Diffraction analysis of two-dimensional pupil mapping for high-contrast imaging

Pupil mapping is a technique whereby a uniformly illuminated input pupil, such as from starlight, can be mapped into a nonuniformly illuminated exit pupil, such that the image formed from this pupil will have suppressed sidelobes, many orders of magnitude weaker than classical Airy ring intensities. Pupil mapping is therefore a candidate technique for coronagraphic imaging of extrasolar planets around nearby stars. Unlike most other high-contrast imaging techniques, pupil mapping is lossless and preserves the full angular resolution of the collecting telescope. So it could possibly give the highest signal-to-noise ratio of any proposed single-telescope system for detecting extrasolar planets. Prior analyses based on pupil-to-pupil ray-tracing indicate that a planet fainter than 10^-10 times its parent star, and as close as about 2λ/D, should be detectable. In this paper we describe the results of careful diffraction analysis of pupil-mapping systems. These results reveal a serious unresolved issue. Namely, high-contrast pupil mappings distribute light from very near the edge of the first pupil to a broad area of the second pupil, and this dramatically amplifies diffraction-based edge effects, resulting in a limiting attainable contrast of about 10^-5. We hope that by identifying this problem, others will provide a solution.