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

Abstract

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][590][591][592][593][594][595][596][597][598][599][600][601][602] is proposed for calculation of the first derivative of the complete smeared scattering curve, which is then explicitly used in direct collimationcorrection 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 SoUer-slit collimation systems or desmeared with direct methods using frequency filtering.

Computer simulations of x‐ray scattering curves: Gelation and crystallization process in amylose solutions

“…The distortion of the scattering curves caused by the diffractometer slits in the small-angle part was corrected by using AKIMA polynomials. 18 The subroutine is included in the PC program system SAXS-PC.I9 And for the sample scattering as well as for the background scattering, produced by slits, air, sample holder, and solvent, the intensity was measured for at least five runs. The resulting mean statistical error amounts to about 2% for the discussed experimental scattering curves.…”

Scanning Microbeam X‐Ray Scattering of Fibers Analyzed by One‐Dimensional Tomography

“…Scattering curves from the Kratky camera,37 have frequently been desmeared by application of Equation (3). For that purpose, the measured data must be smoothed and derived in the direction of ρ f 38. In order to avoid derivation, loss of a background, and generation of excess noise, several iterative numerical algorithms have been devised 39–45.…”