Abstract
We have developed a theory of electron energy loss (EEL) spectra that includes the effects of sample surface roughness and the electromagnetic retardation. The energy loss probability is given by the sum of the term arising from a perfect flat surface and the contribution from surface roughness. The theoretical predictions are compared with experimental EEL spectra of an evaporated Au film. We find that the effects of both roughness and the electromagnetic retardation must be incorporated in the theory to understand the experimental spectra.