Abstract

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with π phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

© 2009 Optical Society of America

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  1. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977-3982 (1983).
    [CrossRef] [PubMed]
  2. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
    [CrossRef]
  3. J. Li, X. Su, and L. Guo, “Improved Fourier transform profilometry of the automatic measurement of three-dimensional object shapes,” Opt. Eng. (Bellingham) 29, 1439-1444 (1990).
    [CrossRef]
  4. W. Chen, P. Bu, and S. Zheng, “Study on Fourier transform profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821-827 (2007).
    [CrossRef]
  5. W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43, 1267-1276 (2005).
    [CrossRef]
  6. Xu Qinghong, Zhong Yuexian, and You Zhifu, “Study on phase demodulation technique based on wavelet transform,” Acta Opt. Sin. 20, 1617-1622 (2000).
  7. M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482-489 (2006).
    [CrossRef]
  8. S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617-643 (1992).
    [CrossRef]
  9. S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674-693 (1989).
    [CrossRef]
  10. W. Chen, J. Sun, and X. Su, “Discuss the structure condition and sampling condition of wavelet transform profilometry,” J. Mod. Opt. 54, 2747-2762 (2007).
    [CrossRef]
  11. 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. London, Ser. A 454, 903-995 (1998).
    [CrossRef]
  12. F. Wu and L. Qu, “An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of large rotating machinery,” J. Sound Vib. 314, 586-602 (2008).
    [CrossRef]
  13. M. Blanco-Velasco, B. Weng, and K. E. Barner, “ECG signal denoising and baseline wander correction based on the empirical mode decomposition,” Comput. Biol. Med. 38, 1-13 (2008).
    [CrossRef]
  14. Q. Gao, C. Duan, H. Fan, and Q. Meng, “Rotating machine fault diagnosis using empirical mode decomposition,” Mech. Syst. Signal Process. 22, 1072-1081 (2008).
    [CrossRef]
  15. P. D. Spanos, A. Giaralis, and N. P. Politis, “Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition,” Soil Dyn. Earthquake Eng. 27, 675-689 (2002).
    [CrossRef]
  16. A. Boudraa and J. Cexus, “EMD-based signal filtering,” IEEE Trans. Instrum. Meas. 56, 2196-2202 (2007).
    [CrossRef]
  17. Tang Yan, Chen Wen-jing, and Su Xian-yu, “Neural network applied to reconstruction of complex objects based on fringe projection,” Opt. Commun. 278, 274-278 (2007).
    [CrossRef]
  18. N. E. Huang, “Introduction to the Hilbert-Huang transform and its related mathematical problems,” Interdisciplinary Mathematics 5, 1-26 (2005).
    [CrossRef]
  19. Zhao Zhidong and Wang Yang, “A new method for processing end effect in empirical mode decomposition,” in Proceedings of 2007 IEEE Conference on Communications, Circuits and Systems (IEEE, 2007), pp. 841-845.
  20. K. Zeng and M. He, “A simple boundary process technique for empirical mode decomposition,” in Proceedings of 2004 IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2004), pp. 4258-4261.
  21. G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” in IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, GRADO(I) (IEEE, 2003).
  22. R. Deering and J. F. Kaiser, “The use of a mask signal to improve empirical mode decomposition,” in Proceedings of IEEE 2005 Conference on Acoustics, Speech, and Signal Processing (IEEE, 2005), pp. 485-488.
    [CrossRef]
  23. C. Damerval and S. Meignen, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701-704 (2005).
    [CrossRef]
  24. G. Hu, Z. Ren, and Y. Tou “Symmetrical wavelet construction and its application for electrical machine fault signal reconstruction,” in Proceedings of the Fifth IEEE Conference on Machine Learning and Cybernetics (IEEE, 2006), pp. 3734-3737.
    [CrossRef]

2008

F. Wu and L. Qu, “An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of large rotating machinery,” J. Sound Vib. 314, 586-602 (2008).
[CrossRef]

M. Blanco-Velasco, B. Weng, and K. E. Barner, “ECG signal denoising and baseline wander correction based on the empirical mode decomposition,” Comput. Biol. Med. 38, 1-13 (2008).
[CrossRef]

Q. Gao, C. Duan, H. Fan, and Q. Meng, “Rotating machine fault diagnosis using empirical mode decomposition,” Mech. Syst. Signal Process. 22, 1072-1081 (2008).
[CrossRef]

2007

A. Boudraa and J. Cexus, “EMD-based signal filtering,” IEEE Trans. Instrum. Meas. 56, 2196-2202 (2007).
[CrossRef]

Tang Yan, Chen Wen-jing, and Su Xian-yu, “Neural network applied to reconstruction of complex objects based on fringe projection,” Opt. Commun. 278, 274-278 (2007).
[CrossRef]

W. Chen, P. Bu, and S. Zheng, “Study on Fourier transform profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821-827 (2007).
[CrossRef]

W. Chen, J. Sun, and X. Su, “Discuss the structure condition and sampling condition of wavelet transform profilometry,” J. Mod. Opt. 54, 2747-2762 (2007).
[CrossRef]

2006

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482-489 (2006).
[CrossRef]

2005

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43, 1267-1276 (2005).
[CrossRef]

N. E. Huang, “Introduction to the Hilbert-Huang transform and its related mathematical problems,” Interdisciplinary Mathematics 5, 1-26 (2005).
[CrossRef]

C. Damerval and S. Meignen, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701-704 (2005).
[CrossRef]

2002

P. D. Spanos, A. Giaralis, and N. P. Politis, “Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition,” Soil Dyn. Earthquake Eng. 27, 675-689 (2002).
[CrossRef]

2001

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

2000

Xu Qinghong, Zhong Yuexian, and You Zhifu, “Study on phase demodulation technique based on wavelet transform,” Acta Opt. Sin. 20, 1617-1622 (2000).

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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

1992

S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617-643 (1992).
[CrossRef]

1990

J. Li, X. Su, and L. Guo, “Improved Fourier transform profilometry of the automatic measurement of three-dimensional object shapes,” Opt. Eng. (Bellingham) 29, 1439-1444 (1990).
[CrossRef]

1989

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674-693 (1989).
[CrossRef]

1983

Barner, K. E.

M. Blanco-Velasco, B. Weng, and K. E. Barner, “ECG signal denoising and baseline wander correction based on the empirical mode decomposition,” Comput. Biol. Med. 38, 1-13 (2008).
[CrossRef]

Blanco-Velasco, M.

M. Blanco-Velasco, B. Weng, and K. E. Barner, “ECG signal denoising and baseline wander correction based on the empirical mode decomposition,” Comput. Biol. Med. 38, 1-13 (2008).
[CrossRef]

Boudraa, A.

A. Boudraa and J. Cexus, “EMD-based signal filtering,” IEEE Trans. Instrum. Meas. 56, 2196-2202 (2007).
[CrossRef]

Bu, P.

W. Chen, P. Bu, and S. Zheng, “Study on Fourier transform profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821-827 (2007).
[CrossRef]

Burton, D. R.

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482-489 (2006).
[CrossRef]

Cao, Y.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43, 1267-1276 (2005).
[CrossRef]

Cexus, J.

A. Boudraa and J. Cexus, “EMD-based signal filtering,” IEEE Trans. Instrum. Meas. 56, 2196-2202 (2007).
[CrossRef]

Chen, W.

W. Chen, P. Bu, and S. Zheng, “Study on Fourier transform profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821-827 (2007).
[CrossRef]

W. Chen, J. Sun, and X. Su, “Discuss the structure condition and sampling condition of wavelet transform profilometry,” J. Mod. Opt. 54, 2747-2762 (2007).
[CrossRef]

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43, 1267-1276 (2005).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Damerval, C.

C. Damerval and S. Meignen, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701-704 (2005).
[CrossRef]

Deering, R.

R. Deering and J. F. Kaiser, “The use of a mask signal to improve empirical mode decomposition,” in Proceedings of IEEE 2005 Conference on Acoustics, Speech, and Signal Processing (IEEE, 2005), pp. 485-488.
[CrossRef]

Duan, C.

Q. Gao, C. Duan, H. Fan, and Q. Meng, “Rotating machine fault diagnosis using empirical mode decomposition,” Mech. Syst. Signal Process. 22, 1072-1081 (2008).
[CrossRef]

Fan, H.

Q. Gao, C. Duan, H. Fan, and Q. Meng, “Rotating machine fault diagnosis using empirical mode decomposition,” Mech. Syst. Signal Process. 22, 1072-1081 (2008).
[CrossRef]

Flandrin, P.

G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” in IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, GRADO(I) (IEEE, 2003).

Gao, Q.

Q. Gao, C. Duan, H. Fan, and Q. Meng, “Rotating machine fault diagnosis using empirical mode decomposition,” Mech. Syst. Signal Process. 22, 1072-1081 (2008).
[CrossRef]

Gdeisat, M. A.

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482-489 (2006).
[CrossRef]

Giaralis, A.

P. D. Spanos, A. Giaralis, and N. P. Politis, “Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition,” Soil Dyn. Earthquake Eng. 27, 675-689 (2002).
[CrossRef]

Goncalves, P.

G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” in IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, GRADO(I) (IEEE, 2003).

Guo, L.

J. Li, X. Su, and L. Guo, “Improved Fourier transform profilometry of the automatic measurement of three-dimensional object shapes,” Opt. Eng. (Bellingham) 29, 1439-1444 (1990).
[CrossRef]

He, M.

K. Zeng and M. He, “A simple boundary process technique for empirical mode decomposition,” in Proceedings of 2004 IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2004), pp. 4258-4261.

Hu, G.

G. Hu, Z. Ren, and Y. Tou “Symmetrical wavelet construction and its application for electrical machine fault signal reconstruction,” in Proceedings of the Fifth IEEE Conference on Machine Learning and Cybernetics (IEEE, 2006), pp. 3734-3737.
[CrossRef]

Huang, N. E.

N. E. Huang, “Introduction to the Hilbert-Huang transform and its related mathematical problems,” Interdisciplinary Mathematics 5, 1-26 (2005).
[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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

Hwang, W. L.

S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617-643 (1992).
[CrossRef]

Kaiser, J. F.

R. Deering and J. F. Kaiser, “The use of a mask signal to improve empirical mode decomposition,” in Proceedings of IEEE 2005 Conference on Acoustics, Speech, and Signal Processing (IEEE, 2005), pp. 485-488.
[CrossRef]

Lalor, M. J.

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482-489 (2006).
[CrossRef]

Li, J.

J. Li, X. Su, and L. Guo, “Improved Fourier transform profilometry of the automatic measurement of three-dimensional object shapes,” Opt. Eng. (Bellingham) 29, 1439-1444 (1990).
[CrossRef]

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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

Mallat, S.

S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617-643 (1992).
[CrossRef]

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674-693 (1989).
[CrossRef]

Meignen, S.

C. Damerval and S. Meignen, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701-704 (2005).
[CrossRef]

Meng, Q.

Q. Gao, C. Duan, H. Fan, and Q. Meng, “Rotating machine fault diagnosis using empirical mode decomposition,” Mech. Syst. Signal Process. 22, 1072-1081 (2008).
[CrossRef]

Mutoh, K.

Politis, N. P.

P. D. Spanos, A. Giaralis, and N. P. Politis, “Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition,” Soil Dyn. Earthquake Eng. 27, 675-689 (2002).
[CrossRef]

Qinghong, Xu

Xu Qinghong, Zhong Yuexian, and You Zhifu, “Study on phase demodulation technique based on wavelet transform,” Acta Opt. Sin. 20, 1617-1622 (2000).

Qu, L.

F. Wu and L. Qu, “An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of large rotating machinery,” J. Sound Vib. 314, 586-602 (2008).
[CrossRef]

Ren, Z.

G. Hu, Z. Ren, and Y. Tou “Symmetrical wavelet construction and its application for electrical machine fault signal reconstruction,” in Proceedings of the Fifth IEEE Conference on Machine Learning and Cybernetics (IEEE, 2006), pp. 3734-3737.
[CrossRef]

Rilling, G.

G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” in IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, GRADO(I) (IEEE, 2003).

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. London, Ser. 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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

Spanos, P. D.

P. D. Spanos, A. Giaralis, and N. P. Politis, “Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition,” Soil Dyn. Earthquake Eng. 27, 675-689 (2002).
[CrossRef]

Su, X.

W. Chen, J. Sun, and X. Su, “Discuss the structure condition and sampling condition of wavelet transform profilometry,” J. Mod. Opt. 54, 2747-2762 (2007).
[CrossRef]

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43, 1267-1276 (2005).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

J. Li, X. Su, and L. Guo, “Improved Fourier transform profilometry of the automatic measurement of three-dimensional object shapes,” Opt. Eng. (Bellingham) 29, 1439-1444 (1990).
[CrossRef]

Sun, J.

W. Chen, J. Sun, and X. Su, “Discuss the structure condition and sampling condition of wavelet transform profilometry,” J. Mod. Opt. 54, 2747-2762 (2007).
[CrossRef]

Takeda, M.

Tou, Y.

G. Hu, Z. Ren, and Y. Tou “Symmetrical wavelet construction and its application for electrical machine fault signal reconstruction,” in Proceedings of the Fifth IEEE Conference on Machine Learning and Cybernetics (IEEE, 2006), pp. 3734-3737.
[CrossRef]

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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

Weng, B.

M. Blanco-Velasco, B. Weng, and K. E. Barner, “ECG signal denoising and baseline wander correction based on the empirical mode decomposition,” Comput. Biol. Med. 38, 1-13 (2008).
[CrossRef]

Wen-jing, Chen

Tang Yan, Chen Wen-jing, and Su Xian-yu, “Neural network applied to reconstruction of complex objects based on fringe projection,” Opt. Commun. 278, 274-278 (2007).
[CrossRef]

Wu, F.

F. Wu and L. Qu, “An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of large rotating machinery,” J. Sound Vib. 314, 586-602 (2008).
[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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

Xiang, L.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43, 1267-1276 (2005).
[CrossRef]

Xian-yu, Su

Tang Yan, Chen Wen-jing, and Su Xian-yu, “Neural network applied to reconstruction of complex objects based on fringe projection,” Opt. Commun. 278, 274-278 (2007).
[CrossRef]

Yan, Tang

Tang Yan, Chen Wen-jing, and Su Xian-yu, “Neural network applied to reconstruction of complex objects based on fringe projection,” Opt. Commun. 278, 274-278 (2007).
[CrossRef]

Yang, Wang

Zhao Zhidong and Wang Yang, “A new method for processing end effect in empirical mode decomposition,” in Proceedings of 2007 IEEE Conference on Communications, Circuits and Systems (IEEE, 2007), pp. 841-845.

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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

Yuexian, Zhong

Xu Qinghong, Zhong Yuexian, and You Zhifu, “Study on phase demodulation technique based on wavelet transform,” Acta Opt. Sin. 20, 1617-1622 (2000).

Zeng, K.

K. Zeng and M. He, “A simple boundary process technique for empirical mode decomposition,” in Proceedings of 2004 IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2004), pp. 4258-4261.

Zhang, Q.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43, 1267-1276 (2005).
[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. London, Ser. A 454, 903-995 (1998).
[CrossRef]

Zheng, S.

W. Chen, P. Bu, and S. Zheng, “Study on Fourier transform profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821-827 (2007).
[CrossRef]

Zhidong, Zhao

Zhao Zhidong and Wang Yang, “A new method for processing end effect in empirical mode decomposition,” in Proceedings of 2007 IEEE Conference on Communications, Circuits and Systems (IEEE, 2007), pp. 841-845.

Zhifu, You

Xu Qinghong, Zhong Yuexian, and You Zhifu, “Study on phase demodulation technique based on wavelet transform,” Acta Opt. Sin. 20, 1617-1622 (2000).

Acta Opt. Sin.

Xu Qinghong, Zhong Yuexian, and You Zhifu, “Study on phase demodulation technique based on wavelet transform,” Acta Opt. Sin. 20, 1617-1622 (2000).

Appl. Opt.

Comput. Biol. Med.

M. Blanco-Velasco, B. Weng, and K. E. Barner, “ECG signal denoising and baseline wander correction based on the empirical mode decomposition,” Comput. Biol. Med. 38, 1-13 (2008).
[CrossRef]

IEEE Signal Process. Lett.

C. Damerval and S. Meignen, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701-704 (2005).
[CrossRef]

IEEE Trans. Inf. Theory

S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617-643 (1992).
[CrossRef]

IEEE Trans. Instrum. Meas.

A. Boudraa and J. Cexus, “EMD-based signal filtering,” IEEE Trans. Instrum. Meas. 56, 2196-2202 (2007).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674-693 (1989).
[CrossRef]

Interdisciplinary Mathematics

N. E. Huang, “Introduction to the Hilbert-Huang transform and its related mathematical problems,” Interdisciplinary Mathematics 5, 1-26 (2005).
[CrossRef]

J. Mod. Opt.

W. Chen, J. Sun, and X. Su, “Discuss the structure condition and sampling condition of wavelet transform profilometry,” J. Mod. Opt. 54, 2747-2762 (2007).
[CrossRef]

J. Sound Vib.

F. Wu and L. Qu, “An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of large rotating machinery,” J. Sound Vib. 314, 586-602 (2008).
[CrossRef]

Mech. Syst. Signal Process.

Q. Gao, C. Duan, H. Fan, and Q. Meng, “Rotating machine fault diagnosis using empirical mode decomposition,” Mech. Syst. Signal Process. 22, 1072-1081 (2008).
[CrossRef]

Opt. Commun.

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482-489 (2006).
[CrossRef]

Tang Yan, Chen Wen-jing, and Su Xian-yu, “Neural network applied to reconstruction of complex objects based on fringe projection,” Opt. Commun. 278, 274-278 (2007).
[CrossRef]

Opt. Eng. (Bellingham)

J. Li, X. Su, and L. Guo, “Improved Fourier transform profilometry of the automatic measurement of three-dimensional object shapes,” Opt. Eng. (Bellingham) 29, 1439-1444 (1990).
[CrossRef]

Opt. Laser Technol.

W. Chen, P. Bu, and S. Zheng, “Study on Fourier transform profilometry based on bi-color projecting,” Opt. Laser Technol. 39, 821-827 (2007).
[CrossRef]

Opt. Lasers Eng.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43, 1267-1276 (2005).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
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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. London, Ser. A 454, 903-995 (1998).
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P. D. Spanos, A. Giaralis, and N. P. Politis, “Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition,” Soil Dyn. Earthquake Eng. 27, 675-689 (2002).
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Other

Zhao Zhidong and Wang Yang, “A new method for processing end effect in empirical mode decomposition,” in Proceedings of 2007 IEEE Conference on Communications, Circuits and Systems (IEEE, 2007), pp. 841-845.

K. Zeng and M. He, “A simple boundary process technique for empirical mode decomposition,” in Proceedings of 2004 IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2004), pp. 4258-4261.

G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” in IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, GRADO(I) (IEEE, 2003).

R. Deering and J. F. Kaiser, “The use of a mask signal to improve empirical mode decomposition,” in Proceedings of IEEE 2005 Conference on Acoustics, Speech, and Signal Processing (IEEE, 2005), pp. 485-488.
[CrossRef]

G. Hu, Z. Ren, and Y. Tou “Symmetrical wavelet construction and its application for electrical machine fault signal reconstruction,” in Proceedings of the Fifth IEEE Conference on Machine Learning and Cybernetics (IEEE, 2006), pp. 3734-3737.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Experimental geometry.

Fig. 2
Fig. 2

Flow chart of EMD.

Fig. 3
Fig. 3

(a) Fringe pattern and its upper and lower envelopes during the first step. (b) Signal with the low frequency component subtracted by the first step. (c) Final result. (d) Fringe with zero component eliminated.

Fig. 4
Fig. 4

Cross section of the object.

Fig. 5
Fig. 5

(a) Deformed fringe pattern. (b) Intensity distribution of the 256th row. (c) Frequency distribution of that row. (d) Retrieved depth-related phase.

Fig. 6
Fig. 6

(a), (b) Spectrum treated by the Daubechies wavelet and the retrieved phase, respectively. (c), (d) Spectrum treated by Symlets wavelet and the retrieved phase, respectively. (e), (f) Spectrum treated by EMD and the restored depth-related phase, respectively.

Fig. 7
Fig. 7

(a) Cat’s face model. (b) Spectrum of the fringe pattern. (c) Spectrum of the fringe pattern with zero spectrum eliminated. (d) Restored depth-related phase distribution.

Equations (8)

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I ( x ) = A ( x ) + B ( x ) cos [ 2 π f 0 x + φ ( x ) ] ,
φ ( x ) = 2 π f 0 d L 0 h ( x ) .
N ( x ) = I ( x ) I max ( x ) + I min ( x ) 2 .
SD = x = 0 m h k 1 ( x ) h k ( x ) 2 h 2 k 1 ( x ) .
r 1 ( x ) c 2 ( x ) = r 2 ( x ) ,
r 2 ( x ) c 3 ( x ) = r 3 ( x ) ,
r n 1 ( x ) c n ( x ) = r n ( x ) .

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