Fundamental limitations of high contrast imaging set by small sample statistics

TL;DR

This paper analyzes how small sample statistics fundamentally limit the detection thresholds and confidence levels in high contrast imaging near stars, revealing significant impacts on current and future exoplanet imaging efforts.

Contribution

It provides a rigorous statistical framework to account for small sample effects, highlighting limitations and offering practical recommendations for high contrast imaging.

Findings

False alarm probabilities are higher than expected at small angles.

Detection limits are fundamentally constrained by small sample statistics.

Naive Gaussian assumptions can lead to overestimated contrasts.

Abstract

In this paper, we review the impact of small sample statistics on detection thresholds and corresponding confidence levels (CLs) in high contrast imaging at small angles. When looking close to the star, the number of resolution elements decreases rapidly towards small angles. This reduction of the number of degrees of freedom dramatically affects CLs and false alarm probabilities. Naively using the same ideal hypothesis and methods as for larger separations, which are well understood and commonly assume Gaussian noise, can yield up to one order of magnitude error in contrast estimations at fixed CL. The statistical penalty exponentially increases towards very small inner working angles. Even at 5-10 resolution elements from the star, false alarm probabilities can be significantly higher than expected. Here we present a rigorous statistical analysis which ensures robustness of the CL, but also imposes a substantial limitation on corresponding achievable detection limits (thus contrast) at small angles. This unavoidable fundamental statistical effect has a significant impact on current coronagraphic and future high contrast imagers. Finally, the paper concludes with practical recommendations to account for small number statistics when computing the sensitivity to companions at small angles and when exploiting the results of direct imaging planet surveys.