A formal solution for slit corrections in small-angle x-ray scattering

Abstract

Slit shaped apertures are usually used in small-angle x-ray scattering measurements in order to obtain easily measured intensities of scattered radiation. As a result, the scattering intensity at a given angle determined by the camera, the center of the sample, and the central incident x-ray beam is not simply related to the scattering from the sample only at that angle. The experimentally determined intensities I(x) are related to the true scattering intensities by the following integral equation: [equation not included]. This integral equation has been previously solved only for certain simplified functional forms for W(t) and I(x). In this paper, a formal procedure is developed for calculating I(x) from the observed angular measurements, which does not necessitate making any a priori assumption about the form of W(t) and I(x).