Alternative representation of the linear canonical integral transform

Starting with the Iwasawa decomposition of a first-order optical system (or ABCD-system) as a cascade of a lens, a magnifier, and an ortho-symplectic system (a system that is both symplectic and orthogonal), a further decomposition of the ortho-symplectic system in the form of a separable fractional Fourier transformer embedded in 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