Improvements in real-space deconvolution of small-angle scattering data

In the cases of spherical, cylindrical or lamellar symmetry it is possible to calculate the radial density distribution from small-angle scattering intensities via indirect Fourier transformation and a convolution square-root technique avoiding the phase problem. The density function is expressed in terms of step functions. All this is accomplished by a method described previously. Firstly, the necessary modifications of the method allowing for arbitrary step widths are discussed. Additional background to the scattering intensities is an important problem in practical application, so it is shown that remaining background scattering is mainly eliminated automatically and does not essentially influence the results in the convolution square-root technique. Finally, the introduction of a least-squares variation algorithm allows for the optimization of simple step models.