TIT# Scanning microbeam X-ray scattering of fibers analyzed by one-dimensional
     tomography
AUT# Stribeck, Norbert; N”chel, Ulrich; Almend rez Camarillo, Armando;
SOU# Macromol. Chem. Phys. (2008), submitted
LOC# xv114
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ABS# The investigation of structure gradients in polymer fibers by the
     X-ray microbeam scanning technique is put on its theoretical
     fundament. It is shown that the observed smeared structure
     information is readily reconstructed by the inverse Abel
     transform. Technical improvement of the reconstruction is ongoing
     development in one-dimensional tomography of objects with
     cylindrical symmetry. In this field fast, low-noise algorithms
     for the desmearing have been developed. They are readily
     applicable to scan data in which the X-ray absorption, the
     small-angle X-ray scattering (SAXS) or the wide-angle X-ray
     diffraction (WAXD) is measured.
     The method is demonstrated by application to SAXS scan data from
     a polymer fiber. The measured projection-space data are
     reconstructed to image space. The resulting sequence of
     image-space SAXS patterns is reflecting the structure variation
     along the fiber radius. It can be used for the purpose of
     quantitative structure analysis.
     Mathematically, the microbeam projection of fiber materials is
     identical to the slit smearing known from slit-focus X-ray
     cameras. The well-known collimation correction equation given by
     Guinier and DuMond is the inverse Abel transform.