Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources

TL;DR

This paper develops a comprehensive theory of spatial coherence for X-ray beams from third-generation synchrotron sources, addressing limitations of previous models and providing a rigorous method to analyze coherence properties across various parameters.

Contribution

It introduces a new technique based on statistical and Fourier optics to accurately calculate the cross-spectral density of undulator sources in all cases, surpassing traditional quasi-homogeneous and Gaussian-Schell models.

Findings

The new model accurately describes coherence properties of non-homogeneous sources.

It simplifies analysis across different asymptotic regimes of emittance and wavelength.

The approach is particularly relevant for third-generation synchrotron radiation sources.

Abstract

This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert-Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical(geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude (from 0.1 Angstrom up to 10^3 Angstrom). Sometimes, the so-called Gaussian-Schell model, that is widely used in statistical optics in the description of partially-coherent sources, is applied as an alternative to the quasi-homogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of X-ray beams from non-homogeneous undulator sources. As a result, a more rigorous analysis is required. We propose a technique, based on statistical optics and Fourier optics, to explicitly calculate the cross-spectral density of an undulator source in the most general case, at any position after the undulator. Our theory, that makes consistent use of dimensionless analysis, allows relatively easy treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. Particular emphasis is given to the asymptotic situation when the horizontal emittance is much larger than the radiation wavelength, and the vertical emittance is arbitrary. This case is practically relevant for third generation synchrotron radiation sources.