A cosine-squared flux distribution from a disk-shaped source was used to calculate the spatial deposition profiles for films sputtered onto rotating substrates. Depositions were made by a stable and reproducible d.c. sputtering machine and thicknesses measured by Rutherford backscattering spectroscopy to compare with this calculation. The measured and calculated profiles were compared at a fixed value of target-substrate distance. We showed for the first lime that the thickness variation is largely responsible for the broadening of the X-ray Bragg peaks at low angles of Fe/Pd multilayers. These results have important implications for the classical interpretation of X-ray scattering from multilayered structures.