Analytical model of flux propagation in light-pipe systems

Abstract

An analytical model of light propagation in rectangular light pipes, termed the flux confinement diagram (FCD), is developed. Based on the edge ray concept of nonimaging optics, the FCD is a construction that describes the angular distribution of flux propagating in a light pipe depending on a light pipe's index of refraction and its geometry. With the FCD model, the angular "mode" of a ray can be defined at any plane in the system. The FCD model is developed here and used to describe flux input coupling, transport, and output coupling in light-pipe illumination systems. The practical example of a flux loss prediction due to a geometrical change (a bend) is examined using the FCD and compared to a ray-tracing analysis. We discuss how this model of flux propagation is a useful tool to aid in "first-order" design and layout of light-pipe illumination systems.