OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 12 — Apr. 20, 2009
  • pp: 2401–2409

Steerable spatial phase shifting applied to single-image closed-fringe interferograms

Juan Antonio Quiroga, Manuel Servin, Julio Cesar Estrada, and Jose Antonio Gomez-Pedrero  »View Author Affiliations

Applied Optics, Vol. 48, Issue 12, pp. 2401-2409 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (1719 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It is well known that spatial phase shifting interferometry (SPSI) may be used to demodulate two- dimensional (2D) spatial-carrier interferograms. In these cases the application of SPSI is straightforward because the modulating phase is a monotonic increasing function of space. However, this is not true when we apply SPSI to demodulate a single-image interferogram containing closed fringes. This is because using these algorithms, one would obtain a wrongly demodulated monotonic phase all over the 2D space. We present a technique to overcome this drawback and to allow any SPSI algorithm to be used as a single-image fringe pattern demodulator containing closed fringes. We make use of the 2D spatial orientation direction of the fringes to steer (orient) the one-dimensional SPSI algorithm in order to correctly demodulate the nonmonotonic 2D phase all over the interferogram.

© 2009 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(100.5070) Image processing : Phase retrieval
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: December 22, 2008
Revised Manuscript: March 19, 2009
Manuscript Accepted: March 19, 2009
Published: April 16, 2009

Juan Antonio Quiroga, Manuel Servin, Julio Cesar Estrada, and Jose Antonio Gomez-Pedrero, "Steerable spatial phase shifting applied to single-image closed-fringe interferograms," Appl. Opt. 48, 2401-2409 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977-3982 (1983). [CrossRef] [PubMed]
  2. M. Servin, J. L. Marroquin, and F. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18, 689-695(2001). [CrossRef]
  3. J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez-Vera, and M. Servin, “Regularization methods for processing fringe-pattern images,” Appl. Opt. 38, 788-794 (1999). [CrossRef]
  4. J. L. Marroquin, R. Rodriguez-Vera, and M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536-44 (1998). [CrossRef]
  5. K. Larkin, D. J. Bone, and 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]
  6. J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, “Phase recovery from a single fringe pattern using an orientational vector-field-regularized estimator,” J. Opt. Soc. Am. A 22, 2766-2773 (2005). [CrossRef]
  7. X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286-292 (2007). [CrossRef]
  8. R. Onodera, Y. Yamamoto, and Y. Ishii, “Signal processing of interferogram using a two-dimensional discrete Hilbert transform,” in Proceedings of Fringe 2005, Fifth International Workshop on Automatic Processing of Fringe Patterns, W. Osten, ed. (European Space Agency, 2005), pp. 82-89.
  9. C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Lett. 7, 368-370 (1982). [CrossRef] [PubMed]
  10. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504-2506 (1987). [CrossRef] [PubMed]
  11. J. A. Gomez Pedrero, J. A. Quiroga, and M. Servín, “Asynchronous phase demodulation algorithm for temporal evaluation of fringe patterns with spatial carrier,” J. Mod. Opt. 51, 97-109 (2004). [CrossRef]
  12. M. Servin, J. A. Quiroga, and J. L. Marroquín, “A general n-dimensional quadrature transform and its applications to interferogram demodulation,” J. Opt. Soc. Am. A 20, 925-934 (2003). [CrossRef]
  13. J. Zhong and J. Weng “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993-4998 (2004). [CrossRef] [PubMed]
  14. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007). [CrossRef]
  15. M. Servin, R. Rodriguez-Vera, and D. Malacara, “Noisy fringe pattern demodulation by an iterative phase locked loop,” Opt. Lasers Eng. 23, 355-365 (1995). [CrossRef]
  16. B. Strobel, “Processing of interferometric phase maps as complex-valued phasor images,” Appl. Opt. 35, 2192-2198(1996). [CrossRef] [PubMed]
  17. J. A. Gómez-Pedrero, J. A. Quiroga, and M. Servin, “Adaptive asynchronous algorithm for fringe pattern demodulation,” Appl. Opt. 47, 3954-3961 (2008). [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

OSA is a member of CrossRef.

CrossCheck Deposited