FUNDAMENTAL LIMITATIONS OF HIGH CONTRAST IMAGING SET BY SMALL SAMPLE STATISTICS

Abstract

In this paper, we review the impact of small sample statistics on detection\nthresholds and corresponding confidence levels (CLs) in high contrast imaging\nat small angles. When looking close to the star, the number of resolution\nelements decreases rapidly towards small angles. This reduction of the number\nof degrees of freedom dramatically affects CLs and false alarm probabilities.\nNaively using the same ideal hypothesis and methods as for larger separations,\nwhich are well understood and commonly assume Gaussian noise, can yield up to\none order of magnitude error in contrast estimations at fixed CL. The\nstatistical penalty exponentially increases towards very small inner working\nangles. Even at 5-10 resolution elements from the star, false alarm\nprobabilities can be significantly higher than expected. Here we present a\nrigorous statistical analysis which ensures robustness of the CL, but also\nimposes a substantial limitation on corresponding achievable detection limits\n(thus contrast) at small angles. This unavoidable fundamental statistical\neffect has a significant impact on current coronagraphic and future high\ncontrast imagers. Finally, the paper concludes with practical recommendations\nto account for small number statistics when computing the sensitivity to\ncompanions at small angles and when exploiting the results of direct imaging\nplanet surveys.\n