Investigation of random phase screen influence on topological characteristics of optical vortex

In this paper, we theoretically show that the distribution of the average intensity of the scattered by random phase screen and focused by spherical lens Gaussian optical vortex has a ring shape with non-zero value on the optical axis. The ring radius depends on the optical vortex topological charge and the scattering power of the diffuser. Therefore, measuring of ring radius is not enough for the determination of the topological charge. However, the topological charge can be determined by the number of points with a phase singularity. It is also shown that the distribution of average intensity of the linear combination of two optical vortices has local maxima. The number of local maxima is equal to the difference of the vortices topological charges. The number of these maxima can serve as an indicator for identifying an optical vortex since it does not depend on the degree of diffusion.