New Ray Optics Model for the Directional Distribution of Light Reflected from a Rough Surface

A new ray optics model is presented for the reflection of light both within and without the nominal plane of incidence from the rough airmaterial interface of a randomly rough surface. Such reflection is of particular interest to laser target designation systems. Unlike previous derivations that modeled the rough interface as consisting of microareas randomly oriented but flat facets, this derivation models it as consisting of microareas not only randomly oriented but also randomly curved. Physically, the models are the same, but this new derivation leads to some new and useful results 1 It is found that, for any given rough interface, there exists a single optically smooth curved surface of revolution average irregularity of very restricted shape that will reflect light in the same distribution as that reflected by the rough interface. 2 Modeling this average irregularity as an ellipsoid of revolution gives a surface structure function that is more accurate and useful than previously existing ones. 3 Unlike the facet derivations, this derivation lends itself to a normalization giving the absolute reflectance- distribution function. Reflection by this new interface model, combined with some Lambertain reflection, is tested extensively both within and without the nominal plane of incidence on a variety of rough surfaces and is found to apply rather well.