Time focusing of pulsed-source crystal analyzer spectrometers. Part II: practical expressions

We develop practical expressions for the focusing conditions of fully general crystal analyzer inelastic neutron scattering instruments having two-dimensionally extended sources (moderators), samples, analyzer crystals, and detectors. We show their relationships to focusing conditions for powder diffraction and single-crystal diffraction instruments. We demonstrate that geometries other than the traditional backscattering arrangement, using more general sample, analyzer, and detector orientation angles, can provide high resolution and offer potential advantages in design. The results apply to the use of mosaic as well as perfect single-crystal analyzers.