X-ray free electron lasers (XFEL) provide intense and almost coherent X-ray pulses. They are used for various experiments investigating physical and chemical properties in materials and biological science because of their complete coherence, high intensity, and very short pulse width. In XFEL experiments, specimens are irradiated by XFEL pulses focused by mirror optics. The focused pulse is too intense to measure its coherence by placing an X-ray detector on the focal spot. Previously, a method was proposed for evaluating the coherence of focused pulses from the visibility of the diffraction intensity of colloidal particles by the speckle visibility spectroscopy (SVS). However, the visibility cannot be determined exactly because the diffraction intensity is integrated into each finite size detector pixel. Here, we propose a method to evaluate the coherence of each XFEL pulse by using SVS in combination with a theory for exact sampling of the diffraction pattern and a technique of multiplying the diffraction data by a Gaussian masks, which reduces the influence of data missing in small-angle regions due to the presence of a direct beamstop. We also introduce a method for characterizing the shot-by-shot size of each XFEL pulse by analysing the X-ray irradiated area.
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