# Speckled cross-spectral densities and their associated correlation singularities for a modern source of partially coherent x rays

## TL;DR

This paper models the cross-spectral density of partially coherent x-ray beams, revealing speckled structures with coherence vortices and domain walls, which are crucial for improving imaging and diffraction techniques using synchrotron sources.

## Contribution

It introduces a realistic model for the cross-spectral density of x-ray beams, highlighting the emergence of speckle, vortices, and domain walls as the number of modes increases.

## Key findings

- Speckled cross-spectral density structure observed
- Coherence vortices and domain walls identified
- Enhanced understanding aids x-ray imaging and diffraction

## Abstract

We consider a realistic model for calculating the cross-spectral density of partially coherent beams from an x-ray undulator in a modern storage ring. This two-point coherence function is seen to have a speckled structure associated with the presence of x-ray coherence vortices and domain walls. Such cross-spectral density speckle is associated with a network of spatial pairs of points for which there is zero correlation. X-ray coherence vortices and domain walls are seen to emerge naturally as the number of coherent modes required increases. An understanding of the existence and nature of such correlation singularities enhances our ability to exploit partially coherent x-ray radiation from new or upgraded synchrotron sources, for both imaging and diffraction applications.