J. C. Leader, "An analysis of the spatial coherence of laser light scattered from a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536–546 (1976).

M. H. Lee, J. F. Holmes, and J. R. Kerr, "Statistics of speckle propagation through the turbulent atmosphere," J. Opt. Soc. Am. 66, 1164–1172 (1976).

R. L. Fante, "Two-source spherical wave structure functions in atmospheric turbulence," J. Opt. Soc. Am. 66, 74 (1976).

M. J. Beran, "Coherence equations governing propagation through random media," Radio. Sci. 10, 15–21 (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).

D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).

A. Sommerfeld, "Optics," Lectures on Theoretical Physics (Academic, New York, 1954), Vol IV, pp. 197–201.

A. V. Artem'ev and A. S. Gurvich, "Experimental study of coherence function spectra," Radiophys. Quantum Electron. (USSR) 14, 580–583 (1971).

D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).

M. J. Beran, "Coherence equations governing propagation through random media," Radio. Sci. 10, 15–21 (1975).

M. J. Beran, "Propagations of a finite beam in a random medium," J. Opt. Soc. Am. 60, 518–521 (1970).

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), Eqs. 4–25.

M. Born and E. Wolf, Principzes of Optics, 3rd (revised) edition (Pergamon, New York, 1965), pp. 512–513.

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).

A. Kon and V. Feizulin, "Fluctuations in the parameters of spherical waves propagating in a turbulant atmosphere," Radiophys. Quantum Electron. (USSR) 13, 51–53 (1970).

A. V. Artem'ev and A. S. Gurvich, "Experimental study of coherence function spectra," Radiophys. Quantum Electron. (USSR) 14, 580–583 (1971).

A. Kon and V. Feizulin, "Fluctuations in the parameters of spherical waves propagating in a turbulant atmosphere," Radiophys. Quantum Electron. (USSR) 13, 51–53 (1970).

R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, 1964), pp. 311–319.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), Eqs. 4–25.

A. Sommerfeld, "Optics," Lectures on Theoretical Physics (Academic, New York, 1954), Vol IV, pp. 197–201.

V. I. Tatarskii, "The effects of the turbulent atmosphere on wave propagation," translated from the Russian TT-68-50464, 472 pp., National Technical Information Service, U.S. Dept. of Commerce, Springfield, Va. 22151.

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).

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).

M. Born and E. Wolf, Principzes of Optics, 3rd (revised) edition (Pergamon, New York, 1965), pp. 512–513.

H. T. Yura, "Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium," Appl. Opt. 11, 1399–1406 (1972).

J. R. Dunphy and J. R. Kerr, "Turbulence effects on target illumination by laser sources: phenomonological analysis and experimental results," Appl. Opt. 16, 1345–1358 (1977).

R. F. Lutomirski and H. T. Yura, "Propagation of a finite optical beam in an inhomgeneous medium," Appl. Opt. 10, 1652–1658 (1971).

R. L. Fante and J. L. Poirier, "Mutual coherence function of a finite optical beam in a turbulent medium," Appl. Opt. 12, 2247–2248 (1973).

D. E. Barrick, "Rough surface scattering based on the specular point theory," IEEE Trans. Antennas Propag. AP-16, 449–454 (1968).

R. L. Fante, "Two-source spherical wave structure functions in atmospheric turbulence," J. Opt. Soc. Am. 66, 74 (1976).

D. L. Fried, "Optical resolution through a randomly inhomogeneous medium for very long and very short exposures," J. Opt. Soc. Am. 56, 1372–1384 (1966).

M. J. Beran, "Propagations of a finite beam in a random medium," J. Opt. Soc. Am. 60, 518–521 (1970).

W. P. Brown, "Second moment of a wave propagating in a random medium," J. Opt. Soc. Am. 61, 1051–1059 (1971).

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).

R. L. Fante, "Mutual coherence function and frequency spectrum of a laser beam propagating through atmospheric turbulence," J. Opt. Soc. Am. 64, 592–598 (1974).

J. C. Leader, "An analysis of the spatial coherence of laser light scattered from a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536–546 (1976).

M. H. Lee, J. F. Holmes, and J. R. Kerr, "Statistics of speckle propagation through the turbulent atmosphere," J. Opt. Soc. Am. 66, 1164–1172 (1976).

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).

M. J. Beran, "Coherence equations governing propagation through random media," Radio. Sci. 10, 15–21 (1975).

A. Kon and V. Feizulin, "Fluctuations in the parameters of spherical waves propagating in a turbulant atmosphere," Radiophys. Quantum Electron. (USSR) 13, 51–53 (1970).

A. V. Artem'ev and A. S. Gurvich, "Experimental study of coherence function spectra," Radiophys. Quantum Electron. (USSR) 14, 580–583 (1971).

V. I. Tatarskii, "The effects of the turbulent atmosphere on wave propagation," translated from the Russian TT-68-50464, 472 pp., National Technical Information Service, U.S. Dept. of Commerce, Springfield, Va. 22151.

The vector problem can be treated using the technique described in this paper together with the formalism described in J. C. Leader, "The generalized partial coherence of a radiation source and its far-field" Optica Acta (to be published).

A. Sommerfeld, "Optics," Lectures on Theoretical Physics (Academic, New York, 1954), Vol IV, pp. 197–201.

R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, 1964), pp. 311–319.

M. Born and E. Wolf, Principzes of Optics, 3rd (revised) edition (Pergamon, New York, 1965), pp. 512–513.

Use has been made of the fact that *R*^{-} = (|**p**|^{2} + *z*^{2})^{1/2} - (|**p**′|^{2} + *z*^{2})^{1/2} ≅ (1/2*z*) × (|**p**|^{2} - |p′|^{2}) = **P**^{+} · **p**^{-}/*z*.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), Eqs. 4–25.

Ref 17, pp. 50–52.

J. C. Leader, "Incoherent backscatter from rough surfaces: the two scale model re-examined," Radio. Sci. (to be published June/July 1978).