Abstract

An adaptive approach is presented for noise reduction of optical fringe patterns using multivariate empirical mode decomposition. Adjacent rows and columns of patterns are treated as multichannel signals and are decomposed into multiscale components. Fringe patterns are reconstructed with less noise by simply thresholding coefficients in different scales. The proposed approach can better concentrate local main components of fringe signals into single scale, compared with the conventional multiscale denoising method. A simulated pattern and an actual example are examined. Signal-to-noise ratio (SNR) of the simulated pattern is more than doubled.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
    [CrossRef]
  2. M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, Opt. Laser. Eng. 45, 723 (2007).
    [CrossRef]
  3. S. Li, X. Su, W. Chen, and L. Xiang, J. Opt. Soc. Am. A 26, 1195 (2009).
    [CrossRef]
  4. M. B. Bernini, A. Federico, and G. H. Kaufmann, Appl. Opt. 47, 2592 (2008).
    [CrossRef]
  5. M. Wielgus and K. Patorski, Appl. Opt. 50, 5513 (2011).
    [CrossRef]
  6. X. Zhou, H. Zhao, and T. Jiang, Opt. Lett. 34, 2033 (2009).
    [CrossRef]
  7. M. B. Bernini, A. Federico, and G. H. Kaufmann, Appl. Opt. 50, 641 (2011).
    [CrossRef]
  8. Y. Zhou and H. G. Li, Opt. Express 19, 18207 (2011).
    [CrossRef]
  9. N. Rehman and D. P. Mandic, Soc. Lond. A Mat. 466, 1291 (2010).
    [CrossRef]
  10. Z. Wu and N. E. Huang, Adv. Adapt. Data Anal. 1, 1 (2009).
    [CrossRef]

2011 (3)

2010 (1)

N. Rehman and D. P. Mandic, Soc. Lond. A Mat. 466, 1291 (2010).
[CrossRef]

2009 (3)

2008 (1)

2007 (1)

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

1998 (1)

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Bernini, M. B.

Chen, W.

Federico, A.

Galizzi, G. E.

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

Huang, N. E.

Z. Wu and N. E. Huang, Adv. Adapt. Data Anal. 1, 1 (2009).
[CrossRef]

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Jiang, T.

Kaufmann, G. H.

Li, H. G.

Li, S.

Liu, H. H.

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Long, S. R.

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Mandic, D. P.

N. Rehman and D. P. Mandic, Soc. Lond. A Mat. 466, 1291 (2010).
[CrossRef]

Patorski, K.

Rehman, N.

N. Rehman and D. P. Mandic, Soc. Lond. A Mat. 466, 1291 (2010).
[CrossRef]

Shen, Z.

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Shih, H. H.

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Su, X.

Tung, C. C.

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Wielgus, M.

Wu, M. L. C.

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Wu, Z.

Z. Wu and N. E. Huang, Adv. Adapt. Data Anal. 1, 1 (2009).
[CrossRef]

Xiang, L.

Yen, N. C.

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Zhao, H.

Zheng, Q. N.

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Zhou, X.

Zhou, Y.

Adv. Adapt. Data Anal. (1)

Z. Wu and N. E. Huang, Adv. Adapt. Data Anal. 1, 1 (2009).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Laser. Eng. (1)

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

Opt. Lett. (1)

P. Roy. Soc. Lond. A Mat. (1)

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, P. Roy. Soc. Lond. A Mat. 454, 903 (1998).
[CrossRef]

Soc. Lond. A Mat. (1)

N. Rehman and D. P. Mandic, Soc. Lond. A Mat. 466, 1291 (2010).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

(a) Simulated noisy fringe pattern and (b) its 115th row signal.

Fig. 2.
Fig. 2.

IMFs (levels 1 to 6) generated from (a) MEMD, (b) EMD, and (c) EEMD. (d) DWT details decomposed by a db9 wavelet.

Fig. 3.
Fig. 3.

Denoised results of the 115th row: (a) the ideal signal and the signals denoised by (b) MEMD, (c) EMD, (d) EEMD, and (e) DWT.

Fig. 4.
Fig. 4.

Denoised fringe pattern handled first along rows and then along columns.

Fig. 5.
Fig. 5.

(a) A real fringe-projected pattern and (b) the denoised result. (c) The 115th row before (solid line) and after (dotted line) denoising.

Equations (2)

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

I(x,y)=a(x,y)+b(x,y)cosϕ(x,y)+n(x,y),
u(x)=j=1Pcj(x)+r(x),

Metrics