Regenerated phase-shifted sinusoids assisted EMD for adaptive analysis of fringe patterns

Abstract Fringe patterns are often produced from optical metrology. It is important yet challenging to reduce noise and remove a complicated background in a fringe pattern, for which empirical mode decomposition based methods have been proven useful. However, the mode-mixing problem and the difficulty in automatic mode classification limit the application of these methods. In this paper, a newly developed method named regenerated phase-shifted sinusoids assisted empirical mode decomposition is introduced to decompose a fringe pattern, and subsequently, a new noise-signal-background classification strategy is proposed. The former avoids the mode-mixing problem appearing during the decomposition, while the latter adaptively classifies the decomposition results to remove the noise and background. The proposed method is testified by both simulation and real experiments, which shows effective and robust for fringe pattern analysis under different noise, fringe modulation, and defects.

[1]  Pierre Jacquot,et al.  The empirical mode decomposition: a must-have tool in speckle interferometry? , 2009, Optics express.

[2]  Jingang Zhong,et al.  Generalized Fourier analysis for phase retrieval of fringe pattern. , 2010, Optics express.

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

[4]  Wilson Wang,et al.  An enhanced Hilbert–Huang transform technique for bearing condition monitoring , 2013 .

[5]  Norden E. Huang,et al.  The Multi-Dimensional Ensemble Empirical Mode Decomposition Method , 2009, Adv. Data Sci. Adapt. Anal..

[6]  Xianyu Su,et al.  Wavelet ridge techniques in optical fringe pattern analysis. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  Alejandro Federico,et al.  Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform. , 2009, Applied optics.

[8]  Feipeng Da,et al.  Windowed Fourier transform profilometry based on improved S-transform. , 2012, Optics letters.

[9]  A. Bovik,et al.  A universal image quality index , 2002, IEEE Signal Processing Letters.

[10]  Maciej Trusiak,et al.  Hilbert-Huang processing for single-exposure two-dimensional grating interferometry. , 2013, Optics express.

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

[12]  Krzysztof Patorski,et al.  Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform. , 2012, Optics express.

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

[14]  Patrick Flandrin,et al.  A complete ensemble empirical mode decomposition with adaptive noise , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[15]  Wei-Hung Su,et al.  Noise-reduction for fringe analysis using the empirical mode decomposition with the generalized analysis model , 2010 .

[16]  Danilo P. Mandic,et al.  Emd via mEMD: multivariate noise-Aided Computation of Standard EMD , 2013, Adv. Data Sci. Adapt. Anal..

[17]  María Eugenia Torres,et al.  Improved complete ensemble EMD: A suitable tool for biomedical signal processing , 2014, Biomed. Signal Process. Control..

[18]  R. Sharpley,et al.  Analysis of the Intrinsic Mode Functions , 2006 .

[19]  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.

[20]  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.

[21]  Feipeng Da,et al.  Phase retrieval for noisy fringe pattern by using empirical mode decomposition and Hilbert Huang transform , 2012 .

[22]  Chunmin Zhang,et al.  Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer. , 2013, Optics express.

[23]  Yi Zhou,et al.  Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition. , 2011, Optics express.

[24]  Mostefa Mesbah,et al.  A sampling limit for the empirical mode decomposition , 2005, Proceedings of the Eighth International Symposium on Signal Processing and Its Applications, 2005..

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

[26]  Maciej Trusiak,et al.  Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition , 2014 .

[27]  Qican Zhang,et al.  Dynamic 3-D shape measurement method: A review , 2010 .

[28]  Feipeng Da,et al.  Regenerated Phase-Shifted Sinusoid-Assisted Empirical Mode Decomposition , 2016, IEEE Signal Processing Letters.

[29]  Xiang Zhou,et al.  Morphological operation-based bi-dimensional empirical mode decomposition for automatic background removal of fringe patterns. , 2012, Optics express.

[30]  Qian Kemao,et al.  Statistical analysis for windowed Fourier ridge algorithm in fringe pattern analysis. , 2012, Applied optics.

[31]  Hongguang Li,et al.  A denoising scheme for DSPI fringes based on fast bi-dimensional ensemble empirical mode decomposition and BIMF energy estimation , 2013 .

[32]  Alejandro Federico,et al.  Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes , 2007 .

[33]  Wenjing Chen,et al.  Application of S-transform profilometry in eliminating nonlinearity in fringe pattern. , 2012, Applied optics.

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

[35]  Alejandro Federico,et al.  Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier. , 2008, Applied optics.