title: Fast linear canonical transforms.
abstract: The linear canonical transform provides a mathematical model of paraxial propagation though quadratic phase systems. We review the literature on numerical approximation of this transform, including discretization, sampling, and fast algorithms, and identify key results. We then propose a frequency-division fast linear canonical transform algorithm comparable to the Sande-Tukey fast Fourier transform. Results calculated with an implementation of this algorithm are presented and compared with the corresponding analytic functions.
authors.affiliation: UCD Communications and Optoelectronic Research Centre, College of Engineering, Mathematical and Physical Sciences, University College Dublin, Belfield, Dublin 4, Ireland.
authors.forename: John J
authors.initials: JJ
authors.lastname: Healy
authors.forename: John T
authors.initials: JT
authors.lastname: Sheridan