Edge-ray method for analysis of radiation transfer among specular reflectors

The analysis of radiation transfer in specular reflector configurations, with multiple or distorted images of an extended radiation source, appears to be so complicated that the need for detailed ray tracing is usually considered inescapable. I show that the number of calculations can be greatly reduced when the source is isotropic. Starting from the fact that the radiation received from an isotropic source depends only on the emissive power of the source and on the angular contour subtended by the source, I show that only edge rays need to be traced, no matter what the curvature of the reflector. Edge rays are rays that pass through the edge of the source or of the reflector. This approach makes it possible to obtain the exact solution for configurations for which the number of reflections is not impractically high. For the solution of general configurations I propose a fast numerical procedure. Based on interpolation between the impact points of a small number of edge rays, it offers high accuracy and unli ted resolution; the convergence is rapid as the number of rays is increased. A test that uses the example of a generalizedcompound parabolic concentrator demonstrates that with this method one can achieve accuracies that are far better than with conventional ray-trace methods while tracing a number of rays that are orders of magnitude smaller.