Gloss is a quantity used in the optical industry to quantify and categorize
materials according to how well they scatter light specularly. With the aid of
phase perturbation theory, we derive an approximate expression for this
quantity for a one-dimensional randomly rough surface. It is demonstrated that
gloss depends in an exponential way on two dimensionless quantities that are
associated with the surface randomness: the root-mean-square roughness times
the perpendicular momentum transfer for the specular direction, and a
correlation function dependent factor times a lateral momentum variable
associated with the collection angle. Rigorous Monte Carlo simulations are used
to access the quality of this approximation, and good agreement is observed
over large regions of parameter space.Comment: 5 page