Two alternative theories that describe neutron scattering from periodic nanostructures are compared with each other and with experimental data. Dynamical scattering theory agrees with experiment for all scattering geometries, while the simpler phase-object approximation can only be used reliably under certain conditions.

A method based on the phase-object approximation is used to describe small-angle neutron scattering experiments on silicon gratings.

The real-space sample correlation function for a sphere is derived for kinematic and dynamic scattering.