Abstract

A new algorithm for phase unwrapping of phase maps with noise or logical inconsistencies is proposed. It is based on the use of an adaptive threshold and the second difference of the locally unwrapped phase as a selection criterion for the pixels to be processed.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. A. Vrooman, A. A. M. Mass, “New image processing algorithms for the analysis of speckle interference patterns,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 51–61 (1989).
  2. D. Dirksen, X. Su, D. Vukicevic, G. von Bally, “Optimized phase shifting and use of phase modulation function for high-resolution phase evaluation,” in Fringe ’93, Proceedings of Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), p. 148–153.
  3. J. A. Quiroga, E. Bernabeu, “Phase-unwrapping algorithm for noisy phase map processing,” Appl. Opt. 33, 6725–6731 (1994).
    [CrossRef] [PubMed]
  4. D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “A quasi-heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).
  5. D. J. Bone, “Fourier fringe analysis: the two-dimensional phase-unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991).
    [CrossRef] [PubMed]

1994 (1)

1991 (1)

Bernabeu, E.

Bone, D. J.

Bryanston-Cross, P. J.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “A quasi-heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).

Dirksen, D.

D. Dirksen, X. Su, D. Vukicevic, G. von Bally, “Optimized phase shifting and use of phase modulation function for high-resolution phase evaluation,” in Fringe ’93, Proceedings of Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), p. 148–153.

Judge, T. R.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “A quasi-heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).

Mass, A. A. M.

H. A. Vrooman, A. A. M. Mass, “New image processing algorithms for the analysis of speckle interference patterns,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 51–61 (1989).

Quiroga, J. A.

Su, X.

D. Dirksen, X. Su, D. Vukicevic, G. von Bally, “Optimized phase shifting and use of phase modulation function for high-resolution phase evaluation,” in Fringe ’93, Proceedings of Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), p. 148–153.

Towers, D. P.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “A quasi-heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).

von Bally, G.

D. Dirksen, X. Su, D. Vukicevic, G. von Bally, “Optimized phase shifting and use of phase modulation function for high-resolution phase evaluation,” in Fringe ’93, Proceedings of Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), p. 148–153.

Vrooman, H. A.

H. A. Vrooman, A. A. M. Mass, “New image processing algorithms for the analysis of speckle interference patterns,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 51–61 (1989).

Vukicevic, D.

D. Dirksen, X. Su, D. Vukicevic, G. von Bally, “Optimized phase shifting and use of phase modulation function for high-resolution phase evaluation,” in Fringe ’93, Proceedings of Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), p. 148–153.

Appl. Opt. (2)

Other (3)

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, “A quasi-heterodyne holographic technique and automatic algorithms for phase unwrapping,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 95–119 (1989).

H. A. Vrooman, A. A. M. Mass, “New image processing algorithms for the analysis of speckle interference patterns,” in Fringe Pattern Analysis, G. T. Reid, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1163, 51–61 (1989).

D. Dirksen, X. Su, D. Vukicevic, G. von Bally, “Optimized phase shifting and use of phase modulation function for high-resolution phase evaluation,” in Fringe ’93, Proceedings of Second International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner, W. Osten, eds. (Akademie, Berlin, 1993), p. 148–153.

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 (3)

Fig. 1
Fig. 1

Neighbor set for a given pixel, 0, and directions for the calculation of the second differences.

Fig. 2
Fig. 2

(a) Computer-generated phase map with a discontinuity that produces an integer fringe shift. (b) Phase map of (a) when a linear carrier phase is added. (c) Unwrapped phase map when the second-difference-based algorithm is used. Black points correspond to nonprocessed points. (d) Final unwrapped phase map, when the value of the phase in the nonprocessed points is obtained by interpolation.

Fig. 3
Fig. 3

(a) Phase map with two conflictive areas: 1, abrupt fringe ends and a very high curvature zone, 2, a 2π jump hidden by noise. (b) Final unwrapped phase map.

Equations (4)

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

Δ ( 3 ) = 2 Φ * ( 3 ) Φ * ( 0 ) Φ * ( 11 ) ,
Φ * ( 0 ) = ϕ ( 0 ) , Φ * ( 3 ) = Φ * ( 0 ) + [ ϕ ( 3 ) ϕ ( 0 ) ] , Φ * ( 11 ) = Φ * ( 3 ) + [ ϕ ( 11 ) ϕ ( 3 ) ] ,
Δ ( 3 ) = [ ϕ ( 3 ) ϕ ( 0 ) ] [ ϕ ( 11 ) ϕ ( 3 ) ] .
Φ ( p ) = Φ ( 0 ) + [ ϕ ( p ) ϕ ( 0 ) ] .

Metrics