Measurement and calculation of resolution of time-of-flight small-angle neutron scattering

The resolution of a time-of-flight small-angle scattering spectrometer is complicated because many wavelengths contribute to the intensity for a particular scattering vector. The resolution function varies according to the wavelength distribution as well as with collimation. A rigorous calculation of the instrumental resolution requires averaging the resolution function weighted by the wavelength spectrum within the band of wavelengths used in a given measurement. For each scattering vector an effective wavelength is defined which, after substitution into the resolution expression developed for fixed wavelength, gives the resolution of the time-of-flight measurement. Alternatively, the resolution may be established by Monte Carlo methods. In order to check the calculated resolution function and the overall instrument resolution, measurements have been made on biological samples (myelin and collagen) which give sharp Bragg peaks at small values of scattering vector. The analysis of these results provides a direct comparison with calculations and with a similar measurement on a steady-source instrument.