Precise Measurement of Spatial Coherence and Axial Brightness Based on the Wigner Function Reconstruction in Transmission Electron Microscopes with Field Emission Guns and a Thermionic Emission Gun

The spatial coherence and the axial brightness of a cold field emission gun, a Schottky field emission gun and a $\mathrm{LaB}_6$ thermionic gun are precisely measured. By analyzing the Airy pattern from a selected area aperture, various parameters including the spatial coherence length are determined. Using the determined coherence length, the axial brightness of the field emission guns is estimated using the equation which we previously derived based on the discussion of the Wigner function of an electron beam. We also make some extensions in the method to be applicable to the measurements of the thermionic gun, which has anisotropic intensity distribution in most case unlike the field emission guns. Not conventional average brightness but the axial brightness measured for the three kinds of emitters are compared accurately and precisely without influenced by the measurement conditions.