Various 3-dimensional nano-scaled periodic structures with different configurations and periods deposited on the surface of silicon and silica substrates were investigated by means of the grazing incidence and grazing emission X-ray fluorescence techniques. Apart from the characteristics which are typical for particle- and layer-like samples, the measured angular intensity profiles show additional periodicity-related features. The latter could be explained by a novel theoretical approach based on simple geometrical optics (GO) considerations. The new GO-based calculations were found to yield results in good agreement with experiment, also in cases where other theoretical approaches are not valid, e.g., periodic particle distributions with an increased surface coverage. (C) 2014 Elsevier B.V. All rights reserved.