Under perfect Observer-Lens-Source alignment, the solution to the lens equation describing gravitational lensing around a point mass picks up a spherical symmetry, and a whole ring of solutions are seen. The optics of the system also produce very large (theoretically, infinite) amplification of the source signal on this ring. In fact, this ring is a critical line of the optical system. The corresponding caustic is a single point on the source plane.
The first mpeg shows a source behind a singular isothermal sphere (SIS) moving through the point of perfect Observer-Lens-Source alignment. These characteristics of SIS lensing can be seen:
A second image appears as the source crosses
the caustic.
The two images merge, and then what was the
first image disappears as the source passes out the other side of the lens.
There is extreme amplification of the signal
on the Einstein ring, the caustic of this system.
A second mpeg is like the SIS Einstein Ring except the deflecting lens is elliptical rather than spherical (a psuedo singular isothermal sphere, PSIS.) This breaks the spherical symmetry of the Einstein Ring.
Notice how the ring seems to form from two
images on the caustic that are not along the Source-Lens line.
It's a bit hard to tell, but the extreme
amplification on the caustic is not uniform when the alignment is perfect,
but rather reflects some of the asymmetry of the lens. If you could only
see the brightest of the bright parts of the ring, you'd see two
counter-arcs instead of a perfect ring.