Assessing the stability of an ALPAO deformable mirror for feed-forward operation

A deformable mirror (DM) is a mirror whose surface can be deformed in order to correct for optical aberrations. If a DM is used in a feed-forward operation (i.e. without feed-back, also known as open-loop) it is, among other requirements, crucial that a set of actuator commands repeatedly results in the same surface shape. We have tested an ALPAO DM against this criterion, by repeatedly applying a set of actuator commands over hours and monitoring the DM shape with an interferometer. We found that if the surface shape was held to shape A for several hours, then changed to a second shape, ℬ, the DM surface will drift from this new shape over the course of several hours. During this period the root-mean-square (RMS) of the deviation from shape ℬ can exceed 30% of the RMS of the difference between shapes A and ℬ. This can correspond to a surface deviation with RMS of several hundred nanometers, and would severely impact the resulting performance of an AO system using such a DM in a feed-forward operation. We have developed a model to correct for the time-varying surface shape in software by continuously adapting the actuator commands over the stabilization period. Application of the stabilisation procedure allows the surface to remain stable to within 4 nm RMS after a period of 6 minutes. We also provide a suggestion on how to improve the repeatability of surface response to different sets of actuator commands, which can be affected by the surface drift.