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In material testing applications, Computed Tomography is a well established imaging technique that allows the recovery of the attenuation map of an object. Conventional modalities exploit only primary radiation and although in the energy ranges used in industrial applications Compton scatter radiation is significant, it is removed from the measured data. On the contrary, Compton Scattering Tomography not only accounts for the Compton effect but also uses it to image material electronic density. Despite its promising applications, some aspects of Compton scattering tomography have not been studied so far and, since they are necessary for the design of a operational system, they need to be addressed. In this paper we analyze the effect of some physical influences regarding real detectors for the Circular Compton Scattering tomography, a system recently introduced by the authors. This is accomplished through the formulation of a new weighted Radon transform. In addition, we propose to adapt the acquired data with pre-processing steps so that they are suitable for reconstruction with a filtered back-projection type reconstruction algorithm, and thus, properly deal with missing data of real measurements. Finally, we introduce a bi-imaging configuration that allows recovering simultaneously the electronic density map of the object as well as its attenuation map.