Abstract

Phase-unwrapping algorithms, an active and interesting subject in recent years, are important in a great number of measurement applications. Active research is being undertaken to develop reliable and high-speed procedures. The current process uses a gray-scale mask and the flood-fill concept from image processing for phase unwrapping. The algorithm unwraps phase from an area with higher reliability to one with lower reliability. In addition to robustness, the speed of the algorithm proposed is much faster than conventional routines. The experimental results of different algorithms are compared by analysis of a tooth plaster and a photoelastic specimen.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry two dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
    [CrossRef]
  2. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 23, 3268–3270 (1989).
    [CrossRef]
  3. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991).
    [CrossRef] [PubMed]
  4. H. A. Vrooman, A. A. M. Mass, “Image processing algorithms for the analysis of phase-shifted speckle interference patterns,” Appl. Opt. 30, 1636–1641 (1991).
    [CrossRef] [PubMed]
  5. R. Vandenhouten, R. Grebe, “Phase reconstruction and unwrapping from holographic interferograms of partially absorbent phase objects,” Appl. Opt. 34, 1401–1406 (1995).
    [CrossRef] [PubMed]
  6. D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
    [CrossRef]
  7. X.-Y. Su, W. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Application of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, H. Liu, H. Podbieska, A. O. Wist, L. J. Zamorano, eds., Proc. SPIE2132, 484–489 (1994).
    [CrossRef]
  8. X.-Y. Su, A. Asundi, M. R. Sajan, “Phase unwrapping in photoelasticity,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 338–342 (1997).
    [CrossRef]
  9. J.-L. Li, X.-Y. Su, J.-T. Li, “Phase unwrapping algorithm based on reliability and edge detection,” Opt. Eng. 36, 1685–1690 (1997).
    [CrossRef]
  10. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef] [PubMed]

1997

J.-L. Li, X.-Y. Su, J.-T. Li, “Phase unwrapping algorithm based on reliability and edge detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

1995

1991

1989

J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 23, 3268–3270 (1989).
[CrossRef]

1988

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

1984

Asundi, A.

X.-Y. Su, A. Asundi, M. R. Sajan, “Phase unwrapping in photoelasticity,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 338–342 (1997).
[CrossRef]

Bone, D. J.

Bryanston-Cross, P. J.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Goldstein, R. M.

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

Grebe, R.

Halioua, M.

Huntley, J. M.

J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 23, 3268–3270 (1989).
[CrossRef]

Judge, T. R.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Li, J.-L.

J.-L. Li, X.-Y. Su, J.-T. Li, “Phase unwrapping algorithm based on reliability and edge detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

Li, J.-T.

J.-L. Li, X.-Y. Su, J.-T. Li, “Phase unwrapping algorithm based on reliability and edge detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

Liu, H. C.

Mass, A. A. M.

Sajan, M. R.

X.-Y. Su, A. Asundi, M. R. Sajan, “Phase unwrapping in photoelasticity,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 338–342 (1997).
[CrossRef]

Srinivasan, V.

Su, X.-Y.

J.-L. Li, X.-Y. Su, J.-T. Li, “Phase unwrapping algorithm based on reliability and edge detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

X.-Y. Su, A. Asundi, M. R. Sajan, “Phase unwrapping in photoelasticity,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 338–342 (1997).
[CrossRef]

X.-Y. Su, W. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Application of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, H. Liu, H. Podbieska, A. O. Wist, L. J. Zamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

Towers, D. P.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Vandenhouten, R.

Vrooman, H. A.

Werner, C. L.

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

Zebker, H. A.

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

Zhou, W.

X.-Y. Su, W. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Application of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, H. Liu, H. Podbieska, A. O. Wist, L. J. Zamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

Appl. Opt.

Opt. Eng.

J.-L. Li, X.-Y. Su, J.-T. Li, “Phase unwrapping algorithm based on reliability and edge detection,” Opt. Eng. 36, 1685–1690 (1997).
[CrossRef]

Opt. Lasers Eng.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “Automatic interferogram analysis techniques applied to quasi-heterodyne holography and ESPI,” Opt. Lasers Eng. 14, 239–281 (1991).
[CrossRef]

Radio Sci.

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

Other

X.-Y. Su, W. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Application of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, H. Liu, H. Podbieska, A. O. Wist, L. J. Zamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

X.-Y. Su, A. Asundi, M. R. Sajan, “Phase unwrapping in photoelasticity,” in International Conference on Experimental Mechanics: Advances and Applications, F. S. Chau, C. T. Lim, eds., Proc. SPIE2921, 338–342 (1997).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Optical geometry of the PMP system.

Fig. 2
Fig. 2

Flowchart of the flood-fill phase-unwrapping method.

Fig. 3
Fig. 3

Schematic diagram of the procedural steps of the proposed phase-unwrapping method.

Fig. 4
Fig. 4

Experimental results for a tooth plaster image: (a) Original image of the tooth plaster. (b) One of the fringe patterns. Block A represents a discontinuous fringe area. (c), (d) Two intermediate unwrapping steps. (e) Three-dimensional surface of the tooth plaster.

Fig. 5
Fig. 5

Experimental results for a photoelastic specimen: (a) Fringe pattern of photoelasticity. (b) Gray-scale display of the unwrapped phase.

Equations (4)

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

I n = A x ,   y + B x ,   y cos ϕ x ,   y +   2 π n / N ,
ϕ x ,   y = n = 1 N   I n sin 2 π n / N n = 1 N   I n cos 2 π n / N .
M x ,   y = n = 1 N I n sin 2 π n / N 2 + n = 1 N I n cos 2 π n / N 2 1 / 2 .
M x ,   y = N 2   B x ,   y .

Metrics