Phase apodized vortex coronagraphs for arbitrary apertures: a case study for the Habitable Worlds Observatory

The HWO enables direct characterization of Earth-like exoplanets which will require high-performance starlight suppression across a broad spectral bandwidth. The vector vortex coronagraph is a promising option due to its achromatic and scale-invariant properties. However, realistic telescope apertures with segments and a secondary obscuration present a challenge to its performance. We present optimized phase-apodizer designs for HWO and compare these to traditional amplitude apodizers, highlighting their advantages in terms of efficiency. Our simulations demonstrate the achromaticity of the phase designs when they are implemented using the geometric phase of patterned liquid-crystal retarders. We also show that the phase designs can be optimized for both circular polarization states simultaneously, confirming that no polarization filtering is required.