Characterizing MEMS deformable mirrors for open-loop operation: High-resolution measurements of thin-plate behavior

TL;DR: In this article, a thin-plate equation was used to model the surface deflection of a micro-electrical mechanical system (MEMS) for open-loop control of multiple DMs.

Abstract: New concepts for astronomical adaptive optics are enabled by use of micro-electrical mechanical systems (MEMS) deformable mirrors (DMs). Unlike traditional DMs now used in astronomical AO systems, MEMS devices are smaller, less expensive, and exhibit extraordinarily repeatable actuation. Consequently, MEMS technology allows for novel configurations, such as multi-object AO, that require open-loop control of multiple DMs. At the UCO/Lick Observatory Laboratory for Adaptive Optics we are pursuing this concept in part by creating a phaseto- voltage model for the MEMS DM. We model the surface deflection approximately by the thin-plate equation. Using this modeling technique, we have achieved open-loop control accuracy in the laboratory to ~13-30 nm surface rms in response to ~1-3 μm peak-to-valley commands, respectively. Next, high-resolution measurements of the displacement between actuator posts are compared to the homogeneous solution of the thin-plate equation, to verify the model's validity. These measurements show that the thin-plate equation seems a plausible approach to modeling deformations of the top surface down to lateral scales of a tenth actuator spacing. Finally, in order to determine the physical lower limit to which our model can be expected to be accurate, we conducted a set of hysteresis experiments with a MEMS. We detect only a sub-nanometer amount of hysteresis of 0.6±0.3 nm surface over a 160-volt loop. This complements our previous stability and position repeatability measurements, showing that MEMS DMs actuate to sub-nanometer precision and are hence controllable in open-loop.