L. Mandel and E. Wolf, "Coherence Properties of Optical Fields," Rev. Mod. Phys. 37, 231–287 (1965).

P. Roman, "Correlation Theory of Stationary Electromagnetic Fields, Part III.—The Presence of Random Sources," Nuovo Cimento 20, 759–772 (1961).

P. Roman and E. Wolf, "Correlation Theory of Stationary Electro-magnetic Fields, Part I.—The Basic Field Equation," Nuovo Cimento 17, 462–476 (1960); "Part II.—Conservation Laws," 17, 477–490 (1960).

E. Wolf, "Optics in Terms of Observable Quantities," Nuovo Cimento 12, 884–888 (1954).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (NBS Series 55, Washington, D.C., 1964).

A. Ban¯os, Jr., Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966), Eq. (2.19).

E. Wolf and W. H. Carter, "Coherence and radiant intensity in scalar wave fields generated by fluctuating primary planar sources," J. Opt. Soc. Am. 68, 953–964 (1978).

W. H. Carter, "Radiant Intensity from Inhomogeneous Sources and the Concept of Averaged Cross-Spectral Density," Opt. Commun. 26, 1–4 (1978).

W. H. Carter and E. Wolf, "Coherence and Radiometry with Quasihomogeneous Planar Sources," J. Opt. Soc. Am. 67, 785–796 (1977).

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).

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).

W. H. Carter and E. Wolf, "Correlation Theory of Wavefields Generated by Fluctuating, Three-Dimensional, Primary, Scalar Sources, Part I: General Theory," Opt. Acta (to be published).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1967).

H. Lass, Vector and Tensor Analysis (McGraw-Hill, New York, 1950).

J. Carl Leader, "The Generalized Partial Coherence of a Radiation Source and Its Far Field," Opt. Acta 25, 395–413 (1978).

L. Mandel and E. Wolf, "Coherence Properties of Optical Fields," Rev. Mod. Phys. 37, 231–287 (1965).

A. J. McConnel, Applications of Tensor Analysis (Dover, New York, 1957).

A. S. Marathay and G. B. Parrent, Jr., "Use of scalar theory in optics," J. Opt. Soc. Am. 60, 243–245 (1970).

M. J. Beran and G. B. Parrent, Jr., "On The Equations Governing the Coherence of the Radiation Emitted by Random Charge and Current Distributions," J. Opt. Soc. Am. 52, 98–99 (1962).

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Englewood Clifts, N.J., 1964).

J. Peřna, Coherence of Light (Van Nostrand, New York, 1971), Chap. 8.

P. Roman, "Correlation Theory of Stationary Electromagnetic Fields, Part III.—The Presence of Random Sources," Nuovo Cimento 20, 759–772 (1961).

P. Roman and E. Wolf, "Correlation Theory of Stationary Electro-magnetic Fields, Part I.—The Basic Field Equation," Nuovo Cimento 17, 462–476 (1960); "Part II.—Conservation Laws," 17, 477–490 (1960).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (NBS Series 55, Washington, D.C., 1964).

C. T. Tai, Dyadic Green's Function's in Electromagnetic Theory (Intext, San Francisco, 1971).

E. Wolf and W. H. Carter, "Coherence and radiant intensity in scalar wave fields generated by fluctuating primary planar sources," J. Opt. Soc. Am. 68, 953–964 (1978).

W. H. Carter and E. Wolf, "Coherence and Radiometry with Quasihomogeneous Planar Sources," J. Opt. Soc. Am. 67, 785–796 (1977).

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).

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).

E. W. Marchand and E. Wolf, "Radiometry with Sources of any State of Coherence," J. Opt. Soc. Am. 64, 1219–1226 (1974).

E. W. Marchand and E. Wolf, "Generalized Radiomietry for Radiation from Partially Coherent Sources," Opt. Commun. 6, 305–308 (1972).

E. W. Marchand and E. Wolf, "Angular correlation and the far-zone behavior of partially coherent fields," J. Opt. Soc. Am. 62, 379–385 (1972).

L. Mandel and E. Wolf, "Coherence Properties of Optical Fields," Rev. Mod. Phys. 37, 231–287 (1965).

P. Roman and E. Wolf, "Correlation Theory of Stationary Electro-magnetic Fields, Part I.—The Basic Field Equation," Nuovo Cimento 17, 462–476 (1960); "Part II.—Conservation Laws," 17, 477–490 (1960).

E. Wolf, "Optics in Terms of Observable Quantities," Nuovo Cimento 12, 884–888 (1954).

W. H. Carter and E. Wolf, "Correlation Theory of Wavefields Generated by Fluctuating, Three-Dimensional, Primary, Scalar Sources, Part I: General Theory," Opt. Acta (to be published).

A. S. Marathay and G. B. Parrent, Jr., "Use of scalar theory in optics," J. Opt. Soc. Am. 60, 243–245 (1970).

M. J. Beran and G. B. Parrent, Jr., "On The Equations Governing the Coherence of the Radiation Emitted by Random Charge and Current Distributions," J. Opt. Soc. Am. 52, 98–99 (1962).

E. W. Marchand and E. Wolf, "Angular correlation and the far-zone behavior of partially coherent fields," J. Opt. Soc. Am. 62, 379–385 (1972).

A. Walther, "Radiometry and Coherence," J. Opt. Soc. Am. 58, 1256–1259 (1968).

E. W. Marchand and E. Wolf, "Radiometry with Sources of any State of Coherence," J. Opt. Soc. Am. 64, 1219–1226 (1974).

W. H. Carter and E. Wolf, "Coherence and Radiometry with Quasihomogeneous Planar Sources," J. Opt. Soc. Am. 67, 785–796 (1977).

E. Wolf and W. H. Carter, "Coherence and radiant intensity in scalar wave fields generated by fluctuating primary planar sources," J. Opt. Soc. Am. 68, 953–964 (1978).

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).

E. Wolf, "Optics in Terms of Observable Quantities," Nuovo Cimento 12, 884–888 (1954).

P. Roman and E. Wolf, "Correlation Theory of Stationary Electro-magnetic Fields, Part I.—The Basic Field Equation," Nuovo Cimento 17, 462–476 (1960); "Part II.—Conservation Laws," 17, 477–490 (1960).

P. Roman, "Correlation Theory of Stationary Electromagnetic Fields, Part III.—The Presence of Random Sources," Nuovo Cimento 20, 759–772 (1961).

J. Carl Leader, "The Generalized Partial Coherence of a Radiation Source and Its Far Field," Opt. Acta 25, 395–413 (1978).

E. W. Marchand and E. Wolf, "Generalized Radiomietry for Radiation from Partially Coherent Sources," Opt. Commun. 6, 305–308 (1972).

W. H. Carter, "Radiant Intensity from Inhomogeneous Sources and the Concept of Averaged Cross-Spectral Density," Opt. Commun. 26, 1–4 (1978).

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).

L. Mandel and E. Wolf, "Coherence Properties of Optical Fields," Rev. Mod. Phys. 37, 231–287 (1965).

A. Ban¯os, Jr., Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, New York, 1966), Eq. (2.19).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1967).

C. T. Tai, Dyadic Green's Function's in Electromagnetic Theory (Intext, San Francisco, 1971).

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Englewood Clifts, N.J., 1964).

J. Peřna, Coherence of Light (Van Nostrand, New York, 1971), Chap. 8.

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 p^{2}_{+} + q^{2}_{+} ≤ 1.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (NBS Series 55, Washington, D.C., 1964).

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)].

W. H. Carter and E. Wolf, "Correlation Theory of Wavefields Generated by Fluctuating, Three-Dimensional, Primary, Scalar Sources, Part I: General Theory," Opt. Acta (to be published).

H. Lass, Vector and Tensor Analysis (McGraw-Hill, New York, 1950).

A. J. McConnel, Applications of Tensor Analysis (Dover, New York, 1957).