Spatial coherence of electron beams from field emitters and its effect on the resolution of imaged objects

摘要

Sub-nanometer and nanometer-sized tips provide high coherence electronsources. Conventionally, the effective source size is estimated from the extentof the experimental biprism interference pattern created on the detector byapplying the van Cittert Zernike theorem. Previously reported experimentalintensity distributions on the detector exhibit Gaussian distribution and oursimulations show that this is an indication that such electron sources must beat least partially coherent. This, in turn means that strictly speaking the VanCittert Zernike theorem cannot be applied, since it assumes an incoherentsource. The approach of applying the van Cittert Zernike theorem is examined inmore detail by performing simulations of interference patterns for the electronsources of different size and different coherence length, evaluating theeffective source size from the extent of the simulated interference pattern andcomparing the obtained result with the pre-defined value. The intensitydistribution of the source is assumed to be Gaussian distributed, as it isobserved in experiments. The visibility or the contrast in the simulatedholograms is found to be always less than 1 which agrees well with previouslyreported experimental results and thus can be explained solely by the Gaussianintensity distribution of the source. The effective source size estimated fromthe extent of the interference pattern turns out to be of about 2-3 timeslarger than the pre-defined size, but it is approximately equal to theintrinsic resolution of the imaging system. A simple formula for estimating theintrinsic resolution, which could be useful when employing nano-tips in in-lineGabor holography or point-projection microscopy, is provided.