Moment-actuator influence function for flat circular deformable mirrors

Abstract

In some applications, moment actuators provide a competitive alternative approach to the conventional piston type of actuators. A pi- ezoelectric or similar device placed between two posts on the back surface of a deformable mirror constitutes one type of moment actuator. A closed form solution of the biharmonic equation of Kirchhoff's thin plate theory is obtained by the classical method of boundary value problems of linear elastomechanics and presented in this paper for the influence function of an arbitrarily located and oriented moment actuator of the above type on the back of a flat circular deformable mirror. The solution covers both radial and tangential moments. The results clearly show their global char- acter in contrast to those for the piston type actuators with high stiffness. An application of these functions to the design of a 30-actuator circular deformable mirror with moment actuators, related hardware, and test results has been reported elsewhere.