OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 6 — Jun. 1, 2008
  • pp: 1361–1370

Fast phase recovery from a single closed-fringe pattern

Oscar S. Dalmau-Cedeño, Mariano Rivera, and Ricardo Legarda-Saenz  »View Author Affiliations


JOSA A, Vol. 25, Issue 6, pp. 1361-1370 (2008)
http://dx.doi.org/10.1364/JOSAA.25.001361


View Full Text Article

Enhanced HTML    Acrobat PDF (1345 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A new framework for phase recovery from a single fringe pattern with closed fringes is proposed. Our algorithm constructs an unwrapped phase from previously computed phases with a simple open-fringe-analysis algorithm, twice applied for analyzing horizontal and vertical oriented fringes, respectively. That reduces the closed-fringe-analysis problem to that of choosing the better phase between the two oriented computed phases and then of estimating the local sign. By propagating the phase sign [and a tilewise constant (DC) term] by regions [here named tiles] instead of a pixelwise phase propagation, our analysis of closed-fringe patterns becomes more robust and faster. Additionally, we propose a multigrid refinement for improving the final computed phase.

© 2008 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
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: October 31, 2007
Manuscript Accepted: March 10, 2008
Published: May 19, 2008

Citation
Oscar S. Dalmau-Cedeño, Mariano Rivera, and Ricardo Legarda-Saenz, "Fast phase recovery from a single closed-fringe pattern," J. Opt. Soc. Am. A 25, 1361-1370 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-6-1361


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. 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, 1536-1544 (1998). [CrossRef]
  2. K. G. Larkin, D. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background to the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862-1870 (2001). [CrossRef]
  3. K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1871-1881 (2001). [CrossRef]
  4. K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operator,” Opt. Express 13, 8097-8121 (2005). [CrossRef] [PubMed]
  5. M. Servin, J. Marroquin, and F. Cuevas, “Demodulation of a single interferogram by use of a two-dimesional regularized phase-tracking technique,” Appl. Opt. 36, 4540-4548 (1997). [CrossRef] [PubMed]
  6. M. Servin, J. Marroquin, and J. A. Quiroga, “Regularized quadrature and phase tracking from a single closed-fringe interferogram,” J. Opt. Soc. Am. A 21, 411-419 (2004). [CrossRef]
  7. R. Legarda-Saenz and M. Rivera, “Fast half-quadratic regularized phase tracking for non normalized fringe patterns,” J. Opt. Soc. Am. A 23, 2724-2731 (2006). [CrossRef]
  8. M. Rivera, “Robust phase demodulation of interferograms with open and closed fringes,” J. Opt. Soc. Am. A 22, 1170-1175 (2005). [CrossRef]
  9. J. A. Guerrero, J. L. Marroquin, M. Rivera, and J. A. Quiroga, “Adaptive monogenic filtering and normalization of ESPI fringe patterns,” Opt. Lett. 30, 3018-3020 (2005). [CrossRef] [PubMed]
  10. J. C. Estrada, M. Servin, and J. L. Marroquin, “Local adaptable quadrature filters to demodulate single fringe patterns with closed fringes,” Opt. Express 15, 2288-2298 (2007). [CrossRef] [PubMed]
  11. 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. A 14, 1742-1753 (1997). [CrossRef]
  12. Q. Kemao and H. Soon, “Sequential demodulation of a single fringe pattern guided by local frequencies,” Opt. Lett. 32, 127-129 (2007). [CrossRef]
  13. W. W. Macy, “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22, 3898-3901 (1983). [CrossRef] [PubMed]
  14. T. Kreis, “Digital holographic interference-phase measurement using the Fourier transform method,” J. Opt. Soc. Am. A 3, 847-855 (1986). [CrossRef]
  15. T. R. Judge, C. Quan, and P. J. Bryanston Cross, “Holographic deformation measurements by Fourier transform technique with automatic phase unwrapping,” Opt. Eng. (Bellingham) 31, 533-543 (1992). [CrossRef]
  16. H. Knutsson, “A tensor representation of 3-D structure,” in 5th IEEE-ASSP and EURASIP Workshop on Multidimensional Signal Processing (IEEE, 1987), poster presentation.
  17. M. Rivera, R. Bizuet, A. Martínez, and J. A. Rayas, “Half-quadratic cost for computing arbitrary phase shifts and phase: adaptive out of step phase shifting,” Opt. Express 14, 3204-3213 (2006). [CrossRef] [PubMed]
  18. X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286-292 (2007). [CrossRef]
  19. H. Knutsson, “Representing local structure using tensors,” in The 6th Scandinavian Conference on Image Analysis (Report LiTH-ISY-I-1019, Computer Vision Laboratory, Linköping University, 1989), pp. 244-251.
  20. H. Knutsson and M. Andersson, “Implications of invariance and uncertainty for local structure analysis filter sets,” Signal Process. Image Commun. 20, 569-581 (2000). [CrossRef]
  21. B. Jähne, Digital Image Processing; Concepts, Algorithms, and Scientific Applications, 2nd ed. (Springer-Verlag, 1991). [PubMed]
  22. L. Haglund, H. Knutsson, and G. H. Granlund, “Scale and orientation adaptive filtering,” in Proceedings of the 8th Scandinavian Conference on Image Analysis (NOBIM, May 1993, Report LiTH-ISY-I-1527, Computer Vision Laboratory, Linköping University, 1993), pp. 1-26.
  23. I. W. Bowler and K. Paler, “A Gabor filter approach to fringe analysis, in Proceedings of the International Conference on Pattern Recognition (ICPR'86) (ICPR, 1986), pp. 558-560.
  24. M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136-3144 (2001). [CrossRef]
  25. K. H. Womak, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. (Bellingham) 23, 391-395 (1984).
  26. 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, 156-160 (1982). [CrossRef]
  27. M. Rivera and J. L. Marroquin, “Half-quadratic cost functions for phase unwrapping,” Opt. Lett. 29, 504-506 (2004). [CrossRef] [PubMed]
  28. W. L. Briggs, V. E. Henson, and S. F. McCormick, A Multigrid Tutorial, 2nd ed. (SIAM, 2000). [CrossRef]
  29. M. D. Pritt, “Multigrid phase unwrapping for interferometric SAR,” in Proceedings of IGARSS (IGARSS, 1995), Vol. 1, pp. 562-564.
  30. S. Botello, J. L. Marroquin, and M. Rivera, “Multigrid algorithms for processing fringe pattern images,” Appl. Opt. 37, 7587-7595 (1998). [CrossRef]
  31. G. Dardyk and I. Yavneh, “A multigrid approach to two-dimensional phase unwrapping,” Numer. Linear Algebra Appl. 11, 241-259 (2004). [CrossRef]
  32. D. J. Fleet and Y. Weiss, “Optical flow estimation,” in Mathematical Models for Computer Vision: The Handbook, N.Paragios, Y.Chen, and O.Faugeras, eds. (Springer, 2005), Chap. 4.
  33. A. P. Witkin, “Scale-space filtering,” in Proceedings of the 8th International Joint Conference on Artificial Intelligence (Morgan Kaufmann, 1983), 1019-1021.
  34. J. J. Koenderink, “The structure of images,” Biol. Cybern. 50, 363-370 (1984). [CrossRef] [PubMed]
  35. J. A. Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun. 224, 221-227 (2003). [CrossRef]

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