Cassini curves in light field theory (Q1201924)

Let a line segment \(PQ\) in \(E^ 3\) be a light source with the classical Lambert distribution of light intensity. Let \(F(E)\) be the carrier set of all area elements in 3-space having normal vectors parallel to \(PQ\) and fixed illumination intensity \(E>0\). The authors show that the intersection of \(F(E)\) and an arbitrary plane through \(P\) and \(Q\) is a Cassini oval.