Abstract

Quality-guided phase unwrapping is a widely used technique with different quality definitions and guiding strategies reported. It is thus necessary to do a detailed comparison of these approaches to choose the optimal quality map and guiding strategy. For quality maps, in the presence of noise, transform-based methods are found to be the best choice. However in the presence of discontinuities, phase unwrapping is itself unresolved and hence quality-guided phase unwrapping is not sufficient. For guiding strategies, classical, two-section, and stack-chain guiding strategies are chosen for comparison. If accuracy is the foremost criterion then the classical guiding strategy with a data structure of indexed interwoven linked list is best. If speed is of essence then the stack-chain guiding strategy is the one to use.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
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    [CrossRef]
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    [CrossRef] [PubMed]
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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]
  15. A. Asundi and Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416–5420 (1998).
    [CrossRef]
  16. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: A review,” Opt. Lasers Eng. 42, 245–261(2004).
    [CrossRef]
  17. S. Zhang, X. Li, and S.-T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46, 50–57 (2007).
    [CrossRef]
  18. W.-S. Li and X.-Y. Su, “Phase unwrapping algorithm based on phase fitting reliability in structured light projection,” Opt. Eng. 41, 1365–1372 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  21. S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008).
    [CrossRef] [PubMed]
  22. Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5420–5428 (2008).
    [CrossRef] [PubMed]
  23. M. Ramji and K. Ramesh, “Adaptive quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models,” Strain 46, 184–194(2010).
    [CrossRef]
  24. Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier filtered and quality guided phase unwrapping algorithm: on locally high-order polynomial phase,” Appl. Opt. 49, 1075–1079 (2010).
    [CrossRef] [PubMed]
  25. H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368(2011).
    [CrossRef]
  26. H. Wang, J. Weaver, I. Perreard, M. Doyley, and K. Paulsen, “A three-dimensional quality-guided phase unwrapping method for MR elastography,” Phys. Med. Biol. 56, 3935–3852(2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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  29. M. D. Pritt, “Phase unwrapping by means of multigrid techniques for interferometric SAR,” IEEE Trans. Geosci. Remote Sens. 34, 728–738 (1996).
    [CrossRef]
  30. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991).
    [CrossRef] [PubMed]
  31. J. A. Quiroga, A. González-Cano, and E. Bernabeu, “Phase-unwrapping algorithm based on an adaptive criterion,” Appl. Opt. 34, 2560–2563 (1995).
    [CrossRef] [PubMed]
  32. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
    [CrossRef]
  33. Y. Lu, X. Wang, X. Zhong, G. He, Y. Liu, and D. Zheng, “A new quality map for quality-guided phase unwrapping,” Chin. Opt. Lett. 2, 698–700 (2004).
  34. D. J. Bone, H. A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
    [CrossRef] [PubMed]
  35. X. Su and W. Chen, “Fourier transform profilometry: A review,” Opt. Lasers Eng. 35, 263–284 (2001).
    [CrossRef]
  36. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
    [CrossRef] [PubMed]
  37. Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47, 5408–5419 (2008).
    [CrossRef] [PubMed]
  38. Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
    [CrossRef]
  39. R. Sedgewick, Algorithms in C: Parts 1–4, Fundamentals, Data Structures, Sorting, and Searching (Addison-Wesley, 1997), p. 702.
  40. Y. Li and X.-Y. Su, “Fast algorithm for reliability-guided phase unwrapping,” Guangdian Gongcheng/Opto-Electronic Engineering 32, 76–79 (2005).
  41. Y. Li and Z. Hou (personal communications, 2011).

2011 (2)

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368(2011).
[CrossRef]

H. Wang, J. Weaver, I. Perreard, M. Doyley, and K. Paulsen, “A three-dimensional quality-guided phase unwrapping method for MR elastography,” Phys. Med. Biol. 56, 3935–3852(2011).
[CrossRef] [PubMed]

2010 (2)

M. Ramji and K. Ramesh, “Adaptive quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models,” Strain 46, 184–194(2010).
[CrossRef]

Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier filtered and quality guided phase unwrapping algorithm: on locally high-order polynomial phase,” Appl. Opt. 49, 1075–1079 (2010).
[CrossRef] [PubMed]

2008 (4)

2007 (2)

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

S. Zhang, X. Li, and S.-T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46, 50–57 (2007).
[CrossRef]

2006 (1)

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

2005 (2)

Y. Li and X.-Y. Su, “Fast algorithm for reliability-guided phase unwrapping,” Guangdian Gongcheng/Opto-Electronic Engineering 32, 76–79 (2005).

Y. Lu, X. Wang, and G. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

2004 (3)

2003 (1)

2002 (2)

2001 (1)

X. Su and W. Chen, “Fourier transform profilometry: A review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

1998 (1)

1997 (2)

T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A 14, 2692–2701 (1997).
[CrossRef]

C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244(1997).
[CrossRef]

1996 (2)

M. D. Pritt, “Phase unwrapping by means of multigrid techniques for interferometric SAR,” IEEE Trans. Geosci. Remote Sens. 34, 728–738 (1996).
[CrossRef]

D. C. Ghiglia and L. A. Romero, “Minimum Lp-norm two-dimensional phase unwrapping,” J. Opt. Soc. Am. A 13, 1999–2013 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

1991 (1)

1988 (1)

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

1986 (2)

H. A. Zebker and R. M. Goldstein, “Topographic mapping from interferometric synthetic aperture radar observations,” J. Geophys. Res. 91, 4993–4999 (1986).
[CrossRef]

D. J. Bone, H. A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

1980 (1)

L. Ole, “Electronic speckle pattern interferometry,” Phys. Technol. 11, 16 (1980).
[CrossRef]

1966 (1)

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Alexeenko, I.

Asundi, A.

Bachor, H. A.

Bernabeu, E.

Bone, D. J.

Brooks, R. E.

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Burton, D. R.

Chen, M.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368(2011).
[CrossRef]

Chen, W.

Doyley, M.

H. Wang, J. Weaver, I. Perreard, M. Doyley, and K. Paulsen, “A three-dimensional quality-guided phase unwrapping method for MR elastography,” Phys. Med. Biol. 56, 3935–3852(2011).
[CrossRef] [PubMed]

Eichel, P. H.

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, and P. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Flynn, T. J.

Gao, W.

Gdeisat, M. A.

Ghiglia, D. C.

D. C. Ghiglia and L. A. Romero, “Minimum Lp-norm two-dimensional phase unwrapping,” J. Opt. Soc. Am. A 13, 1999–2013 (1996).
[CrossRef]

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, and P. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

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

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]

H. A. Zebker and R. M. Goldstein, “Topographic mapping from interferometric synthetic aperture radar observations,” J. Geophys. Res. 91, 4993–4999 (1986).
[CrossRef]

González-Cano, A.

Halioua, M.

He, G.

Y. Lu, X. Wang, and G. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

Y. Lu, X. Wang, X. Zhong, G. He, Y. Liu, and D. Zheng, “A new quality map for quality-guided phase unwrapping,” Chin. Opt. Lett. 2, 698–700 (2004).

Heflinger, L. O.

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Herráez, M. A.

Hock, L.

L. Hock, W. Xu, and X. Hu, “Two new practical methods for phase unwrapping,” in Geoscience and Remote Sensing Symposium (IEEE, 1995), Vol.  191, pp. 196–198.

Hou, Z.

Y. Li and Z. Hou (personal communications, 2011).

Hu, X.

L. Hock, W. Xu, and X. Hu, “Two new practical methods for phase unwrapping,” in Geoscience and Remote Sensing Symposium (IEEE, 1995), Vol.  191, pp. 196–198.

Huntley, J. M.

Jakowatz, C. V.

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, and P. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Kemao, Q.

Lalor, M. J.

Li, S.

Li, W.-S.

W.-S. Li and X.-Y. Su, “Phase unwrapping algorithm based on phase fitting reliability in structured light projection,” Opt. Eng. 41, 1365–1372 (2002).
[CrossRef]

Li, X.

Li, Y.

Y. Li and X.-Y. Su, “Fast algorithm for reliability-guided phase unwrapping,” Guangdian Gongcheng/Opto-Electronic Engineering 32, 76–79 (2005).

Y. Li and Z. Hou (personal communications, 2011).

Liu, H. C.

Liu, Y.

Lu, Y.

Y. Lu, X. Wang, and G. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

Y. Lu, X. Wang, X. Zhong, G. He, Y. Liu, and D. Zheng, “A new quality map for quality-guided phase unwrapping,” Chin. Opt. Lett. 2, 698–700 (2004).

Ma, H.

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Mutoh, K.

Ole, L.

L. Ole, “Electronic speckle pattern interferometry,” Phys. Technol. 11, 16 (1980).
[CrossRef]

Osten, W.

Paulsen, K.

H. Wang, J. Weaver, I. Perreard, M. Doyley, and K. Paulsen, “A three-dimensional quality-guided phase unwrapping method for MR elastography,” Phys. Med. Biol. 56, 3935–3852(2011).
[CrossRef] [PubMed]

Pedrini, G.

Peng, X.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336–342 (2008).
[CrossRef]

Perreard, I.

H. Wang, J. Weaver, I. Perreard, M. Doyley, and K. Paulsen, “A three-dimensional quality-guided phase unwrapping method for MR elastography,” Phys. Med. Biol. 56, 3935–3852(2011).
[CrossRef] [PubMed]

Pritt, M. D.

M. D. Pritt, “Phase unwrapping by means of multigrid techniques for interferometric SAR,” IEEE Trans. Geosci. Remote Sens. 34, 728–738 (1996).
[CrossRef]

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

Quiroga, J. A.

Ramesh, K.

M. Ramji and K. Ramesh, “Adaptive quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models,” Strain 46, 184–194(2010).
[CrossRef]

Ramji, M.

M. Ramji and K. Ramesh, “Adaptive quality guided phase unwrapping algorithm for whole-field digital photoelastic parameter estimation of complex models,” Strain 46, 184–194(2010).
[CrossRef]

Reich, C.

C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244(1997).
[CrossRef]

Ritter, R.

C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244(1997).
[CrossRef]

Romero, L. A.

Saldner, H.

Sandeman, R. J.

Sedgewick, R.

R. Sedgewick, Algorithms in C: Parts 1–4, Fundamentals, Data Structures, Sorting, and Searching (Addison-Wesley, 1997), p. 702.

Srinivasan, V.

Su, X.

S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008).
[CrossRef] [PubMed]

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

X. Su and W. Chen, “Fourier transform profilometry: A review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

Su, X.-Y.

Y. Li and X.-Y. Su, “Fast algorithm for reliability-guided phase unwrapping,” Guangdian Gongcheng/Opto-Electronic Engineering 32, 76–79 (2005).

W.-S. Li and X.-Y. Su, “Phase unwrapping algorithm based on phase fitting reliability in structured light projection,” Opt. Eng. 41, 1365–1372 (2002).
[CrossRef]

Takeda, M.

Tan, Y.

Tang, J.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368(2011).
[CrossRef]

Thesing, J.

C. Reich, R. Ritter, and J. Thesing, “White light heterodyne principle for 3D-measurement,” Proc. SPIE 3100, 236–244(1997).
[CrossRef]

Thompson, P.

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, and P. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Tian, J.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336–342 (2008).
[CrossRef]

Tiziani, H. J.

Wahl, D. E.

C. V. Jakowatz, D. E. Wahl, P. H. Eichel, D. C. Ghiglia, and P. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach (Kluwer Academic, 1996).
[CrossRef]

Wang, H.

Wang, X.

Y. Lu, X. Wang, and G. He, “Phase unwrapping based on branch cut placing and reliability ordering,” Opt. Eng. 44, 055601 (2005).
[CrossRef]

Y. Lu, X. Wang, X. Zhong, G. He, Y. Liu, and D. Zheng, “A new quality map for quality-guided phase unwrapping,” Chin. Opt. Lett. 2, 698–700 (2004).

Wang, Z.

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Weaver, J.

H. Wang, J. Weaver, I. Perreard, M. Doyley, and K. Paulsen, “A three-dimensional quality-guided phase unwrapping method for MR elastography,” Phys. Med. Biol. 56, 3935–3852(2011).
[CrossRef] [PubMed]

Wensen, Z.

Werner, C. L.

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

Wuerker, R. F.

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, “Holographic interferometry,” J. Appl. Phys. 37, 642–649 (1966).
[CrossRef]

Xu, W.

L. Hock, W. Xu, and X. Hu, “Two new practical methods for phase unwrapping,” in Geoscience and Remote Sensing Symposium (IEEE, 1995), Vol.  191, pp. 196–198.

Yau, S.-T.

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]

H. A. Zebker and R. M. Goldstein, “Topographic mapping from interferometric synthetic aperture radar observations,” J. Geophys. Res. 91, 4993–4999 (1986).
[CrossRef]

Zhang, S.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368(2011).
[CrossRef]

S. Zhang, X. Li, and S.-T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46, 50–57 (2007).
[CrossRef]

Zhao, H.

Zhao, X.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for three-dimensional profilometry,” Opt. Lasers Eng. 46, 336–342 (2008).
[CrossRef]

Zheng, D.

Zhong, H.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8, 364–368(2011).
[CrossRef]

Zhong, X.

Appl. Opt. (16)

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
[CrossRef] [PubMed]

V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
[CrossRef] [PubMed]

D. J. Bone, H. A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
[CrossRef] [PubMed]

D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991).
[CrossRef] [PubMed]

J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[CrossRef] [PubMed]

H. Zhao, W. Chen, and Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497–4500 (1994).
[CrossRef] [PubMed]

A. Asundi and Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416–5420 (1998).
[CrossRef]

J. A. Quiroga, A. González-Cano, and E. Bernabeu, “Phase-unwrapping algorithm based on an adaptive criterion,” Appl. Opt. 34, 2560–2563 (1995).
[CrossRef] [PubMed]

M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41, 7437–7444 (2002).
[CrossRef] [PubMed]

G. Pedrini, I. Alexeenko, W. Osten, and H. J. Tiziani, “Temporal phase unwrapping of digital hologram sequences,” Appl. Opt. 42, 5846–5854 (2003).
[CrossRef] [PubMed]

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

S. Zhang, X. Li, and S.-T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46, 50–57 (2007).
[CrossRef]

S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008).
[CrossRef] [PubMed]

Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt. 47, 5408–5419 (2008).
[CrossRef] [PubMed]

Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47, 5420–5428 (2008).
[CrossRef] [PubMed]

Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier filtered and quality guided phase unwrapping algorithm: on locally high-order polynomial phase,” Appl. Opt. 49, 1075–1079 (2010).
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Figures (12)

Fig. 1
Fig. 1

Concept of of QGPU. (a) Wrapped phase map, (b) quality map, (c) unwrapping path map (pixels in light yellow are unwrapped first and those in dark red are unwrapped last), and (d) unwrapped phase map.

Fig. 2
Fig. 2

Diagram of spatial unwrapping process.

Fig. 3
Fig. 3

Simulated of noisy phase maps. (a) Four-step phase-shifted fringe patterns with speckle and random noise, (b) true wrapped phase, (c) true modulation, (d) retrieved noisy wrapped phase, and (e) retrieved unwrapped phase (with phase noise).

Fig. 4
Fig. 4

Comparison of phase unwrapping from noisy phase maps. The quality maps used are (a)  Q MOD , (b)  Q REL , (c)  Q FT , (d)  Q WFF , (e)  Q WFR , and (f)  Q WT , respectively. From left to right, each group shows quality maps, path maps, and unwrapping error maps. (In unwrapping error maps, correctly unwrapped pixels are shown in gray scale and incorrectly unwrapped pixels are shown in red or blue. Red and blue indicate that the unwrapped phase value is larger and smaller than its true value, respectively. Darker shades indicate larger errors.)

Fig. 5
Fig. 5

Comparison of phase unwrapping from noisy phase maps. The quality maps used are (a)  Q PCC , (b)  Q PDV , (c)  Q FPD , (d)  Q SPD , (e)  Q FT , (f)  Q WFF , (g)  Q WFR , and (h)  Q WT , respectively. From left to right, each group shows quality maps, path maps, and unwrapping error maps. The meanings of colors in the unwrapping error maps are the same as in Fig. 4.

Fig. 6
Fig. 6

Phase unwrapping simulation with wide spectrum and no carrier fringes. (a) Phase-shifted fringe patterns, (b) wrapped phase without noise, (c) modulation distribution, and (d) retrieved wrapped phase with phase noise.

Fig. 7
Fig. 7

Comparison of unwrapping results from transform-based methods in case A. The quality maps used are (a)  Q FT , (b)  Q WFF , (c)  Q WFR , and (d)  Q WT , respectively. From left to right, each group shows quality maps, path maps, and unwrapping error maps.

Fig. 8
Fig. 8

Influence of fringe discontinuity on phase unwrapping. (a) Eight frames of phase-shifted fringe pattern using FPP, (b) retrieved wrapped phase, (c) retrieved modulation map, (d) unwrapped phase by using temporal phase unwrapping technique.

Fig. 9
Fig. 9

Comparison of phase unwrapping under discontinuity condition in case A. The quality maps used are (a)  Q MOD , (b)  Q REL , (c)  Q FT , (d)  Q WFF , (e)  Q WFR , and (f)  Q WT , respectively. From left to right, each group shows quality maps, path maps, and unwrapping error maps.

Fig. 10
Fig. 10

Comparison of phase unwrapping under discontinuity condition in case B. The quality maps used are (a)  Q PCC , (b)  Q PDV , (c)  Q FPD , (d)  Q SPD , (e)  Q FT , (f)  Q WFF , (g)  Q WFR , and (h)  Q WT , respectively. From left to right, each group shows quality maps, path maps, and unwrapping error maps.

Fig. 11
Fig. 11

Failure of QGPU. (a) Wrapped phase and unwrapped phase with temporal phase unwrapping and unwrapping result under case A (b)–(g) and case B (h)–(o). The quality maps used are (b)  Q MOD , (c)  Q REL , (d)  Q FT , (e)  Q WFF , (f)  Q WFR , (g)  Q WT , (h)  Q PCC , (i)  Q P D V , (j)  Q FPD , (k)  Q SPD , (l)  Q FT , (m)  Q WFF , (n)  Q WFR , and (o)  Q WT , respectively. From left to right, each group shows quality maps, path maps, and unwrapping error maps.

Fig. 12
Fig. 12

Data structures for sorting in quality guiding. (a) Array, (b) linked list, (c) indexed linked list, and (d) indexed interwoven linked list.

Tables (5)

Tables Icon

Table 1 Speed Comparison for Different Data Structures in Classical Quality Guiding (C++)

Tables Icon

Table 2 Threshold Level in Two-Section Guiding of Box ( 960 × 1280 ) in Fig. 1 (C++)

Tables Icon

Table 3 Comparison Results of Box ( 960 × 1280 ) in Fig. 1

Tables Icon

Table 4 Comparison Results of Noisy Peaks ( 256 × 256 ) in Fig. 3

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Table 5 Comparison Results of Coffee Cup Cover ( 400 × 400 ) in Fig. 8

Equations (5)

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φ a u = φ a w + 2 π × round ( φ b u φ a w 2 π ) ,
f c = M · exp ( j · φ w ) ,
f n = 1 · exp ( j · φ w ) = f c | f c | .
φ ( x , y ) = 2 π 8 ( x 128 ) + 3 × peaks ( x , y ) ,
M ( x , y ) = 255 2 × normalize ( peaks ( x , y ) ) ,

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