Sorry for not replying earlier, but I went through a stretch of 42hrs of work with only 3 hrs of sleep intermingled in there.
The non-dispersive paraline (as I understand it) relies on the refelctive property of a parabola to have equal pathlengths and have a coherent wavefront at the exit. Because a parabolic surface is used as a reflector, the center region will be 'illuminated' more strongly than the ends. I wish I could cobble up a drawing, but can't right now. It would be a good integration problem to figure out the shading curve the parabolic paraline gives....
The dispersive paraline would uses a hyperbolic reflecting surface, and an elliptical reflective surface would make a 'focusing' paraline. All are possible.