Optical scalars and congruences of light rays: A link between beams and analytic aberrations

Abstract

Optical scalars are functions designed to analyze the behavior of geodesic congruences in general relativity. Refracted rays are three-dimensional congruences of light rays and they can be studied with this formalism. In this work we obtain the optical scalars for such congruences: the expansion Θ, the twist ω, and the shear κ. Furthermore, we apply this machinery to study the aberrations of wavefronts to establish a link between them and the aberration function W.