Reconstruction the phase front of a vortex laser beam is conducted by use of a Hartmann-Shack wavefront sensor. The vortex beam in the form of the Laguerre-Gaussian LG(0)(1) mode is generated with the help of a spiral phase plate. The new reconstruction technique based on measured wavefront gradients allows one to restore the singular phase surface with good accuracy, whereas the conventional least-squares approach fails.

A numerical experiment is used to study the variance of the wandering of a Laguerre–Gaussian laser beam propagating in a turbulent atmosphere. It is shown that a laser beam with an initial intensity distribution coinciding with that of the Laguerre–Gaussian beam but not having a vortex phase distribution is less resistant to the action of atmospheric turbulence than the Laguerre–Gaussian beam except in the near diffraction zone. The regularities of the beam wandering associated with the values of the azimuth and radial indices of the beam as well as with the intensity and the outer scale of the turbulence are determined.

The comparative numerical and analytical analysis of scintillation indices of the vortex Laguerre-Gaussian beam and the и non-vortex doughnut hole and Gaussian beams propagating in the randomly inhomogeneous atmosphere has been performed. It has been found that the dependence of the scintillation index at the axis of the optical vortex on the turbulence intensity at the path has the form of a unit step. It has been shown that the behavior of scintillations in the cross sections of vortex and non-vortex beams differs widely.OCIS codes: 010.1300; 010.1330; 030.1640; 050.4865; 260.6042. Laser beams having the orbital angular momentum (OAM) [1][2][3] LG , and doughnut hole beam (DH) in the turbulent atmosphere [19]. Then the numerical results are compared with the asymptotic estimation of scintillation at the beam axis.We use the following representation of the complex amplitude of the field in the initial plane (z = 0)

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