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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 1 — Jan. 1, 2010
  • pp: 69–75

Estimation of the phase derivative using an adaptive window spectrogram

G. Rajshekhar, Sai Siva Gorthi, and Pramod Rastogi  »View Author Affiliations

JOSA A, Vol. 27, Issue 1, pp. 69-75 (2010)

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The paper introduces an adaptive-window-spectrogram–based method to directly estimate the phase derivative from a single fringe pattern. The proposed method relies on estimating the phase derivative using spectrogram peak detection for a set of different window lengths. Then the optimal window length is selected from the set by resolving the estimator’s bias variance trade-off using the intersection of confidence intervals rule. Finally, the phase derivative estimate corresponding to the optimum window is selected. The method’s applicability to phase derivative estimation is demonstrated using simulation and experimental results.

© 2009 Optical Society of America

OCIS Codes
(090.2880) Holography : Holographic interferometry
(120.2880) Instrumentation, measurement, and metrology : Holographic interferometry
(090.1995) Holography : Digital holography

ToC Category:
Holographic Interferometry

Original Manuscript: July 1, 2009
Revised Manuscript: September 30, 2009
Manuscript Accepted: November 12, 2009
Published: December 9, 2009

G. Rajshekhar, Sai Siva Gorthi, and Pramod Rastogi, "Estimation of the phase derivative using an adaptive window spectrogram," J. Opt. Soc. Am. A 27, 69-75 (2010)

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  1. Q. Kemao, S. H. Soon, and A. Asundi, “Instantaneous frequency and its application to strain extraction in moiré interferometry,” Appl. Opt. 42, 6504-6513 (2003). [CrossRef] [PubMed]
  2. K. Qian, S. H. Soon, and A. Asundi, “Phase-shifting windowed Fourier ridges for determination of phase derivatives,” Opt. Lett. 28, 1657-1659 (2003). [CrossRef] [PubMed]
  3. C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327-336 (2007). [CrossRef]
  4. C. A. Sciammarella and T. Kim, “Frequency modulation interpretation of fringes and computation of strains,” Exp. Mech. 45, 393-403 (2005). [CrossRef]
  5. U. Schnars and W. P. O. Juptner, “Digital recording and reconstruction of holograms in hologram interferometry and shearography,” Appl. Opt. 33, 4373-4377 (1994). [CrossRef] [PubMed]
  6. B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal--part 1: fundamentals,” Proc. IEEE 80, 519-538 (1992).
  7. L. Cohen, Time Frequency Analysis (Prentice Hall, 1995).
  8. L. Stankovic and V. Katkovnik, “Algorithm for the instantaneous frequency estimation using time-frequency distributions with adaptive window width,” IEEE Signal Process. Lett. 5, 224-227 (1998). [CrossRef]
  9. V. Katkovnik and L. J. Stankovic, “Periodogram with varying and data-driven window length,” Signal Process. 67, 345-358 (1998). [CrossRef]
  10. V. Katkovnik and L. Stankovic, “Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length,” IEEE Trans. Signal Process. 45, 2147 (1997).
  11. D. R. Pauluzzi and N. C. Beaulieu, “A comparison of snr estimation techniques for the awgn channel,” IEEE Trans. Commun. 48, 1601 (2000). [CrossRef]
  12. R. Matzner and F. Englberger, “Snr estimation algorithm using fourth-order moments,” Proceedings of the IEEE International Symposium on Information Theory (IEEE, 1994).
  13. S. C. Sekhar and T. V. Sreenivas, “Signal-to-noise ratio estimation using higher-order moments,” Signal Process. 86, 716-732 (2006). [CrossRef]
  14. J. A. Quiroga, J. Antonio Gomez-Pedrero, and A. Garcia-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197, 43-51 (2001). [CrossRef]
  15. S. Lawrence Marple Jr., “Computing the discrete-time analytic signal via fft,” IEEE Trans. Signal Process. 47, 2600-2603 (1999). [CrossRef]

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