Modelling the colour of a coated rough-steel surface

A metal has a typical grey "metallic" look. Different colours can appear when the metallic surface is covered with a thin transparent layer. This is of course the result of interference, and consequently the colour depends on the optical thickness of the layer. Experimental observations can be completely predicted by theoretical modelling. Using the Fresnel equations the colour can be calculated within excellent agreement of the experimental observations. Fresnel, of course, assumes perfectly flat surfaces. Roughness complicates matters: the optical path within the coating no longer depends on the local thickness of the coating only, but also on the angle of scattering at the underlying metal, both varying from point to point. In this presentation we describe how the roughness can be taken into account in predicting the colour. The scattered light was calculated using the "Modeled Integrated Scattering Tool", a computer program developed at the "National Institute of Standards and Technology" (USA). The non-uniformity of the coatings was taken into account by considering different coatings thicknesses. The resulting colour is calculated by taking the average of the obtained reflections. Finally the colours were measured with a spectrophotometer. It turned out that the modelled and the measured colours agree very well, confirming the validity of the used model.