OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2556–2561

Fast two-dimensional simultaneous phase unwrapping and low-pass filtering

Miguel A. Navarro, Julio C. Estrada, M. Servin, Juan A. Quiroga, and Javier Vargas  »View Author Affiliations

Optics Express, Vol. 20, Issue 3, pp. 2556-2561 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (996 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Here, we present a fast algorithm for two-dimensional (2D) phase unwrapping which behaves as a recursive linear filter. This linear behavior allows us to easily find its frequency response and stability conditions. Previously, we published a robust to noise recursive 2D phase unwrapping system with smoothing capabilities. But our previous approach was rather heuristic in the sense that not general 2D theory was given. Here an improved and better understood version of our previous 2D recursive phase unwrapper is presented. In addition, a full characterization of it is shown in terms of its frequency response and stability. The objective here is to extend our previous unwrapping algorithm and give a more solid theoretical foundation to it.

© 2012 OSA

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5088) Image processing : Phase unwrapping

ToC Category:
Image Processing

Original Manuscript: November 9, 2011
Revised Manuscript: December 2, 2011
Manuscript Accepted: January 4, 2012
Published: January 20, 2012

Miguel A. Navarro, Julio C. Estrada, M. Servin, Juan A. Quiroga, and Javier Vargas, "Fast two-dimensional simultaneous phase unwrapping and low-pass filtering," Opt. Express 20, 2556-2561 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Itoh, “Analysis of the phase unwrapping algorithm.” Appl. Opt.21, 2470 (1982). [CrossRef] [PubMed]
  2. D. C. Ghihlia and M. D. Pritt, Two-dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  3. T. Judge, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng.21, 199–239 (1994). [CrossRef]
  4. D. C. Ghihlia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A11107–117 (1994). [CrossRef]
  5. J. L. Marroquin and M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. A12, 2393–2400 (1995). [CrossRef]
  6. M. Servin, F. J. Cuevas, D. Malacara, J. L. Marroquin, and R. Rodriguez-Vera, “Phase unwrapping through demodulation by use of the regularized phase-tracking technique,” Appl. Opt.38, 1934–1941 (1999). [CrossRef]
  7. R. Goldstein, H. Zebker, and C. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Sci.23, 713–720 (1988). [CrossRef]
  8. T. J. Flynn, “Two-dimensional phase unwrapping with minimum weighted discontinuity,” J. Opt. Soc. Am. A14, 2692–2701 (1997). [CrossRef]
  9. J. C. Estrada, M. Servin, and J. A. Quiroga, “Noise robust linear dynamic system for phase unwrapping and smoothing,” Opt. Express19, 5126–5133 (2011). [CrossRef] [PubMed]
  10. B. Jähne, Digital Image Processing (Springer, 2005).
  11. J. G. Proakis and D. G. Manolakis, Digital Signal Processing. Principles, Algorothims, and Applications, 3rd ed. (Prentice-Hall, October5, 1995).
  12. W.-S. Lu and A. Antoniou, Two-Dimensional Digital Filters (Marcel Dekker, Inc., 1992).
  13. R. E. Kalman and R. S. Bucy, “New results in linear filtering and prediction theory,” Trans. ASME, Ser. D83, 95–107 (1961). [CrossRef]

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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited