Circularly Symmetric Apodization via Starshaped Masks

Recently, 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 starshaped masks. Given any circularly symmetric apodization function, we show how to construct a corresponding starshaped mask that has the same point-spread function (out to any given outer working distance) as obtained by the apodization.