Instrumental Smearing Effects in Radially Symmetric Small-Angle Neutron Scattering by Numerical and Analytical Methods

A numerical calculation method for determining the resolution functions for radially symmetric collimation and scattering is described. In the present approach, the total number of integrations is reduced to four by use of the radial symmetry of the geometry. Furthermore, the beam-stop shadowing effect is included exactly. A typical calculation can be completed in minutes on current personal computers. An interactive computer program allows the user to enter the experimental parameters such as aperture size and wavelength spread, allowing smearing calculations to be handled routinely as a `black box' operation. The exact smearing treatment is compared both to an improved technique involving Gaussian resolution functions where corrections for the beam stop are included and to results from Monte Carlo simulations. In most experiments, the use of a Gaussian distribution to approximate the resolution is preferred on account of its ease of calculation. But in a few cases, such as Porod scattering, the present more extensive numerical calculation or inclusion of the developed beam-stop-shadowing correction factors into a Gaussian scheme are needed for an adequate prediction of the smearing effects.