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Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • 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)
http://dx.doi.org/10.1364/OL.32.003531


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Abstract

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

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

Citation
F. Gori and M. Santarsiero, "Devising genuine spatial correlation functions," Opt. Lett. 32, 3531-3533 (2007)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-24-3531


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References

  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]
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  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.
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  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]

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