  Stellar coronagraphs rely on deformable mirrors (DMs) to correct wavefront
errors and create high contrast images. Imperfect control of the DM limits the
achievable contrast and, therefore, the DM control electronics must provide
fine surface height resolution and low noise. Here, we study the impact of
quantization errors due to the DM electronics on the image contrast using
experimental data from the High Contrast Imaging Testbed (HCIT) facility at
NASA's Jet Propulsion Laboratory (JPL). We find that the simplest analytical
model gives optimistic predictions compared to real cases, with contrast up to
3 times better, which leads to DM surface height resolution requirements that
are incorrectly relaxed by 70%. We show that taking into account the DM
actuator shape, or influence function, improves the analytical predictions.
However, we also find that end-to-end numerical simulations of the wavefront
sensing and control process provide the most accurate predictions and recommend
such an approach for setting robust requirements on the DM control electronics.
From our experimental and numerical results, we conclude that a surface height
resolution of approximately 6pm is required for imaging temperate terrestrial
exoplanets around Solar-type stars at wavelengths as small as 450nm with
coronagraph instruments on future space telescopes. Finally, we list the
recognizable characteristics of quantization errors that may help determine if
they are a limiting factor.
