Nonlinear plate equation analysis for the design of large stroke deformable mirror

Abstract

Adaptive Optics (AO) improves the quality of astronomical imaging systems by using real time measurement of the turbulent medium in the optical path. The measurements are then taken and applied to a deformable mirror (DM) that is in the conjugate position of the aberrations in the optical path. The quality of the reconstructed wavefront directly affects the images obtained. One of the limiting factors in current DM technology is the amount of stroke available to correct the wavefront distortions which can be as high as 20 microns of optical path difference. We have developed a simulation analysis using Galerkin's method to solve the nonlinear plate equation. The analysis uses a set of orthogonal equations that satisfied the boundary condition to solve for the linear deformation on the mirror surface. This deformation is used to iteratively converge to the final solution by applying the nonlinear plate equation and the nonlinear actuator forces. This simulation was used to design a microelectromechanical DM with 10 μm of stroke.