Configuring an electrostatic membrane reflector with potentials exerted on distributed electrodes

Electrostatic membrane reflector (EMR) is very promised for optical quality application with the merits of utra-lightweight and flexible. Configuring a circular membrane reflector with electrostatic potentials exerted on distributed electrodes can approximatively produce a parabolic shape. A 300mm EMR (made from polyimide) stretched by distributed electrodes below is designed, and the number of concentric electrodes needed for membrane shape forming is analysed. First, based on an analytical solution of Poisson's equation, determine the membrane control matrix by finding influence functions of 3 concentric electrodes and 6 control points on membrane surface in order to compute the needed voltages exerted on the distributed electrodes by the method of least-squares fitting. Then the final shape solved by finite element analysis with ANSYS is contrasted with the paraboloid and deviates greatly when the central displacement of membrane is beyond 2.5mm, but in this range increasing the number of electrodes and control points will get a better shape. The corresponding errors are analyzed, and the control method is concluded. Only using the integrated method of analytical computation, numerical analysis and experiment, the membrane shape of certain central displacement can be exactly predicted and controlled.