Figure 1

Figure 1: Illustration of the exact lens map. $p O$ is the chosen observation event, $𝒯$ is the chosen source surface. $𝒯$ is a hypersurface ruled by timelike curves (worldlines of light sources) which are labeled by the points of a 2-dimensional manifold $𝒬$ . The lens map is defined on the observer’s celestial sphere $𝒮O$ , given by Equation (1 ), and takes values in $𝒬$ . For each $w ∈ 𝒮O$ , one follows the lightlike geodesic with this initial direction until it meets $𝒯$ and then projects to $𝒬$ . For illustrating the exact lens map, it is an instructive exercise to intersect the light cones of Figures 12, 24, 25, and 29 with various source surfaces $𝒯$ .