Operator Formulation for Centered Optical Systems

Abstract

Currently, there are many mathematical methods in use in geometric optics. This paper presents a new mathematical apparatus: an operator formalism, which describes centered optical systems in the paraxial approximation. This work is an ideological continuation of author’s previous research. The refraction and reflection operators of spherical surfaces are defined here. The mathematical properties of the operators are studied, and their physical interpretations are established. In addition, the relations between the lensing operator and the refraction operators of a spherical surface are determined. The behavior of rays is also considered, which helped to establish the injectivity and nondegeneracy for points with infinite coordinates. The operator formalism is helpful for finding a centered optical system that performs a given transformation. Moreover, the interchangeability of the optical operators is investigated, and it is found that each operator has a unique effect.