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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 36 — Dec. 20, 2009
  • pp: 6893–6906

Spatial carrier fringe pattern phase demodulation by use of a two-dimensional real wavelet

Sikun Li, Xianyu Su, and Wenjing Chen  »View Author Affiliations

Applied Optics, Vol. 48, Issue 36, pp. 6893-6906 (2009)

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A two-dimensional continuous wavelet transform employing a real mother wavelet is applied to phase analysis of spatial carrier fringe patterns. In this method, a Hilbert transform is first performed on a carrier fringe pattern to get an analytic signal. Then a two-dimensional wavelet transform is calculated for the signal that is yielded by the first transform. Finally, the height-demodulated phase information can be gotten from the wavelet transform coefficients at the wavelet ridge position. The performance of the proposed method has been evaluated by using computer-generated and real fringe patterns. The result performed better than that of one-dimensional real wavelet transform algorithms in the area with phase discontinuous points and high phase variation, especially when there is much noise in the fringe patterns. Computer simulations and experiments verified the validity of the proposed method.

© 2009 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(100.7410) Image processing : Wavelets

ToC Category:
Image Processing

Original Manuscript: July 22, 2009
Revised Manuscript: October 23, 2009
Manuscript Accepted: November 19, 2009
Published: December 10, 2009

Sikun Li, Xianyu Su, and Wenjing Chen, "Spatial carrier fringe pattern phase demodulation by use of a two-dimensional real wavelet," Appl. Opt. 48, 6893-6906 (2009)

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  1. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement 3-D object shapes,” Appl. Opt. 22, 3977-3982 (1983). [CrossRef]
  2. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263-284 (2001).
  3. J. Li, X. Su, and L. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439-1444 (1990).
  4. S. Li, X. Su, and W. Chen, “Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition,” J. Opt. Soc. Am. A 26, 1195-1201 (2009). [CrossRef]
  5. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695-2702 (2004). [CrossRef]
  6. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
  7. K. Qian, “Windowed Fourier transform method for demodulation of carrier fringes,” Opt. Eng. 43, 1472-1473 (2004).
  8. J. Zhong and J. Weng, “Dilating Gabor transform for the fringe analysis of 3-D shape measurement,” Opt. Eng. 43, 895-899 (2004).
  9. J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993-4998 (2004). [CrossRef]
  10. J. Zhong and J. Weng, “Phase retrieval of optical fringe patterns from the ridge of a wavelet transform,” Opt. Lett. 30, 2560-2562 (2005). [CrossRef]
  11. M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722-8732 (2006). [CrossRef]
  12. A. Z. Abid, M. A. Gdeisat, and D. R. Burton, “Spatial fringe pattern analysis using the two-dimensional continuous wavelet transform employing a cost function,” Appl. Opt. 46, 6120-6126 (2007). [CrossRef]
  13. S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369-3377 (2008). [CrossRef]
  14. L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141-148 (2010).
  15. Zh. Xiang and Zh. Hong, “Three-dimensional profilometry based on Mexican hat wavelet transform,” Acta Optica Sinica 29, 197-202 (2009).
  16. R. A. Carmona, W. L. Hwang, and B. Torresani, “Characterization of signals by the ridges of their wavelet transforms,” IEEE Trans. Signal Process. 45, 2586-2590 (1997). [CrossRef]
  17. J. F. Kirby, “Which wavelet best reproduces the Fourier power spectrum?,” Comput. Geosci. 31, 846-864 (2005). [CrossRef]
  18. D. Benitez, P. A. Gaydecki, A. Zaidi, and A. P. Fitzpatrick, “The use of the Hilbert transform in ECG signal analysis,” Comput. Biol. Med. 31, 399-406 (2001).
  19. H. Olkkoned, P. Pesola, J. Olkkonen, and H. Zhou, “Hilbert transform assisted complex wavelet transform for neuroelectric signal analysis,” J. Neurosci. Methods 151, 106-113(2006). [CrossRef]
  20. A. A. Nabout and B. Tibken, “Object shape recognition using Mexican hat wavelet descriptors,” in Proceedings of IEEE Conference on Control and Automation (IEEE, 2007), pp. 1313-1318.
  21. S. R. Messer, J. Agzarian, and D. Abbott, “Optimal wavelet denoising for phonocardiograms,” Microelectron. J. 32, 931-941 (2001). [CrossRef]
  22. W. L. Anderson and H. Diao, “Two-dimensional wavelet transform and application to holographic particle velocimetry,” Appl. Opt. 34, 249-255 (1995). [CrossRef]
  23. S. Belaïd, D. Lebrun, and C. Özkul, “Application of two-dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame,” Opt. Eng. 36, 1947-1951 (1997).
  24. J. Weng, J. Zhong, and C. Hu, “Phase reconstruction of digital holography with the peak of the two-dimensional Gabor wavelet transform,” Appl. Opt. 48, 3308-3316 (2009). [CrossRef]
  25. K. Kadooka, K. Kunoo, N. Uda, K. Ono, and T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45-51 (2003). [CrossRef]
  26. J. P. Antoine and R. Murenzi, “Two-dimensional directional wavelets and the scale-angle representation,” Signal Proc. 52, 259-281 (1996). [CrossRef]
  27. J. P. Antoine and P. Vandergheynst, “Two-dimensional directional wavelets in image processing,” Int. J. Imaging Syst. Technol. 7, 152-165 (1996). [CrossRef]
  28. M. Kutter, S. K. Bhattacharjee, and T. Ebrahimi, “Towards second generation watermarking schemes,” in Proceedings of IEEE Conference on Image Processing (IEEE, 1999), pp. 320-323.
  29. L. M. Kaplan and R. Murenzi, “Pose estimation of SAR imagery using the two dimensional continuous wavelet transform,” Patt. Recog. Lett. 24, 2269-2280 (2003). [CrossRef]
  30. Yet Another Wavelet Toolbox (YAWTB) home page (accessed in April 2007), http://www.fyma.ucl.ac.be/projects/yawtb/.

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