E. Wolf and W. H. Carter, Opt. Commun. 13, 205 (1975).
M. Beran and G. Parrent, Nuovo Cimento 27, 1049 (1963).
T. J. Skinner, Ph. D. thesis (Boston University, 1965), p. 46.
A. Walther, J. Opt. Soc. Am. 58, 1256 (1968).
E. W. Marchand and E. Wolf, Opt. Commun. 6, 305 (1972).
In this paper, the assumption of statistical homogeneity of the source is to be understood as meaning the property expressed by Eq. (1). For a fuller discussion of this point see footnote 3 of Ref. 1. We implicitly assume that for a finite source, the function Fω(r), introduced in Eq. (1), can be defined for all values of r by analytic continuation; however, within the accuracy of the present theory (which applies only to sufficiently large sources), the exact form of Fω(r) is immaterial when γ = |r| is large compared with the linear dimensions of the area of coherence on the source.
G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. P., Cambridge, 1922), p. 26, Eq. (5) (with an obvious substitution).
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965), p. 682, formula 2 of 6. 554.
The term "large" is to be understood here in the sense explained in the paragraph that follows Eq. (2).
Somewhat-less-precise versions of this result were obtained previously, in Refs. 2 and 4.
C. L. Mehta and E. Wolf, Phys. Rev. 161, 1328 (1967), Eqs. (3. 9)–(3. 11).
In this connection, see the papers by B. Karczewski: (a) Phys. Lett. 5, 191 (1963); (b) Nuovo Cimento 30, 906 (1963).
E. W. Marchand and E. Wolf, J. Opt, Soc. Am. 64, 1219 (1974).
M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1975), Sec. 8. 5. 2.