OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 11 — May. 21, 2012
  • pp: 12579–12592

A generalized regularized phase tracker for demodulation of a single fringe pattern

Li Kai and Qian Kemao  »View Author Affiliations

Optics Express, Vol. 20, Issue 11, pp. 12579-12592 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1751 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The regularized phase tracker (RPT) is one of the most powerful approaches for demodulation of a single fringe pattern. However, two disadvantages limit the applications of the RPT in practice. One is the necessity of a normalized fringe pattern as input and the other is the sensitivity to critical points. To overcome these two disadvantages, a generalized regularized phase tracker (GRPT) is presented. The GRPT is characterized by two novel improvements. First, a general local fringe model that includes a linear background, a linear modulation and a quadratic phase is adopted in the proposed enhanced cost function. Second, the number of iterations in the optimization process is proposed as a comprehensive measure of fringe quality and used to guide the demodulation path. With these two improvements, the GRPT can directly demodulate a single fringe pattern without any pre-processing and post-processing and successfully get rid of the problem of the sensitivity to critical points. Simulation and experimental results are presented to demonstrate the effectiveness and robustness of the GRPT.

© 2012 OSA

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Image Processing

Original Manuscript: March 19, 2012
Revised Manuscript: May 6, 2012
Manuscript Accepted: May 8, 2012
Published: May 18, 2012

Li Kai and Qian Kemao, "A generalized regularized phase tracker for demodulation of a single fringe pattern," Opt. Express 20, 12579-12592 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Cloud, Optical Methods of Engineering Analysis (Cambridge U. Press, Cambridge, UK, 1995).
  2. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Marcel Deker, 2003).
  3. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt.13(11), 2693–2703 (1974). [CrossRef] [PubMed]
  4. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Technique, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, 1993), Chap. 4, pp. 94–140.
  5. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am.72(1), 156–160 (1982). [CrossRef]
  6. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A3(6), 847–855 (1986). [CrossRef]
  7. J. L. Marroquin, M. Servin, and R. Rodriguez-Vera, “Adaptive quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. A14(8), 1742–1753 (1997). [CrossRef]
  8. 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. A15(6), 1536–1544 (1998). [CrossRef]
  9. K. G. 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. A18(8), 1862–1870 (2001). [CrossRef] [PubMed]
  10. M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A20(5), 925–934 (2003). [CrossRef] [PubMed]
  11. E. Robin and V. Valle, “Phase Demodulation from a Single Fringe Pattern Based on a Correlation Technique,” Appl. Opt.43(22), 4355–4361 (2004). [CrossRef] [PubMed]
  12. E. Robin, V. Valle, and F. Brémand, “Phase demodulation method from a single fringe pattern based on correlation with a polynomial form,” Appl. Opt.44(34), 7261–7269 (2005). [CrossRef] [PubMed]
  13. M. Rivera, “Robust phase demodulation of interferograms with open or closed fringes,” J. Opt. Soc. Am. A22(6), 1170–1175 (2005). [CrossRef] [PubMed]
  14. J. C. Estrada, M. Servin, and J. L. Marroquín, “Local adaptable quadrature filters to demodulate single fringe patterns with closed fringes,” Opt. Express15(5), 2288–2298 (2007), http://www. opticsinfobase.org/ oe/abstract. cfm?URI = oe-15–5-2288 . [CrossRef] [PubMed]
  15. Q. Kemao and S. Hock Soon, “Sequential demodulation of a single fringe pattern guided by local frequencies,” Opt. Lett.32(2), 127–129 (2007). [CrossRef] [PubMed]
  16. O. Dalmau-Cedeño, M. Rivera, and R. Legarda-Saenz, “Fast phase recovery from a single close-fringe pattern,” J. Opt. Soc. Am. A25(6), 1361–1370 (2008). [CrossRef]
  17. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt.36(19), 4540–4548 (1997). [CrossRef] [PubMed]
  18. R. Legarda-Sáenz, W. Osten, and W. Jüptner, “Improvement of the Regularized Phase Tracking Technique for the Processing of Nonnormalized Fringe Patterns,” Appl. Opt.41(26), 5519–5526 (2002). [CrossRef] [PubMed]
  19. R. Legarda-Saenz and M. Rivera, “Fast half-quadratic regularized phase tracking for nonnormalized fringe patterns,” J. Opt. Soc. Am. A23(11), 2724–2731 (2006). [CrossRef] [PubMed]
  20. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A18(3), 689–695 (2001). [CrossRef]
  21. H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express17(17), 15118–15127 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-17-15118 . [CrossRef] [PubMed]
  22. C. Tian, Y. Y. Yang, D. Liu, Y. J. Luo, and Y. M. Zhuo, “Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique,” Appl. Opt.49(2), 170–179 (2010). [CrossRef] [PubMed]
  23. H. Wang, K. Li, and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching,” Opt. Lasers Eng.49(4), 564–569 (2011). [CrossRef]
  24. J. Nocedal and S. J. Wright, Numerical Optimization (Springer, 1999).
  25. J. A. Quiroga, J. Antonio Gómez-Pedrero, and Á. Garcı́a-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun.197(1-3), 43–51 (2001). [CrossRef]
  26. J. Antonio Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun.224(4-6), 221–227 (2003). [CrossRef]
  27. J. A. Guerrero, J. L. Marroquin, M. Rivera, and J. A. Quiroga, “Adaptive monogenic filtering and normalization of ESPI fringe patterns,” Opt. Lett.30(22), 3018–3020 (2005). [CrossRef] [PubMed]
  28. N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise-reduction algorithm for fringe patterns,” Opt. Commun.270(2), 161–168 (2007). [CrossRef]
  29. M. B. Bernini, A. Federico, and G. H. Kaufmann, “Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform,” Appl. Opt.48(36), 6862–6869 (2009). [CrossRef] [PubMed]
  30. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt.43(13), 2695–2702 (2004). [CrossRef] [PubMed]
  31. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng.45(2), 304–317 (2007). [CrossRef]
  32. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1999).
  33. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley & Sons, Inc, 1998).
  34. M. Zhao, L. Huang, Q. Zhang, X. Y. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt.50(33), 6214–6224 (2011). [CrossRef] [PubMed]
  35. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, London, 1998), Chap. 5.

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