Diffraction analysis of pupil mapping systems for planet finding

Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight, can be mapped into a non-uniformly 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. Pupil mapping is lossless and preserves the full angular resolution of the collecting telescope. 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 2 λ/D, could 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 thereby dramatically amplifying diffraction-based edge effects resulting in a limiting attainable contrast of about 10 ^-5. We provide two hybrid designs that provide partial solutions to this problem but a complete resolution remains open.