Pupil-remapping mirrors for a four-quadrant phase mask coronagraph

A coronagraph with a four-quadrant phase mask (FQPM) can perfectly eliminate stellar light under ideal conditions. However, the coronagraphic performance is severely degraded in a telescope with a central obscuration. We show that a high-performance FQPM coronagraph can be realized with a centrally obscured telescope by using a two-mirror pupil-remapping system. We calculate the optimal shapes of the remapping mirrors to transform a centrally obscured pupil into clear circular one. The mirror shapes become parabola-like, and the remapping mirrors are shown to provide good coronagraphic performance. The expected performance with adaptive optics systems is also evaluated.