Optical Equation
Mathematical modeling of light propagation within porous media allows paper manufacturers to predict the opacity and color of paper sheets. The kubelka munk theory describes this behavior by using two fundamental coefficients for light absorption and scattering. This optical model remains the industry standard for formulation and color matching.
Scattering Coefficient
Light travels through the fibrous matrix where it is both absorbed by dye molecules and scattered by mineral pigments. By calculating the ratio of these absorption and scattering coefficients, the theory predicts the reflectance of a sheet of paper at a given basis weight. This calculation is essential when designing lightweight papers that must remain opaque to prevent text from showing through from the reverse side of the sheet.
Application Utility
Calculations using this formula rely on reflectance measurements of the paper sheet over both a black and a white background. These values are used to calculate the scattering coefficient, which is a measure of the light-scattering power of the paper matrix per unit of basis weight. Coating formulators use these results to determine the optimal blend of titanium dioxide and clay to achieve target brightness and opacity at the lowest cost.
By using this mathematical approach, mills minimize expensive trial-and-run testing on the paper machine and ensure consistent optical performance of the paperboard across different production runs.
