An acceptance-diagram description of beams from focusing monochromators

`Acceptance' diagrams are used to describe the beams produced by curved segmented (`focusing') monochromators in the kinematic approximation. This semi-analytic semi-graphical method leads to a complete description which is readily visualized in terms of instrument variables. Focusing both in and perpendicular to the scattering plane is considered. Clear relationships are identified between instrument dimensions and the beam produced. The description is directed towards neutron scattering instruments but the formalism should also apply to photons and electrons. It is demonstrated that a monochromator curved both in and perpendicular to the scattering plane (`double focused') on either a straight or curved neutron guide tube from a reactor source can produce a beam of comparable flux to that achievable at the reactor face. Such a beam has spatial dimensions comparable with modern single-crystal samples for inelastic scattering and could thus provide spectacular signal and, even more interestingly, signal to noise ratios for both elastic and inelastic single-crystal spectrometers.