Modeling the Angular Dependence of Emissivity of Randomly Rough Surfaces

Directional emissivity (DE) describes how the emissivity of an isothermal surface changes with viewing angle across thermal infrared wavelengths. The Oxford Space Environment Goniometer (OSEG) is a novel instrument that has been specifically designed to measure the DE of regolith materials derived from planetary surfaces. The DE of Nextel high emissivity black paint was previously measured by the OSEG and showed that the measured emissivity decreases with increasing emission angle, from an emissivity of 0.97 ± 0.01 at 0° emission angle to an emissivity of 0.89± 0.01 at 71° emission angle. The Nextel target measured was isothermal (<0.1 K surface temperature variation) and the observed change in emissivity was due to Fresnel related effects and was not due to non-isothermal effects. Here we apply several increasingly complex modelling techniques to model the measured DE of Nextel black paint. The modelling techniques used here include the Hapke DE model, the Fresnel equations, a multiple slope Fresnel model and a Monte Carlo ray-tracing model. It was found that only the Monte Carlo raytracing model could accurately fit the OSEG measured Nextel data. We show that this is because the Monte Carlo ray-tracing model is the only model that fully accounts for the surface roughness of the Nextel surface by including multiple scattering effects.