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The structural inhomogeneities of silicon films embedded within W/Si multilayer mirrors were studied by X-ray reflection, grazing-incidence small-angle X-ray scattering (GISAXS) and X-ray photoelectron spectroscopy (XPS). In the diffuse scattering spectra, evidence of laterally and vertically ordered in-layer inhomogeneities was consistently observed. In particular, specific substructures resonant in nature (named here `ridges') were detected. The properties of the ridges were similar to the roughness determined by quasi-Bragg peaks of scattering, which required a high interlayer correlation of particles. The XPS showed the nanocrystalline nature of the Si particles in the amorphous matrix. The geometric characteristics and in-layer and inter-layer correlations of the nanoparticles were determined. In GISAXS imaging, the unusual splitting of the waists between the Bragg sheets into filament structures was observed, whose physical nature cannot yet be explained.