Schematic illustration (not to scale) of the CIO scenario (Lu & Bonnerot 2020) modeled in this work. The BH lies at a distance R_int from the debris stream intersection point from which the CIO is launched. Photons are generated on a sphere of radius R_ph centered on the BH and within a cone of opening angle Δθ aligned with the negative z axis. The electron scattering photosphere where the optical depth is τ = 1 is located at a distance d_{sc_ph} from the intersection point while the surrounding sphere of radius R_max corresponds to the outer radius of our grid. We exploit the model symmetry about the z axis and extract polarization levels for 21 viewing angles in the xz plane, equally spaced in cosine (ΔcosΘ = 0.1) between a north-polar (cosΘ = 1, face-on) and a south-polar (cosΘ = −1, face-off) orientation. Photons are unpolarized when they are injected from the photosphere and they become polarized after scattering with an electron (visualized as blue circles). Depending on the direction they travel, they are scattered toward the observer either with an electric field oscillating in the horizontal direction (i.e., with a negative q, see Eq. (14)) or with an electric field oscillating in the vertical direction (i.e., with a positive q).