Abstract: [Background] Coherence is the most striking and fundamental property of the light waves produced by X-ray free-electron lasers (XFEL). The implementation of many experimental techniques exploiting coherent radiation from XFEL requires accurate characterization of spatial properties of the radiation at the sample positon.[Purpose] This paper aims to investigate the two-dimensional transverse coherence of the self-amplified spontaneous emission (SASE) of a free-electron laser radiation based on near-field heterodyne speckle.[Methods] The laser pulse is irradiated on the nanoparticle solution making Brownian movement to produce near-field heterodyne speckle. Use a splitter to split each single pulse into two equal-amplitude pulses and two statistically independent raw images are obtained simultaneously for accurate extraction of the heterodyne speckle intensity distribution. The square root of the two-dimensional power spatial frequency spectrum of the heterodyne speckle yields the modulus of the complex coherence factor.[Results] Theoretical and simulation results proved that the accurate extraction of heterodyne signal and availability of a full two-dimensional coherence map are possible.[Conclusion] The above-mentioned method has the capability to probe the real-time coherence property of XFEL photon pulses produced from SASE mode.

Key words: Heterodyne speckle, SXFEL, Spatial coherence, Twin measurement