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Applied Optics

Applied Optics


  • Vol. 44, Iss. 12 — Apr. 20, 2005
  • pp: 2359–2365

Fringe-density estimation by continuous wavelet transform

Chenggen Quan, Cho Jui Tay, and Lujie Chen  »View Author Affiliations

Applied Optics, Vol. 44, Issue 12, pp. 2359-2365 (2005)

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For many phase extraction algorithms, a priori knowledge of a fringe-pattern density distribution is beneficial for later processing. A fringe-density estimation method based on a continuous wavelet transform (CWT) is proposed. For a one-dimensional signal the instantaneous frequency detected at the CWT ridge is directly adopted as a measure of the local fringe density. For a two-dimensional signal the instantaneous frequency components in both the x and the y directions are detected. Their reliability is evaluated by the CWT coefficient magnitude, based on which an approximate density value is given. The capability for noise reduction and the accuracy of the method are discussed.

© 2005 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.2650) Image processing : Fringe analysis
(100.7410) Image processing : Wavelets

Original Manuscript: April 27, 2004
Revised Manuscript: September 3, 2004
Manuscript Accepted: November 24, 2004
Published: April 20, 2005

Chenggen Quan, Cho Jui Tay, and Lujie Chen, "Fringe-density estimation by continuous wavelet transform," Appl. Opt. 44, 2359-2365 (2005)

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  1. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds.(Institute of Physics, Bristol, UK, 1993), pp. 94–140.
  2. P. Carré, “Installation et utilization du compateur photoelectrique et interferential du Bureau International des Poids et Mesures,” Metrologia 2, 13–20 (1966). [CrossRef]
  3. X. Le, G. Tao, Y. Yang, “Continual deformation analysis with scanning phase method and time sequence phase method in temporal speckle pattern interferometry,” Opt. Laser Technol. 33, 53–59 (2001). [CrossRef]
  4. C. Joenathan, B. Franze, P. Haible, H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998). [CrossRef]
  5. M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983). [CrossRef] [PubMed]
  6. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986). [CrossRef]
  7. J. Wang, A. Asundi, “Strain contouring with Gabor filters: filter bank design,” Appl. Opt. 41, 7229–7236 (2002). [CrossRef]
  8. M. Servin, J. L. Marroquin, F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997). [CrossRef] [PubMed]
  9. J. L. Marroquin, R. Rodriguez-Vera, M. Servin, “Local phase from local orientation by solution of a sequence of linear systems,” J. Opt. Soc. Am. A 15, 1536–1544 (1998). [CrossRef]
  10. J. L. Marroquin, R. Rodriguez-Vera, M. Servin, “Adaptive quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. A 14, 1742–1753 (1997). [CrossRef]
  11. O. Marklund, “Robust fringe density and direction estimation in noisy phase maps,” J. Opt. Soc. Am. A 18, 2717–2727 (2001). [CrossRef]
  12. P. Stephenson, D. R. Burton, M. I. Lalor, “Data validation techniques in a tiled phase unwrapping algorithm,” Opt. Eng. 33, 3703–3708 (1994). [CrossRef]
  13. M. Cherbuliez, P. Jacquot, X. Colonna de Lega, “Wavelet processing of interferometric signals and fringe patterns,” in Wavelet Applications in Signal and Image Processing VII, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE3813, 692–702 (1999). [CrossRef]
  14. H. Liu, A. N. Cartwright, C. Basaran, “Sensitivity improvement in phase-shifted moiré interferometry using 1-D continuous wavelet transform image processing,” Opt. Eng. 42, 2646–2652 (2003). [CrossRef]
  15. H. Liu, A. N. Cartwright, C. Basaran, “Moiré interferogram phase extraction: a ridge detection algorithm for continuous wavelet transforms,” Appl. Opt. 43, 850–857 (2004). [CrossRef] [PubMed]
  16. S. Mallat, A Wavelet Tour of Signal Processing (Academic, San Diego, Calif., 1999).
  17. A. Davila, G. H. Kaufmann, D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35, 3549–3554 (1996). [CrossRef]
  18. B. Strobel, “Processing of interferometric phase maps as complex-valued phasor images,” Appl. Opt. 35, 2192–2198 (1996). [CrossRef] [PubMed]

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