The resolution of the field emission electron microscope is expressed as a function of the ratio of its magnificationMto the time‐of‐flight &tgr; of an electron from emission tip to screen. It is shown that small protrusions on the surface of the tip can provide areas for whichMis much greater than that computed for a perfectly smooth tip. Resolution of the order of 3 A is possible on these protrusions, so that some of their atomic detail should be observable.