Two-dimensional indirect Fourier transformation for evaluation of small-angle scattering data of oriented samples

An extension of the indirect Fourier transformation method for two-dimensional small-angle scattering patterns is presented. This allows for a model-free investigation of real-space functions of oriented structures. The real-space function is built from two-dimensional basis functions. The Fourier transformed basis functions are approximated to the scattering pattern. The solution to this problem in reciprocal space can be used to compute the corresponding real-space functions. These real-space functions contain information on size, shape, internal structure and orientation of the structures studied. Information on structures that are oriented in different distinct directions can be partly separated. The applicability of the technique is demonstrated on simulated data of oriented cuboids and on two experimental data sets based on the nanostructure of spruce normal wood.