High contrast at small separation -- II. Impact on the dark hole of a realistic optical set-up with two deformable mirrors

Future large space- or ground-based telescopes will offer the resolution and sensitivity to probe the habitable zone of a large sample of nearby stars for exo-Earth imaging. To this end, such facilities are expected to be equipped with a high-contrast instrument to efficiently suppress the light from an observed star to image these close-in companions. These observatories will include features such as segmented primary mirrors, secondary mirrors, and struts, leading to diffraction effects on the star image that will limit the instrument contrast. To overcome these constraints, a promising method consists in combining coronagraphy and wavefront shaping to reduce starlight at small separations and generate a dark region within the image to enhance the exoplanet signal. We aim to study the limitations of this combination when observing short-orbit planets. Our analysis is focused on SPEED, the Nice test bed with coronagraphy, wavefront shaping with deformable mirrors (DMs), and complex telescope aperture shape to determine the main realistic parameters that limit contrast at small separations. We develop an end-to-end simulator of this bench with Fresnel propagation effects to study the impact of large phase and amplitude errors from the test-bed optical components and defects from the wavefront shaping system on the final image contrast. We numerically show that the DM finite stroke and non-functional actuators, coronagraph manufacturing errors, and near-focal-plane phase errors represent the major limitations for high-contrast imaging of exoplanets at small separations. We also show that a carefully defined optical set-up opens the path to high contrast at small separation.