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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 22, Iss. 12 — Dec. 1, 2005
  • pp: 2766–2773

Phase recovery from a single fringe pattern using an orientational vector-field-regularized estimator

Jesús Villa, Ismael De la Rosa, Gerardo Miramontes, and Juan Antonio Quiroga  »View Author Affiliations

JOSA A, Vol. 22, Issue 12, pp. 2766-2773 (2005)

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Recent studies have demonstrated that the phase recovery from a single fringe pattern with closed fringes can be properly performed if the modulo 2 π fringe orientation is estimated. For example, the fringe pattern in quadrature can be efficiently obtained in terms of the orientational phase spatial operator using fast Fourier transformations and a spiral phase spectral operator in the Fourier space. The computation of the modulo 2 π fringe orientation, however, is by far the most difficult task in the global process of phase recovery. For this reason we propose the demodulation of fringe patterns with closed fringes through the computation of the modulo 2 π fringe orientation using an orientational vector-field-regularized estimator. As we will show, the phase recovery from a single pattern can be performed in an efficient manner using this estimator, provided that it requires one to solve locally in the fringe pattern a simple linear system to optimize a regularized cost function. We present simulated and real experiments applying the proposed methodology.

© 2005 Optical Society of America

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: April 14, 2005
Manuscript Accepted: May 14, 2005
Published: December 1, 2005

Jesús Villa, Juan Antonio Quiroga, Ismael De la Rosa, and Gerardo Miramontes, "Phase recovery from a single fringe pattern using an orientational vector-field-regularized estimator," J. Opt. Soc. Am. A 22, 2766-2773 (2005)

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  1. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  2. D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).
  3. M. Servín, J. L. Marroquín, J. A. Quiroga, “Regularized quadrature and phase tracking from a single closed-fringe interferogram,” J. Opt. Soc. Am. A 21, 411–419 (2004). [CrossRef]
  4. R. Legarda-Senz, 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]
  5. J. L. Marroquín, R. Rodríguez-Vera, M. Servín, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1543 (1998). [CrossRef]
  6. M. Servín, J. A. Quiroga, J. L. Marroquín, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 925–934 (2003). [CrossRef]
  7. K. G. Larkin, D. J. 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]
  8. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, 2000).
  9. J. A. Quiroga, M. Servín, F. Cuevas, “Modulo 2π fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm,” J. Opt. Soc. Am. A 19, 1524–1531 (2002). [CrossRef]
  10. B. Ströbel, “Processing of interferometric phase maps as complex-valued phasor images,” Appl. Opt. 35, 2192–2198 (1996). [CrossRef] [PubMed]
  11. J. Villa, J. A. Quiroga, M. Servín, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt. 39, 502–508 (2000). [CrossRef]
  12. J. A. Quiroga, J. A. Gómez-Pedrero, A. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197, 43–51 (2001). [CrossRef]

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