OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 4 — Apr. 1, 2006
  • pp: 829–834

Self-Fourier functions and self-Fourier operators

Theodoros P. Horikis and Matthew S. McCallum  »View Author Affiliations

JOSA A, Vol. 23, Issue 4, pp. 829-834 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (88 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The concept of self-Fourier functions, i.e., functions that equal their Fourier transform, is almost always associated with specific functions, the most well known being the Gaussian and the Dirac delta comb. We show that there exists an infinite number of distinct families of these functions, and we provide an algorithm for both generating and characterizing their distinct classes. This formalism allows us to show the existence of these families of functions without actually evaluating any Fourier or other transform-type integrals, a task often challenging and frequently not even possible.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.3870) General : Mathematics
(070.2590) Fourier optics and signal processing : ABCD transforms

ToC Category:
Fourier Optics and Optical Signal Processing

Original Manuscript: August 11, 2005
Revised Manuscript: October 12, 2005
Manuscript Accepted: November 4, 2005

Theodoros P. Horikis and Matthew S. McCallum, "Self-Fourier functions and self-Fourier operators," J. Opt. Soc. Am. A 23, 829-834 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Coffey, "Self-reciprocal Fourier functions," J. Opt. Soc. Am. A 11, 2453-2455 (1994). [CrossRef]
  2. A. Lohmann and D. Mendlovic, "Self-Fourier objects and other self-transform objects," J. Opt. Soc. Am. A 9, 2009-2012 (1992). [CrossRef]
  3. J. Glimm and A. Jaffe, Quantum Physics (Springer, 1981).
  4. S. Lipson, "Self-Fourier objects and other self-transform objects: comment," J. Opt. Soc. Am. A 10, 2088-2089 (1993). [CrossRef]
  5. E. Titchmarsh, Introduction to the Theory of Fourier Integrals (Clarendon, 1937).
  6. H. Edwards, Riemann's Zeta Function (Dover, 2001).
  7. K. Nishi, "Generalized comb function: a new self-Fourier function," in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2004), Vol. 2, pp. 573-576 (2004).
  8. C. Corcoran and K. Pasch, "Self-Fourier functions and coherent laser combination," J. Phys. A 37, L461-L469 (2004). [CrossRef]
  9. C. Corcoran and K. Pasch, "Modal analysis of a self-Fourier laser cavity," J. Opt. A, Pure Appl. Opt. 7, L1-L7 (2005). [CrossRef]
  10. G. Cincotti, F. Gori, and M. Santarsiero, "Generalized self-Fourier functions," J. Phys. A 25, L1191-L1194 (1992). [CrossRef]
  11. M. Caola, "Self-Fourier functions," J. Phys. A 24, L1143-L1144 (1991). [CrossRef]
  12. I. Stakgold, Green's Functions and Boundary Value Problems (Wiley-Interscience, 1997).
  13. H. Dym and H. McKean, Fourier Series and Integrals (Academic, 1972).
  14. B. Gelbaum and J. Olmsted, Counterexamples in Analysis (Dover, 2003).
  15. M. Lighthill, Introduction to Fourier Analysis (Cambridge U. Press, 1958).
  16. T. Alieva and A. Barbe, "Self-fractional Fourier functions and selection of modes," J. Phys. A 30, L2111-L215 (1997). [CrossRef]

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