Solid lines: fraction of rays arriving in delayed pulses, as a function of colatitude θ measured on the sphere at infinity, for a range of BH spins (a/M = 0, 0.5, 0.7, 0.9, 0.95, 0.99, bottom to top). Dotted horizontal lines: fraction of rays arriving in delayed pulses, averaged over colatitude. The ray fluence is weighted more strongly to the equator for higher a/M; hence, each dotted line is not a direct θ-average of the corresponding solid line.