OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 40, Iss. 23 — Aug. 10, 2001
  • pp: 3901–3908

Three-dimensional noise-immune phase unwrapping algorithm

Jonathan M. Huntley  »View Author Affiliations

Applied Optics, Vol. 40, Issue 23, pp. 3901-3908 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (317 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The classical problem of phase unwrapping in two dimensions, that of how to create a path-independent unwrapped map, is extended to the case of a three-dimensional phase distribution. Whereas in two dimensions the path dependence problem arises from isolated phase singularity points, in three dimensions the phase singularities are shown to form closed loops in space. A closed path that links one such loop will cross a nonzero number of phase discontinuities. In two dimensions, path independence is achieved when branch-cut lines are placed between singular points of opposite sign; an equivalent path-independent algorithm for three dimensions is developed that places branch-cut surfaces so as to prevent unwrapping through the phase singularity loops. The placing of the cuts is determined uniquely by the phase data, which contrasts with the two-dimensional case for which there are many possible ways in which to pair up the singular points. The performance of the new algorithm is demonstrated on three-dimensional phase data from a high-speed phase-shifting speckle pattern interferometer.

© 2001 Optical Society of America

OCIS Codes
(100.6890) Image processing : Three-dimensional image processing
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.6160) Instrumentation, measurement, and metrology : Speckle interferometry

Original Manuscript: January 23, 2001
Revised Manuscript: May 17, 2001
Published: August 10, 2001

Jonathan M. Huntley, "Three-dimensional noise-immune phase unwrapping algorithm," Appl. Opt. 40, 3901-3908 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470 (1982). [CrossRef] [PubMed]
  2. J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26, 5245–5258 (1987). [CrossRef] [PubMed]
  3. M. Servin, D. Malacara, F. J. Cuevas, “Path-independent phase unwrapping of subsampled phase maps,” Appl. Opt. 35, 1643–1649 (1996). [CrossRef] [PubMed]
  4. R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry—two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988). [CrossRef]
  5. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989). [CrossRef] [PubMed]
  6. 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-optical-astronomy observatories,” Opt. Eng. 30, 1405–1414 (1991).
  7. 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]
  8. D. C. Ghiglia, L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994). [CrossRef]
  9. D. C. Ghiglia, L. A. Romero, “Minimum Lp-norm two-dimensional phase unwrapping,” J. Opt. Soc. Am. A 13, 1999–2013 (1996). [CrossRef]
  10. T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A 14, 2692–2701 (1997). [CrossRef]
  11. M. Constantini, “A novel phase unwrapping method based on network programming,” IEEE Trans. Geosci. Remote Sens. 36, 813–821 (1998). [CrossRef]
  12. C. W. Chen, H. A. Zebker, “Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms,” J. Opt. Soc. Am. A 17, 401–414 (2000). [CrossRef]
  13. D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley, New York, 1998).
  14. R. Cusack, “Unwrapping 3d maps of magnetic field deviations for use in undistorting fMRI images of the brain,” paper presented at the Institute of Physics Applied Optics Divisional Conference, Loughborough, UK, September 2000.
  15. J. M. Huntley, G. H. Kaufmann, D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38, 6556–6563 (1999). [CrossRef]
  16. P. Haible, M. P. Kothiyal, H. J. Tiziani, “Heterodyne temporal speckle-pattern interferometry,” Appl. Opt. 39, 114–117 (2000). [CrossRef]
  17. D. J. Bone, “Fourier fringe analysis—the two-dimensional phase unwrapping problem,” Appl. Opt. 30, 3627–3632 (1991). [CrossRef] [PubMed]
  18. J. M. Huntley, J. R. Buckland, “Characterization of sources of 2π phase discontinuity in speckle interferograms,” J. Opt. Soc. Am. A 12, 1990–1996 (1995). [CrossRef]
  19. J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited