Analysis on partial coherence propagation using the four-dimensional coherence function

The mutual optical intensity (MOI) is a four-dimensional coherence function and contains the full coherence information of the beam. The propagation of mutual optical intensity through a soft x-ray beamline is analyzed with a new developed model named MOI. The MOI model is based on statistical optics. The wavefront is separated into many elements and every element is assumed to has full coherence and constant complex amplitude, which is reasonable if the dimension of element is much smaller than the coherent length and beam spot size. The propagation of MOI for every element can be analytically solved with Fraunhofer or Fresnel approximations. The total MOI propagation through free space can be obtained by summing the contribution of all elements. Local stationary phase approximation is implemented to simulate MOI propagating through ideal mirrors and gratings. The MOI model provides not only intensity profile, but also wavefront and coherence information of the beam. These advantages make MOI model a useful tool for beamline design and optimization. The nano-ARPES beamline at SSRF is analyzed using the MOI model. A zone plate is used to focus the beam. The intensity profile and local coherence degree at the zone plate are acquired. The horizontal coherence is much worse than the vertical one. By cutting the horizontal beam with the exit slit the horizontal coherence can be improved but at the flux loss. The quantitative analysis on the coherence improvement and flux loss at different exit slit size are obtained with the MOI model.