A tip-tilt adaptive optics system for amateur astronomers and optimum placement of actuators

A major concern in the design of a tip-tilt adaptive optics system, for ama teur astronomical telescopes, is to find optimum positions of the actuators that result in least distortions of the mirror surface. A semi-analytical approach has been used, wherein the mirror is modelled as a thin circular p late with a peripheral ring mass and an elastic edge support. Modal analysi s is performed to determine the natural frequencies and mode shapes of the system. The results of the modal analysis are incorporated in the subsequen t harmonic analysis, where the response of the system to harmonic forces, a pplied by the three actuators? is expressed in terms of the Green functions . For various positions of the actuators, the maximum distortions on the mi rror surface are evaluated, and from these results, the optimum positions o f the actuators are located. The semi-analytical results are vertified by p urely numerical results obtained from finite element analysis. (C) 1999 Aca demic Press.