The Gaussian Schell-model source theory is used to describe the hard X-ray micro focusing beamline with an undulator of the Shanghai Synchrotron Radiation Facility.Based on the model and general Huygens-Fresnel principle

propagation of cross-spectral density function in free space is studied.Equivalent source hypothesis is proposed and the effect of toroidal mirror on spatial coherence of the hard X-ray beams is studied.The theoretical results are consistent with the experimental results.Only divergence angles of the incident and outgoing X-rays are considered in the equivalent source hypothesis

hence an easy extension of the hypothesis to other beamline optical elements.