Dependence of ray fluence on latitude above and below the equatorial caustic on the sphere at infinity, as see in Figure 2. BH spins range from a = 0 (black points) to a/M = 0.9 (red points). Angular dependence is ﹩| \theta -\pi /2{| }^{-1}﹩ in the simplest case of a nonspinning BH (dotted line).