OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 3 — Feb. 2, 2009
  • pp: 1746–1752

The van Cittert-Zernike theorem for electromagnetic fields

Andrey S. Ostrovsky, Gabriel Martínez-Niconoff, Patricia Martínez-Vara, and Miguel A. Olvera-Santamaría  »View Author Affiliations

Optics Express, Vol. 17, Issue 3, pp. 1746-1752 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (127 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.

© 2009 Optical Society of America

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

ToC Category:
Coherence and Statistical Optics

Original Manuscript: December 5, 2008
Revised Manuscript: January 9, 2009
Manuscript Accepted: January 16, 2009
Published: January 29, 2009

Andrey S. Ostrovsky, Gabriel Martínez-Niconoff, Patricia Martínez-Vara, and Miguel A. Olvera-Santamaría, "The van Cittert-Zernike theorem for electromagnetic fields," Opt. Express 17, 1746-1752 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. H. van Cittert, "Die Wahrscheinliche Schwingungsverteilung in Einer von Einer Lichtquelle Direkt Oder Mittels Einer Linse Beleuchteten Ebene," Physica 1, 201-210 (1934). [CrossRef]
  2. F. Zernike, "The concept of degree of coherence and its application to optical problems," Physica 5, 785-795 (1938). [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1997).
  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995).
  5. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge, UK, 2007).
  6. A. S. Ostrovsky, P. Martínez-Vara, M. A. Olvera-Santamaría, and G. Martínez-Niconoff, "Vector coherence theory: An overview of Basic concepts and definitions," in Recent Research Developments in Optics, S.G. Pandalai, ed. (Research Signpost, Trivandrum, Kerala, India, to be published).
  7. J. Tervo, T. Setälä, and A. T. Friberg, "Degree of coherence for electromagnetic fields," Opt. Express 11, 1137-1143 (2003). [CrossRef] [PubMed]
  8. J. Tervo, T. Setälä, and A. T. Friberg, "Theory of partially coherent electromagnetic fields in the space-frequency domain," J. Opt. Soc. Am. A 21, 2205-2215 (2004). [CrossRef]
  9. E. Wolf, "Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation," Opt. Lett. 28, 1078-1080 (2003). [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.


Fig. 1

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited