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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 4 — Apr. 1, 2006
  • pp: 902–905

Efficient deconvolution of noisy periodic interference signals

Feredoon Behroozi and Peter S. Behroozi  »View Author Affiliations


JOSA A, Vol. 23, Issue 4, pp. 902-905 (2006)
http://dx.doi.org/10.1364/JOSAA.23.000902


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Abstract

The interference signal formed by combining two coherent light beams carries information on the path difference between the beams. When the path difference is a periodic function of time, as, for example, when one beam is reflected from a vibrating surface and the other from a fixed surface, the interference signal is periodic with the same period as the vibrating surface. Bessel functions provide an elegant and efficient means for deconvoluting such periodic interference signals, thus making it possible to obtain the displacement of the moving surface with nanometer resolution. Here we describe the mathematical basis for the signal deconvolution and employ this technique to obtain the amplitude of miniature capillary waves on water as a test case.

© 2006 Optical Society of America

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: July 1, 2005
Revised Manuscript: October 17, 2005
Manuscript Accepted: October 18, 2005

Citation
Feredoon Behroozi and Peter S. Behroozi, "Efficient deconvolution of noisy periodic interference signals," J. Opt. Soc. Am. A 23, 902-905 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-4-902


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References

  1. T. M. Bohanon, J. M. Mikrut, B. M. Abraham, J. B. Ketterson, and P. Datta, "Fiber-optic detection system for capillary waves: an apparatus for studying liquid surfaces and spread monolayers," Rev. Sci. Instrum. 62, 2959-2962 (1991). [CrossRef]
  2. See, for example, G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, 1958).
  3. J. Kauppinen and J. Partanen, Fourier Transforms in Spectroscopy (Wiley-VCH, 2002).
  4. J. Markham and J. A. Conchello, "Numerical evaluation of Hankel transforms for oscillating functions," J. Opt. Soc. Am. A 20, 621-630 (2003). [CrossRef]
  5. J. Alda, C. Fumeaue, I. Codreanu, J. A. Schaefer, and D. Boreman, "Deconvolution method for two-dimensional spatial-response mapping of lithographic infrared antennas," Appl. Opt. 38, 3993-4000 (1999). [CrossRef]
  6. See, for example, A. Runnemalm, N. Molin, and E. Jansson, "On operating deflection shapes of the violin body including in-plane motions," J. Acoust. Soc. Am. 107, 3452-3459 (2000). [CrossRef] [PubMed]
  7. F. Behroozi, "Fluid viscosity and the attenuation of surface waves: a derivation based on conservation of energy," Eur. J. Phys. 25, 115-122 (2004). [CrossRef]
  8. F. Behroozi, B. Lambert, and B. Buhrow, "Noninvasive measurement of viscosity from damping of capillary waves," ISA Trans. 42, 3-8 (2003). [CrossRef] [PubMed]
  9. F. Behroozi, "A miniature laser interferometer for noninvasive viscometry," presented at the Technical Proceedings of Nanotech 2003 Conference, San Francisco, Calif., February 24-26, 2003, Vol. 1, pp. 166-169.
  10. F. Behroozi, "Apparatus and method for measurement of fluid viscosity," U.S. patent 6,563,588 B2 (May 13, 2003).
  11. F. Behroozi, B. Lambert, and B. Buhrow, "Direct measurement of the attenuation of capillary waves by laser interferometry: noncontact determination of viscosity," Appl. Phys. Lett. 78, 2399-2401 (2001). [CrossRef]
  12. M.Abramowitz and I.A.Stegun, eds., Handbook of Mathematical Functions, 10th printing (U.S. Government Printing Office, 1972) p. 361.

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