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Journal articles on the topic 'Unwrapped phase'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Spagnolini, Umberto. "2-D phase unwrapping and phase aliasing." GEOPHYSICS 58, no. 9 (September 1993): 1324–34. http://dx.doi.org/10.1190/1.1443515.

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The phase of complex signals is measured modulo-2π (wrapped phase); continuous‐phase information is obtained by adding properly chosen multiples of 2π shift to the wrapped phase. Unwrapping searches for the 2π combinations that minimize the discontinuity of the unwrapped phase as only the unwrapped phase can be analyzed and interpreted by further processing. The key problem of phase unwrapping is phase aliasing, a condition mainly caused by rapid phase variations. The extension of the one‐dimensional (1-D) phase unwrapping algorithms to a two‐dimensional (2-D) domain by 1-D slicing gives unsatisfactory results even in the presence of low‐phase aliasing, whereas 2-D phase unwrapping deals with the complete problem, overcoming the limitations of 1-D unwrapping. The 2-D unwrapped phase is obtained as the solution of a variational problem that minimizes the differences between the gradients of the wrapped and unwrapped phase. The Euler equation is then integrated using the boundary conditions obtained from the wrapped phase. In addition to determining a unique unwrapped phase, this approach has the advantage that it limits the influence of phase aliasing. It is also more attractive than iterative 1-D unwrapping since it limits the propagation of unwrapping errors. Error propagation in phase unwrapping can strongly influence the result of any phase processing. Examples in this paper apply 2-D phase unwrapping to problems of refraction statics and interferometrical imaging using a remote system (SAR) and demonstrate how limited error propagation allows phase processing.

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2

Zhao, Xiaxia, Rong Mo, and Zhiyong Chang. "Enhanced geometric constraint-based phase unwrapping algorithm in binocular stereo vision fringe projection system." Insight - Non-Destructive Testing and Condition Monitoring 63, no. 9 (September 1, 2021): 540–46. http://dx.doi.org/10.1784/insi.2021.63.9.540.

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Phase unwrapping plays an important and central role in phase-based digital fringe projection profilometry. The unwrapping quality directly influences the three-dimensional measurement accuracy. Recently, an effective geometric constraint-based phase unwrapping algorithm has been proposed to obtain the continuous absolute phase map and the unwrapped phase accuracy was found to be high. However, in this technique the virtual depth plane at z = zmin is often created empirically, which increases the manual measurement error. For this reason, this paper proposes a method for accurately constructing the virtual plane and further applies it to phase unwrapping of objects with a larger depth range. In this method, a binocular stereo vision system is used as the measurement set-up for the virtual depth plane construction and a series of virtual depth planes at z = zimin (i ≥ 2) is automatically built using a computational framework. Then, the phase is unwrapped for each region according to the continuity of the unwrapped phase and a complete absolute phase map is obtained by merging the unwrapped phases in all regions for 3D reconstruction. In this process, the virtual depth planes are created automatically and quantitatively by the measurement system. No human intervention is required and it greatly reduces the manual measurement error. Experiments show that the artificial virtual planes can be built accurately and the phase is unwrapped correctly and readily.

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3

Dudczyk, J., and A. Kawalec. "Optimizing the minimum cost flow algorithm for the phase unwrapping process in SAR radar." Bulletin of the Polish Academy of Sciences Technical Sciences 62, no. 3 (September 1, 2014): 511–16. http://dx.doi.org/10.2478/bpasts-2014-0055.

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Abstract The last three decades have been abundant in various solutions to the problem of Phase Unwrapping in a SAR radar. Basically, all the existing techniques of Phase Unwrapping are based on the assumption that it is possible to determine discrete ”derivatives” of the unwrapped phase. In this case a discrete derivative of the unwrapped phase means a phase difference (phase gradient) between the adjacent pixels if the absolute value of this difference is less than π. The unwrapped phase can be reconstructed from these discrete derivatives by adding a constant multiple of 2π. These methods differ in that the above hypothesis may be false in some image points. Therefore, discrete derivatives determining the unwrapped phase will be discontinuous, which means they will not form an irrotational vector field. Methods utilising branch-cuts unwrap the phase by summing up specific discrete partial derivatives of the unwrapped phase along a path. Such an approach enables internally cohesive results to be obtained. Possible summing paths are limited by branch-cuts, which must not be intersected. These branch-cuts connect local discontinuities of discrete partial derivatives. The authors of this paper performed parametrization of the Minimum Cost Flow algorithm by changing the parameter determining the size of a tile, into which the input image is divided, and changing the extent of overlapping of two adjacent tiles. It was the basis for determining the optimum (in terms of minimum Phase Unwrapping time) performance of the Minimum Cost Flow algorithm in the aspect of those parameters.

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4

Yi, Tian, and Chang Li. "Phase Unwrapped Method of Modified Fringe Order." American Journal of Electrical and Computer Engineering 6, no. 1 (2022): 40. http://dx.doi.org/10.11648/j.ajece.20220601.15.

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5

Kam, Dong-Uk, Jeong Hee Kim, and Kunwoo Lee. "Unwrapped phase correction for robust 3D scanning." Applied Optics 58, no. 14 (May 2, 2019): 3676. http://dx.doi.org/10.1364/ao.58.003676.

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6

Choi, Yunseok, and Tariq Alkhalifah. "Unwrapped phase inversion with an exponential damping." GEOPHYSICS 80, no. 5 (September 2015): R251—R264. http://dx.doi.org/10.1190/geo2014-0498.1.

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7

Liu, Wanli, Jian Shao, Zhenguo Liu, and Yang Gao. "A Refined Phase Unwrapping Method for High Noisy Dense Fringe Interferogram Based on Adaptive Cubature Kalman Filter." Mathematical Problems in Engineering 2021 (August 9, 2021): 1–14. http://dx.doi.org/10.1155/2021/7141091.

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Cubature Kalman filter phase unwrapping (CKFPU) is an effective algorithm in unwrapping the interferograms. The local phase slope estimation is a key factor that affects the unwrapped accuracy. However, the estimation accuracy of local phase slop is relatively low in high noisy and dense stripes areas, which usually leads to the unsatisfactory unwrapped results. In order to effectively solve this issue, the rewrapped map of the unwrapped phase (obtained by CKFPU algorithm), which is a filtered interferogram with clearer fringes and more detailed information, is proposed in this paper to improve the phase slope estimation. In order to solve the problem of imprecise error variance for the new phase slope estimation, an adaptive factor is introduced into the CKFPU algorithm to increase the stability and reliability of the phase unwrapping algorithm. The proposed method is compared with the standard CKFPU algorithm using both simulated and real data. The experimental results validate the feasibility and superiority of the proposed method for processing those high noise dense fringe interferograms.

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8

Wu, Xinming, and Guangfa Zhong. "Generating a relative geologic time volume by 3D graph-cut phase unwrapping method with horizon and unconformity constraints." GEOPHYSICS 77, no. 4 (July 1, 2012): O21—O34. http://dx.doi.org/10.1190/geo2011-0351.1.

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Construction of a relative geologic time (RGT) volume is vital to seismic geomorphological and sedimentological interpretation. Seismic instantaneous phase unwrapping provides an excellent approach for generating an RGT volume. Although several 2D or 3D seismic phase unwrapping results have been published, there is a clear need for discussions on concrete methods for seismic phase unwrapping. We have developed the graph-cut phase unwrapping method, which performs well in the interferometric synthetic aperture radar image processing. It has advantages of strong discontinuity-preserving ability and high computing efficiency. To make it suitable for 3D seismic phase unwrapping, the method is improved by extending it from 2D to 3D, and by introducing the seismic horizon and unconformity constraints. The strong and continuous conformable seismic events, which can be easily tracked by certain autopicking methods, are introduced as horizon constraints for guiding the phase unwrapping to ensure a constant unwrapped phase on a constraining horizon. This idea is based on the fact that continuous seismic horizons are of time-stratigraphic significance. The horizon constraints can promise a correct unwrapped result on the constraining horizons and avoid the possible phase unwrapping errors propagating across a horizon. An unconformity represents a geologic time discontinuity, which is difficult to recover in an RGT volume by phase unwrapping. What’s worse, incorrect phase unwrapping on an unconformity will result in some discontinuities of unwrapped phase in the conformable data areas outside the unconformity. Interpreted unconformities are used as unconformity constraints to recover the discontinuities of the unwrapped phase at the constraining unconformities. As a test, our improved 3D graph-cut phase unwrapping method is successfully applied to the late Permian to early Triassic carbonate reservoirs in northern Sichuan Basin, southwest China. The results match well with the regional geologic background.

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9

Liu, Wei Ke, Gou Lin Liu, and Xiao Qing Zhang. "Least Squares Phase Unwrapping Algorithm Based on Topographic Factors." Applied Mechanics and Materials 105-107 (September 2011): 1876–79. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.1876.

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The phase of complex signals is wrapped since it can only be measured modulo-2; unwrapping searches for the 2-combinations that minimize the discontinuity of the unwrapped phase, as only the unwrapped phase can be analyzed and interpreted by further processing. Weighted least squares phase unwrapping algorithm could avoid errors transmission in the whole phase images, but it could not avoid defect and overlay of interference fringes caused by topographic factors. Therefore, a new phase unwrapping and weights choosing method based on local phase frequency estimate of topographic factors was presented. Experiments show it is an efficient phase unwrapping method which well overcome the defect of under-estimate slopes by least squares algorithm, and has higher accuracy and stability than other methods.

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10

Draper, Douglas C., J. Fred Holmes, and John Peacock. "Unwrapped-phase distribution model for speckle and turbulence." Applied Optics 31, no. 18 (June 20, 1992): 3481. http://dx.doi.org/10.1364/ao.31.003481.

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11

Simopoulos, Constantine, and Kutay F. Ustuner. "Phase unwrapped velocity display for ultrasound medical imaging." Journal of the Acoustical Society of America 128, no. 3 (2010): 1569. http://dx.doi.org/10.1121/1.3490394.

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12

Yuan, Zhihui, Tianjiao Chen, Xuemin Xing, Wei Peng, and Lifu Chen. "BM3D Denoising for a Cluster-Analysis-Based Multibaseline InSAR Phase-Unwrapping Method." Remote Sensing 14, no. 8 (April 11, 2022): 1836. http://dx.doi.org/10.3390/rs14081836.

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Multibaseline (MB) phase unwrapping (PU) is a key processing technique in MB interferometric synthetic aperture radar (InSAR). As one of the most popular methods, the cluster analysis (CA)-based MBPU method often suffers from the problem of low noise robustness. Therefore, the block-matching and 3D filtering (BM3D) algorithm, one of the most effective filtering methods for image denoising, is applied to improve the performance of the method. Five different filtering strategies for applying BM3D are proposed in the paper: interferogram filtering (IFF), intercept filtering (ICF), cluster number filtering (CNF), unwrapped phase filtering (UPF), and simultaneous filtering (STF). In particular, while keeping the general structure of BM3D, four different similarity measures are defined for interferograms, intercepts, clusters, and unwrapped phases to accommodate the special characteristics of different filtering objects. Experiments on synthesized and real InSAR datasets prove their feasibility and effectiveness, and the experiment results show that (1) the PU accuracy and robustness of the CA-based MBPU method can be greatly improved by adding BM3D denoising; (2) simultaneous filtering of interferograms, intercepts, cluster numbers, and unwrapped phases works best, but with the worst time complexity; (3) when filtering is performed for only one object of the CA-based MBPU method, the filtering effect of CNF and UPF is better than that of IFF and ICF; and (4), considering the three indicators of PUSR, NRSE, and time consumption, CNF and UPF should be the best choices.

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13

Zhao, M. R., Yu Cheng Lin, X. B. Niu, and D. M. Cheng. "Accurate Estimation of Phase Distribution on Reference Plane in Grating Projection Measurement." Key Engineering Materials 295-296 (October 2005): 221–26. http://dx.doi.org/10.4028/www.scientific.net/kem.295-296.221.

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A binary second order rational polynomial is adopted to simulate and extend the phase distribution on reference plane. In order to get the coefficients of the polynomial accurately, iterative least-square method based on the first order Taylor series expansion is used. The effect of the real reference plane profile error on measuring result is reduced by using extended unwrapped phase to substitute the original unwrapped phase. The effects of the random phase error and the system geometrical parameter error are decreased. The measuring accuracy of the system is improved. The principle of the 3D profile measuring system based on grating projection, the theoretic analysis for accurate estimate of phase distribution on reference plane, and the experimental results are presented.

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14

Gao, Yue Hua, Bing Luo, Zhong Yu Sun, and Su Fang Zhao. "Combined Phase Unwrapping Method Using 2D Image Information in PMP 3D Measurement." Advanced Materials Research 765-767 (September 2013): 2148–52. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.2148.

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In SMT solder paste deposit 3D measurement based on PMP, conventional phase unwrapping method suffered from shadow, noise and holes. Considering practical engineering condition, phase unwrapping method can be improved using 2D image information: basic principle method was applied to smooth area, quality-guided unwrapping and least-square method were taken in shadow or break area for phase unwrapping respectively. Experimental results show that desired phases can be correctly and quickly unwrapped in proposed method.

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15

Kim, Sang-Wan. "Development of Unwrapped InSAR Phase to Height Conversion Algorithm." Korean Journal of Remote Sensing 28, no. 2 (April 30, 2012): 227–35. http://dx.doi.org/10.7780/kjrs.2012.28.2.227.

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16

Wang, Yongxin, and Corinne Darvennes. "Improving noise source location using the unwrapped phase method." Journal of the Acoustical Society of America 112, no. 5 (November 2002): 2448. http://dx.doi.org/10.1121/1.4780079.

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17

Venkatesh, Bharath Ambale, Himanshu Gupta, Steven G. Lloyd, Louis Dell 'Italia, and Thomas S. Denney. "3D left ventricular strain from unwrapped harmonic phase measurements." Journal of Magnetic Resonance Imaging 31, no. 4 (April 2010): 854–62. http://dx.doi.org/10.1002/jmri.22099.

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18

Mao, Wenfei, Guoxiang Liu, Xiaowen Wang, Yakun Xie, Xiaoxing He, Bo Zhang, Wei Xiang, et al. "Using Range Split-Spectrum Interferometry to Reduce Phase Unwrapping Errors for InSAR-Derived DEM in Large Gradient Region." Remote Sensing 14, no. 11 (May 29, 2022): 2607. http://dx.doi.org/10.3390/rs14112607.

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The use of the conventional interferometric synthetic aperture radar (InSAR) to generate digital elevation models (DEMs) always encounters phase unwrapping (PU) errors in areas with a sizeable topographic gradient. Range split-spectrum interferometry (RSSI) can overcome this issue; however, it loses the spatial resolution of the SAR image. We propose the use of the RSSI-assisted In-SAR-derived DEM (RID) method to address this challenge. The proposed approach first applies the RSSI method to generate a prior DEM, used for simulating terrain phases. Then, the simulated terrain phases are subtracted from the wrapped InSAR phases to obtain wrapped residual phases. Finally, the residual phases are unwrapped by the minimum cost flow (MCF) method, and the unwrapped residual phases are added to the simulated phases. Both the simulated and TerraSAR-X data sets are used to verify the proposed method. Compared with the InSAR and RSSI methods, the proposed approach can effectively decrease the PU errors of large gradients, ensure data resolution, and guarantee the DEM’s accuracy. The root mean square error between the topographic phase simulated from the real DEM and the topographic phase generated from the proposed method is 2.22 rad, which is significantly lower than 6.60 rad for InSAR, and the improvement rate is about 66.36%.

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19

Kulkarni, Rishikesh, and Pramod Rastogi. "Direct unwrapped phase estimation in phase shifting interferometry using Levenberg–Marquardt algorithm." Journal of Optics 19, no. 1 (December 9, 2016): 015608. http://dx.doi.org/10.1088/2040-8986/19/1/015608.

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20

Kulkarni, Rishikesh, and Pramod Rastogi. "Simultaneous estimation of unwrapped phase and phase derivative from a closed fringe pattern." Optics and Lasers in Engineering 87 (December 2016): 168–75. http://dx.doi.org/10.1016/j.optlaseng.2016.03.016.

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21

Chen, Cheng, Yiping Cao, Yingying Wan, Guangkai Fu, Yapin Wang, and Chengmeng Li. "Full-field phase error compensation method based on relationship between unwrapped phase and phase error." Journal of Modern Optics 65, no. 16 (May 11, 2018): 1902–9. http://dx.doi.org/10.1080/09500340.2018.1471530.

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22

Chu, Junqiu, Xingling Liu, Haotong Ma, Xuegang Yu, and Ge Ren. "Noised Phase Unwrapping Based on the Adaptive Window of Wigner Distribution." Remote Sensing 14, no. 21 (November 6, 2022): 5603. http://dx.doi.org/10.3390/rs14215603.

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A noised phase-unwrapping method is presented by using the Wigner distribution function to filter the phase noise and restore the gradient of the phase map. By using Poisson’s equation, the unwrapped phase map was obtained. Compared with the existing methods, the proposed method is theoretically simple, provides a more accurate representation, and can be implemented in light-field hardware devices, such as Shack-Hartmann sensors.

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23

Zhong, Heping, Jinsong Tang, and Sen Zhang. "Phase quality map based on local multi-unwrapped results for two-dimensional phase unwrapping." Applied Optics 54, no. 4 (January 26, 2015): 739. http://dx.doi.org/10.1364/ao.54.000739.

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24

Xu, Huaping, Shuo Li, Yanan You, Aifang Liu, and Wei Liu. "Unwrapped Phase Estimation via Normalized Probability Density Function for Multibaseline InSAR." IEEE Access 7 (2019): 4979–88. http://dx.doi.org/10.1109/access.2018.2886702.

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25

Djebbi, R., and T. Alkhalifah. "Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase." Geophysical Journal International 197, no. 2 (February 18, 2014): 975–86. http://dx.doi.org/10.1093/gji/ggu025.

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26

Long, D. G. "Exact computation of the unwrapped phase of finite-length time series." IEEE Transactions on Acoustics, Speech, and Signal Processing 36, no. 11 (1988): 1787–90. http://dx.doi.org/10.1109/29.9019.

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27

del Pozo, Virginia Urruchi, Jose Francisco Algorri Genaro, Juan Carlos Torres Zafra, and Jose Manuel Sanchez-Pena. "Modeling of Unwrapped Phase Defects in Modal Liquid Crystal Cylindrical Microlenses." IEEE Photonics Technology Letters 26, no. 2 (January 2014): 198–201. http://dx.doi.org/10.1109/lpt.2013.2291863.

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28

Wu, Haibing, Bo Tao, Zeyu Gong, Zhouping Yin, and Han Ding. "A Fast UHF RFID Localization Method Using Unwrapped Phase-Position Model." IEEE Transactions on Automation Science and Engineering 16, no. 4 (October 2019): 1698–707. http://dx.doi.org/10.1109/tase.2019.2895104.

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29

Adi, Kusworo, Tati L. R. Mengko, Andriyan B. Suksmono, and H. Gunawan. "Phase Unwrapping Using Energy Minimization Methods for MRI Phase Image." International Journal of E-Health and Medical Communications 1, no. 3 (July 2010): 50–56. http://dx.doi.org/10.4018/jehmc.2010070105.

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Phase Unwrapping (PU) is reconstruction of absolute phase data from its wrapped phase. The absolute phase cannot be extracted from the wrapped phase data directly. Without phase noise, singularity, and aliasing problems, the phase information can be unwrapped easily. However, the phase data are always contaminated by noise and discontinuities, making the PU process more complicated. Therefore, a suitable PU algorithm is required to address the problems properly. In this method, the energy difference between neighborhood pixels in level 3 is counted, followed by getting the probability value to obtain its total fringes. The capability of the proposed method to unwrap simulated and actual MRI phase images is also demonstrated. In actual MRI phase image, PU can be implemented for water and fat separation.

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30

He, Wei, Yiyuan Cheng, Ling Xia, and Feng Liu. "A New Particle Swarm Optimization-Based Method for Phase Unwrapping of MRI Data." Computational and Mathematical Methods in Medicine 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/475745.

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A new method based on discrete particle swarm optimization (dPSO) algorithm is proposed to solve the branch-cut phase unwrapping problem of MRI data. In this method, the optimal order of matching the positive residues with the negative residues is first identified by the dPSO algorithm, then the branch cuts are placed to join each pair of the opposite polarity residues, and in the last step phases are unwrapped by flood-fill algorithm. The performance of the proposed algorithm was tested on both simulated phase image and MRI wrapped phase data sets. The results demonstrated that, compared with conventionally used branch-cut phase unwrapping algorithms, the dPSO algorithm is rather robust and effective.

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31

He, Yan Bin, Xin Zhong Li, Wei Min Chen, and Jun Song Wen. "Phase Unwrapping Method Based on Windowed Fourier Transform." Applied Mechanics and Materials 307 (February 2013): 321–26. http://dx.doi.org/10.4028/www.scientific.net/amm.307.321.

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Phase unwrapping is one of the key technologies in electronic speckle pattern interferometry. A new phase unwrapping algorithm, based on windowed Fourier transform is proposed. The high noisy phase map is denoised by the window Fourier transform approach and then is uwrapped by the discrete cosine transform. The method is tested in this paper using a circumferentially fixed circular plate with a point load at the centre and compared with not denoised wrapped phase map and unwrapped phase map. The result shows the new proposed phase unwrapping method in denoising and improving image quality has obvious superiority.

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32

Tang, Tao, Jianping Peng, Jinlong Li, Yingying Wan, Xingzi Liu, and Ruyu Ma. "Wheel Tread Reconstruction Based on Improved Stoilov Algorithm." Optics 3, no. 2 (April 18, 2022): 150–58. http://dx.doi.org/10.3390/opt3020016.

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With the development of rail transit in terms of speed and carrying capacity, train safety problems caused by wheel tread defects and wear have become more prominent. The wheel is an important part of the train, and the wear and defects of the wheel tread are directly related to the safety of the train; therefore, wheel tread testing is a key element of train testing. In phase measuring profilometry (PMP), the virtual sine grating generated by the computer is projected onto the measured wheel tread by a digital projector, and then a camera is used to obtain the modulated deformed grating on the surface of the wheel tread. Next, the wrapped phase is obtained by the improved Stoilov algorithm, and the unwrapped phase is obtained by the phase unwrapped algorithm. Finally, the three-dimensional (3D) profile of the wheel tread is reconstructed. This paper presents an improved Stoilov algorithm based on probability and statistics. Supposing that the probability of real data was the highest, we chose the cosine square matrix value of the phase shift for processing. After ruling out the singular points of large error, we obtained the closest value to the true phase shift using the method of probability and statistics. The experimental results show that this method can effectively restrain the singular phenomenon, and the 3D profile of wheel tread can be reconstructed successfully.

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Venkatesh, Bharath Ambale, Chun G. Schiros, Himanshu Gupta, Steven G. Lloyd, Louis Dell'Italia, and Thomas S. Denney. "Three-dimensional plus time biventricular strain from tagged MR images by phase-unwrapped harmonic phase." Journal of Magnetic Resonance Imaging 34, no. 4 (July 18, 2011): 799–810. http://dx.doi.org/10.1002/jmri.22665.

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34

Alkhalifah, Tariq. "Research Note: Full-waveform inversion of the unwrapped phase of a model." Geophysical Prospecting 62, no. 2 (December 6, 2013): 397–403. http://dx.doi.org/10.1111/1365-2478.12089.

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35

Huang, Lei, and Anand Krishna Asundi. "Practical Framework for Phase Retrieval and Invalidity Identification with Temporal Phase Unwrapping Method in Fringe Projection Profilometry." Applied Mechanics and Materials 83 (July 2011): 179–84. http://dx.doi.org/10.4028/www.scientific.net/amm.83.179.

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Phase retrieval from fringe patterns is a primary procedure in fringe projection profilometry. Only accurate phase values result in three dimensions with certain accuracy. Phase shifting method plus temporal phase unwrapping approach provides not only the unwrapped absolute phase, but also the modulation map, background map, root mean square errors of least squares fitting, and phase relationship between two neighboring pixels, which can be used for the identification of phase invalidity. A practical phase retrieval frame work is presented to accurately calculate the absolute phase within reliable regions only, with which those unavailable phase points can be automatically identified with thresholds selection and criterion testing and then removed or interpolated according to applications. Experimental results show practical feasibility of the proposed framework.

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36

Chang, Caixia, Zonghua Zhang, Nan Gao, and Zhaozong Meng. "Measurement of the Three-Dimensional Shape of Discontinuous Specular Objects Using Infrared Phase-Measuring Deflectometry." Sensors 19, no. 21 (October 24, 2019): 4621. http://dx.doi.org/10.3390/s19214621.

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Phase-measuring deflectometry (PMD)-based methods have been widely used in the measurement of the three-dimensional (3D) shape of specular objects, and the existing PMD methods utilize visible light. However, specular surfaces are sensitive to ambient light. As a result, the reconstructed 3D shape is affected by the external environment in actual measurements. To overcome this problem, an infrared PMD (IR-PMD) method is proposed to measure specular objects by directly establishing the relationship between absolute phase and depth data for the first time. Moreover, the proposed method can measure discontinuous surfaces. In addition, a new geometric calibration method is proposed by combining fringe projection and fringe reflection. The proposed IR-PMD method uses a projector to project IR sinusoidal fringe patterns onto a ground glass, which can be regarded as an IR digital screen. The IR fringe patterns are reflected by the measured specular surfaces, and the deformed fringe patterns are captured by an IR camera. A multiple-step phase-shifting algorithm and the optimum three-fringe number selection method are applied to the deformed fringe patterns to obtain wrapped and unwrapped phase data, respectively. Then, 3D shape data can be directly calculated by the unwrapped phase data on the screen located in two positions. The results here presented validate the effectiveness and accuracy of the proposed method. It can be used to measure specular components in the application fields of advanced manufacturing, automobile industry, and aerospace industry.

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Mousavi, Asma Alsadat, Chunwei Zhang, Sami F. Masri, and Gholamreza Gholipour. "Structural Damage Localization and Quantification Based on a CEEMDAN Hilbert Transform Neural Network Approach: A Model Steel Truss Bridge Case Study." Sensors 20, no. 5 (February 26, 2020): 1271. http://dx.doi.org/10.3390/s20051271.

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Vibrations of complex structures such as bridges mostly present nonlinear and non-stationary behaviors. Recently, one of the most common techniques to analyze the nonlinear and non-stationary structural response is Hilbert–Huang Transform (HHT). This paper aims to evaluate the performance of HHT based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique using an Artificial Neural Network (ANN) as a proposed damage detection methodology. The performance of the proposed method is investigated for damage detection of a scaled steel-truss bridge model which was experimentally established as the case study subjected to white noise excitations. To this end, four key features of the intrinsic mode function (IMF), including energy, instantaneous amplitude (IA), unwrapped phase, and instantaneous frequency (IF), are extracted to assess the presence, severity, and location of the damage. By analyzing the experimental results through different damage indices defined based on the extracted features, the capabilities of the CEEMDAN-HT-ANN model in detecting, addressing the location and classifying the severity of damage are efficiently concluded. In addition, the energy-based damage index demonstrates a more effective approach in detecting the damage compared to those based on IA and unwrapped phase parameters.

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Ashokan, K., and K. Ramesh. "Plotting of Isoclinic Phasemap from Finite Element Results and its Use in Digital Photoelasticity." Applied Mechanics and Materials 7-8 (August 2007): 89–94. http://dx.doi.org/10.4028/www.scientific.net/amm.7-8.89.

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Digital photoelasticity is an experimental method for determining stresses in 2D and 3D models. In digital photoelasticity one gets a wrapped isoclinic phasemap. The main issue with wrapped isoclinic phasemaps is that the isoclinic values obtained do not uniformly represent the principal stress direction of one of the principal stresses consistently over the entire domain. These zones are labelled as inconsistent zones. Such zones need to be identified and corrected to get unwrapped values of continuous isoclinic phase values. In this paper, a method is developed to plot the simulated wrapped and unwrapped isoclinic phasemap from 2D Finite Element (FE) results so that one can use this as a convenient tool for identification and correction of inconsistent zones in isoclinic phasemaps obtained experimentally for complex problems. The method is explained by using the problem of a circular disc under diametral compression. The application of this method for handling complex problems is demonstrated by solving the cantilever bending of a binocular specimen.

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39

Watson, Stephen M., and Kevin D. Ridley. "Wrapped and unwrapped phase of radiation scattered by a discrete number of particles." Journal of Physics A: Mathematical and Theoretical 40, no. 19 (April 24, 2007): 4989–95. http://dx.doi.org/10.1088/1751-8113/40/19/004.

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ICHIGE, K., K. SAITO, and H. ARAI. "High Resolution DOA Estimation Using Unwrapped Phase Information of MUSIC-Based Noise Subspace." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E91-A, no. 8 (August 1, 2008): 1990–99. http://dx.doi.org/10.1093/ietfec/e91-a.8.1990.

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41

Lv, Shanshan, Mingshun Jiang, Chenhui Su, Lei Zhang, Faye Zhang, Qingmei Sui, and Lei Jia. "Improved unwrapped phase retrieval method of a fringe projection profilometry system based on fewer phase-coding patterns." Applied Optics 58, no. 32 (November 8, 2019): 8993. http://dx.doi.org/10.1364/ao.58.008993.

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42

Liu, Shu Gui, Li Shuan Ji, Shu Jian Han, Xiao Jie Zhang, and Hong Wei Zhang. "An Improved Composite Grating for Phase Unwrapping in 3-D Measurement of Specular Objects." Advanced Materials Research 468-471 (February 2012): 753–57. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.753.

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The paper proposes a novel method of improving the traditional composite grating in 3-D measurement of the specular objects. The traditional composite grating is improved by altering the intensity of the center stripe in one of the fringes. The improved composite grating not only includes the primary phase information, which is modulated by the object's surface, but also includes the code information, which is necessary for the phase unwrapping. The paper introduces the formation of the improved composite grating, demodulating the composite grating and computing the unwrapped phase based on the altered fringe. Simulated and actual experiments prove that this method is valid. Because of projecting a single composite grating, the method is suitable for dynamical measurement.

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Risholm, Petter, Trine Kirkhus, Jens Thielemann, and Jostein Thorstensen. "Adaptive Structured Light with Scatter Correction for High-Precision Underwater 3D Measurements." Sensors 19, no. 5 (March 1, 2019): 1043. http://dx.doi.org/10.3390/s19051043.

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High-precision underwater 3D cameras are required to automate many of the traditional subsea inspection, maintenance and repair (IMR) operations. In this paper we introduce a novel multi-frequency phase stepping (structured light) method for high-precision 3D estimation even in turbid water. We introduce an adaptive phase-unwrapping procedure which uses the phase-uncertainty to determine the highest frequency that can be reliably unwrapped. Light scattering adversely affects the phase estimate. We propose to remove the effect of forward scatter with an unsharp filter and a model-based method to remove the backscatter effect. Tests in varying turbidity show that the scatter correction removes the adverse effect of scatter on the phase estimates. The adaptive frequency unwrapping with scatter correction results in images with higher accuracy and precision and less phase unwrap errors than the Gray-Code Phase Stepping (GCPS) approach.

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Pu, Liming, Xiaoling Zhang, Zenan Zhou, Liang Li, Liming Zhou, Jun Shi, and Shunjun Wei. "A Robust InSAR Phase Unwrapping Method via Phase Gradient Estimation Network." Remote Sensing 13, no. 22 (November 13, 2021): 4564. http://dx.doi.org/10.3390/rs13224564.

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Phase unwrapping is a critical step in synthetic aperture radar interferometry (InSAR) data processing chains. In almost all phase unwrapping methods, estimating the phase gradient according to the phase continuity assumption (PGE-PCA) is an essential step. The phase continuity assumption is not always satisfied due to the presence of noise and abrupt terrain changes; therefore, it is difficult to get the correct phase gradient. In this paper, we propose a robust least squares phase unwrapping method that works via a phase gradient estimation network based on the encoder–decoder architecture (PGENet) for InSAR. In this method, from a large number of wrapped phase images with topography features and different levels of noise, the deep convolutional neural network can learn global phase features and the phase gradient between adjacent pixels, so a more accurate and robust phase gradient can be predicted than that obtained by PGE-PCA. To get the phase unwrapping result, we use the traditional least squares solver to minimize the difference between the gradient obtained by PGENet and the gradient of the unwrapped phase. Experiments on simulated and real InSAR data demonstrated that the proposed method outperforms the other five well-established phase unwrapping methods and is robust to noise.

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Liang, Jian, Junchao Zhang, Jianbo Shao, Bofan Song, Baoli Yao, and Rongguang Liang. "Deep Convolutional Neural Network Phase Unwrapping for Fringe Projection 3D Imaging." Sensors 20, no. 13 (July 1, 2020): 3691. http://dx.doi.org/10.3390/s20133691.

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Phase unwrapping is a very important step in fringe projection 3D imaging. In this paper, we propose a new neural network for accurate phase unwrapping to address the special needs in fringe projection 3D imaging. Instead of labeling the wrapped phase with integers directly, a two-step training process with the same network configuration is proposed. In the first step, the network (network I) is trained to label only four key features in the wrapped phase. In the second step, another network with same configuration (network II) is trained to label the wrapped phase segments. The advantages are that the dimension of the wrapped phase can be much larger from that of the training data, and the phase with serious Gaussian noise can be correctly unwrapped. We demonstrate the performance and key features of the neural network trained with the simulation data for the experimental data.

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Meaney, P. M., K. D. Paulsen, B. W. Pogue, and M. I. Miga. "Microwave image reconstruction utilizing log-magnitude and unwrapped phase to improve high-contrast object recovery." IEEE Transactions on Medical Imaging 20, no. 2 (2001): 104–16. http://dx.doi.org/10.1109/42.913177.

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Wu, Songbo, Lei Zhang, Xiaoli Ding, and Daniele Perissin. "Pixel-Wise MTInSAR Estimator for Integration of Coherent Point Selection and Unwrapped Phase Vector Recovery." IEEE Transactions on Geoscience and Remote Sensing 57, no. 5 (May 2019): 2659–68. http://dx.doi.org/10.1109/tgrs.2018.2876115.

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Zhang, Yao Ting, and Min Jui Huang. "Surface Crack Search and Marking on Materials with Regional Phase Unwrapping Technology." Advanced Materials Research 291-294 (July 2011): 1074–81. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.1074.

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Depending on the size of sets, a wrapped phase map is unwrapped by either region or pixel. In region phase unwrapping, the jump point threshold value is adjusted to search the region boundary after filtering a wrapped map with higher noise and then phase unwrapping ±2nπ in each region without filtering. The latter compares if the phase difference of adjacent pixels is greater than π as a reference for determining pixel point ±2π to perform phase unwrapping point by point. Although the former unwraps phase by means of boundary search and the latter with the phase difference of adjacent pixels, phase unwrapping errors occur in both cases in detecting surface cracks on materials as data on both sides of a crack are discontinuous. This paper proposes a solution for phase unwrapping on discontinuous surfaces by means of crack search and marking with region assembly phase unwrapping technology to locate boundaries in both region splits and crack splits and further extends the scope of application of region assembly phase unwrapping.

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Auber--Le Saux, Jessica, Vincent Detalle, Xueshi Bai, Michalis Andrianakis, Nicolas Wilkie-Chancellier, and Vivi Tornari. "Surface Displacement Measurements of Artworks: New Data Processing for Speckle Pattern Interferometry." Applied Sciences 12, no. 23 (November 23, 2022): 11969. http://dx.doi.org/10.3390/app122311969.

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Curators have developed preventive conservation strategies and usually try to control the temperature (T) and relative humidity (RH) variations in the museum rooms to stabilise the artworks. The control systems chosen by museums depend on the size and age of the building, the financial means and the strategies that can be adapted. However, there is a lack of methods that can monitor mechanical changes or chemical reactions of objects in real-time or regularly. It would therefore ideally be preferable to monitor each of them to alert them to preserve them. For this purpose, a non-destructive, non-contact, full-field technique, Digital Holographic Speckle Pattern Interferometry (DHSPI), has already been developed and allows direct tracking of changes on the surface of artworks. This technique is based on phase-shifting speckle interferometry and gives the deformation of the surface below the level of the micro-meter of the analysed object. In order to monitor the deformation continuously, a large number of images are acquired by DHSPI and have to be processed. The existing process consists of removing noise from the interferogram, unwrapping this image, and deriving and displaying a 2D or 3D deformation map. In order to improve the time and accuracy of processing the imaging data, a simpler and faster processing method is developed. Using Matlab®, a denoising methodology for the interference pattern generated during data acquisition is created, based on a stationary wavelet transform. The unwrapped image is calculated using the CPULSI (Calibrated Phase Unwrapping based on Least-Squares and Iterations) algorithm as it gives the fastest results among the tested methods. The unwrapped phase is then transformed into surface displacement. This process performs these steps for each interferogram automatically. It allows access to 2D or 3D deformation maps.

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Romijn, R. L., B. J. Oosterveld, and J. M. Thijssen. "Phase-Derivative Imaging I: Methods and Stabilization Analysis." Ultrasonic Imaging 9, no. 3 (July 1987): 147–61. http://dx.doi.org/10.1177/016173468700900301.

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The potential of using the phase derivative (PD) for echographic imaging was investigated. The PD data were calculated by four methods: zero crossing (ZCS) with squelch addition, analytic signal either with squelch addition (ASS) or with employment of a Wiener kernel (ASW), and unwrapped phase (UWP). The large peaks which occur in an unprocessed PD signal were “stabilized” by some kind of smoothing algorithm. The effects of the amplitude of the squelch signal and of the degree of smoothing were systematically investigated for experimental and simulated 1-D and 2-D rf echograms. The optimal pictures obtained for all four PD estimation methods were compared to the amplitude modulated (AM) image obtained from the same rf data. It is concluded that three different PD images can be derived: AM dominated (ZCS, ASS), mixed AM-PD (ASW) and pure PD (UWP) images. Some preliminary conclusions regarding the potential of PD imaging for medical diagnostics were drawn. These conclusions were based on quantitative 1st order statistics and on a qualitative assessment of 2nd order statistics of the PD image texture.

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