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A method for collimation correction and combination of anisotropic scattering patterns recorded in tandem experiments is proposed. It includes both an advanced two-dimensional extrapolation procedure for the center of the pattern and (compared with the `blind deconvolution' method) a more justified procedure for desmearing from an unknown broad primary beam profile. This semi-blind deconvolution rests on the availability of unsmeared data in a region of the smeared image. Materials exhibiting both ultra-small-angle X-ray scattering (USAXS) and small-angle X-ray scattering (SAXS) must be studied in both angular bands (tandem experiment), in order to collect the complete range of discrete scattering for nanostructure analysis. Merging of the patterns requires desmearing of at least the SAXS pattern from its point-spread function, i.e. the primary beam profile. The distorting effect of single-band experiments on the reconstructed nanostructure of polymer materials is demonstrated.

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