Design and experiment of microelectrode arrays for deformable membrane mirror

In this paper, a new method which simplifies the design process of micromachined deformable miners is presented By varying the widths of an array of constant-pitched electrodes, the electrostatic-force profile needed to shape the mirror can be precisely controlled by using only one voltage input. A mirror was formed by a thin membrane micromachined from a silicon wafer and is coated with a thin metallic film. The electrodes were deposited on a ground plane over which the membrane is suspended Viewing the mirror as a surface composed of many small patches with the same pitch, we can calculate the required traction of each patch from the deformed shape by using basic elasticity formulae. The analytical solution of the electrostatic field between the mirror and a electrode of one pitch can be obtained by adopting conformal mapping method. Once the relationship between the traction and the width of the electrode was established, the widths of all the electrodes can be obtained by fitting the electrode width to that of the design goal. This new method applies equally well to design both membrane electrostatic actuators and capacitive sensors. The design method is not necessary to solve the PDEs (Partial Differential Equations) of the structure governing equations, and is always valid for any deformation.