Abstract

An approach based on a novel technique, called ensemble empirical mode decomposition, is proposed to adaptively reduce noise and remove background intensity from a two-dimensional fringe pattern. It can solve the mode-mixing problem of the original empirical mode decomposition caused by the existence of intermittent noise in fringe signals. Then a strategy is developed to automatically identify and group the resulting intrinsic mode functions for the purpose of eliminating noise and background of the fringe pattern. This approach is applied to process the simulated and practical fringe patterns, compared with Fourier transform and wavelet methods.

© 2009 Optical Society of America

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Z. Wu and N. E. Huang, Ensemble Empirical Mode Decomposition: a Noise Assisted Data Analysis Method, Tech. Rep. No. 193 (Centre for Ocean-Land-Atmosphere Studies, 2005).

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N. E. Huang, Z. Shen, S. R. Long, M. L. C. Wu, H. H. Shih, Q. N. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, Proc. R. Soc. London, Ser. A 454, 903 (1998).
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N. E. Huang, Z. Shen, S. R. Long, M. L. C. Wu, H. H. Shih, Q. N. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, Proc. R. Soc. London, Ser. A 454, 903 (1998).
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Appl. Opt.

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M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, Opt. Lasers Eng. 45, 723 (2007).
[CrossRef]

Opt. Lett.

Proc. R. Soc. London, Ser. A

N. E. Huang, Z. Shen, S. R. Long, M. L. C. Wu, H. H. Shih, Q. N. Zheng, N. C. Yen, C. C. Tung, and H. H. Liu, Proc. R. Soc. London, Ser. A 454, 903 (1998).
[CrossRef]

Other

Z. Wu and N. E. Huang, Ensemble Empirical Mode Decomposition: a Noise Assisted Data Analysis Method, Tech. Rep. No. 193 (Centre for Ocean-Land-Atmosphere Studies, 2005).

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Figures (6)

Fig. 1
Fig. 1

(a) Simulated noisy fringe pattern and (b) its 256th row signal.

Fig. 2
Fig. 2

Averaged IMFs (c1–c5) and overall trend (c6) extracted by the EEMD (continuous curve) and by EMD (dotted curve).

Fig. 3
Fig. 3

(a) Variations in P ( K ) and (b) its ratio waveform R ( K ) for grouping IMFs.

Fig. 4
Fig. 4

(a) Retrieved fundamental frequency component of the 256th row by the proposed approach; (b) phase distributions: ideal (continuous curve), using the proposed approach (dashed curve), Fourier transform (dotted curve), and continuous wavelet (dashed-dotted curve) methods, respectively.

Fig. 5
Fig. 5

(a) Noise, (b) fundamental frequency component, and (c) background of the fringe pattern by the proposed approach.

Fig. 6
Fig. 6

(a) Deformed fringe pattern on a face model, (b) noise, (c) fundamental frequency component, (d) background of the fringe pattern by the proposed approach, (e) absolute phase extracted by Hilbert transform.

Equations (4)

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I ( x ) = a ( x ) + b ( x ) cos   ϕ ( x ) + n ( x ) ,
I ( x ) = j = 1 N d j ( x ) + r N ( x ) ,
I ( x ) = j = 1 K d ¯ j ( x ) + j = K + 1 N d ¯ j ( x ) + r ¯ N ( x ) ,
P ( K ) = [ r s ( x ) ] 2 d x [ r n ( x ) ] 2 d x ,

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