Special affine Fourier transformation in frequency-domain

Special affine Fourier transformation (SAFT) can be considered as an extens ion of the fractional Fourier transformation (FRT) and the most general lin ear mapping in phase space. A general formula for SAFT in frequency-domain is derived, which gives a direct relationship between the input and output spatial frequency spectra of a light held. It shows that the SAFT has simil ar and symmetric feature in both space- and frequency-domains. As its speci al cases, Collins formula in frequency-domain, the spatial frequency repres entations of the almost-FRT, almost-Fresnel and almost-Fourier transformati ons are explicitly obtained. These formulae may provide a tool for investig ating the performance of a lossless optical system including small deformat ions in both domains in a unified way within the framework of linear theory . (C) 2000 Elsevier Science B.V. All rights reserved.