[[abstract]]In this paper, a new method which simplifies the design process of micromachined deformable mirrors 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 using only one voltage input. In the past, either several independent voltages were necessary or, if only one voltage was available, numerical schemes were required to search for the optimal sizes and locations of a few electrodes. 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. Viewing the mirror as a surface composed of many small patches with the same pitch, we can calculate the average force of each patch from the deformed shape using basic elasticity formulae. Using conformal mapping method, we can solve the analytical solution of the electrostatic field between the mirror and the electrode in one pitch. The relationship between the force and the width of the electrode is established. Finally, the widths of all the electrodes are obtained, and this new method applies equally well to the designs of both membrane electrostatic actuators and capacitive sensors.
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