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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

  • Vol. 21, Iss. 3 — Mar. 1, 2004
  • pp: 388–392

Walsh–Hadamard analysis applied to the study of light propagation in a tapered gradient-index medium

Osvaldo Trabocchi and Carlos Gómez-Reino  »View Author Affiliations


JOSA A, Vol. 21, Issue 3, pp. 388-392 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000388


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Abstract

The analysis of light propagation in a tapered gradient-index (GRIN) medium when the input signal is a binary function is considered with the Walsh–Hadamard analysis. The study of the evolution of the sequency spectrum through the GRIN medium by the Walsh–Hadamard transform confirms the self-imaging effect.

© 2004 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings
(110.2350) Imaging systems : Fiber optics imaging
(110.6760) Imaging systems : Talbot and self-imaging effects

History
Original Manuscript: July 15, 2003
Revised Manuscript: October 30, 2003
Manuscript Accepted: October 30, 2003
Published: March 1, 2004

Citation
Osvaldo Trabocchi and Carlos Gómez-Reino, "Walsh–Hadamard analysis applied to the study of light propagation in a tapered gradient-index medium," J. Opt. Soc. Am. A 21, 388-392 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-3-388


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References

  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  2. K. G. Beauchamp, Walsh Functions and Their Applications (Academic, New York, 1975).
  3. H. F. Harmuth, “Applications of Walsh functions in communications,” IEEE Spectrum 6, 82–91 (1969). [CrossRef]
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  5. H. C. Andrews, Computer Techniques in Image Processing (Academic, New York, 1970).
  6. K. Patorski, “Self-imaging phenomenon and its applications,” in Progress in Optics, Vol. XXVII, E. Wolf, ed. (North-Holland, Amsterdam, 1989), pp. 3–101 and references therein.
  7. C. Colautti, B. Ruiz, E. E. Sicre, M. Garavaglia, “Walsh functions: analysis of their properties under Fresnel diffraction,” J. Mod. Opt. 34, 1385–1391 (1987). [CrossRef]
  8. O. Trabocchi, C. Colautti, E. E. Sicre, “Diffraction properties of a periodic multiple-aperture system: an approach based on the Walsh functions,” Opt. Eng. 35, 94–101 (1996). [CrossRef]
  9. O. Trabocchi, C. Colautti, G. Saavedra, E. E. Sicre, “Spatial coherence properties of a multiple aperture system. An analysis based on the Walsh functions,” J. Mod. Opt. 44, 715–729 (1997). [CrossRef]
  10. O. Trabocchi, C. Gómez-Reino, “Integer and fractional Talbot effect of Walsh functions in a tapered gradient-index medium,” J. Mod. Opt. (to be published).
  11. N. M. Blachman, “Sinusoids versus Walsh functions,” in Proc. IEEE 62, 346–354 (1974). [CrossRef]
  12. C. Gómez-Reino, M. V. Pérez, C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chaps. 1 and 2.

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