Spatial Unwrapping Research Articles

High performance holographic video compression using spatio-temporal phase unwrapping

In this work, we present a high-performance holographic data compression technique. This approach is based in the temporal correlation found in a holographic video generated using an optimized random phase. This temporal correlation makes possible high levels of compression by using a spatio-temporal (ST) representation, partial phase unwrapping, and a lossless compression algorithm like DEFLATE. In this approach, two holographic videos are created using the optimized random phase (ORAP) technique and the Gerchberg-Saxton (GS) algorithm. The phase holograms corresponding to each frame of the videos are arranged into a ST representation, enabling spatial and temporal phase unwrapping. We test phase unwrapping along the spatial and temporal dimensions separately, followed by volume reduction after applying the DEFLATE lossless compression algorithm to the unwrapped phase in each case. The holographic video is then reconstructed from the compressed temporal and spatial unwrapped phase. The results demonstrate the high efficiency of the proposed method, with ORAP holograms achieving a compression percentage of 92.670 % after applying DEFLATE to a ST representation with partial phase unwrapping along the temporal dimension.

Error analysis and 3D reconstruction using airborne array InSAR images

Multi-temporal synthetic aperture radar interferometry (MT-InSAR) is able to detect surface deformation and reconstruct a 3D surface model with high precision but requires a long observation period to accumulate the multi-baseline SAR images. The airborne array InSAR system is able to acquire a stack of multi-baseline SAR images in a single acquisition, which significantly improves the 3D modeling capability. However, processing the images obtained by the low-altitude platform using the conventional model will lead to geometric approximation (GA) errors, such as flattened phase error and reference error, which degrade the precision of the 3D reconstruction. In this paper, we quantitatively analyze the error sources of the array-InSAR interferograms and design a hybrid 3D phase unwrapping approach for 3D reconstruction. A hypothesis test is developed to identify the phase ambiguity by comparing the initial solution of the least-square with that of the beam-forming. Three indicators are proposed to identify the reliable arcs, achieving a reliable phase unwrapping. The L1 norm approach is adopted to detect the unwrapping errors during the spatial unwrapping and a two-tie network strategy is used to process the data in the individual blocks from the perspective of global optimization. Furthermore, an iterative scheme is recommended to compensate the geometric approximation errors. The main advantage of the proposed algorithm is the compensation of the GA error and reliable phase unwrapping. The experimental results by both simulated and real SAR data show that the proposed algorithm can eliminate the GA error and provide a viable solution to rapid 3D SAR imaging with an airborne platform.

Multi-echo gradient-recalled-echo phase unwrapping using a Nyquist sampled virtual echo train in the presence of high-field gradients.

To develop a spatio-temporal approach to accurately unwrap multi-echo gradient-recalled echo phase in the presence of high-field gradients. Using the virtual echo-based Nyquist sampled (VENyS) algorithm, the temporal unwrapping procedure is modified by introduction of one or more virtual echoes between the first lower and the immediate higher echo, so as to reinstate the Nyquist condition at locations with high-field gradients. An iterative extension of the VENyS algorithm maintains spatial continuity by adjusting the phase rotations to make the neighborhood phase differences less than π. The algorithm is evaluated using simulated data, Gadolinium contrast-doped phantom, and in vivo brain, abdomen, and chest data sets acquired at 3 T and 9.4 T. The unwrapping performance is compared with the standard temporal unwrapping algorithm used in the morphology-enabled dipole inversion-QSM pipeline as a benchmark for validation. Quantitative evaluation using numerical phantom showed significant reduction in unwrapping errors in regions of large field gradients, and the unwrapped phase revealed an exact match with the linear concentration profile of vials in a gadolinium contrast-doped phantom data acquired at 9.4 T. Without the need for additional spatial unwrapping, the iterative VENyS algorithm was able to generate spatially continuous phase images. Application to in vivo data resulted in better unwrapping performance, especially in regions with large susceptibility changes such as the air/tissue interface. The iterative VENyS algorithm serves as a robust unwrapping method for multi-echo gradient-recalled echo phase in the presence of high-field gradients.

Absolute phase unwrapping with SVM for fringe‐projection profilometry

Phase unwrapping is a fundamental task in phase-based profilometry. Existing spatial and temporal approaches are facing challenges such as error propagation and low efficiency. In this study, the authors propose a learning-based method that uses a support vector machine (SVM) to perform phase unwrapping, where the problem is solved as a classification task. To be specific, seven elements, extracted from the captured patterns and the wrapped phase, form the input feature vector and the fringe order is the output class. Besides, a radial basis function kernel SVM is adopted as the model. The proposed method is conducted independently for every pixel, and does not suffer from error propagation in the spatial unwrapping. Moreover, it needs fewer patterns than temporal unwrapping since only one phase map is required. Simulation and experimental results demonstrate that the proposed scheme produces precise depth maps, which are comparable with the complex quality-guided methods but at a much faster speed.

Development and application of spatial carrier interferometry for whole field real-time investigation of temperatures in liquid media

This paper presents interferometric measurement of dynamic phenomena in transparent media. The method is based on differential spatial carrier interferometry that provides interesting features for experimental fluid mechanics. The method is particularly suitable for progressively changing phenomena. Temperature is automatically evaluated from a single interferogram, and a differential approach allows to decrease dynamic range of the measurement. As a consequence, in case of high temporal sampling of the phenomena, no spatial phase unwrapping is needed. Otherwise, the spatial unwrapping is performed on low fringe density phase maps and the fringe order is unambiguously determined. The interferometric method was experimentally tested by measuring dynamically varying temperature fields in water. The inspected phenomenon was a convection of water layers within a glass tank, where a heat sink was positioned at the bottom of the tank. Interferometric and temperature measurements were simultaneously conducted. Temperature was measured using four thermocouples to verify the reliability of the method. Results of both approaches are in a good agreement.

Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry

In this work we review and combine two techniques that have been recently published for three-dimensional (3D) fringe projection profilometry and phase unwrapping, namely: co-phased profilometry and 2-steps temporal phase-unwrapping. By combining these two methods we get a more accurate, higher signal-to-noise 3D profilometer for discontinuous industrial objects. In single-camera single-projector (standard) profilometry, the camera and the projector must form an angle between them. The phase-sensitivity of the profilometer depends on this angle, so it cannot be avoided. This angle produces regions with self-occluding shadows and glare from the solid as viewed from the camera׳s perspective, making impossible the demodulation of the fringe-pattern there. In other words, the phase data is undefined at those shadow regions. As published recently, this limitation can be solved by using several co-phased fringe-projectors and a single camera. These co-phased projectors are positioned at different directions towards the object, and as a consequence most shadows are compensated. In addition to this, most industrial objects are highly discontinuous, which precludes the use of spatial phase-unwrappers. One way to avoid spatial unwrapping is to decrease the phase-sensitivity to a point where the demodulated phase is bounded to one lambda, so the need for phase-unwrapping disappears. By doing this, however, the recovered non-wrapped phase contains too much harmonic distortion and noise. Using our recently proposed two-step temporal phase-unwrapping technique, the high-sensitivity phase is unwrapped using the low-frequency one as initial gross estimation. This two-step unwrapping technique solves the 3D object discontinuities while keeping the accuracy of the high-frequency profilometry data. In scientific research, new art are derived as logical and consistent result of previous efforts in the same direction. Here we present a new 3D-profilometer combining these two recently published methods: co-phased profilometry and two-steps temporal phase-unwrapping. By doing this, we obtain a new and more powerful 3D profilometry technique which overcomes the two main limitations of previous fringe-projection profilometers namely: high phase-sensitivity digitalization of discontinuous objects and solid׳s self-generated shadow minimization. This new 3D profilometer is demonstrated by an experiment digitizing a discontinuous 3D industrial-solid where the advantages of this new profilometer with respect to previous art are clearly shown.

The present status of subsiding land vulnerable to roof collapse in the Jharia Coalfield, India, as obtained from shorter temporal baseline C-band DInSAR by smaller spatial subset unwrapped phase profiling

ABSTRACTIn this paper, we identified recently subsiding areas in Jharia Coalfield, Jharkhand, India from the shorter temporal baseline Radarsat-2 C-band interferometric synthetic aperture radar (InSAR) data pairs of 2012. Although shorter wavelength C-band differential InSAR (DInSAR) is more sensitive to slow deformation and better suited for higher precision land subsidence measurement, the dynamic and adverse land cover in mining areas and resulting temporal decorrelation problem poses a serious problem for DInSAR observation in mining areas. We used smaller temporal baseline data pairs and adopted InSAR coherence-guided incremental filtering with smaller moving windows to highlight the deformation fringes over temporal decorrelation noise. We identified the deformation fringes and validated them based on ground information to prepare the land subsidence map of the coalfield in 2012. Several new, previously unreported subsidence areas were detected in the present study with a total subsiding area of 6.9 km2. The recent incidence of roof collapse on 15 November 2014 at Angar Patra village in Katras region of the coalfield where 45 houses collapsed and 10 people were injured is situated in a highly subsiding vulnerable area as obtained from the present study. Due to spatial discontinuities of InSAR coherence, DInSAR phase unwrapping for the entire study area in one go did not appear feasible. To avoid this problem, we performed DInSAR processing in smaller spatial subsets and unwrapping of the subset interferograms by a ‘minimum cost flow’ algorithm. Subsequently, we plotted unwrapped phase profiles across the deformation fringes and retrieved the maximum deformation phase with respect to background phase and translated them into radar line of sight (LOS) displacement rates. For obtaining the average subsidence rates, we adopted InSAR coherence-weighted LOS displacement rates taking into account the contribution of each data pair as a function of DInSAR phase quality of the fringe areas. Ground-based subsidence measurements by precision levelling were conducted in four test sites that had been undergoing active underground mining during the observation period. We compared space-borne DInSAR-based subsidence rates obtained by the adopted technique with precision levelling measurements. Overall, the results are found to agree well. In the four test sites with gentle to flat topography, land subsidence occurs at slow to moderate rates due to compression of in-filled material (resulting from sand stowing in underground mining), without any evidence of roof collapse. In such cases, the horizontal displacement component is less significant, and overall surface displacement occurs essentially in the vertical direction. However, we assessed the nature of subtle horizontal strain to infer relative shrinkage or dilation of the land surface which could be additive or subtractive to vertical displacement in DInSAR-based LOS displacement.

Isochromatic photoelastic phase map unwrapping: temporal versus spatial approach

A comparison of temporal and spatial unwrapping on a photoelastic isochromatic phase map is discussed. The analytical results show that the two-dimensional Macy’s spatial unwrapping can yield a quite good retrieval if an inconsistency-free isochromatic map is to be treated as is true in most of the photoelastic problem cases. While only temporal wrapped data are provided for the phase retrieving work, the success strongly depends on providing the correct changing ratio between the two (or more) temporal states, (e.g., percentage variation of load or wavelength step). The simulation of an incorrect ratio of the temporal isochromatic work on the accuracy of the retrieving work is performed. Experimental results show that temporal unwrapping error is more easily occurs near a highly stressed zone.

Accurate Dynamic 3D Sensing With Fourier-Assisted Phase Shifting

Phase shifting profilometry (PSP) and Fourier transform profilometry (FTP) are two well-known fringe analysis methods for 3D sensing. PSP offers high accuracy but requires multiple images; FTP uses a single image but is limited in its accuracy. In this paper, we propose a novel Fourier-assisted phase shifting (FAPS) method for accurate dynamic 3D sensing. Our key observation is that the motion vulnerability of multi-shot PSP can be overcome through single-shot FTP, while the high accuracy of PSP is preserved. Moreover, to solve the phase ambiguity of complex scenes without additional images, we propose an efficient parallel spatial unwrapping strategy that embeds a sparse set of markers in the fringe patterns. Our dynamic 3D sensing system based on the above principles demonstrates superior performance over previous structured light techniques, including PSP, FTP, and Kinect.

Time series ground subsidence inversion in mining area based on CRInSAR and PSInSAR integration

The subsidence of the mining area was monitored by analyzing the phase of permanent scatters (PS) which maintained high coherence in magnitude of SAR images. A new method of spatial unwrapping was presented which used the subsidence rates calculated on corner reflector (CR) points as constraints for PS network to perform the spatial unwrapping using the parametric adjustment method. The algorithm achieved the integration of CR data and PSInSAR algorithm. The colliery dense distributed area around Baisha reservoir was chosen as the study area in the experiment. The time series of subsidence from February in 2007 to February in 2010 is successfully inversed by using the periodic function to simulate the linear and nonlinear components of the deformation. The simulation results show that the accuracy can be ± 2.1 mm with the leveling data being used as the external validation data.

The Multidimensional Phase Unwrapping Integral and Applications to Microwave Tomographical Image Reconstruction

Spatial unwrapping of the phase component of time varying electromagnetic fields has important implications in a range of disciplines including synthetic aperture radar (SAR) interferometry, MRI, optical confocal microscopy, and microwave tomography. This paper presents a fundamental framework based on the phase unwrapping integral, especially in the complex case where phase singularities are enclosed within the closed path integral. With respect to the phase unwrapping required when utilized in Gauss-Newton iterative microwave image reconstruction, the concept of dynamic phase unwrapping is introduced where the singularity location varies as a function of the iteratively modified property distributions. Strategies for dynamic phase unwrapping in the microwave problem were developed and successfully tested in simulations and clinical experiments utilizing large, high contrast targets to validate the approach.

Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector

A fringe projector based on a low-cost spatial light modulator has been used to measure the shapes of discontinuous objects. By changing the fringe phase and the fringe pitch, a sequence of wrapped phase maps can be acquired at different sensitivities. This sequence can then be converted to a surface profile by the recently proposed method of temporal unwrapping rather than by a conventional spatial unwrapping approach. The main advantages are that the method is simple and ro- bust, and that objects with surface discontinuities are profiled as easily and accurately as smooth ones. The absolute distance from the camera to an object is measured at each pixel independently of the other pixels in the image. In addition to accurate measurement of surface shape, one possible application may therefore be as a 3-D robot vision system. A simple calibration procedure is described which avoids the need for ac- curate positioning of the camera and projector and which takes account of instrumental artifacts. A measurement accuracy better than 1/1000 of the field of view has been achieved. A number of practical applications of the technique are illustrated. © 1997 Society of Photo-Optical Instrumentation En- gineers.