On the basis of the extended Huygens-Fresnel principle, a general expression is derived for the mutual coherence function (MCF) of a finite optical beam propagating in a weakly inhomogeneous medium. The results obtained here for the beam MCF are valid both in the near and far field of the laser transmitting aperture and for an arbitrary complex disturbance in the exit pupil of the aperture. A general expression is also derived for the propagation distance zB such that for distances much less (greater) than zB, the MCF is well approximated by the plane (spherical) wave results. An analytic expression is pre-sented for a Gaussian beam such that a numerical error in previous results is corrected. Finally, some comments regarding higher order statistical moments of the field are given.
H. T. Yura, "Mutual Coherence Function of a Finite Cross Section Optical Beam Propagating in a Turbulent Medium," Appl. Opt. 11, 1399-1406 (1972)