Analysis of azimuthal phase mask coronagraphs

TL;DR

This paper provides an analytical framework for azimuthal phase-mask coronagraphs, detailing conditions for optimal performance and exploring various phase functions to improve detection of exoplanets.

Contribution

It introduces necessary conditions for full extinction in azimuthal phase-mask coronagraphs and reviews different phase functions, including new insights for designing advanced masks.

Findings

Conditions for zero average complex amplitude and even Fourier coefficients are established.

Examples of phase functions like optical vortices and four-quadrant masks are reviewed.

A simplified expression for light leaks due to mask imperfections is proposed.

Abstract

In this paper is presented an analytical study of the azimuthal phase-mask coronagraph currently envisioned for detecting and characterizing extra-solar planets. Special emphasis is put on the physical and geometrical interpretation of the mathematical development. Two necessary conditions are defined for achieving full extinction in the pupil plane of the coronagraph, stating that the complex amplitude generated by the phase mask should have zero average, on the one hand, and its Fourier coefficients should only be even, on the other hand. Examples of such phase functions are reviewed, including optical vortices, four-quadrant phase masks, and azimuthal cosine phase functions. Hints for building more sophisticated functions are also given. Finally, a simplified expression of light leaks due to mask imperfection is proposed