Propagation of Aberrations through Phase Induced Amplitude Apodization coronagraph

TL;DR

This paper introduces an analytical model to accurately predict how optical aberrations propagate through PIAA coronagraphs, aiding in the design and manufacturing of high-precision exo-planet imaging instruments.

Contribution

It provides the first analytical derivation of aberration propagation and chromatic response in PIAA coronagraphs, enhancing optical modeling capabilities.

Findings

Derived the analytical form of harmonic ripple propagation in PIAA units

Quantified the chromaticity of the field at various optical planes

Assessed wavefront correction requirements for PIAA mirror manufacturing

Abstract

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