Diffraction of Apodized Pupil Mapping Systems with Aberrations
  Pupil mapping is a promising and unconventional new method for high contrast imaging being considered for terrestrial exoplanet searches. It employs two (or more) specially designed aspheric mirrors to create a high-contrast amplitude profile across the telescope pupil that does not appreciably attenuate amplitude. As such, it reaps significant benefits in light collecting efficiency and inner working angle, both critical parameters for terrestrial planet detection. While much has been published on various aspects of pupil mapping systems, the problem of sensitivity to wavefront aberrations remains an open question. In this paper, we present an efficient method for computing the sensitivity of a pupil mapped system to Zernike aberrations. We then use this method to study the sensitivity of a particular pupil mapping system and compare it to the concentric-ring shaped pupil coronagraph. In particular, we show how contrast and inner working angle degrade with increasing Zernike order and rms amplitude, which has obvious ramifications for the stability requirements and overall design of a planet-finding observatory. 
Ruslan Belikov, N. Jeremy Kasdin, Robert J. Vanderbei