  By the use of both perturbative and non-perturbative solutions of the reduced
Rayleigh equation, we present a detailed study of the scattering of light from
two-dimensional weakly rough dielectric films. It is shown that for several
rough film configurations, Sel\'enyi interference rings exist in the diffusely
scattered light. For film systems supported by dielectric substrates where only
one of the two interfaces of the film is weakly rough and the other planar,
Sel\'enyi interference rings are observed at angular positions that can be
determined from simple phase arguments. For such single-rough-interface films,
we find and explain by a single scattering model that the contrast in the
interference patterns is better when the top interface of the film (the
interface facing the incident light) is rough than when the bottom interface is
rough. When both film interfaces are rough, Sel\'enyi interference rings exist
but a potential cross-correlation of the two rough interfaces of the film can
be used to selectively enhance some of the interference rings while others are
attenuated and might even disappear. This feature may in principle be used in
determining the correlation properties of interfaces of films that otherwise
would be difficult to access.
