Studies on small circular membrane mirrors with electrostatic actuation and closed loop control

This paper discusses small deformable mirrors based on thin metallized membranes and designed for steering and focusing of beams as well as providing correction for a small number of optical aberration modes. We consider circular membranes driven electrostatically by four electrodes deposited on or milled into a light weight substrate. The metallized surface on the membrane, while acting as a mirror also provides the ground electrode to enable actuation. Here we discuss prototype testing of the mirrors based on different production techniques, and report on closed loop control studies using two formulations: (1) an approximate lumped-parameter model based on a single-input-single-output linearized treatment, and (2) a linearized, continuous parameter model leading to a multiple-input-multiple-output state space system via modal expansion. A quadrant photo-detector ("quad cell") is used as an output sensor.