Optimization of detectors in time-focusing geometry for RTOF neutron diffractometers

The quality of a neutron time-of-flight diffractometer can be significantly improved by setting up its detectors in time-focusing geometry. In order to fully exploit the time-focusing method, the nominal resolution of the spectrometer must be thoroughly investigated by analysing the contributions of several different factors. In this paper analytic formulae are given, which describe the different components contributing to the resolution function and the conditions which optimize the resolution are derived. It is shown how the analytic integral equations can be solved numerically. The programs allow iterative computations to optimize a detector system composed of many individual detector elements, considering the specimen size and instrumental resolution. The flow diagram of the programs to calculate numerically the detector system is briefly discussed and the precision of the individual optimal detector position coordinates is given.