Resolution of neutron three-axis spectrometers using acceptance diagrams

Two-dimensional `acceptance diagrams' are used to discuss the transmission function and the resolution of neutron three-axis spectrometers. The discussion is simplified by assuming rectangular rather than the usual Gaussian transmission profiles for the beam elements, i.e. collimators and crystal mosaic spreads, but the results can be applied to the Gaussian profile approximation. The formalism clearly shows the effects of beam elements on the instrument transmission to the detector. Suitable choices of beam elements are determined to match the transmission functions of the primary and secondary spectrometers and hence optimize measurements. The effect of sample mosaic is addressed. The `focusing angle' for inelastic scattering is determined and discussed.