Matrix formulation of higher-order moments of partially coherent beams propagating through atmospheric turbulence along a slanted path

Based on the extended Huygens–Fresnel principle, the matrix formulae of higher-order moments of partially coherent beams propagating through atmospheric turbulence along a slanted path are derived by using the Wigner distribution function (WDF). The same matrix formulae for propagation along a vertical path, a horizontal path and in free space are discussed as special cases of our general results. Analytical expressions for the important turbulence parameters contained in the matrix formulae of higher-order moments are also derived. (paper)