Alieva Krasheninnikova, TatianaBastiaans, Martin J.2023-06-202023-06-202005-12-150146-959210.1364/OL.30.003302https://hdl.handle.net/20.500.14352/51275© 2005 Optical Society of America. The Spanish Ministry of Education and Science is acknowledged for financial support through a “Ramon y Cajal” grant and projects TIC 2002-01846 (T. Alieva, talieva@fis.ucm.es) and SAB2004-0018 (M. J. Bastiaans, m.j.bastiaans@tue.nl).Starting with the Iwasawa-type decomposition of a first-order optical system (or ABCD system) as a cascade of a lens, a magnifier, and an orthosymplectic system (a system that is both symplectic and orthogonal), a further decomposition of the orthosymplectic system in the form of a separable fractional Fourier transformer embedded between two spatial-coordinate rotators is proposed. The resulting decomposition of the entire first-order optical system then shows a physically attractive representation of the linear canonical integral transformation, which, in contrast to Collins integral, is valid for any ray transformation matrix.engjournal articlehttp://dx.doi.org/10.1364/OL.30.003302http://www.opticsinfobase.org/open access535OpticsÓptica (Física)2209.19 Óptica Física