OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 11, Iss. 1 — Jan. 1, 1994
  • pp: 107–117

Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods

Dennis C. Ghiglia and Louis A. Romero  »View Author Affiliations

JOSA A, Vol. 11, Issue 1, pp. 107-117 (1994)

View Full Text Article

Enhanced HTML    Acrobat PDF (3867 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Two-dimensional (2D) phase unwrapping continues to find applications in a wide variety of scientific and engineering areas including optical and microwave interferometry, adaptive optics, compensated imaging, and synthetic-aperture-radar phase correction, and image processing. We have developed a robust method (not based on any path-following scheme) for unwrapping 2D phase principal values (in a least-squares sense) by using fast cosine transforms. If the 2D phase values are associated with a 2D weighting, the fast transforms can still be used in iterative methods for solving the weighted unwrapping problem. Weighted unwrapping can be used to isolate inconsistent regions (i.e., phase shear) in an elegant fashion.

© 1994 Optical Society of America

Original Manuscript: March 1, 1993
Revised Manuscript: May 10, 1993
Manuscript Accepted: June 22, 1993
Published: January 1, 1994

Dennis C. Ghiglia and Louis 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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements,”J. Opt. Soc. Am. 67, 370–375 (1977). [CrossRef]
  2. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,”J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  3. R. J. Noll, “Phase estimates from slope-type wave-front sensors,”J. Opt. Soc. Am. 68, 139–140 (1978). [CrossRef]
  4. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,”J. Opt. Soc. Am. 69, 393–399 (1979). [CrossRef]
  5. H. Takajo, T. Takahashi, “Least-squares phase estimation from phase differences,” J. Opt. Soc. Am. A 5, 416–425 (1988). [CrossRef]
  6. H. T. Takajo, T. Takahashi, “Noniterative method for obtaining the exact solution for the normal equation in least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 1818–1827 (1988). [CrossRef]
  7. D. C. Ghiglia, G. A. Mastin, “Two-dimensional phase correction of synthetic-aperture-radar imagery,” Opt. Lett. 14, 1104–1106 (1989). [CrossRef] [PubMed]
  8. D. C. Ghiglia, L. A. Romero, “Direct phase estimation from phase differences using fast elliptic partial differential equation solvers,” Opt. Lett. 14, 1107–1109 (1989). [CrossRef] [PubMed]
  9. B. L. Busbee, G. H. Gollub, C. W. Nielson, “On direct methods for solving Poisson’s equations,” SIAM J. Numer. Anal. 7, 627–656 (1970). [CrossRef]
  10. 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]
  11. R. M. Goldstein, H. A. Zebker, C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988). [CrossRef]
  12. N. H. Ching, D. Rosenfeld, M. Braun, “Two-dimensional phase unwrapping using a minimum spanning tree algorithm,”IEEE Trans. Image Process. 1, 355–365 (1992). [CrossRef] [PubMed]
  13. J. S. Lim, “The discrete cosine transform,” in Two-Dimensional Signal and Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1990), pp. 148–157.
  14. G. H. Gollub, C. F. Van Loan, “Iterative methods for linear systems,” in Matrix Computations, 2nd ed. (Johns Hopkins U. Press, Baltimore, Md., 1990), pp. 516–538.
  15. cosft must be used in the forward mode in all cases. In addition, the technique mentioned on p. 649 of Ref. 16 for solving Poisson’s equation with Neumann boundary conditions by using cosft alone is not correct and does not work. cosft does not specify the boundary conditions exactly [as defined by Eq. (14)] and therefore does not solve the least-squares problem.
  16. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986).
  17. G. A. Mastin, D. C. Ghiglia, “A research-oriented spotlight synthetic aperture radar polar reformatter,” Publ. SAND90-1793 (Sandia National Laboratories, Albuquerque, N.M., 1990), pp. 23–27.

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