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ABSTRACT
In this paper, the approximation of the geometrical optics, for dioptric and catadioptric systems, is displayed without being limited to the paraxial optics. Moreover, caustics are introduced for the catadioptric systems which naturally lead to the conventional conjugation formulas. Furthermore, theses formulas are approached more traditionally for the dioptric systems. Then, from optical systems conforming to the different symmetries, the light guidance is described through application examples in mediums of constant or variable refractive index.
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Read the articleAUTHORS
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Christophe LABBÉ: Associate Professor, University of Caen Normandie Université, UNICAEN, IUT de Caen, Département Mesures Physiques, Caen, France Normandie Université, ENSICAEN, UNICAEN, CEA, CNRS, CIMAP, Caen, France
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Benoît PLANCOULAINE: Associate Professor, University of Caen Normandie Université, UNICAEN, IUT de Caen, Département Mesures Physiques, Caen, France Normandie Université, UNICAEN, INSERM, ANTICIPE, Caen, France Faculty of medicine, Vilnius University, Vilnius, Lithuania
INTRODUCTION
The first section of this article introduces the approximation of geometrical optics, highlighting two complementary approaches: directional and luminous. The first presents Descartes' law in a moving reference frame, while the second highlights the importance of caustics generated by optical systems with the notion of stigmatism. The latter are then developed solely through catacaustics (reflection caustics), leading to the classical relations of spherical mirrors. A third section, on dioptric systems, returns to the consequences of Descartes' law established in the introduction, deducing the formulas for diopters (plane or spherical) illustrated by examples such as the prism or mirages. The final section is still devoted to Descartes' law, but this time in fixed reference frames (cylindrical or spherical coordinates), in order to address the notion of sphericity defect in lenses, and its correction by means of aspherical surfaces. The matrix model of aspherical lenses is then established in paraxial optics. In particular, it verifies the condition of aplanatism. The gradient index property is discussed through the examples of GRIN lenses and optical fibers, and ends with the potential application of spherical lenses (Maxwell, Lüneburg and Eaton-Lippmann lenses).
The entire article is illustrated by numerical examples and industrial applications, and is also intended to be read at several levels, as the reader can browse through the fundamental results or immerse himself in the theoretical demonstrations aided by the boxes for obtaining them.
A table of acronyms and symbols is provided at the end of the article.
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KEYWORDS
optical fiber | geometric optics | caustic | Descartes' laws | dioptric system | catadioptric system | index gradient lens | spherical lens | aspherical lens | ball lens
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Optics and photonics
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