Kutay, Mehmet AlperÖzaktaş, Haldun M.Rodrigo, J. A.2018-04-122018-04-1220169781493930272http://hdl.handle.net/11693/38353Chapter 6We consider optical implementation of arbitrary one-dimensional and two-dimensional linear canonical and fractional Fourier transforms using lenses and sections of free space. We discuss canonical decompositions, which are generalizations of common Fourier transforming setups. We also look at the implementation of linear canonical transforms based on phase-space rotators. © Springer International Publishing Switzerland 2016.EnglishTransformation matrixOptical setupCylindrical lensCanonical decompositionThin lensBook Chapter10.1007/978-1-4939-3028-9_69781493930289