COMPUTATION OF STATIC SHAPES AND VOLTAGES FOR MICROMACHINED DEFORMABLE MIRRORS WITH NONLINEAR ELECTROSTATIC ACTUATORS

In modeling micromachined deformable mirrors with electrostatic actuat ors whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mir rors modeled by a membrane or plate equation with nonlinear electrosta tic actuator characteristics. Numerical methods for computing the mirr or deformation due to given actuator voltages and the actuator voltage s required for producing the desired deformations at the actuator loca tions are presented. The application of the proposed methods to circul ar deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical c ircular micromachined mirror with electrostatic actuators.