Optical Behaviour of Pigmented Coatings

As a model of a pigmented system, consider a pigmented coating on a flat substrate, the whole illuminated and observed from the coating side. A great number of individual effects can occur in this situation, as Fig. 21 shows (except for refraction at the surface of the coating). 

How much these individual processes contribute to the overall behavior of the system will depend on several factors the vehicle, the pigment, the substrate, and 

A quantitative description does become possible, however, if the system under examination satisfies special conditions. These include diffuse, monochromatic illumination, homogeneous pigmentation, isotropic scattering in the coating, no difference in refractive index between vehicle and air, and a coating so thick that the substrate has no effect on the exiting radiation. This is the special case treated by the Kubelka-Munk theory. 

In this model, the relationship between the fraction R of incident light that exits the coating (the remission) and the constants K and S characterizing absorption and scattering, respectively, is given by the formula 

If K and S are known, R can be calculated. In the case of several pigments together, the constants K and S can be calculated with the formulas [8] 

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