  The specification of polishing requirements for the optics in coronagraphs
dedicated to exo-planet detection requires careful and accurate optical
modelling. Numerical representations of the propagation of 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 Apodisation (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
sequential DM wavefront actuator correcting such a corrugated field and thus
quantify the requirements on the manufacturing of PIAA mirrors
