Indirect transformation in reciprocal space: desmearing of small-angle scattering data from partially ordered systems

Indirect Fourier transformation is a widely used technique for the desmearing of instrumental broadening effects, for data smoothing and for Fourier transformation of small-angle scattering data. This technique, however, can only be applied to scattering curves with a band-limited Fourier transform, i.e. separated and noninteracting scattering centers. It can therefore not be used for scattering data from partially ordered systems. In this paper, a modified technique for partially ordered systems working in reciprocal space is presented. A peak-recognition technique allows its application to scattering functions with narrow peaks, such as the scattering functions of layered systems like lamellar stacks or strongly interacting particles. Arbitrary geometry effects and wavelength effects can be corrected. Examples of simulations show the merits and limits of this new method. One example shows its applicability to real data.