In order for computer generated imagery to recreate the characteristic visual appearance of phenomena such as smoke and fog it is necessary to compute the way in which light interacts with participating media. In this work we present a novel technique for computing volumetric single scattering lighting solutions for particle-based inhomogeneous participating media data sets. We seek to calculate volumetric lighting solutions for particle-based data sets as such data sets have the advantage of being spatially unbounded and relatively unrestricted with regard to memory as compared to uniform grids. In order to perform the calculations which are required for computing such a lighting solution, we introduce a novel octree based data structure. We refer to this new data structure as a density octree. The design of the density octree allows for efficiently computing light attenuation throughout the spatial extent. Using our data structure, we are able to produce high quality output imagery of arbitrary particle data sets in the presence of arbitrary numbers of lights.