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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 18459–18477

Phase demodulation using adaptive windowed Fourier transform based on Hilbert-Huang transform

Chenxing Wang and Feipeng Da  »View Author Affiliations

Optics Express, Vol. 20, Issue 16, pp. 18459-18477 (2012)

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The phase demodulation method of adaptive windowed Fourier transform (AWFT) is proposed based on Hilbert-Huang transform (HHT). HHT is analyzed and performed on fringe pattern to obtain instantaneous frequencies firstly. These instantaneous frequencies are further analyzed based on the condition of AWFT to locate local stationary areas where the fundamental spectrum will not be interfered by high-order spectrum. Within each local stationary area, the fundamental spectrum can be extracted accurately and adaptively by using AWFT with the background, which has been determined previously with the presented criterion during HHT, being eliminated to remove the zero-spectrum. This method is adaptive and unconstrained by any precondition for the measured phase. Experiments demonstrate its robustness and effectiveness for measuring the object with discontinuities or complex surface.

© 2012 OSA

OCIS Codes
(100.5070) Image processing : Phase retrieval
(110.2960) Imaging systems : Image analysis
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis

ToC Category:
Image Processing

Original Manuscript: May 30, 2012
Revised Manuscript: July 18, 2012
Manuscript Accepted: July 19, 2012
Published: July 27, 2012

Chenxing Wang and Feipeng Da, "Phase demodulation using adaptive windowed Fourier transform based on Hilbert-Huang transform," Opt. Express 20, 18459-18477 (2012)

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  1. S. Gai and F. Da, “A novel phase-shifting method based on strip marker,” Opt. Lasers Eng.48(2), 205–211 (2010). [CrossRef]
  2. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am.72(1), 156–160 (1982). [CrossRef]
  3. J. Zhong and H. Zeng, “Multiscale windowed Fourier transform for phase extraction of fringe patterns,” Appl. Opt.46(14), 2670–2675 (2007). [CrossRef] [PubMed]
  4. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt.43(13), 2695–2702 (2004). [CrossRef] [PubMed]
  5. J. Zhong and J. Weng, “Phase retrieval of optical fringe patterns from the ridge of a wavelet transform,” Opt. Lett.30(19), 2560–2562 (2005). [CrossRef] [PubMed]
  6. S. Li, X. Su, and W. Chen, “Wavelet ridge techniques in optical fringe pattern analysis,” J. Opt. Soc. Am. A27(6), 1245–1254 (2010). [CrossRef] [PubMed]
  7. S. Özder, Ö. Kocahan, E. Coşkun, and H. Göktaş, “Optical phase distribution evaluation by using an S-transform,” Opt. Lett.32(6), 591–593 (2007). [CrossRef] [PubMed]
  8. M. Zhong, W. Chen, and M. Jiang, “Application of S-transform profilometry in eliminating nonlinearity in fringe pattern,” Appl. Opt.51(5), 577–587 (2012). [CrossRef] [PubMed]
  9. S. Zheng, W. Chen, and X. Su, “Adaptive Windowed Fourier transform in 3-D shape measurement,” Opt. Eng.45(6), 063601 (2006). [CrossRef]
  10. J. Zhong and J. Weng, “Generalized Fourier analysis for phase retrieval of fringe pattern,” Opt. Express18(26), 26806–26820 (2010). [CrossRef] [PubMed]
  11. Z. Wang, J. Ma, and M. Vo, “Recent progress in two-dimensional continuous wavelet transform technique for fringe pattern analysis,” Opt. Lasers Eng.50(8), 1052–1058 (2012). [CrossRef]
  12. 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(12), 2797–2807 (2011). [CrossRef]
  13. X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett.34(13), 2033–2035 (2009). [CrossRef] [PubMed]
  14. W. Gao and Q. Kemao, “Statistical analysis for windowed Fourier ridge algorithm in fringe pattern analysis,” Appl. Opt.51(3), 328–337 (2011). [CrossRef] [PubMed]
  15. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt.22(24), 3977–3982 (1983). [CrossRef] [PubMed]
  16. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. N. 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. Lond. A454(1971), 903–995 (1998). [CrossRef]
  17. S. Equis and P. Jacquot, “The empirical mode decomposition: a must-have tool in speckle interferometry?” Opt. Express17(2), 611–623 (2009). [CrossRef] [PubMed]
  18. G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” in IEEE-EURASIP Workshop on Nonlinear signal and Image Processing, NSTP-03, GRADO (I) (2003).
  19. G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process.56(1), 85–95 (2008). [CrossRef]
  20. Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Adv. Adapt. Data Anal.1(1), 1–41 (2009). [CrossRef]
  21. S. Li, X. Su, W. Chen, and L. Xiang, “Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition,” J. Opt. Soc. Am. A26(5), 1195–1201 (2009). [CrossRef]
  22. S. Zhang, X. Li, and S. T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt.46(1), 50–57 (2007). [CrossRef] [PubMed]
  23. S. Gai and F. Da, “Fringe image analysis based on the amplitude modulation method,” Opt. Express18(10), 10704–10719 (2010). [CrossRef] [PubMed]

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