The scattering of light from a one-dimensional randomly rough dielectric film deposited on a flat reflecting substrate is studied by means of a small-amplitude perturbation theory and rigorous numerical simulations. In particular, we study the appearance of well-defined fringes in the angular distribution of the diffusely scattered intensity and their dependence on the angle of incidence, the roughness of the film, and the film’s mean thickness. We find that, for slightly rough films, the angle of incidence modulates the intensity of the fringes but has no effect on their angular position. For rougher films the contrast of the pattern decreases, and the fringes move with the angle of incidence in such a way that there are always bright fringes in the specular and backscattering directions. Eventually, for very rough films, the fringe pattern disappears, and a well-defined backscattering peak emerges in the retroreflection direction.
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