If you are indoors and reading this document on paper, then the page may be lit by a fluorescent light bulb. The gases inside the bulb absorb high-energy electrons, and then fluoresce, or re-radiate that absorbed energy at a different frequency. The particular gases in common fluorescent bulbs are chosen to be efficient at re-radiating this energy in the visible wavelengths.

If you are reading this on-line, then you may be reading it on a cathode-ray tube (CRT). The face of the CRT is lined with phosphors, which absorb the high-energy electrons directed at them, and gradually release that energy over time in the visible band.

The two phenomena of fluorescence and phosphorescence are not as common as simple reflection and transmission, but do have an important part to play in the complete description of macroscopic physical behavior that should be modeled by image synthesis programs. This paper presents a mathematical model for global energy balancing which includes these phenomena.

Let's look first at phosphorescence. Here we see a set of three watches. The hands are painted with a phosphorescent ink, which absorbs light when illuminated and then radiates that light back out (note that gamma setting on your monitor may make these pictures darker than they should be). On the far left we see the watch illuminated at 1:00:00, just before the lights are turned off. One second later, at 1:00:01, the hands are glowing brightly enough to see the watch hands and some of the hour markers pretty well. The third picture shows the watch 640 seconds after the lights were turned off: it's 1:10:40, and the hands are much harder to read. At around 2:34 (not shown), about 5700 seconds after the lights are turned off, the hands are giving back only 0.003 percent of the illumination they absorbed.

Three-dimensional image synthesis programs have pushed the theory of geometric optics methods about as far as it can go. Two significant macroscopic phenomena have been notable for their absence from computer-generated images: phosphorescence, and fluorescence. This work provides a mathematical framework for these phenomena. An interesting result is that the famous parallelism exploited by many ray tracing programs is not inherent in the algorithm, but comes from simplicifation of the physics, which is precisely the eilmination of phosphorescent and fluorescent effects.

We phrase the discussion in the context of the Rendering Equation as presented by Kajiya in his classic 1986 paper, which can be derived by using ideas from transport theory. In general, one may consider rendering to be a light transport problem which is solved for a dynamic equilibrium solution. This matches our intuitive experience of the world: when we turn on the lights in a room, then unless something moves the illumination quickly settles down into a stable distribution. In other words, the number of light particles of each frequency that are flowing through a volume of space remains constant.

In this paper we quickly summarize the transport equation that describes this dynamic equilibrium in a scene of surfaces within a participating medium. We show how it can be easily extended to include fluorescence and phosphorescence, and then discuss implementation issues.

The techniques described here are discussed in detail in my paper "A Model for Fluorescence and Phosphorescence", which appears in the Proceedings of the 1994 Eurographics Rendering Workshop. Here's the citation:

Glassner, Andrew S., "A Model for Fluorescence and Phosphorescence", Proceedings Fifth Eurographics Workshop on Rendering (June 1994), Stefan Haas, Stefan Muller, Georg Sakas, Peter Shirley eds., Springer-Verlag, pp. 57-68