A comparison is made of current approaches to the characterisation of
the abruptness of an interface based upon, on the one hand, attempts t
o derive the exit wavefunction from a through focal image series and,
on the other, indirect methods which seek to quantify the delocalised
contrast seen at such interfaces as a function of the defocus. It is d
emonstrated that the delocalised contrast due to the presence of a lat
eral discontinuity in the projected forward scattering potential is bo
th highly sensitive to the form of the local changes in the scattering
behaviour for images at large defoci and also then potentially of ext
remely high contrast under the high spatial coherence conditions chara
cteristic of the use of a FEGTEM. Given the problems inherent in the r
econstruction of the exit wave function it is thus argued that if the
primary interest is in the characterisation of an interface then indir
ect approaches would appear to be currently more useful than those bas
ed on attempts to derive pictures from the amplitude and phase of the
exit wavefunctions. We suggest that this will be the case whether thes
e pictures be obtained by filtering non-linear contributions to the ex
perimental images or by full recursive restorations which potentially
retain these non-linear contributions.