Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations.

We propose an application for a bidimensional empirical mode decomposition and a Hilbert transform algorithm (BEMD-HT) in processing amplitude modulated fringe patterns. In numerical studies we investigate the influence of parameters of the algorithm and a fringe pattern under study on the demodulation results to optimize the procedure. A spiral phase method and the angle-oriented partial Hilbert transform are introduced to the BEMD-HT and tested. A postprocessing filtration method for BEMD-HT is proposed. Results of processing experimental data, such as vibration mode patterns obtained by time-average interferometry, correspond richly with numerical findings. They compare very well with the results of our previous investigations using the temporal phase-shifting (TPS) method and the continuous wavelet transform (CWT). Not needing to perform phase-shifting represents significant simplification of the experimental procedure in comparison with the TPS method.

[1]  Robert J. Sanford,et al.  Interpretation of fringes in stress-holo-interferometry , 1971 .

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

[3]  Olof Bryngdahl,et al.  Characteristics of superposed patterns in optics , 1976 .

[4]  Horst Schreiber,et al.  Phase Shifting Interferometry , 2006 .

[5]  M. Nisida,et al.  A new interferomemtric method of two-dimensional stress analysis , 1964 .

[6]  Qifeng Yu,et al.  A combined method for obtaining fringe orientations of ESPI , 2007 .

[7]  Haizhang Zhang,et al.  Characterizing the Hilbert transform by the Bedrosian theorem , 2008 .

[8]  B. Chatelain.  Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process , 1973 .

[9]  Christophe Damerval,et al.  A fast algorithm for bidimensional EMD , 2005, IEEE Signal Processing Letters.

[10]  Krzysztof Patorski,et al.  Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination. , 2007, Applied optics.

[11]  J. Schwider,et al.  IV Advanced Evaluation Techniques in Interferometry , 1990 .

[12]  Krzysztof Patorski,et al.  Active microelement testing by interferometry using time-average and quasi-stroboscopic techniques , 2003, SPIE Optical Metrology.

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

[14]  Krzysztof Patorski,et al.  Fizeau interferometer for quasi parallel optical plate testing , 2008, Optical Engineering + Applications.

[15]  Robert X. Gao,et al.  Midpoint-based empirical decomposition for nonlinear trend estimation , 2009, 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[16]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

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

[18]  Bor-Wen Shiau,et al.  Phase shifting interferometry of cold atoms. , 2011, Optics express.

[19]  Kieran G. Larkin,et al.  Efficient nonlinear algorithm for envelope detection in white light interferometry , 1996 .

[20]  Silong Peng,et al.  Texture classification through directional empirical mode decomposition , 2004, ICPR 2004.

[21]  Thomas Bülow,et al.  Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case , 2001, IEEE Trans. Signal Process..

[22]  Thomas Bülow,et al.  Riesz Transforms for the Isotropic Estimation of the Local Phase of Moiré Interferograms , 2000, DAGM-Symposium.

[23]  R Czarnek,et al.  Real-time optical differentiation for moire interferometry. , 1987, Applied optics.

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

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

[26]  Krzysztof Patorski,et al.  Interferogram intensity modulation calculations using temporal phase shifting: error analysis , 2006 .

[27]  Jean Claude Nunes,et al.  Image analysis by bidimensional empirical mode decomposition , 2003, Image Vis. Comput..

[28]  Alejandro Federico,et al.  Phase recovery in temporal speckle pattern interferometry using the generalized S-transform. , 2008, Optics letters.

[29]  Sylvain Petitgrand,et al.  Application of microscopic interferometry techniques in the MEMS field , 2003, SPIE Optical Metrology.

[30]  Krzysztof Patorski,et al.  Phase-shifting method contrast calculations in time-averaged interferometry: error analysis , 2005 .

[31]  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.

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

[33]  Alejandro Federico,et al.  Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition. , 2008, Applied optics.

[34]  Minvydas Ragulskis,et al.  Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré , 2005 .

[35]  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.

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

[37]  Michael Felsberg,et al.  The monogenic signal , 2001, IEEE Trans. Signal Process..

[38]  Krzysztof Patorski,et al.  Visualization of additive-type moiré and time-average fringe patterns using the continuous wavelet transform. , 2010, Applied optics.

[39]  Alejandro Federico,et al.  Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition. , 2011, Applied optics.

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

[41]  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.

[42]  Pierre Jacquot,et al.  Phase Extraction in Dynamic Speckle Interferometry with Empirical Mode Decomposition and Hilbert Transform , 2010 .

[43]  Y. Ishii,et al.  Signal processing of interferogram using a two-dimensional discrete Hilbert transform , 2006 .

[44]  G O Rosvold,et al.  Video-based vibration analysis using projected fringes. , 1994, Applied optics.

[45]  H. Osterberg,et al.  An Interferometer Method of Studying the Vibrations of an Oscillating Quartz Plate , 1932 .

[46]  Sylvain Petitgrand,et al.  Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization , 2001, Lasers in Metrology and Art Conservation.

[47]  Krzysztof Patorski,et al.  Examination of singular scalar light fields using wavelet processing of fork fringes. , 2011, Applied optics.

[48]  Y. Y. Hung,et al.  Moiré contour-sum contour-difference, and vibration analysis of arbitrary objects. , 1971, Applied optics.