Abstract
We consider the formulation and analysis of a problem of automatic control: correcting for the distortion induced in an optical wave front due to propagation through a turbulent atmosphere. It has recently been demonstrated that high-resolution optical wave-front distortion suppression can be achieved using feedback systems based on high-resolution spatial light modulators and phase-contrast techniques. We examine the modeling and analysis of such adaptive optic systems, and show that under certain conditions, the nonlinear dynamical system models obtained are gradient systems (with energy functions that also serve as Lyapunov functions). These gradient systems (employing fixed phase-contrast sensors) serve as a starting point for understanding the design of practical high-resolution wave-front correction systems, in which the phase-contrast sensor itself is subject to control.
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