  Sub-nanometer and nanometer-sized tips provide high coherence electron
sources. Conventionally, the effective source size is estimated from the extent
of the experimental biprism interference pattern created on the detector by
applying the van Cittert Zernike theorem. Previously reported experimental
intensity distributions on the detector exhibit Gaussian distribution and our
simulations show that this is an indication that such electron sources must be
at least partially coherent. This, in turn means that strictly speaking the Van
Cittert Zernike theorem cannot be applied, since it assumes an incoherent
source. The approach of applying the van Cittert Zernike theorem is examined in
more detail by performing simulations of interference patterns for the electron
sources of different size and different coherence length, evaluating the
effective source size from the extent of the simulated interference pattern and
comparing the obtained result with the pre-defined value. The intensity
distribution of the source is assumed to be Gaussian distributed, as it is
observed in experiments. The visibility or the contrast in the simulated
holograms is found to be always less than 1 which agrees well with previously
reported experimental results and thus can be explained solely by the Gaussian
intensity distribution of the source. The effective source size estimated from
the extent of the interference pattern turns out to be of about 2-3 times
larger than the pre-defined size, but it is approximately equal to the
intrinsic resolution of the imaging system. A simple formula for estimating the
intrinsic resolution, which could be useful when employing nano-tips in in-line
Gabor holography or point-projection microscopy, is provided.
