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

In this work, we investigate the transverse coherence properties of X-ray radiation from micron-sized electron beams in undulator sources. We evidence deviations from the well-known Van Cittert and Zernike theorem when the beam emittance becomes comparable to, or smaller than, the radiation wavelength. In these conditions, we show that the coherence properties of the emitted X-rays strongly depend on the absolute position across the observation plane and exhibit unexpected oscillations caused by the peculiar features of the single-electron radiation pattern. Relevance to current facilities and future fourth-generation light sources approaching the diffraction limit is also highlighted.