Adaptive focusing of an optical beam by a system with delay in the control channel

An aberration-free description of the propagation of a light beam is used to analyze and identify the characteristic features of continuous control of beam focusing by a system with a delay. It is shown that some control regimes may be oscillatory or diverging. The conditions for the appearance of these regimes are found. It is concluded that the conditions governing the operation of a system with a delay and a continuous control algorithm are equivalent to those for a system without a delay and with a discrete control algorithm.