Phase Extraction in Dynamic Speckle Interferometry with Empirical Mode Decomposition and Hilbert Transform

In many respects, speckle interferometry (SI) techniques are being considered as mature tools in the experimental mechanics circles. These techniques have enlarged considerably the field of optical metrology, featuring nanometric sensitivities in whole-field measurements of profile, shape and deformation of mechanical rough surfaces. Nonetheless, when we consider classical fringe processing techniques, e.g. phase-shifting methods, the deformation range is intrinsically limited to the correlation volume of the speckle field. In addition, the phase evaluation from such patterns is still computationally intensive, especially in the characterisation of dynamic regimes, for which there is a growing interest in a wide range of research and engineering activities. A promising approach lies in the pixel history analysis. We propose in this paper to implement the empirical mode decomposition (EMD) algorithm in a fast way, to put the pixel signal in an appropriate shape for accurate phase computation with the Hilbert transform. © 2008 Blackwell Publishing Ltd.

[1]  Gabriel Rilling,et al.  on the Influence of Sampling on the Empirical Mode Decomposition , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[2]  K. W. Cattermole.  The Fourier Transform and its Applications , 1965 .

[3]  Xavier Colonna de Lega,et al.  Wavelet processing of interferometric signals and fringe patterns , 1999, Optics & Photonics.

[4]  P Jacquot,et al.  Deformation measurement with object-induced dynamic phase shifting. , 1996, Applied optics.

[5]  E Vikhagen,et al.  Nondestructive testing by use of TV holography and deformation phase gradient calculation. , 1990, Applied optics.

[6]  Pierre Jacquot,et al.  Phase Extraction in Dynamic Speckle Interferometry by Empirical Mode Decomposition , 2007 .

[7]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.

[8]  Satoru Toyooka,et al.  Dynamic electronic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform. , 2003, Optics express.

[9]  M. A. Oldfield,et al.  Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  P. Loughlin,et al.  On the amplitude‐ and frequency‐modulation decomposition of signals , 1996 .

[11]  L. Mandel.  Interpretation of Instantaneous Frequencies , 1974 .

[12]  Wei An,et al.  Speckle interferometry for measurement of continuous deformations , 2001, Lasers in Metrology and Art Conservation.

[13]  Gabriel Rilling,et al.  On empirical mode decomposition and its algorithms , 2003 .

[14]  S. S. Shen,et al.  A confidence limit for the empirical mode decomposition and Hilbert spectral analysis , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[15]  Guillermo H. Kaufmann.  Phase measurement in temporal speckle pattern interferometry using the Fourier transform method with and without a temporal carrier , 2003 .

[16]  M. Takeda,et al.  Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry , 1982 .

[17]  Valéry Valle,et al.  Phase demodulation method from a single fringe pattern based on correlation with a polynomial form. , 2005, Applied optics.

[18]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[19]  Alejandro Federico,et al.  Evaluation of dynamic speckle activity using the empirical mode decomposition method , 2006 .

[20]  E. Bedrosian.  A Product Theorem for Hilbert Transforms , 1963 .

[21]  D J Bone,et al.  Fringe-pattern analysis using a 2-D Fourier transform. , 1986, Applied optics.

[22]  K Larkin,et al.  A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns. , 2001, Optics express.

[23]  Alejandro Federico,et al.  Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition , 2007 .

[24]  K. Larkin.  Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.