Convenient expressions are derived for incremental length diffraction coeff
icients (ILDCs) in terms of the far fields of arbitrary cylindrical canonic
al scatterers composed of linear electromagnetic material. The derivation o
f these general expressions for ILDCs is based on a surface-current equival
ence theorem that states that the electromagnetic fields outside cylindrica
l sources can be generated to any degree of accuracy by localized electric
and magnetic surface currents that lie in a single plane within the source
region. This equivalence theorem is proven with the help of cylindrical wav
e expansions and the Kottler-Franz formulas. It combines with a general eve
n and odd decomposition of cylindrical electromagnetic fields to allow the
use of previous formulas for planar surface-current ILDCs in the derivation
of the general expressions for ILDCs in terms of cylindrical far fields.