Low-order aberration sensitivity of eighth-order coronagraph masks

In a recent paper, Kuchner, Crepp, and Ge describe new image-plane coronagraph mask designs that reject to eighth order the leakage of starlight caused by image motion at the mask, resulting in a substantial relaxation of image centroiding requirements compared to previous fourth-order and second-order masks. They also suggest that the new masks are effective at rejecting leakage caused by low-order aberrations (e.g., focus, coma, and astigmatism). In this paper, we derive the sensitivity of eighth-order masks to aberrations of any order and provide simulations of coronagraph behavior in the presence of optical aberrations.We find that the masks leak light as the fourth power of focus, astigmatism, coma, and trefoil. This has tremendous performance advantages for the Terrestrial Planet Finder Coronagraph.