Aplanatic corrector designs for the extremely large telescope

The next century is knocking on our door, bringing with it the possibility of telescopes even bigger than the 8-10-m-class instruments that have proliferated over the past decade. The fixed spherical reflector is the most economical and pragmatic way to construct an extremely large primary mirror (30-50 m in diameter). Although spherical mirrors have virtues such as manufacturability and identically figured segments, they also create great amounts of spherical aberration and coma. Here we show that there are several catoptric (all-reflecting) corrector designs that enable a fast telescope based on a spherical primary mirror.