Circularly symmetric apodization via star-shaped masks

In a recent paper, we introduced a class of shaped pupil masks, called spiderweb masks, that produce point-spread functions having annular dark zones. With such masks, a single image can be used to probe a star for extrasolar planets. In this paper, we introduce a new class of shaped pupil masks that also provide annular dark zones. We call these masks star-shaped masks. Given any circularly symmetric apodization function, we show how to construct a corresponding star-shaped mask that has the same point-spread function (out to any given outer working angle) as obtained by the apodization.