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Light Scattering from Red Pigment Particles: Multiple Scattering in a Strongly Absorbing System
L. E. McNeil a) Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3255 R. H. French DuPont Central Research and Development, Wilmington, Delaware 19880-0356 ~Received 15 May 2000; accepted for publication 16 October 2000 In the optical analysis of collections of particles embedded in a matrix, the ultimate goal is to predict the optical properties of the final film, given the optical characteristics of the materials of which it is made, the particle 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 individual particles. The second is to relate the calculated far-field scattering and absorption cross sections for a single particle to the measured optical characteristics of real films. Here we accomplish these tasks for a regime that is rarely considered in the literature but is quite important in applications. This regime is characterized by three conditions: ~a! the extinction 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 negligible. We have measured the visible diffuse reflectance and transmission of films of quinacridone particles in a transparent resin at various particle volume concentrations, and used the Kubelka–Munk formalism as a parametrization method to extract scattering and absorption parameters for this strongly absorbing, multiple-scattering system in the resonant regime. We have modeled the scattering parameter S* as a convolution of the angular distribution of the scattering from a single particle ~derived from Mie theory! and a multiple-scattering function that characterizes the effects of the concentration and arrangement of the particles in the film. We find that the multiple-scattering function has an angular distribution that is strongly peaked in the backscattering direction. This accounts for the transformation of the collimated and strongly forward-scattered light in the top layers of the film into diffusely reflected light as the film is traversed. The multiple-scattering function also accounts for the differences in diffuse reflection observed for films of identical volume fraction occupied by particles ~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 accessible 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 Kubelka–Munk analysis.
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Comment: (c) 2010 Roger H. French , frenchrh@lrsm.upenn.edu |
