Open-loop control demonstration of micro-electro-mechanical-system MEMS deformable mirror

New astronomical challenges revolve around the observation of faint galaxies, nearby star-forming regions and the direct imaging of exoplanets. The technologies required to progress in these fields of research rely on the development of custom Adaptive Optics (AO) instruments such as Multi-Object AO (MOAO) or Extreme AO (ExAO). Many obstacles remain in the development of these new technologies. A major barrier to the implementation of MOAO is the utilisation of deformable mirrors (DMs) in an open-loop control system. Micro-Electro-Mechanical-System (MEMS) DMs show promise for application in both MOAO and ExAO. Despite recent encouraging laboratory results, it remains an immature technology which has yet to be demonstrated on a fully operational on-sky AO system. Much of the research in this area focuses on the development of an accurate model of the MEMS DMs. In this paper, a thorough characterization process of a MEMS DM is performed, with the goal of developing an open-loop control strategy free of computationally heavy modelling (such as the use of plate equations). Instead, a simpler approach, based on the additivity of the influence functions, is chosen. The actuator stroke-voltage relationship and the actuator influence functions are carefully calibrated. For 100 initial phase screens with a mean rms of 97 nm (computer generated following a Von Karman statistic), the resulting mean residual open-loop rms error is 16.5 nm, the mean fitting error rms is 13.3 nm and the mean DM error rms is 10.8 nm (error reflecting the performances of the model under test in this paper). This corresponds to 11% of residual DM error.