Electrostatic condensing lenses of very short focal length were invest
igated via trajectory calculations with the goal of determining the mi
nimum spot diameter that could be formed by focusing positrons of nega
tive work function emitted from a 100 mu m diameter portion of a Ni(10
0) foil re-moderator. The specific applications for which the calculat
ions were carried out were brightness enhancement and transmission-mod
e positron re-emission microscopy, in which positrons are accelerated
to 5 keV onto the target, which also serves to terminate the electric
field of the condensing lens. The minimum spot size that could be form
ed was 3 mu m using a 1 mm diameter two-cylinder lens with a tapered s
econd cylindrical element.