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Future large space- or ground-based telescopes will offer the resolution andsensitivity to probe the habitable zone of a large sample of nearby stars forexo-Earth imaging. To this end, such facilities are expected to be equippedwith a high-contrast instrument to efficiently suppress the light from anobserved star to image these close-in companions. These observatories willinclude features such as segmented primary mirrors, secondary mirrors, andstruts, leading to diffraction effects on the star image that will limit theinstrument contrast. To overcome these constraints, a promising method consistsin combining coronagraphy and wavefront shaping to reduce starlight at smallseparations and generate a dark region within the image to enhance theexoplanet signal. We aim to study the limitations of this combination whenobserving short-orbit planets. Our analysis is focused on SPEED, the Nice testbed with coronagraphy, wavefront shaping with deformable mirrors (DMs), andcomplex telescope aperture shape to determine the main realistic parametersthat limit contrast at small separations. We develop an end-to-end simulator ofthis bench with Fresnel propagation effects to study the impact of large phaseand amplitude errors from the test-bed optical components and defects from thewavefront shaping system on the final image contrast. We numerically show thatthe DM finite stroke and non-functional actuators, coronagraph manufacturingerrors, and near-focal-plane phase errors represent the major limitations forhigh-contrast imaging of exoplanets at small separations. We also show that acarefully defined optical set-up opens the path to high contrast at smallseparation.

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