designed shaped apertures delivering 1e-7 contrast at 4 $\lambda$/D. Similarly, [@2011arXiv1108.4050C] showed that shaped pupil can be designed for  1e-6 contrast and $\approx 4 \lambda$/D inner working angle for a variety of centrally obscured and segmented apertures. ]{}

A different approach to this problem is to remap the entrance aperture to remove central obstruction and/or spiders. [@2005PASP..117..295M] propose a 2-mirror system to remove central obstruction and spiders for a four-quadrant coronagraph. [@2006PASP..118..860G] propose a high efficiency nulling coronagraph concept adapted to central obstruction and spiders by performing destructive interferences between pairs of unobstructed off-axis subapertures. [@2009PASP..121.1232L] demonstrate that a prism-like transmissive device and aspheric optics can be used to remove both central obstruction and spiders from the Subaru Telescope pupil, theoretically allowing high performance coronagraphy with the full telescope aperture. These remapping solutions are complex, challenging to implement and align, and extremely sensitive to tip-tilt and stellar angular size [@2009ApJ...702..672C] at high contrast: when points on either size of an obstruction are brought next to each other in the remapped pupil, a small tip-tilt in the entrance beam leads to a phase discontinuity in the remapped beam. When due to finite stellar angular diameters, diffraction due to this discontinuity cannot 