Mendlovic, D.Özaktaş, Haldun M.Lohmann, A. W.2015-07-282015-07-2819940003-6935http://hdl.handle.net/11693/13641Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.EnglishFourier opticsOptical information processingFractional fourier transformsWignerdistribution functionsGraded-index mediaSpatial filteringArticle10.1364/AO.33.006188