Confocal prolate spheroids in an off-axis system

Abstract

The design of an off-axis mirror system, based on a pair of prolate spheroids with a common focus but not a common axis, is considered. With the focus as a pupil, any ray through one focus of a spheroid must pass through all others as each such ray becomes a chief ray. A pseudo- (optical) axis is defined as that chief ray about which other rays are symmetric. A condition to ensure the existence of the pseudoaxis is derived based on a relation between the two eccentricities, the angle that the pseudoaxis makes with the axis of the first spheroid and the angle between the axes of the two spheroids. Data are presented to compare theoretical calculations with computerized real ray-tracing data. A brief discussion is presented to consider the problem of imaging formation.