Xray reflectometry (XRR)
The scattering geometry of an incident plane wave is scetched in Fig.1 and Fig.2.
Fig. 1 Scattering geometry of XRR 
Fig. 2 Reflection and transmission at a plane surface 
Because the refractive index of Xrays n differs for matter only by small amounts(e.g., δ ~ 10^{5}, β ~ 10^{6}) from the vacuum value (n_{0}=1), n = 1  δ  iβ, and n<1, total extrernal reflection occurs for incident angles α_{i} smaller than the critical angle α_{c}. The critical angle is (for β << δ)
α_{c }~ (2δ)^{1/2}~Z (Z  atomic number)
The critical angle of total external reflection is small (~0.2° 1° for a wavelength λ of ~ 0.1 nm) and interferences from thin films are only visible in a small range close to the critical angle.
Reflectometry is sensitive to the electron density and absorption and does not depend on crystallinity and crystal texture. The reflected intensity R_{F }is given by the known Fresnel equations. Fig.3 shows the R_{F} of a perfect Sivacuum interface.
Fig. 3 Reflectivity of a perfect Sivacuum interface for different values of absorption and a wavelength of l =0.154nm 
 For α_{i} << α_{C} and β >> 0 > R = 1
(total reflection)
 For α_{i} > α_{c }> R_{F} ~ K_{z}^{4}
R_{F} ~ α_{i}^{4}
Fig. 4 In some cases the surface roughness σ_{rms} can be described as a Gaussian distribution of the height h of the hills and valleys around a average surface level h_{0} 

Surface roughness σ_{rms} is introduced by a DebyeWaller factor

R_{F}^{rough} = R_{F} exp(K_{z}^{2}σ_{rms}^{2})

if the height distribution is Gaussianlike as shown in Fig.4.
XRR on thin films and Multilayers
The reflected intensity may be calculated using a recurrence formalism which calculates the reflection coefficient starting from the lowest surface boundary (substrate) up to the last (surface / air).
With a code (based on the Parratt or matrix formalism) a simulation of XRR spectra can be done. The parameters film thickness (d), density (ρ) and roughness (σ_{rms}) can be exctracted from the interference spectra, the critical angle, and the decrease of the reflectivity as schematically shown in Fig.5 for a Ta layer on silicon substrate.
Fig. 5 Specular reflectivity of an oxidized Ta layer deposited on a Siwafer (measured at ROBL with a wavelength of l=0.1033 nm) 
Experimental setup for XRR
The Figs. 6 and 7 show the diffractometer D5000 (SIEMENS) in thetatheta geometry with the special cutting slit device for reflecometry. The divergent beam of a sealed copper tube is matched into a parallel beam by a Göbel mirror. With such a beam the cutting slit may have a larger slit width and furthermore in the most cases one does not need a collimatoranalyzer device. The gain in intensity reduces the measuring time for specular scans extended to higher incidence angles. This is of special interest for the study of multilayers.
XRR is nondestructive technique and can be used for samples with a sufficently smooth surface.
Fig. 6 Scheme of experimental setup 
Fig. 7 D5000 (SIEMENS) in thetatheta geometry with Göbel mirror and cutting slit device.
