. Concurrently, the DEM data were optimized using the natural neighbor interpolation method to enhance its accuracy. Finally, the optimized DEM data were combined with the surface deformation information extracted through the PS-InSAR technique for a detailed analysis of the land subsidence in Wan’an Town. The research results indicate that the DEM data optimized by the natural neighbor interpolation method have higher accuracy and spatial resolution, providing a more accurate reflection of the topographical features of Wan’an Town. The research found that the optimized DEM provided a more accurate reflection of Wan’an Town’s topographical features. By combining PS-InSAR data, subsidence information from 2016 to 2024 was calculated. The study area showed varying degrees of subsidence, with rates ranging from 6 mm/year to 10 mm/year. Four characteristic deformation areas were analyzed for causes and influencing factors. The findings contribute to understanding urban land subsidence, guiding urban planning, and providing data support for geological disaster warning and prevention.

3D measurement method based on Gray code and single sine fringe image

FPP has been widely used in the industrial field and with the development of this technology, improving the measurement efficiency becomes a hot direction. Based above, a new single phase-shifting method is proposed in this paper. First, the background intensity is reduced in the sine fringe image and the processed image is normalized to double precision number [-1,1]. Then, we perform arcsine operation and adjust the results according to the Gray code array to get the wrapped phase. Finally, the wrapped phase is combined with the Gray code array and compensated according to the actual situation to get the unwrapped phase. The proposed method could obtain the relevant 3D information from single sine fringe image. Experiments show that the corresponding measurement efficiency is improved by 50% compared with the complementary Gray code combines 2+1 phase-shifting profilometry and the complementary Gray code combines N+2 phase-shifting profilometry.

Three-dimensional reconstruction of a light field based on phase restoration for highly reflective surfaces

This paper proposes, a novel, to our knowledge, phase-restoration-based light field method to achieve 3D reconstruction of highly reflective surfaces. First, a focused light field camera whose angular and spatial resolutions can be adjusted according to the needs has been designed and fabricated to capture 4D light field information. Then, according to the pixel offsets between different sub-aperture images, a phase restoration method based on multi-view complementary information is proposed to restore the missing absolute phase information caused by highlights. Finally, a cubic B-spline curve method is used to directly fit the relationship between absolute phase and coordinates to achieve 3D reconstruction of highly reflective surfaces. The experimental results demonstrate that the proposed method effectively utilizes the multi-view information from the light field to restore missing absolute phase data in the phase unwrapping, ensuring accurate 3D reconstruction of highly reflective surfaces. What is more, our method requires no additional hardware, camera angle calibration, or point cloud fusion, which significantly reduces both hardware complexity and computational demands.

Fringe projection profilometry based on deep learning phase demodulation combined with temporal phase unwrapping

Fringe projection profilometry based on deep learning phase demodulation combined with temporal phase unwrapping

Research on hydroacoustic signal processing algorithm based on B-spline and Hilbert transform

Purpose This paper aims to solve the problems of baseline drift, susceptibility to abnormal data interference during baseline drift processing, and phase inconsistency in underwater acoustic target detection and signal processing of single microelectromechanical systems (MEMS) vector hydrophone. To this end, this paper proposes a baseline drift removal algorithm based on Huber regression model with B-spline interpolation (H-BS) and a phase compensation algorithm based on the Hilbert transform. Design/methodology/approach First, the Huber regression model is innovatively introduced into the conventional B-spline interpolation (B-spline) to solve the control point vectors more accurately and to improve the anti-interference ability of the abnormal data when the B-spline interpolation fitting removes baseline drift and the baseline drift components in the signals are fitted accurately and removed by the above method. Next, the Hilbert transform is applied to the three-channel output signals of the MEMS vector hydrophone to calculate the instantaneous phase and the phase compensation is performed on the vector X/Y signals with the scalar P signal as the reference. Findings Through simulation experiments, it is found that H-BS proposed in this paper has smaller processing error and better robustness than variational modal decomposition and B-spline, but the H-BS algorithm takes slightly longer than the B-spline. In the actual lake test experiments, the H-BS algorithm can effectively remove the baseline drift component in the original signal and restore the signal waveform, and after the Hilbert transform phase compensation, the direction of arrival estimation accuracy of the signal is improved by 1°∼2°, which realizes high-precision orientation to the acoustic source target. Originality/value In this paper, the Huber regression model is introduced into B-spline interpolation fitting for the first time and applied in the specialized field of hydroacoustic signal baseline drift removal. Meanwhile, the Hilbert transform is applied to phase compensation of hydroacoustic signals. After simulation and practical experiments, these two methods are verified to be effective in processing hydroacoustic signals and perform better than similar methods. This study provides a new research direction for the signal processing of MEMS vector hydrophone, which has important practical engineering application value.

Crystallization-driven formation of cluster assemblies on surface for super-hydrophobic poly (L-lactic acid)/ZnO composite membrane.

The poly(L-lactic acid) (PLLA)/ZnO composite membrane with cluster assemblies microstructure was constructed by a combination of non-solvent induced phase separation (NIPS) and the Breath-Figure method. In this novel method, the controllable diffusion rate between solvent and non-solvent was introduced to the system by adjusting the non-solvent solubility parameters. The humidity was adjusted to control non-solvent solubility parameters in the Breath-Figure method, which avoids the instantaneous phase separation induced by direct coagulation of water droplets. Hydrophobic modified ZnO nanoparticles were used as heterogeneous nucleation points to induce PLLA crystallization and formation of micro-nano structures. Controlling molecular chain growth with crystal nuclei as templates and constructing cluster assemblies microscopic morphology at 99 % humidity, and the size of the cluster decreases gradually from 10 μm to 3 μm as the nanoparticles content increased up to 5 wt%. The surface water contact angle could reach 153.8° with cluster morphology. In addition, the porous structure formed by the polymer-lean phase could increase the porosity to 93.1 % and exhibit an excellent oil absorption capacity up to 12.64 g/g. It is foreseeable that porous PLLA/ZnO composite membranes have potential applications as biodegradable oil-water separation materials.

Sinusoidal Fitting Decomposition for Instantaneous Characteristic Representation of Multi-Componential Signal.

The research on how to effectively extract the instantaneous characteristic components of non-stationary signals continues to be both a research hotspot and a very challenging topic. In this paper, a new method of multi-component decomposition is proposed to decompose a signal into finite mono-component signals and extract their Instantaneous Amplitude (IA), Instantaneous Phase (IP), and Instantaneous Frequency (IF), which is called Sinusoidal Fitting Decomposition (SFD). The proposed method can ensure that the IA extracted from the given signal must be positive, the IP is monotonically increasing, and the signal synthesized by both IA and IP must be mono-componential and smooth. It transforms the decomposition process into a synthesis iterative process and does not rely on any dictionary or basis function space or carry out the sifting operation. In addition, the proposed method can describe the instantaneous-frequency-amplitude characteristics of the signal very well on the time-frequency plane. The results of numerical simulation and the qualitative analysis of the amount of calculation show that the proposed method is effective.

Novel CMR-assessed right ventricular-pulmonary artery coupling index independently associates with exercise capacity and clinical risk in pulmonary arterial hypertension

Abstract Background We defined a novel noninvasive right ventricle (RV)–pulmonary artery (PA) coupling index as the ratio of cardiovascular magnetic resonance (CMR)-assessed RV direct flow (RVDF) and PA pulse wave velocity (PWV), and investigated its associations with exercise capacity and clinical risk in pulmonary arterial hypertension (PAH). Method 43 PAH patients (mean age 46±12 years, M:F 7:36) and 60 healthy volunteers (mean age 46±13 years, M:F 11:48) underwent CMR and cardiopulmonary exercise test (CPET) within one week. From cine CMR, RV ejection fraction (EF) and RV end-diastolic volume (RVEDV) were calculated using volumetric analysis; and tricuspid annular plane systolic excursion (TAPSE), feature tracking. PAPWV was the ratio of early systolic DPA flow and DPA area measured from instantaneous phase and magnitude through plane 2D flow CMR images across the pulmonary trunk, respectively. RVDF was the 4D flow CMR-assessed blood volume entering and exiting the RV in one cardiac cycle, indexed to RVEDV. RV-PA coupling was RVDF/PAPWV. Based on CPET-assessed peak oxygen consumption (PVO2), all 103 participants were stratified into two groups: PVO2>15 ml/kg/min; and PVO2≤15 ml/kg/min. Based on the REVEAL (Registry to Evaluate Early and Long-term PAH Disease Management) 2.0 score, the 43 PAH patients were stratified into low risk (score ≤6) and intermediate to high risk (score >6) groups. Results RVDF/PAPWV was significantly lower in PAH vs. controls (7.9 vs. 20.4 %/(m/s), P<0.001); and in PAH patients with intermediate to high risk vs. low risk (4.6 vs. 9.4 %/(m/s), P=0.001). On multivariable analyses, RVDF/PAPWV was an independent predictor of PVO2≤15 ml/kg/min (=0.302, P=0.001) among all participants, and of REVEAL 2.0 score >6 (=0.621, P=0.009) among PAH patients. Compared to RVEF and TAPSE, RVDF/PAPWV had numerically higher discrimination (p values non-significant based on Delong test) for PVO2≤15 ml/kg/min (AUC=0.914 vs. 0.872, 0.843); and among PAH patients, REVEAL 2.0 score >6 (AUC=0.851 vs. 0.723 and 0.728) (Figure). Conclusion CMR-derived noninvasive RVDF/PAPWV independently associates with exercise capacity and PAH clinical risk, supporting its utility as an imaging marker of disease progression and therapeutic response.

Coherent linking between confocal amplitude image and confocal phase image in dual-comb microscopy

We propose a method for integrating confocal amplitude and phase images obtained through dual-comb microscopy (DCM). DCM combines the benefits of confocal laser microscopy and quantitative phase microscopy, offering high axial resolution and scan-less imaging. By leveraging the coherence between confocal amplitude and phase images within the same DCM system, we accurately determine the number of phase wrapping iterations, thereby eliminating ambiguity in phase wrapping. We demonstrate this approach using samples with micrometer-range optical thickness and nanometer-scale surface roughness. The results demonstrate an expanded axial range, spanning from micrometers to millimeters, while maintaining nanometer-level axial resolution. This integrated DCM imaging technique enables the simultaneous acquisition of confocal amplitude image and absolute phase image, thus enhancing its potential for wide-axial-dynamic-range imaging across various applications.

Fringe photometric stereo

In fringe projection profilometry (FPP), a high spatial frequency of fringe typically indicates powerful error suppression capability; however, it complicates phase unwrapping, necessitating a greater number of patterns and thus compromising the real-time performance of scanning. In this letter, we report a fringe photometric stereo (FPS) to completely bypass phase unwrapping for recovering the continuous 3D surface. We reveal the linear mapping relationship between the phase gradient and depth gradient, thereby facilitating the computation of depth gradients from phase gradients. Thus, we can employ depth gradients to reconstruct high-quality 3D profiles. Experimental results demonstrate that our FPS surpasses traditional phase-shifting profilometry in mitigating Gaussian noise. Our approach enables high-quality and unambiguous 3D reconstruction using single-frequency fringe patterns, relying solely on a camera and a projector without the need for dual, multiple, or light field cameras, thereby paving a path to high-speed and precision 3D imaging.

Dual frequency composite pattern temporal phase unwrapping for 3D surface measurement

Phase shifting profilometry (PSP) is widely used in three-dimensional (3D) optical metrology applications such as mechanical engineering, industrial monitoring, computer vision, and biomedicine because of its high measurement accuracy. In PSP, multi-frequency temporal phase unwrapping (TPU) plays a dominant role due to its high-accuracy measurement of surfaces with discontinuities and isolated objects. However, it requires a large number of fringe patterns. To reduce the number of required patterns, a new dual-frequency composite-pattern TPU method is developed, which needs only three patterns. The new method combines two fringe patterns of different frequencies into three composite fringe patterns, reconstructs rough 3D points by demodulating the low-frequency fringe pattern using geometric constraints, and reprojects it to obtain a rough low-frequency absolute phase, which is then refined to correct edge errors. Finally, the high-frequency wrapped phase is unwrapped under the guidance of the refined low-frequency phase, thereby the accurate 3D points are reconstructed based on stereo-vision technology. Experimental results demonstrated that the proposed method can achieve 3D surface measurement with only three images, which greatly improves the measurement efficiency. The proposed method has great application potential for the rapid 3D measurement of discontinuous surfaces and isolated objects.