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J. Cosmet. Sci. J 56, 193-204 (May/June 2005) Spatial and angular distribution of light incident on coatings using Mie-scattering Monte Carlo simulations MASAKO YAMADA, MATTHEW D. BUTTS, and KAREN K. KALLA, General Electric Global Research CenterJ 1 Research Circle, Niskayuna} NY 12309 (M. Y., M.D.B.), and Procter and Gamble, 11810 East Miami River Road, Cincinnati, Ohio 45252 (K.K.K.). Accepted for publication March 14, 2005. Synopsis We show the results of Mie-scattering Monte Carlo models developed to simulate the optical properties of light incident on particle-containing coatings. The model accommodates mixtures of particles with different sizes and complex refractive indices, enabling the simulation of formulations, including pigments. The simulation tracks trajectories of photons as they propagate through the turbid medium, calculating both angular and spatial light intensity distributions. Scalar quantities such as total transmission and reflection, and haze and diffuse reflectance, are also calculated. INTRODUCTION This paper describes the optical properties of hypothetical formulations using Mie- scattering Monte Carlo simulations. Radiative transport of light through a turbid film can be calculated using methods such as Kubelka-Munk (1), discrete ordinates (2), and adding-doubling (3), leading to the ability to predict parameters such as transmission, reflection, and angular intensity distribution. However, the Monte Carlo method has the advantage of allowing trajectories of individual photons to be tracked as they propagate through the film, enabling a more thorough analysis of both angular and spatial dis- tributions of the photons. Volumetric scattering properties of photons within a material are considered crucial in achieving a realistic look in turbid media such as marble, milk, and skin (4). The Henyey-Greenstein phase function (or the even simpler anisotropic phase function) is often used in Monte Carlo simulations to approximate the angular scattering distri- bution of light incident on a single sphere (5 ). Although this simplification is effective in many scenarios, it disregards subtleties in the phase function that may contribute to differences in appearance. We have developed a simulation that calculates the exact Mie phase function of light incident on a sphere based on its complex refractive index (RI) and size parameter (6-8) Address all correspondence to Matthew D. Butts. 193