Elliptical reflector: efficiency gain by defocusing

Elliptical reflectors are widely used to couple the radiation of a light source into an optical system. Such a system usually collects the light with an integrating rod, a fiber, or any other kind of light guide. Its entrance window can be conceived as an aperture and an acceptance angle. In illumination designs with elliptical reflectors, sources and apertures are usually positioned in the focal points of the ellipse, probably due to the fact that the foci form a stigmatic pair. This is then implicitly generalized to the case of extended sources and apertures. Surprisingly, a careful investigation revealed that the maximum coupling efficiency is achieved if source and target are not positioned in the focal points. In this paper, a theoretical explanation of this effect is given by a calculation of higher-order magnification properties of an elliptical reflector. Finally, applications in current reflector designs for video projection lamps are shown.