2024/12/16 by Drogoul, Audric · 2 citations
#14P10 #14P25 #14Q30 #Algebraic Geometry (math.AG) #F.2.1 #F.2.2 #FOS: Mathematics #FOS: Physical sciences #I.1.2 #I.1.4 #Instrumentation and Methods for Astrophysics (astro-ph.IM) #J.6 #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2412.11546
This paper is devoted to an intrinsic geometrical classification of three-mirror telescopes. The problem is formulated as the study of the connected components of a semi-algebraic set. Under first order approximation, we give the general expression of the transfer matrix of a reflexive optical system. Thanks to this representation, we express the semi-algebraic set for focal telescopes and afocal telescopes as the set of non-degenerate real solutions of first order optical conditions. Then, in order to study the topology of these sets, we address the problem of counting and describe their connected components. In a same time, we introduce a topological invariant which encodes the topological features of the solutions. For systems composed of three mirrors, we give the semi-algebraic description of the connected components of the set and show that the topological invariant is exact.