On the transverse coherence of X-ray radiation from micron-sized electron beams.

Light sources with finite physical size emit radiation endowed with limited transverse coherence. For light sources composed by many independent point-like emitters (also known as incoherent, or quasi-homogeneous, thermal sources), this is expressed by the well-known Van Cittert and Zernike theorem. Here we present the first systematic characterization of the transverse coherence properties of X-ray radiation emitted by micron-sized ultra-relativistic electron beams wiggling in an undulator, indicating deviations from the quasi-homogeneous model. Measurements are performed at the NCD-SWEET beamline at the ALBA Synchrotron Light Source by varying the vertical beam size below 10 micrometers. We use the Heterodyne Near Field Speckle technique to assess the full 2D transverse coherence of 12.4 keV and 16 keV X-ray radiation. We compare results with predictions relying on the Van Cittert and Zernike theorem, and with a more rigorous approach based on statistical optics. We also discuss relevance to third- and next-generation synchrotron light sources approaching the diffraction limit, where the electron beam emittance becomes comparable to, or smaller than, the radiation wavelength.