Minimum-variance control of astronomical adaptive optic systems with actuator dynamics under synchronous and asynchronous sampling

摘要

Adaptive optic (AO) systems are now routinely used in ground-based telescopes to counter the effects of atmospheric turbulence. A deformable mirror (DM) generates a correction wavefront, which is subtracted from the turbulent wavefront using measurements of the residual phase provided by a wavefront sensor (WFS). Minimizing the variance of the residual phase defines a sampled data control problem combining a continuous time minimum-variance (MV) performance criterion with a discrete-time controller. For a fairly general class of linear time-invariant DM and turbulence WFS models, this control problem can be transformed into an equivalent discrete-time LQ optimization problem involving a set of (discrete-time) control-sufficient statistics of the incoming continuous-time turbulence. This paper shows how to constructively solve this MV problem in the presence of DM's dynamics, starting from continuous-time models of DM and turbulence. This result is extended to the case of asynchronous DM/WFS sampling. An illustrative application to optimal control of tip-tilt turbulent modes for the European extremely large telescope in the presence of first-order DM's dynamics is presented.