Earlier we discussed examples of adaptive phase correction for laser beams and images formed in turbulent atmospheres. Thermal blooming, along with turbulent distortions, is a serious factor that limits concentration of the energy of laser beams on an object. In some situations, in particular, when using an IR laser, thermal blooming is almost the sole obstacle to achieving a high level of intensity on a target.
Various methods are used to make the transfer of energy of an optical beam more efficient. Relatively simple methods are the optimization of power, intensity distribution, focal length , and time conditions of radiation. The methods of a priori (programmed) phase correction (APC), phase conjugation, and wavefront reversal are more complex.
The first two sections in this chapter are devoted to the capabilities of optimization and a priori phase correction on vertical paths with allowance made for the altitude profile of the wind vector and the finite spatial resolution of the corrector in an adaptive system applied to beams with different initial intensity distributions in the cross section. The problem is considered in the approximation of a phase screen, and this allows us to estimate the correction efficiency for extremely wide beams on vertical paths.
Note that the effect of the initial intensity distribution in the beam cross section on the concentration of energy in the receiving aperture has been considered in a number of papers. For example, the problem of thermal blooming of a scanning beam was considered in Ref.  and it was shown that the homogeneous (like a super-Gaussian) intensity distribution gives better results than the Gaussian beam. Various beams having on-axis null and propagating along a homogeneous path without scanning were considered in Ref. . It was shown that in this situation the non-Gaussian intensity distribution gives no significant gain. Nevertheless, for vertical paths such beams can give a marked gain .
The peculiarities of thermal blooming for hyper-Gaussian beams were considered in Ref. . In other papers, square (hyper-Gaussian) and Gaussian beams were compared for a homogeneous (horizontal) path . However, so far there has been no systematic study of thermal blooming for beams of different types propagating along a vertical path.
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