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Cone-beam type X-ray computed tomography (CBCT) is a potential method to measure three-dimensional phase distributions in vessels. An example for that is the measurement of gas profiles in stirred chemical reactors. Such data are highly valuable for the assessment and evaluation of chemical processes, for optimisation of the reactor and stirrer design, and for evaluation of computational fluid dynamics codes used to model the fluid flow and heat transfer in reactive systems. However, there are considerable difficulties for accurate quantitative measurements due to beam hardening and radiation scattering effects. In a theoretical and experimental work we have investigated the non-linear effects of both physical phenomena and developed a suitable measurement setup as well as calibration and software correction methods to achieve a highly accurate measurement of void fraction profiles with CBCT.