Abstract:
Ground based modern telescopes with AO (Adaptive Optics) are at par with
the space borne telescopes in providing unprecedented quality images. Recently, deformable
mirrors using MEMS (Micro-Electro-Mechanical Systems) have become a popular choice for
adaptive mirrors due to various advantages. The continuous facesheet of the MEMS mirror can
be modeled with the help of theory developed for thin plates [1], [2] and [3]. In this paper we
discuss the modeling techniques using energy principles and variational methods [4] and [5].
For modeling and simulations we will follow the specifications of a commercially available
144 actuator continuous facesheet deformable MEMS mirror by Boston Micromachines
Corporation [6]. The dynamics of this mirror is very fast and hence is neglected when
compared to the rate of corrections to be applied and it is assumed that the boundaries of the
mirror are simply supported. Thus our problem simplifies to that of a simply supported thin
plates static under equilibrium condition. The MEMS mirror equation under the influence
of point load matrix is obtained using superposition principle and Navier solution method is
used for solving the deformation matrix for a given force matrix. In the case of an AO system,
first the atmospheric wavefront is measured which then gives the desired shape of the mirror.
Hence the deformation matrix is known and it is required to derive the force matrix, which
essentially means solving the inverse problem. If the measured wavefront has noise which is
normally the case, or the transformation matrix is rank deficient, the inverse problem becomes
ill-posed [7] and [8].
