Propagation of aberrations through phase-induced amplitude apodization coronagraph

The specification of polishing requirements for the optics in coronagraphs dedicated to exoplanet detection requires careful and accurate optical modeling. Numerical representations of propagated aberrations through the system as well as simulations of the broadband wavefront compensation system using multiple DMs are critical when one devises an error budget for such a class of instruments. In this communication, we introduce an analytical tool that serves this purpose for phase-induced amplitude apodization (PIAA) coronagraphs. We first start by deriving the analytical form of the propagation of a harmonic ripple through a PIAA unit. Using this result, we derive the chromaticity of the field at any plane in the optical train of a telescope equipped with such a coronagraph. Finally, we study the chromatic response of a two-sequential-DM wavefront actuator correcting such a corrugated field and thus quantify the requirements on the manufacturing of PIAA mirrors.