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Applied Optics

Applied Optics


  • Vol. 43, Iss. 13 — May. 1, 2004
  • pp: 2695–2702

Windowed Fourier transform for fringe pattern analysis

Qian Kemao  »View Author Affiliations

Applied Optics, Vol. 43, Issue 13, pp. 2695-2702 (2004)

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Fringe patterns in optical metrology systems need to be demodulated to yield the desired parameters. Time-frequency analysis is a useful concept for fringe demodulation, and a windowed Fourier transform is chosen for the determination of phase and phase derivative. Two approaches are developed: the first is based on the concept of filtering the fringe patterns, and the second is based on the best match between the fringe pattern and computer-generated windowed exponential elements. I focus on the extraction of phase and phase derivatives from either phase-shifted fringe patterns or a single carrier fringe pattern. Principles as well as examples are given to show the effectiveness of the proposed methods.

© 2004 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(100.7410) Image processing : Wavelets
(120.3940) Instrumentation, measurement, and metrology : Metrology
(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

Original Manuscript: October 29, 2003
Revised Manuscript: January 27, 2004
Published: May 1, 2004

Qian Kemao, "Windowed Fourier transform for fringe pattern analysis," Appl. Opt. 43, 2695-2702 (2004)

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  1. D. W. Robinson, G. T. Reid(eds.), Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics, Bristol, England, 1993).
  2. M. Servin, M. Kujawinska, “Modern fringe analysis in interferometry,” in Handbook of Optical Engineering, D. Malacara, B. J. Thompson, eds. (Marcel Dekker, New York, 2001), pp. 373–426.
  3. J. M. Huntley, “Automated fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998). [CrossRef]
  4. M. Servin, J. L. Marroguin, 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]
  5. M. Servin, R. Rodriguez-Vera, J. L. Marraquin, D. Malacara, “Phase-shifting interferometry using a two-dimensional regularized phase-tracking technique,” J. Mod. Opt. 45, 1809–1819 (1998). [CrossRef]
  6. M. Servin, F. J. Cuevas, D. Malacara, J. L. Marroguin, R. Rodriguez-Vera, “Phase unwrapping through demodulation by use of the regularized phase-tracking technique,” Appl. Opt. 38, 1934–1941 (1999). [CrossRef]
  7. L. R. Watkins, S. M. Tan, T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999). [CrossRef]
  8. K. Kadooka, K. Kunoo, N. Uda, K. Ono, T. Nagayasu, “Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform,” Exp. Mech. 43, 45–51 (2003). [CrossRef]
  9. J. Fang, C. Y. Xiong, H. J. Li, Z. L. Zhang, “Digital transform processing of carrier fringe patterns from speckle-shearing interferometry,” J. Mod. Opt. 48, 507–520 (2001). [CrossRef]
  10. K. Qian, H. S. Seah, A. Asundi, “Instantaneous frequency and its application in strain extraction in moiré interferometry,” Appl. Opt. 42, 6504–6513 (2003). [CrossRef]
  11. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. (Academic, San Diego, 1999).
  12. K. Kröchenig, Foundations of Time-Frequency Analysis (Birkhäuser, Boston, 2001).
  13. matlab codes for both WFF and WFR are available upon request.
  14. M. Servin, F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995). [CrossRef]
  15. K. Qian, H. S. Seah, A. Asundi, “Filtering the complex field in phase shifting interferometry,” Opt. Eng. 42, 2792–2793 (2003). [CrossRef]
  16. M. Takeda, H. Ina, S. Kobayashi, “Fourier transform methods of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  17. N. Delprat, B. Escudié, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torrésani, “Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies,” IEEE Trans. Inf. Theory 38, 644–664 (1992). [CrossRef]
  18. P. Guillemain, R. Kronland-Martinet, “Characterization of acoustic signals through continuous linear time-frequency representations,” Proc. IEEE 84, 561–585 (1996). [CrossRef]
  19. H. Miao, “The studies on real time phase measurement technique and its application to protein crystal growth,” Ph.D Dissertation (University of Science and Technology of China, Beijing, 1999).

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