Black-Body SNR Formulation of Astronomical Camera Systems

In this paper, we present a formulation for the computation of the SNR of an image system designed for astronomical star observations by combining research results from different disciplines such as physics, astronomy, optics, and electronics. Starting from the energy emitted by the stars and their catalogued magnitudes, we formulate the amount of electrons formed in the pixels of an image sensor using the camera parameters and then compute the quality of the signal in terms of SNR. We provide formulations for both space bound and earth bound observations of stars and present example numerical data for a camera and a telescope system. The formulation given here, although not novel if considered separately in its components, combines the information from different disciplines in an effort to present a complete resource that relates the full image chain from the source to the finally formed image in the hope that it will be a self-contained reference for other researchers working on astronomical camera systems.