Abstract

Phase unwrapping still plays an important role in many data-processing chains based on phase information. Here, we introduce a new phase unwrapping approach for noisy wrapped phase maps of continuous objects to improve the accuracy and computational time requirements of phase unwrapping using a rotational compensator (RC) method. The proposed algorithm is based on compensating the singularity of discontinuity sources. It uses direct compensation for adjoining singular point (SP) pairs and uses RC for other SP pairs. The performance of the proposed method is tested through both simulated and real wrapped phase data. The proposed algorithm is faster than the original algorithm with the RC and has proved efficiency compared to other phase unwrapping methods.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010

2008

2007

S. A. Karout, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Two-dimensional phase unwrapping using a hybrid genetic algorithm,” Appl. Opt. 46, 730–743 (2007).
[CrossRef]

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251(2007).
[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

2005

Q. Kemao, S. H. Soon, and A. Asundi, ”A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
[CrossRef]

2002

C. L. Martinez and X. Fabergas, “Modeling and reduction of SAR interferometric phase noise in the wavelet domain,” IEEE Trans. Geosci. Remote Sens. 40, 2553–2566(2002).
[CrossRef]

S. Chavez, Q.-S. Xiang, and L. An, “Understanding phase maps in MRI: a new cutline phase unwrapping method,” IEEE Trans. Med. Imaging 21, 966–977 (2002).
[CrossRef]

2001

C. L. Martinez, X. F. Canovas, and M. Chandra, “SAR interferometric phase noise reduction using wavelet transform,” Electron. Lett. 37, 649–651 (2001).
[CrossRef]

2000

1999

1998

M. Costantine, “A novel phase unwrapping method based on network programming,” IEEE Trans. Geosci. Remote Sens. 36, 813–821 (1998).
[CrossRef]

M. R. Goldstein and C. L. Werner, “Radar interferogram filtering for geophysical applications,” Geophys. Res. Lett. 25, 4035–4038 (1998).
[CrossRef]

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36, 1456–1465 (1998).
[CrossRef]

1995

1994

1993

K. E. Perry, Jr., and J. McKelvie, “A comparison of phase shifting and Fourier methods in the analysis of discontinuous fringe patterns,” Opt. Lasers Eng. 19, 269–284 (1993).
[CrossRef]

1989

1988

1985

1982

1979

1977

1974

Ainsworth, T. L.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36, 1456–1465 (1998).
[CrossRef]

An, L.

S. Chavez, Q.-S. Xiang, and L. An, “Understanding phase maps in MRI: a new cutline phase unwrapping method,” IEEE Trans. Med. Imaging 21, 966–977 (2002).
[CrossRef]

Asundi, A.

Q. Kemao, S. H. Soon, and A. Asundi, ”A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
[CrossRef]

Brangaccio, D. J.

Breuckmann, B.

Bruning, J. H.

Buckland, J. R.

Burton, D. R.

Canovas, X. F.

C. L. Martinez, X. F. Canovas, and M. Chandra, “SAR interferometric phase noise reduction using wavelet transform,” Electron. Lett. 37, 649–651 (2001).
[CrossRef]

Chandra, M.

C. L. Martinez, X. F. Canovas, and M. Chandra, “SAR interferometric phase noise reduction using wavelet transform,” Electron. Lett. 37, 649–651 (2001).
[CrossRef]

Chavez, S.

S. Chavez, Q.-S. Xiang, and L. An, “Understanding phase maps in MRI: a new cutline phase unwrapping method,” IEEE Trans. Med. Imaging 21, 966–977 (2002).
[CrossRef]

Costantine, M.

M. Costantine, “A novel phase unwrapping method based on network programming,” IEEE Trans. Geosci. Remote Sens. 36, 813–821 (1998).
[CrossRef]

Cuche, E.

Cusack, R.

Depeursinge, C.

Fabergas, X.

C. L. Martinez and X. Fabergas, “Modeling and reduction of SAR interferometric phase noise in the wavelet domain,” IEEE Trans. Geosci. Remote Sens. 40, 2553–2566(2002).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edition (Cambridge University, 2007).

Fried, D. L.

Gallagher, J. E.

Gao, W.

Gdeisat, M. A.

Ghiglia, D. C.

Glover, G. H.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, “Phase unwrapping of MR phase images using Poisson equation,” IEEE Trans. Image Process. 4, 667–676 (1995).
[CrossRef]

Goldrein, H. T.

Goldstein, M. R.

M. R. Goldstein and C. L. Werner, “Radar interferogram filtering for geophysical applications,” Geophys. Res. Lett. 25, 4035–4038 (1998).
[CrossRef]

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Grunes, M. H.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36, 1456–1465 (1998).
[CrossRef]

Gutmann, B.

Herriott, D. R.

Heshmat, S.

Hirose, A.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251(2007).
[CrossRef]

Hudgin, R. H.

Hunt, B. R.

Huntley, J. M.

Ina, H.

Karout, S. A.

Kemao, Q.

Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5408–5428 (2008).
[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

Q. Kemao, S. H. Soon, and A. Asundi, ”A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
[CrossRef]

Kobayashi, S.

Lalor, M. J.

Lee, J. S.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36, 1456–1465 (1998).
[CrossRef]

Lyuboshenko, I.

Maitre, H.

Marquet, P.

Martinez, C. L.

C. L. Martinez and X. Fabergas, “Modeling and reduction of SAR interferometric phase noise in the wavelet domain,” IEEE Trans. Geosci. Remote Sens. 40, 2553–2566(2002).
[CrossRef]

C. L. Martinez, X. F. Canovas, and M. Chandra, “SAR interferometric phase noise reduction using wavelet transform,” Electron. Lett. 37, 649–651 (2001).
[CrossRef]

McKelvie, J.

K. E. Perry, Jr., and J. McKelvie, “A comparison of phase shifting and Fourier methods in the analysis of discontinuous fringe patterns,” Opt. Lasers Eng. 19, 269–284 (1993).
[CrossRef]

Miyamoto, N.

Napel, S.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, “Phase unwrapping of MR phase images using Poisson equation,” IEEE Trans. Image Process. 4, 667–676 (1995).
[CrossRef]

Nishiyama, S.

Papathanassiou, K. P.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36, 1456–1465 (1998).
[CrossRef]

Pelc, N. J.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, “Phase unwrapping of MR phase images using Poisson equation,” IEEE Trans. Image Process. 4, 667–676 (1995).
[CrossRef]

Perry, K. E.

K. E. Perry, Jr., and J. McKelvie, “A comparison of phase shifting and Fourier methods in the analysis of discontinuous fringe patterns,” Opt. Lasers Eng. 19, 269–284 (1993).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edition (Cambridge University, 2007).

Reigber, A.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36, 1456–1465 (1998).
[CrossRef]

Romero, L. A.

Rosenfeld, D. P.

Song, S. M.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, “Phase unwrapping of MR phase images using Poisson equation,” IEEE Trans. Image Process. 4, 667–676 (1995).
[CrossRef]

Soon, S. H.

Q. Kemao, S. H. Soon, and A. Asundi, ”A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
[CrossRef]

Takahashi, T.

Takajo, H.

Takeda, M.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edition (Cambridge University, 2007).

Thieme, W.

Tomioka, S.

Turner, S. R. E.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edition (Cambridge University, 2007).

Wang, H.

Weber, H.

Werner, C. L.

M. R. Goldstein and C. L. Werner, “Radar interferogram filtering for geophysical applications,” Geophys. Res. Lett. 25, 4035–4038 (1998).
[CrossRef]

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

White, A. D.

Xiang, Q.-S.

S. Chavez, Q.-S. Xiang, and L. An, “Understanding phase maps in MRI: a new cutline phase unwrapping method,” IEEE Trans. Med. Imaging 21, 966–977 (2002).
[CrossRef]

Yamaki, R.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251(2007).
[CrossRef]

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Appl. Opt.

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef]

B. Breuckmann and W. Thieme, “Computer-aided analysis of holographic interferograms using the phase-shift method,” Appl. Opt. 24, 2145–2149 (1985).
[CrossRef]

J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
[CrossRef]

B. Gutmann and H. Weber, “Phase unwrapping with the branch-cut method: clustering of discontinuity sources and reverse simulated annealing,” Appl. Opt. 38, 5577–5593 (1999).
[CrossRef]

R. Cusack, J. M. Huntley, and H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781–789 (1995).
[CrossRef]

J. R. Buckland, J. M. Huntley, and S. R. E. Turner, “Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm,” Appl. Opt. 34, 5100–5108 (1995).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

S. A. Karout, M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Two-dimensional phase unwrapping using a hybrid genetic algorithm,” Appl. Opt. 46, 730–743 (2007).
[CrossRef]

Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5408–5428 (2008).
[CrossRef]

S. Tomioka, S. Heshmat, N. Miyamoto, and S. Nishiyama, “Phase unwrapping for noisy phase maps using rotational compensator with virtual singular points,” Appl. Opt. 49, 4735–4745 (2010).
[CrossRef]

Electron. Lett.

C. L. Martinez, X. F. Canovas, and M. Chandra, “SAR interferometric phase noise reduction using wavelet transform,” Electron. Lett. 37, 649–651 (2001).
[CrossRef]

Geophys. Res. Lett.

M. R. Goldstein and C. L. Werner, “Radar interferogram filtering for geophysical applications,” Geophys. Res. Lett. 25, 4035–4038 (1998).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36, 1456–1465 (1998).
[CrossRef]

M. Costantine, “A novel phase unwrapping method based on network programming,” IEEE Trans. Geosci. Remote Sens. 36, 813–821 (1998).
[CrossRef]

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251(2007).
[CrossRef]

C. L. Martinez and X. Fabergas, “Modeling and reduction of SAR interferometric phase noise in the wavelet domain,” IEEE Trans. Geosci. Remote Sens. 40, 2553–2566(2002).
[CrossRef]

IEEE Trans. Image Process.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, “Phase unwrapping of MR phase images using Poisson equation,” IEEE Trans. Image Process. 4, 667–676 (1995).
[CrossRef]

IEEE Trans. Med. Imaging

S. Chavez, Q.-S. Xiang, and L. An, “Understanding phase maps in MRI: a new cutline phase unwrapping method,” IEEE Trans. Med. Imaging 21, 966–977 (2002).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Laser Technol.

Q. Kemao, S. H. Soon, and A. Asundi, ”A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
[CrossRef]

Opt. Lasers Eng.

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

K. E. Perry, Jr., and J. McKelvie, “A comparison of phase shifting and Fourier methods in the analysis of discontinuous fringe patterns,” Opt. Lasers Eng. 19, 269–284 (1993).
[CrossRef]

Opt. Lett.

Radio Sci.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[CrossRef]

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edition (Cambridge University, 2007).

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