OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 6 — Jun. 1, 2005
  • pp: 1170–1175

Robust phase demodulation of interferograms with open or closed fringes

Mariano Rivera  »View Author Affiliations

JOSA A, Vol. 22, Issue 6, pp. 1170-1175 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (449 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present two robust algorithms for fringe pattern analysis with partial-field and closed fringes. The algorithm for partial-field fringe patterns is presented as a refinement method for precomputed coarse phases. Such an algorithm consists of the minimization of a regularized cost function that incorporates an outlier rejection strategy, which causes the algorithm to become robust. On the basis of the phase refinement method, we propose a propagative scheme for phase retrieval from closed-fringe interferograms. The algorithm performance is demonstrated by demodulating closed-fringe interferograms with complex spatial distribution of stationary points and gradients in the illumination components.

© 2005 Optical Society of America

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

Original Manuscript: October 7, 2004
Revised Manuscript: December 16, 2004
Manuscript Accepted: December 17, 2004
Published: June 1, 2005

Mariano Rivera, "Robust phase demodulation of interferograms with open or closed fringes," J. Opt. Soc. Am. A 22, 1170-1175 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 4, 156–160 (1982). [CrossRef]
  2. K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. (Bellingham) 23, 391–395 (1984). [CrossRef]
  3. D. W. Robinson and G. T. Reid, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, UK, 1993).
  4. J. L. Marroquin, J. E. Figueroa, M. Servin, “Robust quadrature filters,” J. Opt. Soc. Am. A 14, 779–791 (1997). [CrossRef]
  5. J. L. Marroquin, M. Servin, R. Rodriguez-Vera, “Adaptive quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. A 14, 1742–1753 (1997). [CrossRef]
  6. M. Servin, J. L. Marroquin, F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997). [CrossRef] [PubMed]
  7. J. L. Marroquin, R. Rodriguez-Vera, M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1544 (1998) [CrossRef]
  8. J. Villa, J. A. Quiroga, M. Servin, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms” Appl. Opt. 39, 502–508 (2000). [CrossRef]
  9. M. Servin, J. L. Marroquin, F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18, 689–695 (2001). [CrossRef]
  10. K. G. Larkin, D. Bone, M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862–1870 (2001). [CrossRef]
  11. K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1871–1881 (2001). [CrossRef]
  12. R. Legarda-Saenz, W. Osten, W. Jüptner, “Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns,” Appl. Opt. 41, 5519–5526 (2002). [CrossRef] [PubMed]
  13. M. Servin, J. A. Quiroga, J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 925–934 (2003) [CrossRef]
  14. M. Servin, J. L. Marroquin, J. A. Quiroga, “Regularized quadrature and phase tracking from a single closed-fringe interferogram,” J. Opt. Soc. Am. A 21, 411–419 (2004). [CrossRef]
  15. D. Geman, G. Reynolds, “Constrained restoration and the recovery of discontinuities,” IEEE Trans. Image Process. 14, 367–383 (1992).
  16. M. J. Black, A. Rangarajan, “Unification of line process, outlier rejection, and robust statistics with application in early vision,” Int. J. Comput. Vis. 19, 57–91 (1996). [CrossRef]
  17. P. Charbonnier, L. Blanc-Féraud, G. Aubert, M. Barlaud, “Deterministic edge-preserving regularization in computer imaging,” IEEE Trans. Image Process. 6, 298–311 (1997). [CrossRef]
  18. M. Rivera, J. L. Marroquin, “Adaptive rest condition potentials: Second order edge-preserving regularization,” Comput. Vis. Image Underst. 88, 76–93 (2002). [CrossRef]
  19. M. Rivera, J. L. Marroquin, “Efficient half-quadratic regularization with granularity control,” Image Vis. Comput. 21, 345–357 (2003). [CrossRef]
  20. M. Rivera, J. L. Marroquin, “Half-quadratic cost functions for phase unwrapping,” Opt. Lett. 29, 504–506 (2004). [CrossRef] [PubMed]
  21. B. Jahne, Digital Image Processing, 5th ed., (Springer-Verlag, Berlin, 2002). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited