In this paper, we deal with the time-harmonic scattering by one-dimens
ional rough surfaces separating two homogeneous and isotropic media. T
he method is based on a rigorous integral formalism. The unknown of th
e integral equation is projected onto a Fourier basis while the equati
on itself is sampled as in a classical method of moments. The accuracy
is tested against both other methods and experimental results. One of
the main interests in choosing a Fourier basis lies in the ability to
solve rigorously the scattering of a p polarized incident beam by a s
hallow metallic rough surface. The role of the surface waves is accura
tely taken into account and phenomena such as enhanced backscattering
are well described. With this method, one can consider that the gap be
tween the domain of validity of perturbation theories and the domain o
f practical use of rigorous methods is filled.