Generalization of Hamilton’s formalism for geometrical optics

Abstract

A generalization of Hamilton's formalism for geometrical optics is given to provide more convenient descriptions of the optical properties of certain classes of systems. This generalization is made by replacement of the usual points and planes that are effectively used as references from which to measure optical path length in the definition of characteristic functions by more general surfaces. In this way an unlimited number of options are made available. Some particular cases that are well suited to the study of asymmetric systems are investigated.