Focal shift of the partially coherent vortex beams focused by an aperture lens

Based on the propagation law of partially coherent beams, the propagation equations of the partially coherent vortex beams focused by an aperture lens are derived. Based on these equations, the focal shift of partially coherent vortex beams is studied, and illustrative numerical results are given. It is found that the focal shift of the partially coherent vortex is dependent not only on the Fresnel number but also on the relative coherent length and the topological charge of the vortex.