OSA's Digital Library

Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 32, Iss. 24 — Dec. 15, 2007
  • pp: 3531–3533

Devising genuine spatial correlation functions

F. Gori and M. Santarsiero  »View Author Affiliations

Optics Letters, Vol. 32, Issue 24, pp. 3531-3533 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (79 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The choice of the mathematical form of spatial correlation functions for optical fields is restricted by the constraint of nonnegative definiteness. We discuss a sufficient condition for ensuring the satisfaction of such a constraint.

© 2007 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(260.5430) Physical optics : Polarization

ToC Category:
Physical Optics

Original Manuscript: September 19, 2007
Revised Manuscript: November 19, 2007
Manuscript Accepted: November 19, 2007
Published: December 10, 2007

F. Gori and M. Santarsiero, "Devising genuine spatial correlation functions," Opt. Lett. 32, 3531-3533 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  2. P. De Santis, F. Gori, G. Guattari, and C. Palma, J. Opt. Soc. Am. A 3, 1258 (1986). [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  4. J. W. Goodman, Statistical Optics (Wiley, 1983).
  5. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  6. F. Gori, Opt. Commun. 46, 149 (1983). [CrossRef]
  7. F. Gori and E. Wolf, Opt. Commun. 61, 369 (1987). [CrossRef]
  8. F. Gori, Opt. Lett. 4, 354 (1979). [CrossRef] [PubMed]
  9. The authors are indebted to A. T. Friberg for calling this point to their attention.
  10. N. Aronszajn, Trans. Am. Math. Soc. 68, 337 (1950). [CrossRef]
  11. E. Parzen, Ann. Math. Stat. 32, 951 (1961). [CrossRef]
  12. G. Wahba, Spline Models for Observational Data, CBMS-NSF Regional Conference Series in Applied Mathematics 59 (Society for Industrial and Applied Mathematics, 1990). [CrossRef]
  13. S. Saitoh, Integral Transforms, Reproducing Kernels and Their Applications (Addison Wesley Longman, 1997).
  14. A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2003).
  15. For any nonnegative definite kernel there exists a unique functional Hilbert space whose functions are reproduced when they are multiplied by the kernel by means of the scalar product holding for such space. This is the origin of the phrase 'Reproducing kernel Hilbert space.'
  16. F. Gori, Opt. Acta 27, 1025 (1980). [CrossRef]
  17. F. Gori and C. Palma, Opt. Commun. 27, 185 (1978). [CrossRef]
  18. P. Vahimaa and J. Turunen, Opt. Express 14, 1376 (2006). [CrossRef] [PubMed]

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