OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 11 — Nov. 1, 2001
  • pp: 2707–2716

Talbot effect interpreted by number theory

Marı́a Teresa Flores-Arias, Marı́a Victoria Pérez, Carlos Gómez-Reino, Carmen Bao, and Carlos R. Fernández-Pousa  »View Author Affiliations

JOSA A, Vol. 18, Issue 11, pp. 2707-2716 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (224 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An interpretation of the Talbot effect in a tapered gradient-index medium by number theory as the output/input relationship between the integer and the noninteger difference of position and the slope of rays is presented. Unit cell and transverse magnification for Talbot images are evaluated, and two criteria for angular magnification are defined. The study is particularized to a finite set of diffracted rays.

© 2001 Optical Society of America

OCIS Codes
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(110.0110) Imaging systems : Imaging systems

Original Manuscript: February 20, 2001
Revised Manuscript: April 26, 2001
Manuscript Accepted: April 30, 2001
Published: November 1, 2001

Marı́a Teresa Flores-Arias, Marı́a Victoria Pérez, Carlos Gómez-Reino, Carmen Bao, and Carlos R. Fernández-Pousa, "Talbot effect interpreted by number theory," J. Opt. Soc. Am. A 18, 2707-2716 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII, E. Wolf, ed. (North-Holland, Amsterdam, 1989), pp. 3–101 and references therein.
  2. M. V. Berry, S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996) and references therein. [CrossRef]
  3. M. T. Flores-Arias, C. Bao, M. V. Pérez, C. Gómez-Reino, “Talbot effect in a tapered gradient-index medium for nonuniform and uniform illumination,” J. Opt. Soc. Am. A 16, 2439–2446 (1999). [CrossRef]
  4. M. T. Flores-Arias, C. R. Fernández-Pousa, M. V. Pérez, C. Bao, C. Gómez-Reino, “Fractional Talbot effect in a tapered gradient-index medium: unit cell,” J. Opt. Soc. Am. A 17, 1007–1011 (2000). [CrossRef]
  5. P. Latimer, R. F. Course, “Talbot effect reinterpreted,” Appl. Opt. 31, 80–89 (1992). [CrossRef] [PubMed]
  6. P. Szwaykowski, “Talbot effect reinterpreted: comment,” Appl. Opt. 32, 3466–3467 (1993). [CrossRef] [PubMed]
  7. P. Latimer, “Talbot effect reinterpreted: reply to comment,” Appl. Opt. 32, 3468–3469 (1993). [CrossRef] [PubMed]
  8. P. Szwaykowski, J. Ojeda-Castañeda, “Nondiffracting beams and the self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991). [CrossRef]
  9. C. Gómez-Reino, “GRIN optics and its applications in optical connections,” Int. J. Optoelectron. 7, 607–680 (1992).
  10. G. H. Gardy, E. M. Wright, An Introduction to the Theory of Number, 5th ed. (Clarendon, Oxford, UK, 1995), pp. 21, 23, 52, 53.
  11. J. C. Fernando, V. Gregori, Matemática Discreta (Editorial Reverté, Barcelona, Spain, 1994), p. 98.

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