Pupil mapping in two dimensions 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. The pupil mapping technique 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. A planet fainter than 10^-10 times its parent star and as close as about 2λ/D should be detectable. We derive the two-dimensional equations of pupil mapping for both two-mirror and two-lens systems. We give examples for both cases. We derive analytical estimates of aberration in a two-mirror system and show that the aberrations are essentially corrected with an added reversed set of mirrors.