We construct models for the characteristic functions describing the mo
und structures induced by a surface diffusion barrier in epitaxial gro
wth fronts. These characteristic functions, including the height-heigh
t correlation functions, are used to calculate the angular distributio
n of diffraction intensity. We compare in detail the characteristics o
f the reciprocal space structure for diffusion-barrier-induced and noi
se-induced roughening of epitaxial growth fronts. It is shown that exc
ept near the out-of-phase (anti-Bragg) diffraction condition, the reci
procal space structure oi the diffusion-barrier-induced growth front c
ontains splitting (ring) and broadening characteristics that are drama
tically different from that obtained from a scale invariant growth fro
nt caused by random noises that exist during growth. This result allow
s us to differentiate unambiguously, using diffraction techniques, the
two mechanisms that can cause the roughening of expitaxial growth fro
nts.