Analytical convolution methods used to explain the interaction of a fi
ne electron beam with a thin segregated layer in a typical electron mi
croscope specimen are described. Expressions are derived which quantif
y the shape of the measured concentration profile determined in the mi
croscope by scanning the beam across the segregated layer. The express
ion contains parameters concerned with the beam profile and the thickn
ess of the segregated layer. The method is applied to grain boundary s
egregation studies of neutron-irradiated ferritic-martensitic steels.