Broadband wavefront control in a pupil mapping coronagraph

Pupil mapping (a.k.a. Phase-Induced Amplitude Apodization, or PIAA) is a promising technique in high-dynamic range stellar coronagraphy that obtains higher throughput and better inner working angle than any other known approach. As with any coronagraph, the optical surface requirements and the diameter of the controllable region in the image plane are tied to the wavefront control system and optical bandpass. For example, in a monochromatic bandpass, a single ideal deformable mirror (DM) can create a dark hole with a diameter limited by its Nyquist frequency, even for highly aberrated optics. In broadband light, the depth of the dark hole is linked to the wavelength dependence of aberrations, their spatial frequency content, and their propagation through the system. We derive requirements on the surface height and reflectivity power spectral densities for optics in the PIAA system and describe a sequential-DM architecture that will achieve high-contrast over a large optical bandwidth.