Procedure for Simulating Divergent-Light Halos

Divergent-light halos are halos produced by light from nearby light sources, like street lamps being scattered by small crystals of ice floating in the air. The use of "brute-force " Monte Carlo methods to simulate such halos is extremely inefficient, as most scattered rays will not hit the eye of the observer. I present a new procedure for Monte Carlo simulations of divergent-light halos. This procedure uses rotational symmetries to make a selected sampling of events that greatly improves the computational efficiency of the algorithm. We can typically generate a simulated halo display in minutes using a personal computer, several orders of magnitude more rapid than a simple brute-force method. The algorithm can also optionally generate three-dimensional pictures of divergent-light halo displays.