Light scattering from red pigment particles: Multiple scattering in a strongly absorbing system

In the optical analysis of collections of particles embedded in a matrix, t he ultimate goal is to predict the optical properties of the final film, gi ven the optical characteristics of the materials of which it is made, the p article size, and the fraction of the volume occupied by the particles. The first task in the pursuit of this goal is to make connections between the optical properties of the bulk materials of which the particles and medium are made and the spatial distribution of the scattered intensity from the i ndividual particles. The second is to relate the calculated far-field scatt ering and absorption cross sections for a single particle to the measured o ptical characteristics of real films. Here we accomplish these tasks for a regime that is rarely considered in the literature but is quite important i n applications. This regime is characterized by three conditions: (a) the e xtinction coefficient of the particle is significant; (b) the particle size is comparable to the wavelength in the medium; and (c) the optical density of the films is large enough that multiple scattering is significant, and yet direct transmission of collimated radiation through the film is not neg ligible. We have measured the visible diffuse reflectance and transmission of films of quinacridone particles in a transparent resin at various partic le volume concentrations, and used the Kubelka-Munk formalism as a parametr ization method to extract scattering and absorption parameters for this str ongly absorbing, multiple-scattering system in the resonant regime. We have modeled the scattering parameter S-* as a convolution of the angular distr ibution of the scattering from a single particle (derived from Mie theory) and a multiple-scattering function that characterizes the effects of the co ncentration and arrangement of the particles in the film. We find that the multiple-scattering function has an angular distribution that is strongly p eaked in the backscattering direction. This accounts for the transformation of the collimated and strongly forward-scattered light in the top layers o f the film into diffusely reflected light as the film is traversed. The mul tiple-scattering function also accounts for the differences in diffuse refl ection observed for films of identical volume fraction occupied by particle s (particle volume concentration) but different grinding time. This method of analysis begins to allow one to make an explicit connection between the fundamental optical properties of the particles and the experimentally acce ssible parameters. We have thus developed a way to begin to bridge the gap between the fundamental physics of the scattering of light from individual particles and the practical characterization of a film using the simple Kub elka-Munk analysis. (C) 2001 American Institute of Physics.