Grazing emission x-ray fluorescence from multilayers

In x-ray fluorescence spectrometry, the sensitivity to subsurface layers is considerably enhanced by measuring intensities at grazing angles. By using wavelength dispersive detection, elements of low atomic number can be measured. We derive explicit formulas for the intensity of the emitted fluorescence from multilayers consisting of an arbitrary number of layers. Multiple reflections at the interfaces between the layers and contributions of secondary, tertiary, etc., fluorescence are taken into account. The derived expressions are compared with experimental results. Furthermore, some properties of the inverse problem are discussed.