Ray optics regime for Gaussian random spheres

Abstract

We examine the validity regime of the ray optics approximation for Gaussian random spheres. The Gaussian sphere is fully characterized by the mean and the covariance function of the radius. We calculate the first two moments of the total, Gaussian curvature on such particles, and utilize the second moment in establishing the ray optics regime. As an intermediate result, we obtain the 6 × 6 covariance matrix for the logarithmic radius and its first and second partial derivatives with respect to the spherical angles. The results are useful when analysing the applicability of our earlier ray optics computations for ensembles of Gaussian spheres.