An original classification of obscuration-free telescopes designs unfolded in two dimensions

TL;DR

This paper introduces a novel classification method for unobscured two-dimensional telescope designs, utilizing topology and algebraic geometry to enhance system understanding and optimization potential.

Contribution

It presents an original classification framework based on topology and algebraic geometry, enabling systematic exploration of unobscured telescope configurations.

Findings

Provides a systematic classification for unobscured telescopes

Demonstrates the method on three- and four-mirror systems

Offers a foundation for optimized telescope design

Abstract

In this article we propose an original classification method for unobscured imaging systems unfolded in two dimensions. This classification is based on a study of off-axis properties, and relies on topology and algorithm of real algebraic geometry to find at least one instance by connected component of a semialgebraic set. Our corresponding nomenclature provides intrinsic information about the system, in terms of geometry and manufacturability. The proposed systems for each name of the nomenclature, can be used as starting points for parallel optimizations, allowing for a much more comprehensive search of an unobscured solution, given a set of specifications. We exemplify our method on three and four mirrors imaging systems.