  Telescope pupil fragmentation from spiders generates specific aberrations
observed at various telescopes and expected on the large telescopes under
construction. This so-called island effect induces differential pistons, tips
and tilts on the pupil petals, deforming the instrumental PSF, and is one of
the main limitations to the detection of exoplanets with high-contrast imaging.
These aberrations have different origins such as the low-wind effect or
petaling errors in the adaptive-optics reconstruction. In this paper, we
propose to alleviate the impact of the aberrations induced by island effects on
high-contrast imaging by adapting the coronagraph design in order to increase
its robustness to petal-level aberrations. Following a method first developed
for errors due to primary mirror segmentation (segment phasing errors, missing
segments...), we develop and test Redundant Apodized Pupils (RAP), i.e.
apodizers designed at the petal-scale, then duplicated and rotated to mimic the
pupil petal geometry. We apply this concept to the ELT architecture, made of
six identical petals, to yield a 10^-6 contrast in a dark region from 8 to
40lambda/D. Both amplitude and phase apodizers proposed in this paper are
robust to differential pistons between petals, with minimal degradation to
their coronagraphic PSFs and contrast levels. In addition, they are also more
robust to petal-level tip-tilt errors than apodizers designed for the whole
pupil, with which the limit of contrast of 10^-6 in the coronagraph dark zone
is achieved for constraints up to 2 rad RMS of these petal-level modes. The RAP
concept proves its robustness to island effects (low-wind effect and
post-adaptive optics petaling), with an application to the ELT architecture. It
can also be considered for other 8- to 30-meter class ground-based units such
as VLT/SPHERE, Subaru/SCExAO, GMT/GMagAO-X, or TMT/PSI.

Instrumentation and Methods for Astrophysics