Second moments of partially coherent beams in atmospheric turbulence.

Based on the extended Huygens-Fresnel principle, the propagation law of the beam matrix in terms of second moments of the Wigner distribution function for partially coherent beams propagating through atmospheric turbulence was obtained. The general formulas for the mean-squared spatial and angular widths, as well as the beam propagation factor (M(2) factor) of partially coherent beams in turbulence were also derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations of the turbulent atmosphere.