Resolution effects and analysis of small-angle neutron scattering data

A discussion of the instrumental smearing effects for small-angle neutron scattering (SANS) data sets is given. It is shown that these effects can be described by a resolution function, which describes the distribution of scattering vectors probed for the nominal values of the scattering vector. The resolution function is independent of the scattering cross section of the sample and can be calculated once and for all for any instrumental setting. For scattering from isotropic system the resolution function allows the smeared intensity to be calculated by computing only one numerical integral. It is discussed how the resolution function can be calculated analytically. determined by Monte Carlo simulations, and measured. It is demonstrated that for typical SANS setups, the resolution function can be described by a Gaussian function to a good approximation. The incorporation of the function in computer programs for least-squares fits of known cross sections and for indirect Fourier transformations is discussed. Finally, some examples are given which demonstrate the application.