Imaging terrestrial planets with a free-flying occulter and space telescope: an optical simulation

In this manuscript, we further develop our concepts for the free-ying occulter space-based mission, Umbral Missions Blocking Radiating Astronomical Sources (UMBRAS). Our optical simulations clearly show that an UMBRAS-like mission designed around a 4-m telescope and 10-m occulter could directly image terrestrial planets. Such a mission utilizing existing technology could be built and o wn by the end of the decade. Moreover, many of the other proposed concepts for Terrestrial Planet Finder (TPF) could signican tly benet by using an external occulter. We present simulations for an optical design comprising a square aperture telescope plus square external occulter. We show that the entire diraction pattern, which is propagated from occulter to telescope and through telescope to focal plane, may be characterized by two parameters, the Fresnel number and the ratio of the telescope diameter to the occulter width. Combining the eects of a square occulter with apodization provides a much more rapid roll-o in the PSF intensity between the diraction spikes than may be achieved with an unapodized telescope aperture and occulter. We parameterize our results with respect to wavefront quality and compare,them against other competing methods for exo-planet imaging. The combination of external occulter and apodization yields the required contrast in the region of the PSF essential for exo-planet detection. An occulter external to the telescope (i.e., in a separate spacecraft, as opposed to a classical coronagraph with internal occulter) reduces light scatter within the telescope by approximately 2 orders of magnitude. This is due to less light actually entering the telescope. Reduced scattered light signican tly relaxes the constraints on the mirror surface roughness, especially in the mid-spatial frequencies critical for planet detection. This study, plus our previous investigations of engineering as well as spacecraft rendezvous and formation ying, clearly indicates that the UMBRAS concept is very competitive with, or superior to, other proposed concepts for TPF