  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.
