With uniform partially coherent illumination of a sufficiently small c
oherence width, linear holographic axicons produce an extended axial l
ine image of a desired length and a nearly uniform intensity. This res
ult is demonstrated by numerical diffractive simulations based on gene
ralized axicon phase functions and the space-frequency theory of optic
al coherence. The conclusions are also verified through analytical cal
culations employing the asymptotic method of stationary phase.