The ABCD matrix formalism, the Collins formula and the complex amplitude distributions on two spherical surfaces of given curvature and spacing are adapted to the mathematical expression of fractional order Fourier transform.This result provides a general expression as a tool for analyzing complicated systems involving several lenses and mirrors separated by arbitrary distances; for this class of system it is sufficient to specify the ray transfer matrix and the order of fractional Fourier transform to characterize the system completely.2002 Optical Society of America