Small-angle neutron scattering resolution with refractive optics

The resolution of small-angle neutron scattering instruments is investigated for the case where refractive optics (lenses or prisms) are used. The appropriate equations are derived to describe the position and the spatial variance of the neutron beam at the detector in the horizontal and vertical directions, and the minimum value of the scattering vector. This is given for the spectrometer without any additional optics, and with the insertion of converging lenses or prisms. The addition of the lenses decreases the sample-aperture contribution to the resolution to enable an increase of neutron current at the sample. They also reduce the size of the penumbra of the beam at the detector, thereby lowering the minimum value of the scattering vector. The prisms correct the effect of gravity on the vertical beam position, and make the beam spot less asymmetric.