Abstract
This study presents a novel means of simplifying the design process of micro machined deformable mirrors. Varying the widths of an array of constant-pitched electrodes allows us to precisely control the electrostatic-force profile needed to shape the mirror using only one voltage input. A mirror is formed by a thin membrane micromachined from a silicon wafer and is coated with a thin metallic film. The electrodes are deposited on a ground plane over which the membrane is suspended. By viewing the mirror as a surface composed of many small patches with the same pitch, the required traction of each patch can be calculated from the desired deformation by using basic elasticity formulae. The analytical solution of the electrostatic field between the mirror and an electrode of one pitch can be obtained by adopting the conformal mapping method. Once establishing the relationship between the traction and the width of the electrode, the widths of all the electrodes can be obtained by correlating the electrode width to that of the design goal. The proposed method applies equally well to design both membrane electrostatic actuators and capacitive sensors. Moreover, the design method is not necessary to solve the PDE (Partial Differential Equations) of the structure governing equations, and is always valid for any axisymmetric deformation.
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