Abstract

In most phase unwrapping algorithms, the image reconstruction results are obtained by shifting the phase jumps in the wrapped phase map by 2π. The performance of such algorithms is degraded by the presence of speckle noise, residual noise, noise at the height discontinuities and holes in the wrapped phase map. Thus, a filtering operation is performed prior to the unwrapping process in order to remove the noise. However, the filtering process smears the phase jumps in the wrapped phase map and therefore causes a phase shifting error during the reconstruction process. Moreover, the noise errors, hole errors and shifting errors are accumulated path-by-path during unwrapping. Accordingly, the present study proposes a new rotation algorithm for phase unwrapping applications which resolves the noise error, the error of hole, the shifting error. Existing phase unwrapping algorithms are designed to operate only on those pixels whose phase values have no noise or holes. Or they are designed to operate the three-dimensional unwrapping paths in the row and column directions to avoid the noise or holes. By contrast, the rotation algorithm proposed in this study operates on all the pixels in the wrapped phase map, including those affected by noise or holes. As a result, the noise errors and hole errors produced in existing 2π phase shifting unwrapping algorithms are eliminated. Furthermore, since in the proposed approach, the wrapped phase map is not filtered prior to the unwrapping process, the phase shifting errors induced in existing algorithms are also eliminated. The robustness of the proposed algorithm to various noise errors, hole errors and phase shifting errors is demonstrated both numerically and experimentally.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  24. K. A. Stetson, J. Wahid, and P. Gauthier, “Noise-immune phase unwrapping by use of calculated wrap regions,” Appl. Opt. 36(20), 4830–4838 (1997).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  29. J. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: a review and comparison,” Opt. Eng. 50(8), 1026–1029 (2011).
  30. X. Xianming and P. Yiming, “Multi-baseline phase unwrapping algorithm based on the unscented Kalman filter,” IET Radar Sonar Nav. 5(3), 296–304 (2011).
    [CrossRef]
  31. J. J. Martinez-Espla, T. Martinez-Marin, and J. M. Lopez-Sanchez, “Using a Grid-Based Filter to Solve InSAR Phase Unwrapping,” IEEE Geosci. Remote Sens. 5(2), 147–151 (2008).
    [CrossRef]
  32. K. Liu, Y. C. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  34. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987).
    [CrossRef] [PubMed]

2012 (2)

2011 (4)

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]

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[CrossRef]

J. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: a review and comparison,” Opt. Eng. 50(8), 1026–1029 (2011).

X. Xianming and P. Yiming, “Multi-baseline phase unwrapping algorithm based on the unscented Kalman filter,” IET Radar Sonar Nav. 5(3), 296–304 (2011).
[CrossRef]

2010 (2)

2009 (2)

2008 (3)

A. Wada, M. Kato, and Y. Ishii, “Large step-height measurements using multiple-wavelength holographic interferometry with tunable laser diodes,” J. Opt. Soc. Am. A 25(12), 3013–3020 (2008).
[CrossRef] [PubMed]

J. J. Martinez-Espla, T. Martinez-Marin, and J. M. Lopez-Sanchez, “Using a Grid-Based Filter to Solve InSAR Phase Unwrapping,” IEEE Geosci. Remote Sens. 5(2), 147–151 (2008).
[CrossRef]

M. J. Huang and J. K. Liou, “Retrieving ESPI map of discontinuous objects via a novel phase unwrapping algorithm,” Strain 44(3), 239–247 (2008).
[CrossRef]

2007 (3)

2005 (2)

2001 (1)

1999 (1)

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4–6), 205–210 (1999).
[CrossRef]

1998 (1)

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30(6), 487–502 (1998).
[CrossRef]

1997 (5)

1995 (1)

1993 (1)

1991 (1)

A. Spik and D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14(1), 25–37 (1991).
[CrossRef]

1988 (1)

R. Goldstein, H. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[CrossRef]

1987 (2)

1985 (1)

1983 (1)

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4–6), 205–210 (1999).
[CrossRef]

Bertani, D.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36(9), 2466–2472 (1997).
[CrossRef]

Brady, D.

Capanni, A.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36(9), 2466–2472 (1997).
[CrossRef]

Cetica, M.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36(9), 2466–2472 (1997).
[CrossRef]

Chang, H. Y.

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30(6), 487–502 (1998).
[CrossRef]

Chen, C. W.

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30(6), 487–502 (1998).
[CrossRef]

Cheng, J.

Cheng, X.

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[CrossRef]

Creath, K.

Cui, H.

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[CrossRef]

Dai, N.

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[CrossRef]

Dubey, S. K.

Eiju, T.

Estrada, J. C.

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. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: a review and comparison,” Opt. Eng. 50(8), 1026–1029 (2011).

Fetterman, M.

Flynn, T. J.

Francini, F.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36(9), 2466–2472 (1997).
[CrossRef]

Gauthier, P.

Ghiglia, D. C.

Goldstein, R.

R. Goldstein, H. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[CrossRef]

Hahn, J.

Hao, Q.

Hariharan, P.

Hassebrook, L. G.

Hirose, A.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Rem. Sens. 45(10), 3240–3251 (2007).
[CrossRef]

Hossain, M. M.

Hu, C. P.

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30(6), 487–502 (1998).
[CrossRef]

Huang, M. J.

M. J. Huang and J. K. Liou, “Retrieving ESPI map of discontinuous objects via a novel phase unwrapping algorithm,” Strain 44(3), 239–247 (2008).
[CrossRef]

Huntley, J. M.

Ishii, Y.

Javidi, B.

Jiang, J.

Kato, M.

Kim, E. H.

Kim, H.

Krishnaswamy, S.

Lau, D. L.

Lee, B.

Lee, C. K.

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30(6), 487–502 (1998).
[CrossRef]

Li, X. L.

Liao, W.

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[CrossRef]

Liou, J. K.

M. J. Huang and J. K. Liou, “Retrieving ESPI map of discontinuous objects via a novel phase unwrapping algorithm,” Strain 44(3), 239–247 (2008).
[CrossRef]

Liu, K.

Liu, Z.

Lo, Y. L.

Lopez-Sanchez, J. M.

J. J. Martinez-Espla, T. Martinez-Marin, and J. M. Lopez-Sanchez, “Using a Grid-Based Filter to Solve InSAR Phase Unwrapping,” IEEE Geosci. Remote Sens. 5(2), 147–151 (2008).
[CrossRef]

Luong, B.

Macy, W. W.

Martinez-Espla, J. J.

J. J. Martinez-Espla, T. Martinez-Marin, and J. M. Lopez-Sanchez, “Using a Grid-Based Filter to Solve InSAR Phase Unwrapping,” IEEE Geosci. Remote Sens. 5(2), 147–151 (2008).
[CrossRef]

Martinez-Marin, T.

J. J. Martinez-Espla, T. Martinez-Marin, and J. M. Lopez-Sanchez, “Using a Grid-Based Filter to Solve InSAR Phase Unwrapping,” IEEE Geosci. Remote Sens. 5(2), 147–151 (2008).
[CrossRef]

Mastin, G.

Mehta, D. S.

Moon, I.

Navarro, M. A.

Oreb, B. F.

Pezzati, L.

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36(9), 2466–2472 (1997).
[CrossRef]

Potuluri, P.

Pouet, B. F.

Quiroga, J. A.

Reichard, K.

Robinson, D. W.

A. Spik and D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14(1), 25–37 (1991).
[CrossRef]

Romero, L. A.

Saldner, H.

Saldner, H. O.

Servin, M.

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. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: a review and comparison,” Opt. Eng. 50(8), 1026–1029 (2011).

Shakher, C.

Shi, K.

Spik, A.

A. Spik and D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14(1), 25–37 (1991).
[CrossRef]

Stetson, K. A.

Su, W. H.

Vargas, J.

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. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: a review and comparison,” Opt. Eng. 50(8), 1026–1029 (2011).

Wada, A.

Wahid, J.

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4–6), 205–210 (1999).
[CrossRef]

Wang, B.

Wang, Y. C.

Weng, J. F.

Werner, C.

R. Goldstein, H. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[CrossRef]

Xianming, X.

X. Xianming and P. Yiming, “Multi-baseline phase unwrapping algorithm based on the unscented Kalman filter,” IET Radar Sonar Nav. 5(3), 296–304 (2011).
[CrossRef]

Yamaki, R.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Rem. Sens. 45(10), 3240–3251 (2007).
[CrossRef]

Yau, S. T.

Yiming, P.

X. Xianming and P. Yiming, “Multi-baseline phase unwrapping algorithm based on the unscented Kalman filter,” IET Radar Sonar Nav. 5(3), 296–304 (2011).
[CrossRef]

Yin, S.

Yuqing, S.

Zebker, H.

R. Goldstein, H. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[CrossRef]

Zhang, S.

Appl. Opt. (10)

J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32(17), 3047–3052 (1993).
[CrossRef] [PubMed]

K. A. Stetson, J. Wahid, and P. Gauthier, “Noise-immune phase unwrapping by use of calculated wrap regions,” Appl. Opt. 36(20), 4830–4838 (1997).
[CrossRef] [PubMed]

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997).
[CrossRef] [PubMed]

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997).
[CrossRef] [PubMed]

W. W. Macy., “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22(23), 3898–3901 (1983).
[CrossRef] [PubMed]

K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24(18), 3053–3058 (1985).
[CrossRef] [PubMed]

D. S. Mehta, S. K. Dubey, M. M. Hossain, and C. Shakher, “Simple multifrequency and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry,” Appl. Opt. 44(35), 7515–7521 (2005).
[CrossRef] [PubMed]

S. Zhang, X. L. Li, and S. T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46(1), 50–57 (2007).
[CrossRef] [PubMed]

P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987).
[CrossRef] [PubMed]

J. Jiang, J. Cheng, and B. Luong, “Unsupervised-clustering-driven noise-residue filter for phase images,” Appl. Opt. 49(11), 2143–2150 (2010).
[CrossRef] [PubMed]

IEEE Geosci. Remote Sens. (1)

J. J. Martinez-Espla, T. Martinez-Marin, and J. M. Lopez-Sanchez, “Using a Grid-Based Filter to Solve InSAR Phase Unwrapping,” IEEE Geosci. Remote Sens. 5(2), 147–151 (2008).
[CrossRef]

IEEE Trans. Geosci. Rem. Sens. (1)

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Rem. Sens. 45(10), 3240–3251 (2007).
[CrossRef]

IET Radar Sonar Nav. (1)

X. Xianming and P. Yiming, “Multi-baseline phase unwrapping algorithm based on the unscented Kalman filter,” IET Radar Sonar Nav. 5(3), 296–304 (2011).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162(4–6), 205–210 (1999).
[CrossRef]

Opt. Eng. (3)

A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, “Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping,” Opt. Eng. 36(9), 2466–2472 (1997).
[CrossRef]

H. Cui, W. Liao, N. Dai, and X. Cheng, “Reliability-guided phase-unwrapping algorithm for the measurement of discontinuous three-dimensional objects,” Opt. Eng. 50(6), 063602 (2011).
[CrossRef]

J. C. Estrada, M. Servin, and J. Vargas, “2D simultaneous phase unwrapping and filtering: a review and comparison,” Opt. Eng. 50(8), 1026–1029 (2011).

Opt. Express (8)

P. Potuluri, M. Fetterman, and D. Brady, “High depth of field microscopic imaging using an interferometric camera,” Opt. Express 8(11), 624–630 (2001).
[CrossRef] [PubMed]

W. H. Su, K. Shi, Z. Liu, B. Wang, K. Reichard, and S. Yin, “A large-depth-of-field projected fringe profilometry using supercontinuum light illumination,” Opt. Express 13(3), 1025–1032 (2005).
[CrossRef] [PubMed]

E. H. Kim, J. Hahn, H. Kim, and B. Lee, “Profilometry without phase unwrapping using multi-frequency and four-step phase-shift sinusoidal fringe projection,” Opt. Express 17(10), 7818–7830 (2009).
[CrossRef] [PubMed]

K. Liu, Y. C. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[CrossRef] [PubMed]

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

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, “Integration of robust filters and phase unwrapping algorithms for image reconstruction of objects containing height discontinuities,” Opt. Express 20(10), 10896–10920 (2012).
[CrossRef] [PubMed]

Opt. Lasers Eng. (2)

A. Spik and D. W. Robinson, “Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor,” Opt. Lasers Eng. 14(1), 25–37 (1991).
[CrossRef]

H. Y. Chang, C. W. Chen, C. K. Lee, and C. P. Hu, “The Tapestry Cellular Automata phase unwrapping algorithm for interferogram analysis,” Opt. Lasers Eng. 30(6), 487–502 (1998).
[CrossRef]

Opt. Lett. (2)

Radio Sci. (1)

R. Goldstein, H. Zebker, and C. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23(4), 713–720 (1988).
[CrossRef]

Strain (1)

M. J. Huang and J. K. Liou, “Retrieving ESPI map of discontinuous objects via a novel phase unwrapping algorithm,” Strain 44(3), 239–247 (2008).
[CrossRef]

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