Refraction and scattering of X-rays in analyzer-based imaging

A new algorithm is introduced for separation of the scattered and non-scattered parts of a monochromatic and well collimated synchrotron radiation beam transmitted through a sample and analyzed by reflection from a perfect crystal in the non-dispersive setting. The observed rocking curve is described by the Voigt function, which is a convolution of Lorentzian and Gaussian functions. For the actual fitting, pseudo-Voigtians are used. The fit yields the scaled integrated intensity (the effect of absorption), the center of the rocking curve (the effect of refraction), and the intensity of the transmitted beam is divided into the scattered and non-scattered parts. The algorithm is tested using samples that exhibit various degrees of refraction and scattering. Very close fits are achieved in an angular range that is 15 times the full width at half-maximum of the intrinsic rocking curve of the analyzer. The scattering part has long tails of Lorentzian shape owing to the `long-slit geometry' of the set-up. Quantitative images of absorption, refraction and scattering are constructed and compared with results of earlier treatments. The portion of scattering and the second moment of the observed rocking curve both increase linearly with the sample thickness and yield identical maps of the effects of scattering. The effects of refraction are calculated using the geometrical optics approximation, and a good agreement with experiment is found. The fits with reduced number of data points (minimum number is five) yield closely the same results as fits to the full data set.