Bastiaans, Martin J.Alieva Krasheninnikova, Tatiana2023-06-202023-06-202006-08-150146-959210.1364/OL.31.002414https://hdl.handle.net/20.500.14352/51271© 2006 Optical Society of America. T. Alieva thanks the Spanish Ministry of Education and Science for financial support (TEC2005-02180/MIC). M. J. Bastiaans can be reached at m.j.bastiaans@tue.nl, and T. Alieva at talieva@fis.ucm.es.On the basis of the modified Iwasawa decomposition of a lossless first-order optical system as a cascade of a lens, a magnifier, and a so-called orthosymplectic system, we show how to synthesize an arbitrary ABCD system (with two transverse coordinates) by means of lenses and predetermined sections of free space such that the lenses are located at fixed positions.engjournal articlehttp://dx.doi.org/10.1364/OL.31.002414http://www.opticsinfobase.org/open access5351st-order opticsRepresentationTransformÓptica (Física)2209.19 Óptica Física