Stability of topological properties of optical vortices after diffraction on a phase screen

It is theoretically shown that the distribution of the average intensity of Gaussian optical vortex in the focal plane of a spherical lens scattered by random phase screen has the form of a ring with non-zero value on the optical axis. The radius of the ring depends on the topological charge of the optical vortex and the scattering power of the diffuser. Therefore the topological charge cannot be determined only by the radius of the formed ring. However, it can be determined by the number of points with phase singularity for which detection Shack-Hartmann sensor is used. It is also shown that when using a linear combination of two optical vortices than the distribution of the average intensity will have local maxima the quantity of which is equal to the difference of their topological charges. The number of these maxima does not depend on the degree of diffusion and can serve as an indicator for identifying an optical vortex. Numerical simulation and experiment confirm the theoretical conclusions.