X-ray Coherent diffraction interpreted through the fractional Fourier transform

TL;DR

This paper introduces a novel approach using the fractional Fourier transform to analyze coherent x-ray diffraction, bridging the Fresnel and Fraunhofer regimes and providing new insights into wave propagation and uncertainty principles.

Contribution

It presents a new framework applying the fractional Fourier transform to interpret coherent x-ray diffraction across different regimes, extending traditional theories.

Findings

Fractional Fourier transform effectively models diffraction from Fresnel to Fraunhofer regimes.

A generalized uncertainty principle is derived within this framework.

The approach offers a unified perspective on wave propagation in diffraction experiments.

Abstract

Diffraction of coherent x-ray beams is treated through the Fractionnal 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 and a generalized uncertainty principle is introduced.