The perfomance of generalized Davies-Cotton optical systems with infinitesimal mirror facets

TL;DR

This paper analyzes the imaging and timing performance of generalized Davies-Cotton optical systems with infinitesimal mirror facets, providing Taylor expansions to understand their aberrations and dispersion characteristics.

Contribution

It introduces a mathematical framework using Taylor expansions for modified Davies-Cotton telescopes with discontinuous spherical mirrors, highlighting configurations that optimize aberration and timing.

Findings

Identifies configurations minimizing spherical aberration

Derives Taylor expansions for imaging and timing characteristics

Provides insights into optimizing telescope design

Abstract

This paper presents Taylor expansions for the imaging and timing characteristics of spherical optical systems with infinitesimal mirror facets, sometimes referred to as ''modified Davies-Cotton'' telescopes. Such a system comprises a discontinuous spherical mirror surface whose curvature radius is different from its focal length, and whose mirrors are aligned to suppress spherical aberration. Configurations that range between two ''optima'' are, one of which minimises tangential comatic aberration and the other that minimises timing dispersion.