Determination of the overlap integral from differential-scanning measurements by merged beams

A recent description by C.J. Keyser et al. (see J. Phys. B (GB), Vol.10, p.3797 (1977) of a beam scanning system for determining beam profiles and form factors in a merged electron-ion beam experiment (MEIBE) included a derivation of expressions for the overlap integral and the form factor in terms of the measured output signals obtained from the scanning system. The derivation of these expressions was based on the assumption that the distributions of current density in both the electron and ion beams were Gaussian. This note shows that the assumption of Gaussian beams is not a necessary assumption and that the expressions for form factor and overlap integral given are in fact valid for beam profiles of a much more general functional form.