The open-loop control of MEMS: Modeling and experimental results

As adaptive optics (AO) technology progresses, both wide-field and high-order wavefront correction systems become reachable. Deformable mirrors (DMs) in these advanced architectures must exhibit exemplary performance to give low wavefront error. Such DMs must be economically attainable, meet stroke as well as flatness requirements, and show stable and repeatable actuation. Micro-electrical mechanical systems (MEMS) deformable mirrors, undergoing testing and characterization in the Laboratory for Adaptive Optics (LAO) at the University of California at Santa Cruz, show promise on these fronts. In addition to requiring advanced deformable mirror technology, these progressive AO architectures require advanced DM control algorithms. We therefore present a formulation for accurate open-loop control of MEMS deformable mirrors. The electrostatic actuators in a discrete-actuator MEMS device are attached via posts to a thin reflective top plate. The plate itself can be well-modeled by the thin plate equation. The actuators, although nonlinear in their response to applied voltage and deformation, are independent of each other except through forces transmitted by the top plate and can be empirically modeled via a calibration procedure we will describe. In this paper we present the modeling and laboratory results. So far in the lab we have achieved open loop control to ∼15 nm accuracy in response to arbitrary commands of ∼500 nm amplitude. Open-loop control enables a wealth of new applications for astronomical adaptive optics instruments, particularly in multi-object integral field spectroscopy, which we will describe.