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Applied Optics

Applied Optics


  • Vol. 51, Iss. 12 — Apr. 20, 2012
  • pp: 2026–2034

Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis

Sikun Li, Xiangzhao Wang, Xianyu Su, and Feng Tang  »View Author Affiliations

Applied Optics, Vol. 51, Issue 12, pp. 2026-2034 (2012)

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This paper theoretically discusses modulus of two-dimensional (2D) wavelet transform (WT) coefficients, calculated by using two frequently used 2D daughter wavelet definitions, in an optical fringe pattern analysis. The discussion shows that neither is good enough to represent the reliability of the phase data. The differences between the two frequently used 2D daughter wavelet definitions in the performance of 2D WT also are discussed. We propose a new 2D daughter wavelet definition for reliability-guided phase unwrapping of optical fringe pattern. The modulus of the advanced 2D WT coefficients, obtained by using a daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter that represents the reliability of the retrieved phase data. Computer simulation and experimentation show the validity of the proposed method.

© 2012 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(100.7410) Image processing : Wavelets
(100.5088) Image processing : Phase unwrapping

ToC Category:
Image Processing

Original Manuscript: October 20, 2011
Revised Manuscript: January 3, 2012
Manuscript Accepted: January 4, 2012
Published: April 16, 2012

Sikun Li, Xiangzhao Wang, Xianyu Su, and Feng Tang, "Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis," Appl. Opt. 51, 2026-2034 (2012)

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  1. 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, 156–160(1982). [CrossRef]
  2. X. Su, and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001). [CrossRef]
  3. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004). [CrossRef]
  4. 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]
  5. S. Li, X. Su, and W. Chen, “Wavelet ridge techniques in optical fringe pattern analysis,” J. Opt. Soc. Am. A 27, 1245–1254 (2010). [CrossRef]
  6. 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). [CrossRef]
  7. C. Quan, W. Chen, and C. J. Tay, “Phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. 48, 235–243 (2010). [CrossRef]
  8. M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009). [CrossRef]
  9. C. J. Tay, C. Quan, and W. Sun, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007). [CrossRef]
  10. L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999). [CrossRef]
  11. M. Cherbuliez, P. Jacquot, and X. de Lega, “Wavelet processing of interferometric signals and fringe patterns,” Proc. SPIE 3813, 692–702 (1999). [CrossRef]
  12. 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]
  13. W. L. Anderson, and H. Diao, “Two-dimensional wavelet transform and application to holographic particle velocimetry,” Appl. Opt. 34, 249–255 (1995). [CrossRef]
  14. 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). [CrossRef]
  15. J. Weng, and J. Zhong, “Phase reconstruction of digital holography with the peak of the two-dimensional Gabor wavelet transform,” Appl. Opt. 48, 3308–3316 (2009). [CrossRef]
  16. 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]
  17. 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]
  18. S. Li, X. Su, and W. Chen, “Spatial carrier fringe pattern phase demodulation by use of a two-dimensional real wavelet,” Appl. Opt. 48, 6893–6906 (2009). [CrossRef]
  19. H. Niu, C. Quan, and C. J. Tay, “Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform,” Opt. Lasers Eng. 47, 1334–1339 (2009). [CrossRef]
  20. Z. Wang, and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006). [CrossRef]
  21. D. C. Ghiglia, and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).
  22. S. Zhang, X. Li, and S. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46, 50–57 (2007). [CrossRef]
  23. X. Su, and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261(2004).
  24. Y. Lu, X. Wang, X. Zhong, G. He, Y. Liu, and D. Zheng, “A new quality map for quality-guided phase unwrapping,” Chin. Opt. Lett. 2, 698–700 (2004).
  25. X. Su, G. Bally, and D. Vukicevic, “phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993). [CrossRef]
  26. X. Su, A. M. Zarubin, and G. Bally, “Modulation analysis of phase-shifting holographic interferograms,” Opt. Commun. 105, 379–387 (1994). [CrossRef]
  27. X. Su and L. Xue, “Phase unwrapping algorithm based on fringe frequency analysis in Fourier-transform profilometry,” Opt. Eng. 40, 637–643 (2001). [CrossRef]
  28. L. Xue and X. Su, “Phase-unwrapping algorithm based on frequency analysis for measurement of a complex object by the phase-measuring profilometry method,” Appl. Opt. 40, 1207–1215 (2001). [CrossRef]

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