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Applied Optics

Applied Optics


  • Vol. 38, Iss. 26 — Sep. 10, 1999
  • pp: 5577–5593

Phase unwrapping with the branch-cut method: clustering of discontinuity sources and reverse simulated annealing

Bernd Gutmann and Herbert Weber  »View Author Affiliations

Applied Optics, Vol. 38, Issue 26, pp. 5577-5593 (1999)

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The branch-cut method is a powerful tool for correct unwrapping of phase maps in optical metrology. However, this method encounters the problem of the correct setting of the cuts, which belongs to the class of nondeterministic-polynomial-time-complete problems. Simulated annealing is an algorithm used to solve problems of this kind in a polynomial-time execution. However, the algorithm still requires an enormous calculation time if the number of discontinuity sources and thus the number of branch cuts is high. We illustrate the motivation for the use of this algorithm and show how the running time can be severely reduced by use of reverse simulated annealing, starting from the nearest-neighbor solution to find a proper initial configuration, and by clustering of discontinuity sources.

© 1999 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Original Manuscript: December 21, 1998
Revised Manuscript: April 13, 1999
Published: September 10, 1999

Bernd Gutmann and Herbert Weber, "Phase unwrapping with the branch-cut method: clustering of discontinuity sources and reverse simulated annealing," Appl. Opt. 38, 5577-5593 (1999)

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  1. D. C. Ghiglia, G. A. Mastin, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987). [CrossRef]
  2. M. Takeda, “Recent progress in phase unwrapping techniques,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 334–343 (1996). [CrossRef]
  3. R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988). [CrossRef]
  4. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989). [CrossRef] [PubMed]
  5. L. D. Barr, V. Coudé du Foresto, J. Fox, G. A. Poczulp, J. Richardson, C. Roddier, F. Roddier, “Large mirror testing facility at the National Astronomy Observatories,” Opt. Eng. 30, 1405–1414 (1991). [CrossRef]
  6. R. Cusack, J. M. Huntley, H. T. Goldrein, “Improved noise-immune phase unwrapping algorithm,” Appl. Opt. 35, 781–789 (1995). [CrossRef]
  7. M. R. Garey, D. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness (Freeman, New York, 1979).
  8. J. R. Buckland, J. M. Huntley, S. R. E. Turner, “Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm,” Appl. Opt. 34, 5100–5108 (1995). [CrossRef] [PubMed]
  9. J. A. Quiroga, A. González-Cano, E. Bernabeu, “Stable-marriages algorithm for preprocessing phase maps with discontinuity sources,” Appl. Opt. 34, 5029–5038 (1995). [CrossRef] [PubMed]
  10. M. Takeda, T. Abe, “Phase unwrapping by a maximum cross-amplitude spanning tree algorithm: a comparative study,” Opt. Eng. 35, 2345–2351 (1996). [CrossRef]
  11. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983). [CrossRef] [PubMed]
  12. R. V. V. Vidal, ed., Applied Simulated Annealing (Springer-Verlag, Berlin, 1993). [CrossRef]
  13. E. Aarts, J. Korst, Simulated Annealing and Boltzmann Machines, Wiley-Interscience Series in Discrete Mathematics and Optimization (Wiley, Chichester, N.Y., 1989).
  14. Because there are usually some sources connected to the boundary of the measurement range, we have Nbc ≥ (N+ + N-)/2.
  15. Image used with the kind permission of Fabrice Brémand, Laboratoire de Méchaniques des Solides, Université de Poitiers, France.
  16. H. A. Zebker, Y. Lu, “Phase unwrapping algorithms for radar interferometry: residue-cut, least-squares, and synthesis algorithms,” J. Opt. Soc. Am. A 15, 586–598 (1998). [CrossRef]
  17. S. Flügge, ed., Encyclopedia of Physics, Vol. IV: Principles of Electrodynamics and Relativity (Springer, Berlin, 1962).
  18. A. Dittler, B. Gutmann, R. Lichtenberger, H. Weber, G. Kasper, “Optical in situ measurement of dust cake thickness distributions on rigid filter media for gas cleaning,” Powder Technol. 99, 177–184 (1998). [CrossRef]
  19. Image used with the kind permission of the Department of Physics, Applied Optics, Carl von Ossietzky University, Oldenburg, Germany.

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