Demodulation of a Single Interferogram based on Bidimensional Empirical Mode Decomposition and Hilbert Transform

Authors

  • Said Amar  
  • Mustapha Bahich  
  • Hanane Dalimi  
  • Mohammed Bailich  
  • Bentahar Youness  
  • ElMostafa Barj  
  • Mohamed Afifi  

Keywords:

Interferometry, Fourier Transform, Bidimensional Empirical Mode Decomposition, dynamic analysis, Carrier Superposition, Phase Retrieval, wavelet transform

Abstract

The phase calculation is a powerful measurement technique that allows the reconstruction of 3D profiles from interferogram intensity. In this article a new phase extraction algorithm is presented. This algorithm uses the BEMD technique (Bidimensional Empirical Mode Decomposition) for the evaluation of the phase distribution from a single uncarrier interferogram. The proposed method requires the numerical addition of a high spatial frequency carrier and application of the wavelet transform or the Fourier transform. An evaluation was made through a numerical simulation on simulated and real fringes to validate and confirm the performance of the proposed algorithm. The main advantage of this technique is its ability to provide a metrological solution for the fast dynamic analysis.

References

  1. D.C. Williams,"Optical methods in engineering metrology". Chapman and Hall, First edition. (1993).
  2.  José Xavier, Identification de la variabilité des rigidités du bois à l’intérieur de l’arbre par la méthode des champs virtuels, PhD thesis, École Nationale Supérieure d’Arts et Métiers, 2007.
  3. M. Afifi, these d’état, Université Hassan II Mohammedia, (2002).
  4. N. E. Huang, Z. Shen and S. R. Long, ''The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis'' in: Proceedings of the Royal Society of London Series, 1998, 454, pp. 903- 995.
  5. G. Rilling, P. Flandrin, “On empirical mode decomposition and its algorithms”, in: IEEE–EURASIP Workshop Nonlinear Signal Image Process, Grado, Italy, 2003.
  6. Cexus Jean-Christophe," Analyse des signaux non stationnaires par Transformation de Huang,Opérateur de Teager-Kaiser, et Transformation de Huang-Teager (THT)" these de Doctorat, 2005.
  7. EB Saff, AD Snider, “Complex analysis for mathematics, science and engineering”, Prentice- Hall Inc, New York, (1976).
  8. M Bahich, M Afifi, EM Barj, “Optical phase extraction algorithm based on the continuous wavelet and the Hilbert transforms”, Journal Of Computing, vol.2, 5, (2010)
  9. Q. Kemao, et al., Wavelets in optical metrology, in: K. Singh, V.K. Rastogi (Eds.), Perspectives in Engineering Optics, 2003, pp. 117–133.
  10. D.C. Ghiglia, M.D. Pritt, Two-dimensional Phase Unwrapping: Theory Algorithms and Software, Wiley, New York, 1998.

International Journal of Scientific Research in Science and Technology

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Published

2016-08-30

Issue

Volume 2, Issue 4, July-August-2016

Section

Research Articles

License

Copyright (c) IJSRST

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Said Amar, Mustapha Bahich, Hanane Dalimi, Mohammed Bailich, Bentahar Youness, ElMostafa Barj, Mohamed Afifi, " Demodulation of a Single Interferogram based on Bidimensional Empirical Mode Decomposition and Hilbert Transform, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 2, Issue 4, pp.83-89, July-August-2016.