OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 39, Iss. 26 — Sep. 10, 2000
  • pp: 4817–4825

Unwrapping circular interferograms

Igor Lyuboshenko  »View Author Affiliations

Applied Optics, Vol. 39, Issue 26, pp. 4817-4825 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (3016 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The Green’s formulation for phase unwrapping is generalized to the case of circular phase-support regions. A phase-unwrapping method, believed to be new, is developed in which two forms of the Green’s function are used, one in a closed form and the other in the form of a series of Helmholtz equation eigenfunctions to satisfy homogeneous Neumann boundary conditions in a circular domain. The contribution of the rotational part of the wrapped phase gradient that is due to phase-gradient inconsistencies (residues) is accounted for in the unwrapped phase. Computational results on the reconstruction of a simulated wave front in the presence of aberrations, and on unwrapping real synthetic aperture radar interferograms, show the usefulness and reliability of the method when applied to regions where the conventional rectangular support regions are impractical.

© 2000 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval
(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(280.6730) Remote sensing and sensors : Synthetic aperture radar

Original Manuscript: January 3, 2000
Revised Manuscript: June 12, 2000
Published: September 10, 2000

Igor Lyuboshenko, "Unwrapping circular interferograms," Appl. Opt. 39, 4817-4825 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. 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]
  2. G. H. Glover, E. Schneider, “Three-point Dixon technique for true water/fat decomposition with B0 inhomogeneity correction,” Magn. Reson. Med. 18, 371–383 (1991). [CrossRef] [PubMed]
  3. G. Páez, M. Strojnik, “Phase-shifted interferometry without phase unwrapping: reconstruction of a decentered wave front,” J. Opt. Soc. Am. A 16, 475–480 (1999). [CrossRef]
  4. M. S. Scivier, T. J. Hall, M. A. Fiddy, “Phase unwrapping using the complex zeros of a band-limited function and the presence of ambiguities in two dimensions,” Opt. Acta 31, 619–623 (1984). [CrossRef]
  5. E. G. Abramochkin, V. G. Volostnikov, “Relationship between two-dimensional intensity and phase in a Fresnel diffraction zone,” Opt. Commun. 74, 144–148 (1989). [CrossRef]
  6. 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]
  7. 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]
  8. R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988). [CrossRef]
  9. W. Xu, I. Cumming, “A region-growing algorithm for InSAR phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 37, 124–134 (1999). [CrossRef]
  10. M. Constantini, “A novel phase unwrapping method based on network programming,” IEEE Trans. Geosci. Remote Sens. 36, 813–821 (1998). [CrossRef]
  11. G. Franceschetti, R. Lanari, Synthetic Aperture Radar Processing (CRC Press, Boca Raton, Fla., 1999).
  12. I. Lyuboshenko, H. Maı̂tre, “Phase unwrapping for interferometric synthetic aperture radar by use of Helmholtz equation eigenfunctions and the first Green’s identity,” J. Opt. Soc. Am. A 16, 378–395 (1999). [CrossRef]
  13. I. Lyuboshenko, A. Maruani, H. Maı̂tre, “Residue influence on phase unwrapping by use of Green–Helmholtz formulation,” in Proceedings of International Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. III, pp. 1537–1539.
  14. L. Axel, D. Morton, “Correction of phase wrapping in magnetic resonance imaging,” Med. Phys. 16, 284–287 (1989). [CrossRef] [PubMed]
  15. B. D. Bobrov, “Screw dislocations of laser speckle fields in interferograms with a circular line structure,” Sov. J. Quantum Electron. 21, 802–806 (1991). [CrossRef]
  16. S. Stramaglia, L. Guerriero, G. Pasquariello, N. Veneziani, “Mean-field annealing for phase unwrapping,” Appl. Opt. 38, 1377–1383 (1999). [CrossRef]
  17. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  18. M. Abramowitz, C. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972).
  19. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, New York, 1970).
  20. M. D. Pritt, J. S. Shipman, “Least-squares two-dimensional phase unwrapping using FFT’s,” IEEE Trans. Geosci. Remote Sens. 32, 706–708 (1994). [CrossRef]
  21. U. Spagnolini, “2-D phase unwrapping and phase aliasing,” Geophysics 58, 1324–1334 (1993). [CrossRef]
  22. H. Takajo, T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425 (1988). [CrossRef]
  23. J. C. Curlander, R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley, New York, 1991).

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