Resolution of VISION, a crystal-analyzer spectrometer

We present both analytic and Monte Carlo calculations of the resolution of VISION, which is a crystal-analyzer spectrometer based on the TOSCA design. The analyzer crystal in VISION is configured to focus in time, radial, and transverse directions (“triple focused”). Previously published analytical results have two serious flaws in the handling of the statistics, which gave misleading results. First, Gaussian distributions were assumed for all resolution components, so that full-width-half-maximum could be used. Not only is this a very poor approximation for most terms, it is also completely unnecessary because standard deviations can be combined in quadrature for any shape distribution (except Lorentzian). The second flaw was the choice of variables that are not independent, so that significant correlations were ignored. An example of the effect of including correlations is that the mosaic spread of the analyzer crystals does not contribute to the resolution in first order. Monte Carlo simulation is not limited to first order, and we find a mild optimum value for mosaic spread. A complete set of six independent variables is: neutron emission time, incident flight-path variation (due to moderator tilt), sample thickness, mean path in the analyzer (due to multiple reflections), sample-to-detector radial distance, and detector thickness. We treat separately the resolution contributions from histogramming and rebinning during data acquisition and reduction, and describe a scheme for VISION that minimizes the effect on resolution. We compare the contributions of the six variables to the total resolution, both analytically and by Monte Carlo simulations of a complete VISION model using the Neutron Instrument Simulation Package (NISP).