On the kinematic approximation to specular reflectivity data

Abstract

The kinematic approximation to specular reflectivity is very useful for understanding neutron and X-ray scattering observations, because it provides a simple analytical formula that relates the scattering-length density profile of a layered surface or interface, β(z), to the data, R (q_z ). Although its derivation from the wave equation, or the optical transfer model, for large q_z , is straightforward, the origin of the q_z -factor in the denominator is less obvious when the problem is viewed in the limit of Fraunhofer diffraction from the outset. This paper, which is principally educational, aims to bring clarity to the issue.

Acknowledgments

I am grateful to Rob Dalgliesh, Nikitas Gidopoulos, Bill Hamilton, Stephen Holt, Sean Langridge, Stephen Lovesey, Jerry Mayers, Jeff Penfold, Roger Pynn, Jorge Quintanilla, Rob Richardson, Greg Smith and John Webster for useful discussions.