Comparison of two different methods for direct structure analysis from small-angle scattering data

Two methods for direct structure analysis from small-angle scattering data of spherically symmetric monodisperse particles have been developed during recent years. Both methods assume ideal data from particles with perfect symmetry. The test uses simulated data from a core-shell model with systematic errors in the scattering curve, caused by a constant background or by an angle-dependent background as can occur from higher terms in an expansion in spherical harmonics. The direct structure analysis method gives an excellent fit to the data points. However, this means that the background is evaluated as a contribution from a spherically symmetric structure. This leads to artificial oscillations in the resulting density distribution. The convolution square root method cannot interpret the background terms as spherically symmetric structures and leads therefore to excellent results in the density distribution but to a rather poor fit to the scattering data. From these examples we can learn that a perfect fit to the data does not always give the best possible structure and that a poor fit may be caused by systematic deviations from the assumed symmetry, and that the resulting structure is much better than indicated by the fit.