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.