Figure 1: Illustration of the exact lens
map. is the chosen
observation event, is the
chosen source surface.
is a hypersurface ruled by timelike curves
(worldlines of light sources) which are labeled by the points of a 2-dimensional
manifold . The lens map is
defined on the observer’s celestial
sphere , given by
Equation (1), and takes values in . For each , one follows the lightlike geodesic with this initial
direction until it meets and
then projects to .
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 .
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