I'm thinking about building an all-sky camera, i.e. an automated camera that points straight up to the zenith and that captures the entire sky down to the horizon. The idea is to capture celestial phenomena like meteors.
A lot of the all-sky cameras on the web suffer from suboptimal image quality. I was wondering if, perhaps outside of the classical photography market, there are any lenses that offer a 180° FOV with very little chromatic aberrations, coma and astigmatism, but that are "faster" than about f/4.
If not, is it even possible (from a theoretical optics point of view) to design such a lens?