  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.
