that emanate from all volume elements of the cylinder of matter inside the object that are simultaneously irradiated by the penetrant X-ray microbeam are recorded. Thus, rather than recording (in parallel) a series of line integrals of the linear absorption coefficient during a one-dimensional ω-scan (as is the case in absorption tomography – see Eqn 1), a (sequential) series of line integrals of the secondary signals (fluorescence or diffraction) that emerge from the irradiated object are recorded during a two-dimensional (x, ω) or three-dimensional (x, z, ω) scan. A marked disadvantage of first-generation tomography is therefore the much lower degree of parallelism that can be achieved during data acquisition. In what follows, we exclusively deal with data obtained during two-dimensional (x, ω) scans.