Reflectivity and optical surface height requirements in a broadband coronagraph. 1. Contrast floor due to controllable spatial frequencies.

We derive the broadband contrast floor in a coronagraphic telescope having nonideal optical surfaces. We consider only fundamental spatial frequencies within the control bandwidth of the coronagraph's deformable mirror. Cross terms arising from the beating of spatial frequencies beyond the deformable mirror control bandwidth will be considered in a second paper. Two wavefront control systems are analyzed:a zero-path difference Michelson interferometer with two deformable mirrors at a pupil image, and a sequential pair of deformable mirrors with one placed at a pupil image. We derive requirements on optical surface figure and reflectivity uniformity for both cases.