title: Alternative representation of the linear canonical integral transform.
abstract: 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.
authors.affiliation: Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, Madrid 28040, Spain. talieva@fis.ucm.es
authors.forename: Tatiana
authors.initials: T
authors.lastname: Alieva
authors.forename: Martin J
authors.initials: MJ
authors.lastname: Bastiaans