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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 11 — Apr. 10, 2014
  • pp: 2297–2301

Total variation regularization cost function for demodulating phase discontinuities

Ricardo Legarda-Saenz, Carlos Brito-Loeza, and Arturo Espinosa-Romero  »View Author Affiliations

Applied Optics, Vol. 53, Issue 11, pp. 2297-2301 (2014)

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We introduce a method based on the minimization of a total variation regularization cost function for computing discontinuous phase maps from fringe patterns. The performance of the method is demonstrated by numerical experiments with both synthetic and real data.

© 2014 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 25, 2013
Revised Manuscript: March 5, 2014
Manuscript Accepted: March 6, 2014
Published: April 4, 2014

Ricardo Legarda-Saenz, Carlos Brito-Loeza, and Arturo Espinosa-Romero, "Total variation regularization cost function for demodulating phase discontinuities," Appl. Opt. 53, 2297-2301 (2014)

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  1. D. W. Robinson and G. T. Reid, Interferogram Analysis, Digital Fringe Pattern Measurement Techniques (Taylor & Francis, 1993).
  2. G. Rajshekhar and P. Rastogi, “Fringe analysis: premise and perspectives,” Opt. Lasers Eng. 50, iii–x (2012). [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. Villa, J. A. Quiroga, and M. Servin, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt. 39, 502–508 (2000). [CrossRef]
  5. R. Legarda-Saenz, W. Osten, and W. P. Juptner, “Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns,” Appl. Opt. 41, 5519–5526 (2002). [CrossRef]
  6. M. Rivera, “Robust phase demodulation of interferograms with open or closed fringes,” J. Opt. Soc. Am. A 22, 1170–1175 (2005). [CrossRef]
  7. C. Galvan and M. Rivera, “Second-order robust regularization cost function for detecting and reconstructing phase discontinuities,” Appl. Opt. 45, 353–359 (2006). [CrossRef]
  8. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992). [CrossRef]
  9. R. Acar and C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994). [CrossRef]
  10. P. Getreuer, “Rudin-Osher-Fatemi total variation denoising using split Bregman,” IPOL 2012, 1–20 (2012). [CrossRef]
  11. J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).
  12. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).
  13. H. Liao, F. Li, and M. K. Ng, “Selection of regularization parameter in total variation image restoration,” J. Opt. Soc. Am. A 26, 2311–2320 (2009). [CrossRef]
  14. T. Kreis, Holographic Interferometry: Principles and Methods (Wiley-VCH, 1996).
  15. M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 925–934 (2003). [CrossRef]
  16. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley-Interscience, 1998).
  17. K. J. Gasvik, Optical Metrology, 3rd ed. (Wiley, 2002).
  18. D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Probl. 19, S165–S187 (2003). [CrossRef]

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