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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 43, Iss. 33 — Nov. 20, 2004
  • pp: 6139–6146

Fast algorithm for estimation of the orientation term of a general quadrature transform with application to demodulation of an n-dimensional fringe pattern

Daniel Crespo, Juan Antonio Quiroga, and Jose Antonio Gomez-Pedrero  »View Author Affiliations


Applied Optics, Vol. 43, Issue 33, pp. 6139-6146 (2004)
http://dx.doi.org/10.1364/AO.43.006139


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Abstract

The spatial orientation of fringes has been demonstrated to be a key point in reliable phase demodulation from a single n-dimensional fringe pattern, regardless of the frequency spectrum of the signal. Recent publications have shown a general method for determination of the orientation factor by use of a regularized phase-tracking (RPT) algorithm. We propose a generalization of a RPT algorithm for estimation of the spatial orientation in a general n-dimensional case. The proposed algorithm makes use of a simplified cost function that remains one dimensional regardless of the dimension of the problem. This makes the calculation faster than with a standard RPT algorithm, with which it is necessary to minimize an n + 1-dimensional cost function for each point of the sample space. We have applied the method to the three-dimensional demodulation of a time-evolving fringe pattern, with good results.

© 2004 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval

History
Original Manuscript: July 8, 2004
Revised Manuscript: September 2, 2004
Published: November 20, 2004

Citation
Daniel Crespo, Juan Antonio Quiroga, and Jose Antonio Gomez-Pedrero, "Fast algorithm for estimation of the orientation term of a general quadrature transform with application to demodulation of an n-dimensional fringe pattern," Appl. Opt. 43, 6139-6146 (2004)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-43-33-6139


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References

  1. T. Kreis, Holographic Interferometry (Akademie Verlag, Berlin, 1996).
  2. M. Servin, J. A. Quiroga, J. L. Marroquin, “A general n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 925–934 (2003). [CrossRef]
  3. J. A. Quiroga, M. Servin, J. L. Marroquin, D. Crespo, “Estimation of the orientation term of the general quadrature transform from a single n-dimensional fringe pattern,” submitted to J. Opt. Soc. Am. A.
  4. X. Zhou, J. P. Baird, J. F. Arnold, “Fringe-orientation estimation by use of a Gaussian gradient-filter and neighboring-direction averaging,” Appl. Opt. 38, 795–804 (1999). [CrossRef]
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  7. M. Servin, F. J. Cuevas, D. Malacara, J. L. Marroquin, R. Rodriguez-Vera, “Phase unwrapping through demodulation by use of the regularized phase-tracking technique,” Appl. Opt. 35, 2192–2198 (1996).
  8. J. A. Quiroga, M. Servin, J. L. Marroquín, “Robust demodulation of isochromatics from a single tricolour image using an adaptive regularised phase tracking technique,” presented at the international conference, PhotoMechanique 2001, presented at Poitiers, France, 24–26 April, 2001.

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