Computing aberration coefficients for plane-symmetric reflective systems: A Lie algebraic approach

TL;DR

This paper introduces a systematic Lie algebraic method for deriving and analyzing aberration coefficients in plane-symmetric reflective optical systems, enabling high-order aberration treatment with analytical ray-tracing.

Contribution

It presents a novel Lie algebraic approach for calculating aberration coefficients up to arbitrary order in plane-symmetric systems, with explicit second- and third-order results.

Findings

Derived second- and third-order aberration coefficients.

Applied the method to three single-mirror examples.

Provided a systematic framework for high-order aberration analysis.

Abstract

We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in terms of initial ray coordinates. The Lie algebraic method is applied to treat aberrations up to arbitrary order. The presented method provides a systematic and rigorous approach to the derivation, treatment and composition of aberrations in plane-symmetric systems. We give the results for second- and third-order aberrations and apply them to three single-mirror examples.