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 thresholds and corresponding confidence levels (CLs) in highcontrast imaging at small angles. When looking close to the star, the number of resolution elements decreases rapidly toward 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 toward very small inner working angles. Even at 510 resolution elements from the star, false alarm probabilities can be significantly higher than expected. Here we present a rigorous statistical analysis that 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 highcontrast 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 2014
 DOI:
 10.1088/0004637X/792/2/97
 arXiv:
 arXiv:1407.2247
 Bibcode:
 2014ApJ...792...97M
 Keywords:

 methods: statistical;
 techniques: high angular resolution;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 12 pages, 10 figures, accepted to ApJ