Three-dimensional setup for the analytical test cases in Sect. 3.3: The primary source photons (50% linearly polarised along the x-axis) are emitted in the positive z-direction k and observed in a direction k′ after Compton scattering on free electrons at the origin. The photons are emitted at E = 4 keV and observed at E′ = C(θ, x)× E (see Eq. (12)). Having N_e = 10¹⁹ cm⁻², the effect of multiple scattering is negligible.