Monzón Serrano, Juan JoséMontesinos Amilibia, José MaríaSánchez Soto, Luis Lorenzo2023-06-162023-06-162020-020030-394110.1364/JOSAA.378661https://hdl.handle.net/20.500.14352/6123Received 23 September 2019; revised 1 December 2019; accepted 6 December 2019; posted 6 December 2019 (Doc. ID 378661); published 10 January 2020We revisit the basic aspects of first-order optical systems from a geometrical viewpoint. In the paraxial regime, there is a wide family of beams for which the action of these systems can be represented as a Möbius transformation. We examine this action from the perspective of non-Euclidean hyperbolic geometry and resort to the isometric-circle method to decompose it as a reflection followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations for basic elements, such as free propagation and thin lenses, and link them with physical parameters of the system.engjournal articlehttps://doi.org/10.1364/JOSAA.378661https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-37-2-225restricted access535.31514.13Geometric opticsLigth beamsLight fieldsOptocal systemsParaxial waveCoherenceÓptica (Física)Óptica geométrica e instrumental2209.19 Óptica Física2209.06 Óptica geométrica