FRACTIONAL ORDER FOURIER-TRANSFORM AND FOURIER OPTICS

The electromagnetic field transfer from a spherical emitter to a spherical receiver is expressed through a fractional order Fourier transform. Given an emitter and a receiver, the order of the fractional transform is calculated as a function of their distance and their radii of curvature. The continuity of fractional Fourier transforms with respect to their orders corresponds to the continuity of wave propagation and to the continuity between the Fresnel and Fraunhofer diffraction phenomena. The operator composition law applied to fractional transforms is in accordance with Huygens principle. The transfer from an emitter to a receiver, situated in two different media, is analysed and the coherent imaging assumption gives the usual paraxial formulae for the spherical refracting surface and requires the conjugation of vertices and centres of curvature of spherical emitter and receiver.