# Phase-Apodized-Pupil Lyot Coronagraphs for Arbitrary Telescope Pupils

## TL;DR

This paper introduces a numerical optimization method for phase-apodized-pupil Lyot coronagraphs (PAPLCs) that achieve high-contrast imaging for arbitrary telescope pupils, including complex apertures with obscurations and segmentation.

## Contribution

It presents a globally optimal design approach for PAPLCs applicable to any telescope pupil, enhancing high-contrast imaging capabilities for various astronomical instruments.

## Key findings

- PAPLCs with annular masks perform like APLCs in contrast.
- Knife-edge PAPLCs achieve inner working angles of 1.4λ/D at 10^{-10} contrast.
- Designs are effective for realistic telescope pupils with structural features.

## Abstract

The phase-apodized-pupil Lyot coronagraph (PAPLC) is a pairing of the apodized-pupil Lyot coronagraph (APLC) and the apodizing phase plate (APP) coronagraph. We describe a numerical optimization method to obtain globally-optimal solutions for the phase apodizers for arbitrary telescope pupils, based on the linear map between complex-amplitude transmission of the apodizer and the electric field in the post-coronagraphic focal plane. PAPLCs with annular focal-plane masks and point-symmetric dark zones perform analogous to their corresponding APLCs. However with a knife-edge focal-plane mask and one-sided dark zones, the PAPLC yields inner working angles as close as $1.4\lambda/D$ at contrasts of $10^{-10}$ and maximum post-coronagraphic throughput of >75% for telescope apertures with central obscurations of up to 30%. We present knife-edge PAPLC designs optimized for the VLT/SPHERE instrument and the LUVOIR-A aperture. These designs show that the knife-edge PAPLC retains its performance, even for realistic telescope pupils with struts, segments and non-circular outer edges.