Phase Errors in Diffraction-Limited Imaging: Contrast Limits for Sparse Aperture Masking

TL;DR

This paper develops formulae to understand phase errors in sparse aperture masking imaging, revealing current observational limits and proposing calibration strategies to improve high-contrast imaging near the diffraction limit.

Contribution

It introduces detailed formulae for third-order phase errors in SAM and kernel-phase techniques, aiding in understanding and mitigating contrast limitations in high-resolution imaging.

Findings

Current observations are limited by temporal phase noise and photon noise.

Formulations enable comparison of phase errors with fundamental noise sources.

Calibration strategies like POISE improve kernel-phase accuracy.

Abstract

Bispectrum phase, closure phase and their generalisation to kernel-phase are all independent of pupil-plane phase errors to first-order. This property, when used with Sparse Aperture Masking (SAM) behind adaptive optics, has been used recently in high-contrast observations at or inside the formal diffraction limit of large telescopes. Finding the limitations to these techniques requires an understanding of spatial and temporal third-order phase effects, as well as effects such as time-variable dispersion when coupled with the non-zero bandwidths in real observations. In this paper, formulae describing many of these errors are developed, so that a comparison can be made to fundamental noise processes of photon- and background-noise. I show that the current generation of aperture-masking observations of young solar-type stars, taken carefully in excellent observing conditions, are consistent with being limited by temporal phase noise and photon noise. This has relevance for plans to combine pupil-remapping with spatial filtering. Finally, I describe calibration strategies for kernel-phase, including the optimised calibrator weighting as used for LkCa 15, and the restricted kernel-phase POISE technique that avoids explicit dependence on calibrators.