Abstract

Robust phase unwrapping in the presence of high noise remains an open issue. Especially, when both noise and fringe densities are high, pre-filtering may lead to phase dislocations and smoothing that complicate even more unwrapping. In this paper an approach to deal with high noise and to unwrap successfully phase data is proposed. Taking into account influence of noise in wrapped data, a calibration method of the 1st order spatial phase derivative is proposed and an iterative approach is presented. We demonstrate that the proposed method is able to process holographic phase data corrupted by non-Gaussian speckle decorrelation noise. The algorithm is validated by realistic numerical simulations in which the fringe density and noise standard deviation is progressively increased. Comparison with other established algorithms shows that the proposed algorithm exhibits better accuracy and shorter computation time, whereas others may fail to unwrap. The proposed algorithm is applied to phase data from digital holographic metrology and the unwrapped results demonstrate its practical effectiveness. The realistic simulations and experiments demonstrate that the proposed unwrapping algorithm is robust and fast in the presence of strong speckle decorrelation noise.

© 2016 Optical Society of America

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References

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2016 (1)

2015 (8)

J. Poittevin, P. Picart, F. Gautier, and C. Pézerat, “Quality assessment of combined quantization-shot-noise-induced decorrelation noise in high-speed digital holographic metrology,” Opt. Express 23(24), 30917–30932 (2015).
[Crossref] [PubMed]

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Lasers Eng. 64, 51–58 (2015).
[Crossref]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: a review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: A D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

B. Tayebi, M. R. Jafarfard, F. Sharif, Y. S. Song, D. Har, and D. Y. Kim, “Large step-phase measurement by a reduced-phase triple-illumination interferometer,” Opt. Express 23(9), 11264–11271 (2015).
[Crossref] [PubMed]

Z. Cheng, D. Liu, Y. Yang, T. Ling, X. Chen, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique,” Opt. Express 23(25), 32337–32349 (2015).
[Crossref] [PubMed]

P. Girshovitz and N. T. Shaked, “Fast phase processing in off-axis holography using multiplexing with complex encoding and live-cell fluctuation map calculation in real-time,” Opt. Express 23(7), 8773–8787 (2015).
[Crossref] [PubMed]

J. C. de Souza, M. E. Oliveira, and P. A. dos Santos, “Branch-cut algorithm for optical phase unwrapping,” Opt. Lett. 40(15), 3456–3459 (2015).
[Crossref] [PubMed]

2014 (5)

H. Huang, “A fast multi-baseline and multi-frequency band phase-unwrapping algorithm,” Measurement 49, 401–406 (2014).
[Crossref]

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

W. He, L. Xia, and F. Liu, “Sparse-representation-based direct minimum L (p) -norm algorithm for MRI phase unwrapping,” Comput. Math. Methods Med. 2014, 134058 (2014).
[Crossref] [PubMed]

Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Lasers Eng. 63, 25–29 (2014).
[Crossref]

2013 (1)

L. Song, X. Dong, J. Xi, Y. Yu, and C. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Tech. 45, 319–329 (2013).
[Crossref]

2012 (9)

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

F. Da and H. Huang, “A fast, accurate phase unwrapping method for wavelet-transform profilometry,” Opt. Commun. 285(4), 421–432 (2012).
[Crossref]

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50(3), 322–327 (2012).
[Crossref]

Y. T. Zhang, M. J. Huang, H. R. Liang, and F. Y. Lao, “Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point,” Opt. Lasers Eng. 50(5), 619–631 (2012).
[Crossref]

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
[Crossref]

M. A. Navarro, J. C. Estrada, M. Servin, J. A. Quiroga, and J. Vargas, “Fast two-dimensional simultaneous phase unwrapping and low-pass filtering,” Opt. Express 20(3), 2556–2561 (2012).
[Crossref] [PubMed]

J. Weng and Y. Lo, “Novel rotation algorithm for phase unwrapping applications,” Opt. Express 20(15), 16838–16860 (2012).
[Crossref]

H. Y. Huang, L. Tian, Z. Zhang, Y. Liu, Z. Chen, and G. Barbastathis, “Path-independent phase unwrapping using phase gradient and total-variation (TV) denoising,” Opt. Express 20(13), 14075–14089 (2012).
[Crossref] [PubMed]

H. T. Xia, R. X. Guo, Z. B. Fan, H. M. Cheng, and B. C. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52(4), 439–445 (2012).
[Crossref]

2011 (3)

2009 (1)

P. Andris and I. Frollo, “Simple and accurate unwrapping phase of MR data,” Measurement 42(5), 737–741 (2009).
[Crossref]

2007 (1)

2004 (4)

J. J. Chyou, S. J. Chen, and Y. K. Chen, “Two-dimensional phase unwrapping with a multichannel least-mean-square algorithm,” Appl. Opt. 43(30), 5655–5661 (2004).
[Crossref] [PubMed]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[Crossref]

F. Palacios, E. Gonçalves, J. Ricardo, and J. L. Valin, “Adaptive filter to improve the performance of phase-unwrapping in digital holography,” Opt. Commun. 238(4), 245–251 (2004).
[Crossref]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
[Crossref] [PubMed]

2003 (1)

An, N.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

Andris, P.

P. Andris and I. Frollo, “Simple and accurate unwrapping phase of MR data,” Measurement 42(5), 737–741 (2009).
[Crossref]

Asundi, A.

Bai, J.

Barbastathis, G.

Chen, F.

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

Chen, S. J.

Chen, W.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[Crossref]

Chen, X.

Chen, Y. K.

Chen, Z.

Cheng, H. M.

H. T. Xia, R. X. Guo, Z. B. Fan, H. M. Cheng, and B. C. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52(4), 439–445 (2012).
[Crossref]

Cheng, Z.

Chyou, J. J.

Cong, L.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50(3), 322–327 (2012).
[Crossref]

Da, F.

F. Da and H. Huang, “A fast, accurate phase unwrapping method for wavelet-transform profilometry,” Opt. Commun. 285(4), 421–432 (2012).
[Crossref]

Daga, P.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

de Souza, J. C.

Dong, X.

L. Song, X. Dong, J. Xi, Y. Yu, and C. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Tech. 45, 319–329 (2013).
[Crossref]

dos Santos, P. A.

Doubre, C.

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: A D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

Drobnjak, I.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Duncan, J. S.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Estrada, J. C.

Fan, Z. B.

H. T. Xia, R. X. Guo, Z. B. Fan, H. M. Cheng, and B. C. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52(4), 439–445 (2012).
[Crossref]

Frollo, I.

P. Andris and I. Frollo, “Simple and accurate unwrapping phase of MR data,” Measurement 42(5), 737–741 (2009).
[Crossref]

Gautier, F.

Girshovitz, P.

Gonçalves, E.

F. Palacios, E. Gonçalves, J. Ricardo, and J. L. Valin, “Adaptive filter to improve the performance of phase-unwrapping in digital holography,” Opt. Commun. 238(4), 245–251 (2004).
[Crossref]

Gonzalez, A.

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Lasers Eng. 64, 51–58 (2015).
[Crossref]

Guo, R. X.

H. T. Xia, R. X. Guo, Z. B. Fan, H. M. Cheng, and B. C. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52(4), 439–445 (2012).
[Crossref]

Guo, Y.

Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Lasers Eng. 63, 25–29 (2014).
[Crossref]

Har, D.

He, W.

W. He, L. Xia, and F. Liu, “Sparse-representation-based direct minimum L (p) -norm algorithm for MRI phase unwrapping,” Comput. Math. Methods Med. 2014, 134058 (2014).
[Crossref] [PubMed]

Hernandez-Lopez, F. J.

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Lasers Eng. 64, 51–58 (2015).
[Crossref]

Huang, H.

H. Huang, “A fast multi-baseline and multi-frequency band phase-unwrapping algorithm,” Measurement 49, 401–406 (2014).
[Crossref]

F. Da and H. Huang, “A fast, accurate phase unwrapping method for wavelet-transform profilometry,” Opt. Commun. 285(4), 421–432 (2012).
[Crossref]

Huang, H. Y.

Huang, L.

Huang, M. J.

Y. T. Zhang, M. J. Huang, H. R. Liang, and F. Y. Lao, “Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point,” Opt. Lasers Eng. 50(5), 619–631 (2012).
[Crossref]

Huang, W.

Z. Cheng, D. Liu, Y. Yang, T. Ling, X. Chen, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique,” Opt. Express 23(25), 32337–32349 (2015).
[Crossref] [PubMed]

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

Jafarfard, M. R.

Karray, M.

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
[Crossref]

Kemao, Q.

Kim, D. Y.

Kobayashi, E.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

Lao, F. Y.

Y. T. Zhang, M. J. Huang, H. R. Liang, and F. Y. Lao, “Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point,” Opt. Lasers Eng. 50(5), 619–631 (2012).
[Crossref]

Li, B. N.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

Liang, H. R.

Y. T. Zhang, M. J. Huang, H. R. Liang, and F. Y. Lao, “Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point,” Opt. Lasers Eng. 50(5), 619–631 (2012).
[Crossref]

Ling, T.

Liu, D.

Liu, F.

W. He, L. Xia, and F. Liu, “Sparse-representation-based direct minimum L (p) -norm algorithm for MRI phase unwrapping,” Comput. Math. Methods Med. 2014, 134058 (2014).
[Crossref] [PubMed]

Liu, S.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50(3), 322–327 (2012).
[Crossref]

Liu, Y.

Lo, Y.

Lo, Y. L.

Malet, J. P.

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: A D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

Mancini, L.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Masson, F.

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: A D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

McEvoy, A. W.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Miao, L.

Modat, M.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Montresor, S.

Navarro, M. A.

Oliveira, M. E.

Ourselin, S.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Palacios, F.

F. Palacios, E. Gonçalves, J. Ricardo, and J. L. Valin, “Adaptive filter to improve the performance of phase-unwrapping in digital holography,” Opt. Commun. 238(4), 245–251 (2004).
[Crossref]

Pan, F.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50(3), 322–327 (2012).
[Crossref]

Pendse, T.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Pézerat, C.

Picart, P.

Poittevin, J.

Quiroga, J. A.

Ricardo, J.

F. Palacios, E. Gonçalves, J. Ricardo, and J. L. Valin, “Adaptive filter to improve the performance of phase-unwrapping in digital holography,” Opt. Commun. 238(4), 245–251 (2004).
[Crossref]

Rivera, M.

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Lasers Eng. 64, 51–58 (2015).
[Crossref]

Schlögel, R.

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: A D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

Servin, M.

Shaked, N. T.

Shan, X.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

Sharif, F.

Shen, Y.

Slangen, P.

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
[Crossref]

Song, L.

L. Song, X. Dong, J. Xi, Y. Yu, and C. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Tech. 45, 319–329 (2013).
[Crossref]

Song, Y. S.

Su, X.

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref] [PubMed]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[Crossref]

Tayebi, B.

Thornton, J.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Tian, L.

Valin, J. L.

F. Palacios, E. Gonçalves, J. Ricardo, and J. L. Valin, “Adaptive filter to improve the performance of phase-unwrapping in digital holography,” Opt. Commun. 238(4), 245–251 (2004).
[Crossref]

Vargas, J.

Volkov, V. V.

Wang, F.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50(3), 322–327 (2012).
[Crossref]

Weng, J.

Weng, J. F.

White, M.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Winston, G. P.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Xi, J.

L. Song, X. Dong, J. Xi, Y. Yu, and C. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Tech. 45, 319–329 (2013).
[Crossref]

Xia, H. T.

H. T. Xia, R. X. Guo, Z. B. Fan, H. M. Cheng, and B. C. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52(4), 439–445 (2012).
[Crossref]

Xia, L.

W. He, L. Xia, and F. Liu, “Sparse-representation-based direct minimum L (p) -norm algorithm for MRI phase unwrapping,” Comput. Math. Methods Med. 2014, 134058 (2014).
[Crossref] [PubMed]

Xiang, K.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

Xiao, W.

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50(3), 322–327 (2012).
[Crossref]

Xu, J.

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

Yang, B. C.

H. T. Xia, R. X. Guo, Z. B. Fan, H. M. Cheng, and B. C. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52(4), 439–445 (2012).
[Crossref]

Yang, C.

L. Song, X. Dong, J. Xi, Y. Yu, and C. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Tech. 45, 319–329 (2013).
[Crossref]

Yang, Y.

Yousry, T.

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Yu, Y.

L. Song, X. Dong, J. Xi, Y. Yu, and C. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Tech. 45, 319–329 (2013).
[Crossref]

Yuqing, S.

Zhang, L.

Zhang, Q.

Zhang, T.

Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Lasers Eng. 63, 25–29 (2014).
[Crossref]

Zhang, Y. T.

Y. T. Zhang, M. J. Huang, H. R. Liang, and F. Y. Lao, “Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point,” Opt. Lasers Eng. 50(5), 619–631 (2012).
[Crossref]

Zhang, Z.

Zhao, M.

Zhu, Y.

Appl. Opt. (3)

Comput. Biol. Med. (1)

B. N. Li, X. Shan, K. Xiang, N. An, J. Xu, W. Huang, and E. Kobayashi, “Evaluation of robust wave image processing methods for magnetic resonance elastography,” Comput. Biol. Med. 54, 100–108 (2014).
[Crossref] [PubMed]

Comput. Math. Methods Med. (1)

W. He, L. Xia, and F. Liu, “Sparse-representation-based direct minimum L (p) -norm algorithm for MRI phase unwrapping,” Comput. Math. Methods Med. 2014, 134058 (2014).
[Crossref] [PubMed]

Exp. Mech. (2)

M. Karray, P. Slangen, and P. Picart, “Comparison between digital Fresnel holography and digital image-plane holography: the role of the imaging aperture,” Exp. Mech. 52(9), 1275–1286 (2012).
[Crossref]

H. T. Xia, R. X. Guo, Z. B. Fan, H. M. Cheng, and B. C. Yang, “Non-invasive mechanical measurement for transparent objects by digital holographic interferometry based on iterative least-squares phase unwrapping,” Exp. Mech. 52(4), 439–445 (2012).
[Crossref]

Geomorphology (1)

R. Schlögel, C. Doubre, J. P. Malet, and F. Masson, “Landslide deformation monitoring with ALOS/PALSAR imagery: A D-InSAR geomorphological interpretation method,” Geomorphology 231, 314–330 (2015).
[Crossref]

Measurement (2)

P. Andris and I. Frollo, “Simple and accurate unwrapping phase of MR data,” Measurement 42(5), 737–741 (2009).
[Crossref]

H. Huang, “A fast multi-baseline and multi-frequency band phase-unwrapping algorithm,” Measurement 49, 401–406 (2014).
[Crossref]

Med. Image Anal. (1)

P. Daga, T. Pendse, M. Modat, M. White, L. Mancini, G. P. Winston, A. W. McEvoy, J. Thornton, T. Yousry, I. Drobnjak, J. S. Duncan, and S. Ourselin, “Susceptibility artefact correction using dynamic graph cuts: application to neurosurgery,” Med. Image Anal. 18(7), 1132–1142 (2014).
[Crossref] [PubMed]

Opt. Commun. (2)

F. Da and H. Huang, “A fast, accurate phase unwrapping method for wavelet-transform profilometry,” Opt. Commun. 285(4), 421–432 (2012).
[Crossref]

F. Palacios, E. Gonçalves, J. Ricardo, and J. L. Valin, “Adaptive filter to improve the performance of phase-unwrapping in digital holography,” Opt. Commun. 238(4), 245–251 (2004).
[Crossref]

Opt. Express (11)

J. C. Estrada, M. Servin, and J. A. Quiroga, “Noise robust linear dynamic system for phase unwrapping and smoothing,” Opt. Express 19(6), 5126–5133 (2011).
[Crossref] [PubMed]

M. A. Navarro, J. C. Estrada, M. Servin, J. A. Quiroga, and J. Vargas, “Fast two-dimensional simultaneous phase unwrapping and low-pass filtering,” Opt. Express 20(3), 2556–2561 (2012).
[Crossref] [PubMed]

J. F. Weng and Y. L. Lo, “Robust detection scheme on noise and phase jump for phase maps of objects with height discontinuities--theory and experiment,” Opt. Express 19(4), 3086–3105 (2011).
[Crossref] [PubMed]

J. Weng and Y. Lo, “Novel rotation algorithm for phase unwrapping applications,” Opt. Express 20(15), 16838–16860 (2012).
[Crossref]

H. Y. Huang, L. Tian, Z. Zhang, Y. Liu, Z. Chen, and G. Barbastathis, “Path-independent phase unwrapping using phase gradient and total-variation (TV) denoising,” Opt. Express 20(13), 14075–14089 (2012).
[Crossref] [PubMed]

J. Poittevin, P. Picart, F. Gautier, and C. Pézerat, “Quality assessment of combined quantization-shot-noise-induced decorrelation noise in high-speed digital holographic metrology,” Opt. Express 23(24), 30917–30932 (2015).
[Crossref] [PubMed]

S. Montresor and P. Picart, “Quantitative appraisal for noise reduction in digital holographic phase imaging,” Opt. Express 24(13), 14322–14343 (2016).
[Crossref] [PubMed]

S. Yuqing, “Robust phase unwrapping by spinning iteration,” Opt. Express 15(13), 8059–8064 (2007).
[Crossref] [PubMed]

B. Tayebi, M. R. Jafarfard, F. Sharif, Y. S. Song, D. Har, and D. Y. Kim, “Large step-phase measurement by a reduced-phase triple-illumination interferometer,” Opt. Express 23(9), 11264–11271 (2015).
[Crossref] [PubMed]

Z. Cheng, D. Liu, Y. Yang, T. Ling, X. Chen, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique,” Opt. Express 23(25), 32337–32349 (2015).
[Crossref] [PubMed]

P. Girshovitz and N. T. Shaked, “Fast phase processing in off-axis holography using multiplexing with complex encoding and live-cell fluctuation map calculation in real-time,” Opt. Express 23(7), 8773–8787 (2015).
[Crossref] [PubMed]

Opt. Laser Tech. (1)

L. Song, X. Dong, J. Xi, Y. Yu, and C. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Tech. 45, 319–329 (2013).
[Crossref]

Opt. Lasers Eng. (6)

S. Liu, W. Xiao, F. Pan, F. Wang, and L. Cong, “Complex-amplitude-based phase unwrapping method for digital holographic microscopy,” Opt. Lasers Eng. 50(3), 322–327 (2012).
[Crossref]

Y. T. Zhang, M. J. Huang, H. R. Liang, and F. Y. Lao, “Branch cutting algorithm for unwrapping photoelastic phase map with isotropic point,” Opt. Lasers Eng. 50(5), 619–631 (2012).
[Crossref]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[Crossref]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: a review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

Y. Guo, X. Chen, and T. Zhang, “Robust phase unwrapping algorithm based on least squares,” Opt. Lasers Eng. 63, 25–29 (2014).
[Crossref]

M. Rivera, F. J. Hernandez-Lopez, and A. Gonzalez, “Phase unwrapping by accumulation of residual maps,” Opt. Lasers Eng. 64, 51–58 (2015).
[Crossref]

Opt. Lett. (2)

Optik (Stuttg.) (1)

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

Other (5)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Th. Kreis, Holographic Interferometry – Pinciples and Methods (Akademie Verlag 1996).

J. W. Goodman, Speckle Phenomena in Optics (Roberts and Company Publishers, 2006).

T. C. Poon, Digital Holography and Three-Dimensional Display: Principles and Applications (Springer-Verlag, 2010).

P. Picart, New Techniques in Digital Holography (ISTE-Wiley 2015).

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Figures (17)

Fig. 1
Fig. 1 Examples of profiles of phase derivatives of noisy wrapped phase and noise-free wrapped phase, (a) first example, blue points: noisy profile, dark line: noise-free profile, (b) second example, blue points: noisy profile, dark line: noise-free profile; the red line correspond to the standard deviation.
Fig. 2
Fig. 2 Flow chart of the unwrapping algorithm; DCT means Discrete Cosine Transform, IDCT means Inverse Discrete Cosine Transform, <…> means average value.
Fig. 3
Fig. 3 Arrangement to produce speckle phase decorrelation in phase change due to surface deformation.
Fig. 4
Fig. 4 Outputs from the numerical simulation; two sets of phase data with progressive increase of fringe density and phase noise. Two first rows, Set 1, from left to right increase of fringe density and phase noise, two last rows, Set 2, from left to right increase of fringe density and phase noise.
Fig. 5
Fig. 5 Relationships between qualifying parameters, (a) σlmax versus σt for each phase map of the two sets, (b) ρfmax versus σt for each phase map of the two sets.
Fig. 6
Fig. 6 Phase maps n°10 of Set 1, (a) original unwrapped phase, (b) noisy wrapped phase (colorbars given in radian units).
Fig. 7
Fig. 7 Unwrapped phase obtained for phase map n°10 of Set 1, (a) Gold, (b) Quality, (c) Flynn, (d) Lp, (e) PULSI, (f) CPULSI (colorbars given in radian units).
Fig. 8
Fig. 8 Phase maps n°8 of Set 2, (a) original unwrapped phase, (b) noisy wrapped phase (colorbars given in radian units).
Fig. 9
Fig. 9 Unwrapped phase obtained for phase map n°8 of Set 2, (a) Gold, (b) Quality, (c) Flynn, (d) Lp, (e) PULSI, (f) CPULSI (colorbars given in radian units).
Fig. 10
Fig. 10 Error maps of unwrapped phase for fringe pattern n°10 of Set 1, (a) Gold, (b) Quality, (c) Flynn, (d) Lp, (e) PULSI, (f) CPULSI (colorbars given in radian units).
Fig. 11
Fig. 11 Error maps of unwrapped phase for fringe pattern n°8 of Set 2, (a) Gold, (b) Quality, (c) Flynn, (d) Lp, (e) PULSI, (f) CPULSI (colorbars given in radian units).
Fig. 12
Fig. 12 Standard deviations of the errors between the unwrapped phase and the noisy original phase: (a) for Set1, (b) for Set2.
Fig. 13
Fig. 13 Ratio of peak-valley value of unwrapped phase errors divided by that of original phase: (a) for Set 1, (b) for Set 2; PVphase: peak-to-valley of the original unwrapped phase.
Fig. 14
Fig. 14 Evolution of the standard deviation of errors, (a) versus the maximum fringe density, and (b) versus the maximum local standard deviation of noise, for the two sets of fringe patterns and algorithms Flynn, Lp and CPULSI.
Fig. 15
Fig. 15 Experimental wrapped phase maps, (a) phase map related to stress field around a crack in a transparent plate tested by digital transmission holographic interferometry, (b) phase map obtained to mechanical deformation of a rough sample measured with digital Fresnel holography.
Fig. 16
Fig. 16 Unwrapped phases of Fig. 15(a) obtained from (a) Gold, (b) Quality, (c) Flynn, (d) Lp, (e) PULSI, (f) CPULSI.
Fig. 17
Fig. 17 Unwrapped phases of Fig. 15(b) obtained from (a) Gold, (b) Quality, (c) Flynn, (d) Lp, (e) PULSI, (f) CPULSI.

Tables (4)

Tables Icon

Table 1 Standard deviation of noise and fringe density of the phase maps for the two sets.

Tables Icon

Table 2 Standard deviations of phase difference between unwrapped phase and original noisy phase (rad) for Set n°1

Tables Icon

Table 3 Standard deviations of phase difference between unwrapped phase and original noisy phase (rad) for Set n°2

Tables Icon

Table 4 Average computation times of the different algorithms.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

W( ϕ ij )= ψ ij ( i=0,1...,M1;j=0,1...N1 ),
Δ ij x =W( ψ ( i+1 )j ψ ij )( i=0,1...,M2;j=0,1...N1 ) Δ ij x =0otherwise Δ ij y =W( ψ i( j+1 ) ψ ij )( i=0,1...,M1;j=0,1...N2 ) Δ ij y =0otherwise,
Δ ij x =sgn( Δ ij x )| G x |if| Δ ij x | T x Δ ij x = Δ ij x otherwise Δ ij y =sgn( Δ ij y )| G y |if| Δ ij y | T y Δ ij y = Δ ij y otherwise,
{ T x = E[ ( Δ ij x ) 2 ] ( E[ Δ ij x ] ) 2 T y = E[ ( Δ ij y ) 2 ] ( E[ Δ ij y ] ) 2 ,
{ G x = 1 MN i=0 i=M1 j=0 j=N1 Δ ij x G y = 1 MN i=0 i=M1 j=0 j=N1 Δ ij y .
s= i=0 M2 j=0 N1 | ϕ ( i+1 )j ϕ ij Δ ij x | 2 + i=0 M1 j=0 N2 | ϕ i( j+1 ) ϕ ij Δ ij y | 2 .
( ϕ ( i+1 )j 2 ϕ ij + ϕ ( i1 )j )+( ϕ i( j+1 ) 2 ϕ ij + ϕ i( j1 ) )= ρ ij,
ρ ij =( Δ ij x Δ ( i1 )j x )+( Δ ij y Δ i( j1 ) y ).
ϕ ^ ij = ρ ^ ij 2cos( πi/M )+2cos( πj/N )4 ,
φ ij,k = ψ ij +2πround( ϕ ij,k ψ ij 2π ),
φ ij,k ψ ij 2π =round( ϕ ij,k ψ ij 2π ).
Δ ψ ij,k = φ ij,k ϕ ij,k .
ϕ ij,k+1 ϕ ij,k + ϕ ij,k+1 .
ρ f,ij = 1 2πKL p=iK/2 i+K/2 q=jL/2 j+L/2 ( Δ pq x ) 2 + ( Δ pq y ) 2 .

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