Two‐Mirror Apodization for High‐Contrast Imaging

Direct detection of extrasolar planets will require imaging systems capableof unprecedented contrast. Apodized pupils provide an attractive way to achievesuch contrast but they are difficult, perhaps impossible, to manufacture to therequired tolerance and they absorb about 90% of the light in order to createthe apodization, which of course lengthens the exposure times needed for planetdetection. A recently proposed alternative is to use two mirrors to accomplishthe apodization. With such a system, no light is lost. In this paper, weprovide a careful mathematical analysis, using one dimensional mirrors, of theon-axis and off-axis performance of such a two-mirror apodization system. Thereappear to be advantages and disadvantages to this approach. In addition to notlosing any light, we show that the nonuniformity of the apodization implies anextra magnification of off-axis sources and thereby makes it possible to builda real system with about half the aperture that one would otherwise require or,equivalently, resolve planets at about half the angular separation as one canachieve with standard apodization. More specifically, ignoring pointing errorand stellar disk size, a planet at $1.7 \lambda/D$ ought to be at the edge ofdetectability. However, we show that the non-zero size of a stellar disk pushesthe threshold for high-contrast so that a planet must be at least $2.5\lambda/D$ from its star to be detectable. The off-axis analysis oftwo-dimensional mirrors is left for future study.