Sample shape contribution to the resolution function of time-of-flight neutron scattering spectrometers

For high resolution time-of-flight neutron scattering spectrometers, a significant contribution to the instrumental resolution broadening will be due to the flight path uncertainty induced by the sample size. In linear approximation, this contribution is an additional convolution of the resolution function with the scaled distribution of flight path lengths. This distribution, its moments, and its Fourier transform will be calculated for flat film and hollow-cylindrical sample geometry. The minima in the Fourier transform are shown to correspond to experimentally inaccessible ranges of the intermediate scattering function.