Linear polarization pattern at null infinity, corresponding to emission by the upboosting and reflection of the ambient toroidal magnetic field near the emission point. Top panel: a = 0; bottom panel: a/M = 0.95. Color zones are separated by powers of 1.5 (1.7 bottom panel) in intensity. A relatively uniform polarization pattern is seen near the BH equator and also extending above and below the primary caustic for moderate BH spin. A differing magnetic configuration at the ISCO (e.g., a poloidal magnetic field) would imply a systematic rotation of the polarization, but the uniformity in the equatorial polarization pattern would be maintained. These maps are obtained by a Monte Carlo procedure, but now with angular resolution four times coarser than in Figure 2.