Analytical approach to the 4D-resolution function of three axes neutron spectrometers with focussing monochromators and analysers

Three axes neutron spectrometers explore excitations in condensed matter at almost arbitrary points within the 4-dimensional (Q-ω)-space of momentum and energy transfers. The knowledge of resolution is important for both, the preparation and interpretation of experiments. In order to meet the requirements of modern focussing techniques in direct and reciprocal spaces, an analytical algorithm is presented which allows the detailed calculation of the 4D-resolution function. This approach takes into account all essential features of state-of-the-art three axes spectrometers. Complementary to existing numerical simulation methods, the analytical treatment provides neutron users with almost instantaneous information about resolution effects of ongoing experiments. Moreover, it can be used as an efficient tool for the quantitative interpretation of experimental results. Several examples are shown which demonstrate the performance and the accuracy of the present approach.