Direct recovery of interfacial topography from coherent X-ray reflectivity: model calculations for a 1D interface

The use of coherent X-ray reflectivity to recover interfacial topography is described using model calculations for a 1D interface. The results reveal that the illuminated topography can be recovered directly from the measured reflected intensities. This is achieved through an analysis of the Patterson function, the Fourier transform of the scattering intensity (as a function of lateral momentum transfer, Q_//, at fixed vertical momentum transfer, Q_z). Specifically, a second-order Patterson function is defined that reveals the discrete set of separations and contrast factors (i.e. the product of changes in the effective scattering factor) associated with discontinuities in the effective interfacial topography. It is shown that the topography is significantly overdetermined by the measurements, and an algorithm is described that recovers the actual topography through a deterministic sorting of this information.