Scratch-dig is an acknowledged cosmetic specification that is often misused as a specification to limit
scattered light. In spite of its shortcomings, the stray light analyst is often called upon to write this
specification, or at least approve it. An analytic model that relates a bidirectional reflectance distribution
function (BRDF) to a scratch-dig specification is proposed. Applying scalar diffraction theory and some
idealizations for the shape, orientation, and number of scratches and digs; the magnitude and functional form
of the BRDF is derived. The effective BRDF associated with the scratch dig specification is compared with
the magnitude and functional form of the BRDF from surface roughness and contamination.