Introduction

The expressions for reflectance developed in previous chapters of this book implicitly assume that the apparent surface of the particulate medium is smooth on scales large compared with the particle size. Although that assumption may be valid for surfaces in the laboratory, it is certainly not the case for planetary regoliths. In this chapter the expressions that were derived in Chapters 8–10 to describe the light scattered from a planet with a smooth surface will be modified so as to be applicable to a planet with large-scale roughness.

In calculations of this type we are immediately faced with the problem of choosing an appropriate geometric model to describe roughness. Some authors have chosen specific shapes, such as hemispherical cups (Van Diggelen, 1959; Hameen-Anttila, 1967), that approximate impact craters on the surface of a planet. However, such models may not be applicable to other geometries. To make the expressions to be derived as general as possible, it will be assumed that the surfaces are randomly rough. There is a large body of literature that treats shadowing on such surfaces — see, for example, Muhleman (1964), Wagner (1967), Saunders (1967), Hagfors (1968), Lumme and Bowell (1981), and Simpson and Tyler (1982), as well as the references cited in those papers — although many of those papers deal only with specular reflection, such as is involved in analyses of sea glitter or backscattered lunar radar signals.