Left: EVPA as a function of the emission coordinate ϕ along a contour of fixed Z (with both coordinates referring to the location of the background emission). Right: the observable analog, EVPA, as a function of the image coordinate φ along a fixed impact parameter b. In both cases, the curve approaches a step function at the singular point of the TL. Searching for this behavior could shed clues on black hole spin, as the impact parameter for which the EVPA develops this kink depends sensitively on spin.