Iterative approach to deformable membrane design

A continuous deformable membrane mirror can be fabricated using MEMS processes. It will have a highly reflective thin membrane, which is the mirror surface, and a number of actuators below it. The shape of the mirror surface is controlled by inducing an electrostatic force through applying a voltage between the mirror surface and the actuators. Small displacements of a membrane under tension are governed by Poisson's equation. The solutions of this equation determine the deflections in the vertical direction for different pressures applied at various surface points, due to various electrode positions. This thesis examines the influence of number, position, thickness of the electrodes and also the electrostatic pressure applied by each electrode on the surface of the mirror. A Matlab Graphical User Interface is designed that computes the deflections and uses iterative methods to optimize the voltages on the electrodes, their position and thickness. It produces a deformable membrane design that will match the surface of the mirror to that of a spherical mirror of known radius of curvature.