Eur. Phys. J. B 81, 481-487 (2011)
https://doi.org/10.1140/epjb/e2011-20123-1

X-ray coherent diffraction interpreted through the fractional Fourier transform

Laboratoire de Physique des Solides, Bât. 510, Univ. Paris-Sud, CNRS, UMR 8502, 91405 Orsay Cedex, France

Corresponding author: ^a david.le-bolloch@u-psud.fr

Received: 16 February 2011
Revised: 3 May 2011
Published online: 21 June 2011

Abstract

Diffraction of coherent X-ray beams is treated through the fractional Fourier transform. The transformation allow us to deal with coherent diffraction experiments from the Fresnel to the Fraunhofer regime. The analogy with the Huygens-Fresnel theory is first discussed, a generalized uncertainty principle is introduced and the successive diffraction of two objects is interpreted through the fractional Fourier transform.