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The intensity scattered by particles randomly placed beneath a rough interface is studied with rigorous simulations. It is shown that the angular intensity pattern is close to that obtained by adding the intensity scattered by particles under a flat surface to that scattered by a rough homogeneous surface whose permittivity is evaluated with an effective-medium theory. This heuristic splitting rule is accurate for a large range of parameters that are well beyond any perturbative treatment.
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Sentenac et al. (2002) studied this question.
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