Acquisition and Analysis of Bispectral Bidirectional Reflectance and Reradiation Distribution Functions

In fluorescent materials, light from a certain band of incident wavelengths is reradiated at longer wavelengths, i.e., with a reduced per-photon energy. While fluorescent materials are common in everyday life, they have received little attention in computer graphics. Especially, no bidirectional reradiation measurements of fluorescent materials have been available so far. In this paper, we extend the well-known concept of the bidirectional reflectance distribution function (BRDF) to account for energy transfer between wavelengths, resulting in a Bispectral Bidirectional Reflectance and Reradiation Distribution Function (bispectral BRRDF). Using a bidirectional and bispectral measurement setup, we acquire reflectance and reradiation data of a variety of fluorescent materials, including vehicle paints, paper and fabric, and compare their renderings with RGB, RGBxRGB, and spectral BRDFs. Our acquisition is guided by a principal component analysis on complete bispectral data taken under a sparse set of angles. We show that in order to faithfully reproduce the full bispectral information for all other angles, only a very small number of wavelength pairs needs to be measured at a high angular resolution.