On the Impact of Natural Guide-Star Asterism Geometry on Atmospheric Tomography

When imaging a target object in space, atmospheric distortion degrades the angular resolution of an imaging system. Adaptive optics is a method of reducing this degradation by estimating the aberration from the light of a nearby bright guidestar and correcting for the wavefront distortion. Atmospheric tomography can improve the images of astronomical objects that are outside the effective angular distance to a sufficiently bright guide-star. It reconstructs the target wavefront distortion using the wavefront estimates of several guide-stars. The spatial distribution of the guide-stars has a significant impact on the reconstruction performance. Currently, when studying tomography methods, a circular asterism is normally assumed. This holds for laser guide-stars but has limitations when applying atmospheric tomography to natural guide-stars, which are very rarely arranged as a perfect circular asterism with the astronomy target at the centre. This paper uses an empirical approach to investigate the effect of asterism geometry on atmospheric tomographic reconstruction performance. Specifically, several models are developed and compared against one another in terms of predicting the tomographic performance from realworld guide-star coordinates. We find that using support vector regression or a small neural network is sufficient to accurately predict asterism quality using only features calculated from the guide-star geometry (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R^{2}=0.951$</tex>), eliminating the need to compute the projection matrices in real-time for asterism quality evaluation.