The Wigner distribution function (WDF) describes the entire propagation properties of an electromagnetic beam including all information on its spatial coherence. It can be reconstructed from beam profiles taken at different positions along its propagation direction. Here, we present measurements of the WDF conducted at the Free-electron laser FLASH at DESY. As a result, we derive the entire four-dimensional mutual coherence function, the coherence lengths and the global degree of coherence. Additionally, we provide an estimation of the possible error that our algorithm might produce for the derived quantities.
In comparison to existing studies that characterize the photon beam of FLASH, we find significantly lower values for the global degree of coherence. This difference cannot be explained by our error estimation. We explore the possible reasons for this discrepancy and their effect on the value of the global degree of coherence.