Vol. 11, issue 11, article # 12

Kanev F.Yu., Lavrinova L.N., Lukin V.P. Adaptive compensation for time-dependent thermal blooming with local extrema in the space of control coordinates. // Atmospheric and oceanic optics. 1998. V. 11. No. 11. P. 1056-1062.
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Laser beam adaptive control with the use of a multidither algorithm is considered under the conditions of thermal blooming. If the algorithm is applied before the termination of transient processes in a medium, an adaptive system finds the region of the extremum but leaves it in a short while. Time required to find the extremum is defined by the value of a gradient step, lesser is the step, greater is the time. On the contrary, the time interval during which the system remains in the vicinity of the extremum is inversely proportional to the value of the step. The problem becomes even more complicated if local maxima appear in the space of control coordinates. In this case if the value of a gradient step is chosen too small the algorithm stops in a local maximum. It was shown that initially the control should be applied only to the tilt of the beam wave front, the step of the algorithm can be taken large that ensures the termination of the control in the vicinity of the global extremum. After that, to detect precisely the location of the maximum, the control algorithm could be applied to other coordinates.