Different methods of optical vortex detection were investigated. The method of generating optical beams with a nonzero orbital angular momentum using a liquid-crystal HoloEye LC-2002 light modulator was demonstrated, and various methods for detecting optical vortices were tested. The distance at which the structure of the vortex beam decays for the technically possible aperture of the receiving interference system was determined. The results of experimental studies of beam size at different distances were presented. Calculations of the beam and the singularity of the optical vortex divergence angle are performed as a function of the length of the atmospheric path. Additional method for vortices detection based on data from the output of the Shack-Hartmann wavefront sensor using a machine learning system was also presented.