Compensation of nonlinear distortions of light beams in the case of restricted deformation of the control mirror

An analysis is made of the influence of constraints relating to the profile of a flexible mirror on the quality of compensation of nonlinear distortions of light beams which are scanned and have a specific transverse distribution. The effects of propagation across thick and thin nonlinear layers are considered. Studies are made of the problems of control of the focusing and tilt of the wavefront of the scanning beam and of the influence of restrictions on the aberration modes when adaptive systems are tuned using the peak intensity or the beam width. It is shown numerically and analytically that it is desirable to use beams with a specific transverse distribution when restrictions are imposed on the wavefront profile.