Collection efficiency of conical reflectors

Abstract

We investigate a class of illumination systems, which consist of a light source, a conical (elliptical or parabolic) reflector and an optical device that collects the radiation. The collection efficiency of such systems is limited for conventional means of light collection such as rod and fly's eye integrators. The distribution of the collecting etendue in phase space differs from that of the light, which comes from the reflector. The mismatch is caused by a series of optical effects such as the actual shape of the source, a variable magnification of the conical section, and by consequences from skewness conservation. Nevertheless, this situation is accepted as in many commercial devices, and one may at least ask what conditions yield best efficiency. We show, for example, how to calculate optimum eccentricity of an elliptical reflector to be used with a given source and integrator. To go further and to reduce the etendue mismatch, one may either redesign the lamp for a better fit to the collection system or modify the collection method. Based on the analysis of the conical reflector, we discuss options to achieve better collection efficiency and show examples. For a simultaneous treatment of both elliptical and parabolic reflectors, we introduce a new method that describes the lamp by a luminance distribution on the director circle or plane of the conical section.