Calculation of scattering patterns from phase-shifting objects using the Radon transform

In the case of neutron (and X-ray) scattering by objects that are about 10⁵ times larger than the wavelength, the objects can be considered as (inhomogeneous) phase-shifting media. In contrast with small-angle scattering, the scattering patterns from phase-shifting objects are calculated by the superposition of coherent partial waves that penetrate the object. In order to determine the scattering patterns from large complicated objects, it is proposed to use the two-dimensional Radon transform of the objects and Fraunhofer diffraction. This approach is much easier than using the small-angle scattering treatment, as is shown in this paper.