A geometrical constraint on shadowing in rough surfaces

By considering a one-dimensional cross-section through the rough surface, we derive a purely geometrical constraint on the statistical distribution of shadowed facet slopes that should be satisfied by any model of surface emissivity that includes the effect of self-shadowing. Our purpose is not to develop a single shadowing model, but to provide a condition that any valid shadowing model should satisfy. Although the emphasis of the presentation is theoretical, some practical ramifications will also be discussed.