Alternative computation of the Seidel aberration coefficients using the Lie algebraic method

TL;DR

This paper introduces a Lie algebraic approach to systematically compute Seidel aberration coefficients of any order in rotationally symmetric optical systems, linking Hamiltonian optics with aberration analysis.

Contribution

It presents a novel Lie algebraic method for calculating aberration coefficients that maintains the additive property of surface contributions in optical systems.

Findings

Method accurately computes aberration coefficients for complex systems.

Validated approach with three example cases showing good agreement.

Provides a systematic framework linking Hamiltonian optics to aberration analysis.

Abstract

We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction and reflection in phase space. The method offers a systematic way to find aberration coefficients of any order for arbitrary rotationally symmetric optical systems. The coefficients from the Lie method are linked to the Seidel aberration coefficients. Furthermore, the property of summing individual surface contributions is preserved by the Lie algebraic theory. Three examples are given to validate the proposed methodology with good results.