Coherence properties of focused X-ray beams at high brilliance synchrotron sources

TL;DR

This paper presents an analytical method to describe the coherence and focusing properties of partially coherent X-ray beams at synchrotron sources, including effects of apertures and optical elements, with practical application to PETRA III.

Contribution

It introduces a new analytical approach based on statistical optics for predicting beam size and coherence at any point behind optical elements, specifically for Gaussian Schell-model beams.

Findings

Analytical expressions for beam size and coherence length are derived.

The impact of apertures on transverse coherence is quantitatively analyzed.

Application to PETRA III demonstrates the method's practical relevance.

Abstract

An analytical approach describing properties of focused partially coherent X-ray beams is presented. The method is based on the results of statistical optics and gives both the beam size and transverse coherence length at any distance behind an optical element. In particular, here we consider Gaussian Schell-model beams and thin optical elements. Limiting cases of incoherent and fully coherent illumination of the focusing element are discussed. The effect of the beam defining aperture, typically used in combination with focusing elements at synchrotron sources to improve transverse coherence, is also analyzed in detail. As an example the coherence properties in the focal region of compound refractive lenses at the PETRA III synchrotron source are analyzed.