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By the use of both perturbative and non-perturbative solutions of the reducedRayleigh equation, we present a detailed study of the scattering of light fromtwo-dimensional weakly rough dielectric films. It is shown that for severalrough film configurations, Sel\'enyi interference rings exist in the diffuselyscattered light. For film systems supported by dielectric substrates where onlyone 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 bedetermined from simple phase arguments. For such single-rough-interface films,we find and explain by a single scattering model that the contrast in theinterference patterns is better when the top interface of the film (theinterface facing the incident light) is rough than when the bottom interface isrough. When both film interfaces are rough, Sel\'enyi interference rings existbut a potential cross-correlation of the two rough interfaces of the film canbe used to selectively enhance some of the interference rings while others areattenuated and might even disappear. This feature may in principle be used indetermining the correlation properties of interfaces of films that otherwisewould be difficult to access.

Selective enhancement of Sel\'enyi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film