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 NASAs 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.
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