OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 12 — Dec. 1, 2004
  • pp: 2382–2385

Spectral degree of coherence of a random three-dimensional electromagnetic field

Olga Korotkova and Emil Wolf  »View Author Affiliations

JOSA A, Vol. 21, Issue 12, pp. 2382-2385 (2004)

View Full Text Article

Acrobat PDF (129 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The complex spectral degree of coherence of a general random, statistically stationary electromagnetic field is introduced in a manner similar to the way it is defined for a beamlike field, namely, by means of Young’s interference experiment. Both its modulus and its phase are measurable. We illustrate the definition by applying it to blackbody radiation emerging from a cavity. The results are of particular interest for near-field optics.

© 2004 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics
(260.2110) Physical optics : Electromagnetic optics
(260.3160) Physical optics : Interference

Olga Korotkova and Emil Wolf, "Spectral degree of coherence of a random three-dimensional electromagnetic field," J. Opt. Soc. Am. A 21, 2382-2385 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938).
  2. F. Zernike, “Diffraction and optical image formation,” Proc. Phys. Soc. London 61, 158–164 (1948).
  3. E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources II. Fields with a spectral range of arbitrary width,” Proc. R. Soc. London, Ser. A 230, 246–265 (1955).
  4. B. Karczewski, “Coherence theory of the electromagnetic field,” Nuovo Cimento 30, 906–915 (1963).
  5. W. H. Carter and E. Wolf, “Far-zone behavior of electromag-netic fields generated by fluctuating current distributions,” Phys. Rev. A 36, 1258–1269 (1987).
  6. L. Mandel and E. Wolf, “Spectral coherence and concept of cross-spectral purity,” J. Opt. Soc. Am. 66, 529–535 (1976).
  7. E. Wolf and W. H. Carter, “Angular distribution of radiant intensity from sources of different degrees of spatial coherence,” Opt. Commun. 13, 205–209 (1975).
  8. E. Wolf and W. H. Carter, “A radiometric generalization of the van Cittert–Zernike theorem for fields generated by sources of arbitrary state of coherence,” Opt. Commun. 16, 297–302 (1976). see also Ref. 9.
  9. M. J. Bastiaans, “A frequency-domain treatment of partial coherence,” Opt. Acta 24, 261–274 (1977).
  10. E. Wolf, “Unified theory of coherence and polarization of statistical electromagnetic beams,” Phys. Rev. Lett. 312, 263–267 (2003).
  11. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  12. B. Karczewski and E. Wolf, “Comparison of three theories of electromagnetic diffraction at an aperture. Part I: Coherence matrices,” J. Opt. Soc. Am. 56, 1207–1214 (1966).
  13. R. K. Luneberg, Mathematical Theory of Optics (University of California Press, Berkeley and Los Angeles, Calif., 1964), pp. 319–320.
  14. M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, Cambridge, UK, 1999).
  15. Expression (3.14) was noted previously (Ref. 5, Eq. 6.16) as the degree of coherence in a particular case, namely, in the far field generated by three-dimensional fluctuating charge current distribution in free space.
  16. D. F. V. James and E. Wolf, “Determination of the degree of coherence of light from spectroscopic measurements,” Opt. Commun. 145, 1–4 (1998).
  17. V. N. Kumar and D. N. Rao, “Two-beam interference experiments in the frequency-domain to measure the complex degree of spectral coherence,” J. Mod. Opt. 48, 1455–1465 (2001).
  18. An analogous definition of the degree of coherence of a beamlike field in the space–time domain was obtained many years ago by Karczewski in a little-known paper.4
  19. C. L. Mehta and E. Wolf, “Coherence properties of blackbody radiation. III. Cross-spectral tensors,” Phys. Rev. 161, 1328–1334 (1967).

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