Spatial coherence of synchrotron radiation

The spatial coherence properties of a monochromatic component of synchrotron radiation from an insertion device in the Fraunhofer limit are analyzed in the general case when the coherence distance is comparable with the beam width, expressing them by simple products and convolutions of Fourier transforms and autocorrelations on the single-electron field amplitude and the electron-beam position and angular distributions. In particular, the Gaussian approximation is discussed, in which case the far-field amplitude satisfies the Schell condition (its statistical properties can be described by a coherence factor depending only on the difference of the reciprocal space coordinates), and this discussion leads to simple estimates of the coherence widths. The coherence widths deviate from the Van Cittert-Zernike values when one or more of the phase space widths of the electron beam are close to (or smaller than) the diffraction limit.