Inelastic plasmon diffuse scattering (PDS) is treated as an effective position-dependent potential perturbing the incident electron wavelength in a solid surface, resulting in an extra phase grating term in the slice transmission function. This potential is derived for the geometry of reflection electron microscopy (REM) and high-resolution electron microscopy (HREM). The energy-filtered inelastic images can be calculated following the routine image simulation procedures by using different slice transmission functions for the elastic and inelastic waves, by considering the 'transitions' of the elastic scattered electrons to the inelastic scattered electrons. It is predicted that the inelastic scattering could modify the electron intensity distribution at a surface. It is possible to take high-resolution energy-filtered inelastic images of crystals, the resolution of which is about the same as that taken from the elastic scattered electrons.
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