OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

View Full Text Article

Enhanced HTML    Acrobat PDF (160 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

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

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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]
  4. S. G. Tzafestas, Walsh Functions in Signal and Systems Analysis and Design (Van Nostrand Reinhold, New York, 1985).
  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.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited