Overview of modern technologies for measuring, predicting and correcting turbulent distortions in optical waves

This work is an analytical review of the components of modern technology for creating adaptive optics systems for correcting the distortion of optical waves propagating in a turbulent atmosphere. The work consists of the following parts: description of a technique for measuring fluctuations of optical waves in an atmospheric path, theoretical calculations of fluctuations by analytical analysis and mathematical modeling methods, technology for predicting turbulent air movement by the numerical solution of the Navier-Stokes equations and, finally, constructing adaptive optics systems that compensate for the turbulent distortions in optoelectronic image construction systems. Attention is focused on the peculiarities of fluctuations of specially created Laguerre-Gaussian and Bessel-Gaussian beams. Features of the propagation of vortex Laguerre-Gaussian and vortex Bessel-Gaussian beams for the transfer of orbital angular momentum through a turbulent medium are shown. Effects of the relative attenuation of phase and intensity fluctuations of the vortex-free Bessel-Gaussian beams in comparison with similar characteristics of the Gaussian beams are found. The integral scale of the coherence degree of the vortex Bessel-Gaussian beams and vortex conic waves is revealed to be highly sensitive to the influence of atmospheric turbulence, in contrast to the coherence radius of these beams and waves. Arguments are given in favor of the feasibility of constructing adaptive optical systems for a wide-aperture solar telescope operating under a strong atmospheric turbulence.