Using ray matrices to derive analytical expressions of optical aberrations

Abstract

In this work we show an easy way to derive approximated analytical expressions for spherical aberration. It is based on the use of 3×3 ray matrices, where additional elements are included to account for the errors in the ray height and angle propagation. The technique, which is commonly used to analyze misaligned systems in optical resonators, is here applied to account for deviations from the paraxial regime caused by spherical aberration.