Use of the Fourier spectrum of X-ray reflectivity curves for analysis of stacked thin layers

Grazing incidence X-my reflectometry is usually used for the analysis of thin layer stacks. The parameters to be found are thicknesses, roughnesses, and indices. They can be reached by the fitting of the experimental reflectivity curve whith a theoretical one calculated from these parameters (trial and error method). Another method consists to use the Fourier transform in order to study the typical features of the stack. Because the reflectivity curve has no periodicity, the data have to be processed before using the Fourier transformation. Starting from real examples, it will be shown how the Fourier analysis gives informations on the model of the stack The results allows mainly to evaluate the distances between all the interfaces. The accuracy of the results depends on the angular detection scanning range. The width of the peaks in the spectrum depends on the roughness of the related interfaces. A limitation of this method is due to the discretisation of the Fourier transform. The results are refined by the trial and error method as explained above, but with starting roughtly known values of the parameters, that allows to save much time in the curves fitting process.