Grazing x-ray reflectometry allows analysis of thin-layer stacks. The fitting of the reflectivity curve by a trial and error method can determine the parameters of the films. The Fourier analysis of the experimental reflectivity curve can directly give a rough determination of the profile index. Such results can be useful in choosing a starting model. With the choice of an appropriate model a fit to the reflectivity curve can be undertaken to determine the parameters of the stack. The Fourier analysis method can only be used if the reflectivity data undergo a transformation to produce a periodic curve. Associated artifacts are studied and discussed. Each Fourier peak is associated with two interfaces. The interface roughness spreads the Fourier peaks, adding the squared roughness values. The sample's absorption of the x-rays does not limit the Fourier analysis.