Simultaneous determination of the X-ray refractive index and the attenuation length from a single digitally registered radiograph of rectangular prisms

Prisms deflect and disperse X-rays due to refraction very similar to visible light. As X-rays are always attenuated while traversing material, the intensity distribution in the transmitted beam carries information about the prism transmission function. This study will show that sufficient information is contained in a single digitally registered radiograph from a rectangular prism, for deriving both the refractive index of the material and its attenuation length. The measured data can be prepared such that neither intensity fluctuations nor false light content in the incident beam will introduce systematic errors into the result. The strategy is thus very adapted, when single shot pictures are taken at X-ray sources with limited shot reproducibility. This technique is favourably be used at very grazing angles of incidence of the order of the critical angle for the prism material, when the beam deflection becomes significant. In such a geometry dimensional parameters, like sample thickness, do not affect the data analysis, which is particularly insensitive to even significant errors in the tip angle.