Abstract

In the process of phase unwrapping for an image obtained by an interferometer or in-line holography, noisy image data may pose difficulties. Traditional phase unwrapping algorithms used to estimate a two-dimensional phase distribution include much estimation error, due to the effect of singular points. This paper introduces an accurate phase-unwrapping algorithm based on three techniques: a rotational compensator, unconstrained singular point positioning, and virtual singular points. The new algorithm can confine the effect of singularities to the local region around each singular point. The phase-unwrapped result demonstrates that accuracy is improved, compared with past methods based on the least-squares approach.

© 2010 Optical Society of America

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    [CrossRef]
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2007 (3)

S. Tomioka, S. Nisiyama, and T. Enoto, “Nonlinear least square regression by adaptive domain method with multiple genetic algorithms,” IEEE Trans. Evol. Comput. 11, 1–16(2007).
[CrossRef]

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

2000 (1)

1999 (1)

1998 (2)

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

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

1995 (4)

1994 (1)

1993 (1)

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]

1991 (1)

1989 (2)

1988 (3)

1986 (1)

1985 (1)

1982 (1)

1979 (1)

1977 (2)

1974 (1)

1953 (1)

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), pp. 52–54.

Bachor, H.-A.

Bernabeu, E.

Bone, D. J.

Brangaccio, D. J.

Breuckmann, B.

Bruning, J. H.

Buckland, J. R.

Burton, D. R.

Costantini, M.

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

Cuche, E.

Cusack, R.

Depeursinge, C.

Enoto, T.

S. Tomioka, S. Nisiyama, and T. Enoto, “Nonlinear least square regression by adaptive domain method with multiple genetic algorithms,” IEEE Trans. Evol. Comput. 11, 1–16(2007).
[CrossRef]

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), pp. 52–54.

Fried, D. L.

Gallagher, J. E.

Gdeisat, M. A.

Ghiglia, D. C.

Goldrein, H. T.

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]

González-Cano, A.

Grebe, R.

Gutmann, B.

Herriott, D. R.

Hirose, A.

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

Hudgin, R. H.

Hunt, B. R.

Huntley, J. M.

Ina, H.

Karout, S. A.

Kobayashi, S.

Lalor, M. J.

Marquet, P.

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]

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), pp. 52–54.

Nisiyama, S.

S. Tomioka, S. Nisiyama, and T. Enoto, “Nonlinear least square regression by adaptive domain method with multiple genetic algorithms,” IEEE Trans. Evol. Comput. 11, 1–16(2007).
[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]

Pritt, M. D.

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

Quiroga, J. A.

Romero, L. A.

Rosenfeld, D. P.

Sandeman, R. J.

Takahashi, T.

Takajo, H.

Takeda, M.

Thieme, W.

Tomioka, S.

S. Tomioka, S. Nisiyama, and T. Enoto, “Nonlinear least square regression by adaptive domain method with multiple genetic algorithms,” IEEE Trans. Evol. Comput. 11, 1–16(2007).
[CrossRef]

Turner, S. R. E.

Vandenhouten, R.

Weber, H.

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]

White, A. D.

Yamaki, R.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sensing 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. (12)

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]

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]

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

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

R. Vandenhouten and R. Grebe, “Phase reconstruction and unwrapping from holographic interferograms of partially absorbent phase objects,” Appl. Opt. 34, 1401–1406 (1995).
[CrossRef]

J. A. Quiroga, A. González-Cano, and E. Bernabeu, “Stable-marriages algorithm for preprocessing phase maps with discontinuity sources,” Appl. Opt. 34, 5029–5038(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]

IEEE Trans. Evol. Comput. (1)

S. Tomioka, S. Nisiyama, and T. Enoto, “Nonlinear least square regression by adaptive domain method with multiple genetic algorithms,” IEEE Trans. Evol. Comput. 11, 1–16(2007).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (2)

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

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

J. Opt. Soc. Am. (4)

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

Opt. Lasers Eng. (1)

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. (1)

Radio Sci. (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]

Other (2)

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

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), pp. 52–54.

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