This paper discusses the scattering of a plane wave on the uneven surf
ace of an ideal conductor. Integral equations are derived for the scat
tering amplitude in the framework of the Rayleigh hypothesis. The resu
lts of a numerical experiment on scattering at a finite diffraction gr
ating is compared with the values predicted by Kirchhoff's approximati
on. The advantage of the Rayleigh hypothesis in the case of scattering
at shallow irregularities is pointed out. (C) 1996 The Optical Societ
y of America.