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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 9 — Sep. 1, 1980
  • pp: 1067–1074

Properties of electromagnetic radiation from a partially correlated current distribution

William H. Carter  »View Author Affiliations

JOSA, Vol. 70, Issue 9, pp. 1067-1074 (1980)

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A free-space solution is found for the field correlation tensors as a Green’s function integral over the correlation tensor for the source currents. This solution is used to formulate a vector theory of partial coherence in an angular spectrum representation. The theory is used to analyze the angular distribution of radiation into the far field for several special cases of source polarization and coherence. It is found that the radiation pattern from unpolarized, quasihomogeneous sources depends on the coherence properties of the source in the same manner as described in scalar theory. However, for sources that are not unpolarized this is not generally the case.

William H. Carter, "Properties of electromagnetic radiation from a partially correlated current distribution," J. Opt. Soc. Am. 70, 1067-1074 (1980)

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  17. W. H. Carter and E. Wolf, "Coherence and Radiometry with Quasihomogeneous Planar Sources," J. Opt. Soc. Am. 67, 785–796 (1977).
  18. Representing a correlation function by a Dirac delta function in the incoherent limit clearly violates the normalization condition g(0) = 1, but is nevertheless a useful approximation [viz., Ref. 2, Eq. (4.31)].
  19. 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); also see Ref. 17, Eq. (4.19a).
  20. Because J(s) is defined by Eq. (70) only over directions s from the origin into the z ≥ 0 half space, we assume J(s) = 0 for all other s. This limits the integration in Eq. (72) to the domain p2+ + q2+ ≤ 1.
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  23. Lamberts law restricts only the portion of the source correlation function with spatial frequencies less than 1/λ, see W. H. Carter and E. Wolf, "Coherence properties of Lambertian and non-Lambertian sources," J. Opt. Soc. Am. 65, 1067–1071 (1975).
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