Deriving Deformable Mirror Performance Requirements in Simulation

Coronagraphs rely on predictable and stable deformable mirror (DM) surface displacement to achieve the contrast required to detect Earth-sized exoplanets in the habitable zone of their host star. Anomalous DM behavior, such as unstable or pinned actuators, can limit contrast in coronagraphs. Simulating how these undesired behaviors affect the performance of a high contrast imaging architecture is important for developing requirements on their control electronics. Simulating a vortex coronagraph (VC) with two deformable mirrors, this study quantifies how the number of pinned actuators affects the performance of focal plane wavefront control, both with and without periodically aggressive regularization values. The simulations also quantify how various types of voltage noise such as zero-mean Gaussian noise, zero-mean periodic noise, and drift can affect the contrast of a VC during an observation run. A tolerance of a change in the mean normalized intensity of 1 x 10(-11) is allocated to both types of error. If periodically aggressive regularizations are used with electric field conjugation (EFC), only 1 pinned actuator on both DMs can be tolerated. If a regularization grid search is used for EFC, the DMs cannot have any pinned actuators. For the case of zero-mean Gaussian noise and zero-mean periodic noise, one can tolerate a noise standard deviation of no more than sigma = 0.45 mV. For drift, one can only tolerate sigma = 0.30 mV or less. These results show that the DM electronics and the DMs themselves need to be nearly defect free to avoid having more than 1 pinned actuator. It is important that the electronics designer attempts to minimize the noise by not only selecting high quality components but also control the output voltage to minimize drift.