OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 2 — Jan. 19, 2009
  • pp: 611–623

The empirical mode decomposition: a must-have tool in speckle interferometry?

Sébastien Equis and Pierre Jacquot  »View Author Affiliations


Optics Express, Vol. 17, Issue 2, pp. 611-623 (2009)
http://dx.doi.org/10.1364/OE.17.000611


View Full Text Article

Acrobat PDF (455 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In a wider and wider range of research and engineering activities, there is a growing interest for full-field techniques, featuring nanometric sensitivities, and able to be addressed to dynamic behaviors characterization. Speckle interferometry (SI) techniques are acknowledged as good candidates to tackle this challenge. To get rid of the intrinsic correlation length limitation and simplify the unwrapping step, a straightforward approach lies in the pixel history analysis. The need of increasing performances in terms of accuracy and computation speed is ermanently demanding new efficient processing techniques. We propose in this paper a fast implementation of the Empirical Mode Decomposition (EMD) to put the SI pixel signal in an appropriate shape for accurate phase computation. As one of the best way to perform it, the analytic method based on the Hilbert transform (HT) of the so-transformed signal will then be reviewed. For short evaluation, a zero-crossing technique which exploits directly the extrema finding step of the EMD will be presented. We propose moreover a technique to discard the under-modulated pixels which yield wrong phase evaluation. This work is actually an attempt to elaborate a phase extraction procedure which exploits all the reliable information in 3D, – two space and one time coordinates –, to endeavor to make the most of SI raw data.

© 2009 Optical Society of America

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(070.2025) Fourier optics and signal processing : Discrete optical signal processing
(120.6165) Instrumentation, measurement, and metrology : Speckle interferometry, metrology

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: November 6, 2008
Revised Manuscript: December 22, 2008
Manuscript Accepted: December 23, 2008
Published: January 7, 2009

Citation
Sébastien Equis and Pierre Jacquot, "The empirical mode decomposition: a must-have tool in speckle interferometry?," Opt. Express 17, 611-623 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-2-611


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. Cf. Proceedings of the "Fringe" Conferences Series, as e.g.: Osten W. and Jüptner W. Eds., Elsevier (2001), Osten W. Ed., Springer (2005).
  2. K. Creath, Interferogram Analysis (Institute of Physics Publishing, Bristol, UK, 1993), Chap. 4.
  3. J. M. Huntley and H. Saldner, "Temporal phase-unwrapping algorithm for automated interferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
  4. X. Colonna de Lega and P. Jacquot, "Deformation measurement with object-induced dynamic phase-shifting," Appl. Opt. 35, 5115-5121 (1996). [CrossRef]
  5. L. Bruno, "Global approach for fitting 2D interferometric data," Opt. Express 15, 4835-4847 (2007). [CrossRef]
  6. E. Robin and V. Valle, "Phase demodulation method from a single fringe pattern based on correlation technique with a polynomial form," Appl. Opt. 34, 7261-7269 (2005). [CrossRef]
  7. 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]
  8. D.J. Bone, H.-A. Bachor, and R. J. Sandeman, "Fringe-pattern analysis using a 2D Fourier transform," Appl. Opt. 25, 1653-1660 (1986).
  9. K. G. Larkin, D. J. Bone, and M. A. Oldfield, "Natural demodulation of two-dimensional fringe patterns - Part I," J. Opt. Soc. Am. A 18, 1862-1881 (2001). [CrossRef]
  10. J. L. Marroquin, M. Rivera, S. Botello, R. Rodriguez-Vera, and M. Servin, "Regularization methods for processsing fringe-pattern images," Appl. Opt. 38, 788-794 (1999). [CrossRef]
  11. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping (Wiley-Interscience Publication, New-York, 1998).
  12. H. A. Aebischer and S. Waldner, "A simple and effective method for filtering speckle interferometric phase fringe patterns," Opt. Commun. 162, 205-210 (1999). [CrossRef]
  13. M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, "Wavelet processing of interferometric signals and fringe patterns," Proc. SPIE 3813, 692-702 (1999).
  14. V. D. Madjarova, H. Kadono, and S. Toyooka, "Dynamic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform," Opt. Express 11, 617-623 (2003).
  15. S. Equis, A. Baldi, and P. Jacquot, "Phase extraction in dynamic speckle interferometry by empirical mode decomposition," in Proceedings of the International Conference in Experimental Mechanics, E.E. Gdoutos, ed. (Springer, Dordrecht, The Netherlands, 2007), pp. 719-720 & CD-Rom.
  16. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, "The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis," Proc. R. Soc. London Ser. A 454, 903-995 (1998). [CrossRef]
  17. G. Rilling, P. Flandrin, and P. Gonçalves, "On empirical mode decomposition and its algorithms," in Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image ProcessingNSIP-03 (2003).
  18. N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, and K. L. Fan, "A confidence limit for the empirical mode decomposition and Hilbert spectral analysis," Proc. R. Soc. London Ser. A 459, 2317-2345 (2003). [CrossRef]
  19. A. Federico and G. Kaufmann, "Evaluation of dynamic speckle activity using the empirical mode decomposition," Opt. Commun. 267, 287-294 (2006). [CrossRef]
  20. F. A. Marengo Rodriguez, A. Federico, and G. H. Kaufmann, "Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition," Opt. Commun. 275, 38-41 (2007). [CrossRef]
  21. S. Equis and P. Jacquot, "Phase extraction in dynamic speckle interferometry by empirical mode decomposition," Strain (to be published).
  22. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill Book Company, 1965).
  23. E. Bedrosian, "A product theorem for Hilbert transforms," Proc. IEEE 51, 868-869 (1963). [CrossRef]
  24. D. Vakman, "On the analytic signal, the Teager-Kaiser algorithm, and other methods for defining amplitude and frequency," IEEE Trans. Sig. Proc. 44, 791-797 (1996). [CrossRef]
  25. B. Boashash, "Estimating and interpreting the instantaneous frequency of a signal," Proc. IEEE 80, 520-568 (1992). [CrossRef]
  26. M. LehmannDigital Speckle Pattern Interferometry and Related Techniques (John Wiley & Sons, Ltd, Chichester, 2001), Chap. 1.
  27. G. Rilling, P. Flandrin, and P. Gonçalves, "On Empirical Mode Decomposition and its algorithms", Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03 (2003).
  28. K. Zeng and M.-X. He, "A simple boundary process technique for empirical mode decomposition," IEEE Int. Geosci. Remote Sensing 6, 4258-4261 (2004).
  29. N. Stevenson, M. Mesbah, and B. Boashash, "A sampling limit for the empirical mode decomposition," in Proceedings of International Symposium on Signal Processing and its ApplicationsISSPA-05, 647-650 (2005).
  30. G. Rilling and P. Flandrin, "On the influence of sampling on the empirical mode decomposition," in Proceedings of IEEE International Conference on Acoustic, Speech and Signal ProcessingICASSP-06 (2006).
  31. http://perso.ens-lyon.fr/patrick.flandrin/publis.html
  32. G. Rilling and P. Flandrin, "One or two frequencies? The empirical mode decomposition answers," IEEE Trans. Sig. Proc. 56, 85-95 (2008). [CrossRef]
  33. S. Equis and P. Jacquot, "Simulation of speckle complex amplitude: advocating the linear model," Proc. SPIE 6841, 634138−1-634138−6 (2006).
  34. E. Vikhagen, "Nondestructive testing by use of TV holography and deformation phase gradient calculation," Appl. Opt. 29, 137-144 (1990).
  35. W. An and T. E. Carlsson, "Speckle interferometry for measurement of continuous deformations," Opt. Lasers Eng. 40, 529-541 (2003). [CrossRef]
  36. www.qhull.org

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.

Supplementary Material


» Media 1: MOV (2912 KB)     
» Media 2: MOV (2691 KB)     
» Media 3: MOV (2000 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited