Output irradiance of tapered lightpipes

A light cone efficiently transports, distributes, and concentrates the incoming radiation. I derive a formula for the spatial irradiance (or illuminance) distribution at the exit aperture of a tapered light pipe. The theory is demonstrated by Monte Carlo ray-tracing for lightpipes with light-emitting diodes at the input face. The analysis is based on the addition of the radiation patterns of the multiple virtual sources that, as in a three-dimensional kaleidoscope, are seen through a tapered light tube. Given its explicit dependence on the structural and optical parameters, this analysis may be a useful tool in the development and application of light cones.