Phase-object approximation in small-angle neutron scattering experiments on silicon gratings

The phase-object approximation for neutron scattering based on a one-dimensional dynamic forward scattering theory is discussed and used to calculate the differential cross section of an object. It is shown that this approximation is valid in ultra-small-angle neutron scattering (USANS) and spin-echo small-angle neutron scattering (SESANS) experiments on silicon gratings. In the weak scattering limit, the phase-object approximation reduces to the kinematic or first Born approximation. The spatial coherence function is used to describe instrumental resolution effects. Measurements on three different instruments are in good agreement with calculation results. In the experiment with a time-of-flight SESANS instrument, the effect of Pendellösung with object size is observed.