The resolution of TOF low-Q diffractometers: instrumental, data acquisition and reduction factors

The resolution of scattering vector, Q, in small-angle neutron scattering (SANS) measurements derives from uncertainties in scattered neutron wavelength and direction. The manner in which these are manifest on broad-band time-of-flight (TOF) spectrometers at pulsed sources is different from that for instruments using monochromated sources. In TOF instruments the uncertainties arise from the TOF measurement as well as the directional uncertainties due to collimation, finite sample and detector-element size that are present in any small-angle scattering instrument. Further, data from a TOF instrument must be mapped into Q space, and the strategy used to accomplish this affects the final resolution of the measurement. Thus for TOF-SANS instruments the question of resolution is more complicated than for instruments on monochromated sources. There is considerable flexibility in TOF data acquisition and Q mapping that can be utilized to optimize for intensity and Q resolution requirements of a particular measurement. In this work, present understanding of the effects of instrument geometry, TOF data acquisition and Q mapping strategies on the precision of the measurement is outlined. The goal is to establish guidelines on the best manner in which a particular measurement can be set up. Toward this end some new aspects are presented of optimal Q-mapping procedures, the effect of inelastic scattering on the measurement, and the calculation of instrument resolution functions. Some of these ideas are tested by comparison of simulations with measurement.