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We have calculated the lateral resolution (LR) of the electron beams emitted from sharp tips used in the near field emission SEM (NFESEM). To this end we have simulated the tip as an ellipsoid and have used a 3-dimensional WKB approximation. We find a self focusing of the electron beam which can explain the small experimental values of the observed LR of the NFESEM. This self focusing is highly sensitive on the sharpness S=R1/R2 of the tip where R1 and R2 are the big and small radius of the ellipsoid simulating the tip. However it is not sensitive on any particular radius alone.