Paraxial ray analysis of a cat's-eye retroreflector

The cat's-eye retroreflector is a passive optical system consisting of a secondary mirror placed at the focal point of a primary lens. We analyze the cat's eye using the paraxial ray matrix approach. The position of the equivalent reflecting surface and the angular field of view of a realizable cat's eye are functions of the radius of curvature of the secondary mirror. The field of view is maximum for a secondary mirror with a concave radius of curvature equal to the focal length of the primary lens. We further derive the general dependence of retroreflection errors on misadjustment of the secondary mirror.