Abstract

In 3D shape measurement, because deformed fringes often contain low-frequency information degraded with random noise and background intensity information, a new fringe-projection profilometry is proposed based on 2D empirical mode decomposition (2D-EMD). The fringe pattern is first decomposed into numbers of intrinsic mode functions by 2D-EMD. Because the method has partial noise reduction, the background components can be removed to obtain the fundamental components needed to perform Hilbert transformation to retrieve the phase information. The 2D-EMD can effectively extract the modulation phase of a single direction fringe and an inclined fringe pattern because it is a full 2D analysis method and considers the relationship between adjacent lines of a fringe patterns. In addition, as the method does not add noise repeatedly, as does ensemble EMD, the data processing time is shortened. Computer simulations and experiments prove the feasibility of this method.

© 2013 Optical Society of America

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2012

2011

2010

2009

Z. H. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Adv. Adapt. Data Anal. 1, 1–41 (2009).
[CrossRef]

2007

2006

S. Zheng, W. Chen, and X. Su, “Adaptive windowed Fourier transform in 3-D shape measurement,” Opt. Eng. 45, 063601 (2006).
[CrossRef]

2004

2003

S. Yoneyama, Y. Morimoto, M. Fujigaki, and M. Yabe, “Phase-measuring profilometry of moving object without phase-shifting device,” Opt. Lasers Eng. 40, 153–161 (2003).
[CrossRef]

2001

1998

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

1997

1996

R. G. Stockwell, L. Mansinha, and R. P. Lowe, “Localization of the complex spectrum: the S transform,” IEEE Trans. Signal Process. 44, 998–1001 (1996).
[CrossRef]

1983

Burton, D.

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in windowed Fourier transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284, 2797–2807 (2011).
[CrossRef]

Chen, W.

M. Zhong, W. Chen, and M. Jiang, “Application of S-transform profilometry in eliminating nonlinearity in fringe pattern,” Appl. Opt. 51, 577–587 (2012).
[CrossRef]

S. Zheng, W. Chen, and X. Su, “Adaptive windowed Fourier transform in 3-D shape measurement,” Opt. Eng. 45, 063601 (2006).
[CrossRef]

Coskun, E.

Da, F.

C. Wang and F. Da, “Phase retrieval for noisy fringe pattern by using empirical mode decomposition and Hilbert Huang transform,” Opt. Eng. 51, 061306 (2012).
[CrossRef]

Fernandez, S.

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in windowed Fourier transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284, 2797–2807 (2011).
[CrossRef]

Fujigaki, M.

S. Yoneyama, Y. Morimoto, M. Fujigaki, and M. Yabe, “Phase-measuring profilometry of moving object without phase-shifting device,” Opt. Lasers Eng. 40, 153–161 (2003).
[CrossRef]

Gdeisat, M. A.

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in windowed Fourier transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284, 2797–2807 (2011).
[CrossRef]

Göktas, H.

Gu, Q.

Huang, N. E.

Z. H. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Adv. Adapt. Data Anal. 1, 1–41 (2009).
[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Jiang, M.

Kemao, Q.

Kinoshita, M.

Kocahan, Ö.

Li, H.

Li, W.

Liu, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Liu, Z.

Long, S. R.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Lowe, R. P.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, “Localization of the complex spectrum: the S transform,” IEEE Trans. Signal Process. 44, 998–1001 (1996).
[CrossRef]

Lun, D. P.-K.

Mansinha, L.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, “Localization of the complex spectrum: the S transform,” IEEE Trans. Signal Process. 44, 998–1001 (1996).
[CrossRef]

Morimoto, Y.

S. Yoneyama, Y. Morimoto, M. Fujigaki, and M. Yabe, “Phase-measuring profilometry of moving object without phase-shifting device,” Opt. Lasers Eng. 40, 153–161 (2003).
[CrossRef]

Mutoh, K.

Ng, W. W.-L.

Özder, S.

Patorski, K.

Pokorski, K.

Salvi, J.

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in windowed Fourier transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284, 2797–2807 (2011).
[CrossRef]

Shen, Z.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Shih, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Stockwell, R. G.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, “Localization of the complex spectrum: the S transform,” IEEE Trans. Signal Process. 44, 998–1001 (1996).
[CrossRef]

Su, X.

Takahashi, Y.

Takai, H.

Takeda, M.

Tung, C. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Wang, C.

C. Wang and F. Da, “Phase retrieval for noisy fringe pattern by using empirical mode decomposition and Hilbert Huang transform,” Opt. Eng. 51, 061306 (2012).
[CrossRef]

Wu, M. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Wu, Z. H.

Z. H. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Adv. Adapt. Data Anal. 1, 1–41 (2009).
[CrossRef]

Yabe, M.

S. Yoneyama, Y. Morimoto, M. Fujigaki, and M. Yabe, “Phase-measuring profilometry of moving object without phase-shifting device,” Opt. Lasers Eng. 40, 153–161 (2003).
[CrossRef]

Yen, N.-C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Yoneyama, S.

S. Yoneyama, Y. Morimoto, M. Fujigaki, and M. Yabe, “Phase-measuring profilometry of moving object without phase-shifting device,” Opt. Lasers Eng. 40, 153–161 (2003).
[CrossRef]

Zheng, Q.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

Zheng, S.

S. Zheng, W. Chen, and X. Su, “Adaptive windowed Fourier transform in 3-D shape measurement,” Opt. Eng. 45, 063601 (2006).
[CrossRef]

Zhong, M.

Zhou, Y.

Adv. Adapt. Data Anal.

Z. H. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Adv. Adapt. Data Anal. 1, 1–41 (2009).
[CrossRef]

Appl. Opt.

IEEE Trans. Signal Process.

R. G. Stockwell, L. Mansinha, and R. P. Lowe, “Localization of the complex spectrum: the S transform,” IEEE Trans. Signal Process. 44, 998–1001 (1996).
[CrossRef]

Opt. Commun.

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in windowed Fourier transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284, 2797–2807 (2011).
[CrossRef]

Opt. Eng.

C. Wang and F. Da, “Phase retrieval for noisy fringe pattern by using empirical mode decomposition and Hilbert Huang transform,” Opt. Eng. 51, 061306 (2012).
[CrossRef]

S. Zheng, W. Chen, and X. Su, “Adaptive windowed Fourier transform in 3-D shape measurement,” Opt. Eng. 45, 063601 (2006).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

S. Yoneyama, Y. Morimoto, M. Fujigaki, and M. Yabe, “Phase-measuring profilometry of moving object without phase-shifting device,” Opt. Lasers Eng. 40, 153–161 (2003).
[CrossRef]

Opt. Lett.

Proc. R. Soc. A

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. A 454, 903–995 (1998).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Projection system and fringe patterns obtained. (a) Traditional projection system. (b) Single direction fringe. (c) Inclined projection system. (d) Inclined fringe pattern.

Fig. 2.
Fig. 2.

Computer simulation. (a) Original object. (b) Deformed fringe pattern. (c) By Fourier transform. (d) Error by Fourier Transform. (e) Retrieved noise of (b) by 2D-EMD. (f) Retrieved fundamental component IMF of (b) by 2D-EMD. (g) By our method. (h) Error by our method.

Fig. 3.
Fig. 3.

Experiment. (a) A teacup lid. (b) Deformed fringe pattern. (c) Retrieved the noise of (b) by 2D-EMD. (d) Retrieved the fundamental component IMF of (b) by 2D-EMD. (e) By Fourier transform. (f) By our method.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

s(x,y)=i=1nci(x,y)+rn(x,y),
I(x,y)=I0(x,y)[1+V(x,y)cos(2πf0(x+y)+ϕ(x,y))]+n(x,y),
c(x,y)=I0(x,y)V(x,y)cos(2πf0(x+y)+ϕ(x,y)).
c^(x,y)=1πPc(ξ,η)(xξ)(yη)dξdη,
z(x,y)=c(x,y)+jc^(x,y)=λ(x,y)ejφ(x,y),
{λ(x,y)=c(x,y)2+c^(x,y)2φ(x,y)=arctan[c^(x,y)/c(x,y)].
1h(x,y)=a(x,y)+b(x,y)1ϕ(x,y)+d(x,y)1ϕ2(x,y),
I(x,y)=0.5[1+cos(2πf0(x+y)+ϕ(x,y))]+n(x,y),
ϕ(x,y)=15(1(x256)2+(y256)22002),

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