In the present paper a general analytic expression has been obtained and co
nfirmed by a computer simulation which links the surface roughness of an ob
ject under study in an emission electron microscope and it's resolution. A
quantitative derivation was made for the model case when there is a step on
the object surface. It was shown that the resolution is deteriorated asymm
etrically relative to the step. The effect sets a practical limit to the ul
timate lateral resolution obtainable in an emission electron microscope.