Performance of binoculars: Berek's model of target detection

A model of target detection thresholds, first presented by Max Berek of Leitz, is fitted into a simple set of closed equations. These are combined with a recently published universal formula for the human eye's pupil size to yield a versatile formalism that is capable of predicting binocular performance gains. The model encompasses target size, contrast, environmental luminance, binocular's objective diameter, magnification, angle of view, transmission, stray light, and the observer's age. We analyze performance parameters of various common binocular models and compare the results with popular approximations to binocular performance, like the well-known twilight index. The formalisms presented here are of interest in military target detection as well as in civil applications such as hunting, surveillance, object security, law enforcement, and astronomy.