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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2412.11546 |
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| _version_ | 1866917900012486656 |
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| author | Drogoul, Audric |
| author_facet | Drogoul, Audric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A certified classification of first-order controlled coaxial telescopes Drogoul, Audric Instrumentation and Methods for Astrophysics Mathematical Physics Algebraic Geometry 14Q30, 14P25, 14P10 J.6; I.1.2; I.1.4; I.1.2; F.2.1; F.2.2 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. |
| title | A certified classification of first-order controlled coaxial telescopes |
| topic | Instrumentation and Methods for Astrophysics Mathematical Physics Algebraic Geometry 14Q30, 14P25, 14P10 J.6; I.1.2; I.1.4; I.1.2; F.2.1; F.2.2 |
| url | https://arxiv.org/abs/2412.11546 |