Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path

The explicit expression for the cross-spectral density of a radial partially coherent beam array with an initial phase distribution propagating through atmospheric turbulence along a slant path is derived and used to study the propagation of composite coherence vortices formed by the radial partially coherent beam array. The dependence of number, position and topological charge of composite coherence vortices on the beam array and atmospheric turbulence parameters is illustrated by numerical examples.