Akima Interpolation: a Tool used in Direct Slit-Length Desmearing Procedures of Non-Frequency-Limited X-ray Scattering Curves

X-ray small- and medium-angle scattering of partially ordered or semicrystalline materials is composed of background scattering from the form scattering of the components and from the amorphous phase and of peaks from the scattering of the crystallites. By the slit geometry of X-ray diffractometers constructed for registration of small- and medium-angle X-ray scattering, the diffuse scattering and the peaks are distorted and the peak positions and half-widths are changed. A program module based on the Akima interpolation [Akima (1970). J. Assoc. Comput. Math. 17, 589-602] is proposed for calculation of the first derivative of the complete smeared scattering curve, which is then explicitly used in direct collimation correction procedures. The desmearing of scattering curves from semicrystalline starch samples proves the convenience of the method for low-noise conditions and exhibits a significant gain of measuring time in comparison with data of comparable accuracy but measured with Soller-slit collimation systems or desmeared with direct methods using frequency filtering.