Small-Angle X-ray Scattering Measurements and Image Reconstruction by the Maximum Entropy Method

For rapid small-angle X-ray scattering (SAXS) measurements in laboratories, we have designed and assembled a SAXS measurement system, which includes a new point-focusing camera using a doubly curved monochromator of a W/Si multilayer. As the two-dimensional detector and the X-ray source, an imaging plate (IP) and a rotating-anode generator operated at 40 kV and 30 mA with a microfocus of 0.1 × 0.1 mm2 are used. As an example of time-resolved SAXS measurements with our system, an observation of smectic A-nematic transition of a thermotropic liquid crystal 4-[(2‘-methylbutyl)phenyl]-4‘-n-octylbiphenyl-4-carboxylate is reported. To correct the broadening due to the beam divergence and enhance the signal-to-noise ratio of the data, two-dimensional deconvolution based on the maximum entropy method (MaxEnt) has been employed. A SAXS image of a uniaxially extended high-density polyethylene film was reconstructed from noisy data obtained by an X-ray exposure of only 3 s. The deconvolution was shown to give quantitative information regarding the position and breadth of the scattering maxima. It can be concluded that the combined use of the setup, IPs, and the MaxEnt processing facilitates rapid SAXS measurements with laboratory-based X-ray sources.