The Fourier method used by Fan has produced a representation of the field o
f a semi-infinite pole head consisting of a simple analytical approximation
(Karlqvist field) pins an infinite series of correction terms. A method is
developed in this paper by which other approximations to head fields have
their infinite series of correction terms evaluated to make them exact. Exp
ressions with only one correction term produced by Ruigrok and Szczech ct a
l, are studied, and enhancement of them is shown to offer accurate approxim
ations to the exact head fields.