On the kinematic approximation to reflectivity

Devinderjit Singh Sivia (1)

1 ISIS Facility

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, $\beta\left(z\right)$, to the data, $R\left(q_z\right)$. 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.

Mots clés: Physical Sciences

Devinderjit Singh Sivia. On the kinematic approximation to reflectivity. Philosophical Magazine, 2007, 87 (10), pp.1575-1580. ⟨10.1080/14786430601072283⟩. ⟨hal-00513803⟩