Empirical mode decomposition profilometry: small-scale capabilities and comparison to Fourier transform profilometry.

We present the empirical mode decomposition profilometry (EMDP) for the analysis of fringe projection profilometry (FPP) images. It is based on an iterative filter, using empirical mode decomposition, which is free of spatial filtering and adapted for surfaces characterized by a broadband spectrum of deformation. Its performances are compared to Fourier transform profilometry, the benchmark of FPP. We show both numerically and experimentally that using EMDP improves strongly the profilometry small-scale capabilities. Moreover, the height reconstruction distortion is much lower: the reconstructed height field is now both spectrally and statistically accurate. EMDP is thus particularly suited to quantitative experiments.

[1]  Feipeng Da,et al.  Differential signal-assisted method for adaptive analysis of fringe pattern. , 2014, Applied optics.

[2]  Yiping Cao,et al.  Fringe-projection profilometry based on two-dimensional empirical mode decomposition. , 2013, Applied optics.

[3]  Xianyu Su,et al.  Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  Norden E. Huang,et al.  On Instantaneous Frequency , 2009, Adv. Data Sci. Adapt. Anal..

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

[6]  A. Maurel,et al.  Different regimes for water wave turbulence. , 2011, Physical review letters.

[7]  A. Maurel,et al.  Space-time resolved wave turbulence in a vibrating plate. , 2009, Physical review letters.

[8]  Nikolaos E. Myridis.  Handbook of 3D Machine Vision: Optical Metrology and Imaging, Series in Optics and Optoelectronics, edited by Song Zhang , 2013 .

[9]  Xiang Zhou,et al.  Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm. , 2009, Optics letters.

[10]  Vincent Pagneux,et al.  Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry. , 2009, Applied optics.

[11]  Wenjing Chen,et al.  ERROR CAUSED BY SAMPLING IN FOURIER TRANSFORM PROFILOMETRY , 1999 .

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

[13]  Xianyu Su,et al.  Fourier transform profilometry:: a review , 2001 .

[14]  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.

[15]  N. Huang,et al.  A new view of nonlinear water waves: the Hilbert spectrum , 1999 .

[16]  Norden E. Huang,et al.  A review on Hilbert‐Huang transform: Method and its applications to geophysical studies , 2008 .

[17]  Gabriel Rilling,et al.  Detrending and denoising with empirical mode decompositions , 2004, 2004 12th European Signal Processing Conference.

[18]  M. Takeda,et al.  Fourier transform profilometry for the automatic measurement of 3-D object shapes. , 1983, Applied optics.

[19]  Bing Zhao,et al.  Discussion on spatial resolution and sensitivity of Fourier transform fringe detection , 2000 .

[20]  Sai Siva Gorthi,et al.  Fringe projection techniques: Whither we are? , 2010 .

[21]  A. Maurel,et al.  Global measurement of water waves by Fourier transform profilometry , 2009 .

[22]  Gabriel Rilling,et al.  Empirical mode decomposition as a filter bank , 2004, IEEE Signal Processing Letters.

[23]  Feipeng Da,et al.  Phase demodulation using adaptive windowed Fourier transform based on Hilbert-Huang transform. , 2012, Optics express.

[24]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..