Two-Dimensional Desmearing of Centrosymmetric Small-Angle X-ray Scattering Diffraction Patterns

Abstract

Owing to the high dynamic range and resolution of image plates, digitization of the direct-beam profile as well as of two-dimensional small-angle X-ray scattering patterns gives data with enough accuracy to allow desmearing of two-dimensional patterns after corrections of geometrical distortions. A radial conversion of the images is used to compress the images and to isolate a small area of interest. The results obtained by the Wiener filtering method and the iterative method of Van Cittert on simulated patterns are compared.

Everything SAXS: small-angle scattering pattern collection and correction

“…The photographic films in particular had a very nonlinear response to the incident intensity, necessitating complex corrections [23]. The advent of image plates [29] and 2D gas-filled wire detectors [57] mostly replaced the prior solutions, though image plates have a low time resolution (given the need to read and erase them), and the 2D gas-filled wire detectors suffer from a low spatial resolution due to a considerable point-spread function [108]. Charge coupled device (CCD) detectors enjoy a modicum of success, though they suffer from reduced sensitivity alongside a slew of other issues [7].…”

“…If necessary, symmetry in the scattering patterns can be exploited to determine the beam centre of every image. A procedure for achieving this is described by Le Flanchec et al [108].…”

“…Most detectors are flat with uniform, square pixels, but we wish to collect the intensity over a solid angle of a (virtual) sphere. The projection of the detector pixels on the sphere results in a difference in solid angle covered by each pixel (illustrated in figure 6) [14,7,108]. Therefore, we need to correct the intensity for the difference between these areas 13 .…”

“…The electronics and design of image intensifiers in CCD cameras and electronics of wire detectors can give rise to pixels being assigned incorrect geometric positions, leading to geometric distortion [7]. Even image plate readers can show this effect due to the read-out mechanics [108], and it therefore seems a necessary correction for all detectors save those based on direct-detection (e.g. the PILATUS detector).…”

“…This then allows for the evaluation of where on the detector the photons are observed versus where the photons actually arrived through the holes in the mask [108,185].…”