Refractive radiative transfer equation

Abstract

We introduce a refractive radiative transfer equation to the graphics community for the physically based rendering of participating media that have a spatially varying index of refraction. We review principles of geometric nonlinear optics that are crucial to discuss a more generic light transport equation. In particular, we present an optical model that has an integral form suitable for rendering. We show rigorously that the continuous bending of light rays leads to a nonlinear scaling of radiance. To obtain physically correct results, we build on the concept of basic radiance—known from discontinuous refraction—to conserve energy in such complex media. Furthermore, the generic model accounts for the reduction in the speed of light due to the index of refraction to render transient effects like the propagation of light echoes. We solve the refractive volume rendering equation by extending photon mapping with transient light transport in a refractive, participating medium. We demonstrate the impact of our approach on the correctness of rendered images of media that are dominated by spatially continuous refraction and multiple scattering. Furthermore, our model enables us to render visual effects like the propagation of light echoes or time-of-flight imagery that cannot be produced with previous approaches.