Fresnel Lens, Plano-convex Lens, Collimating Lens

I had planed to model a Fresnel lens, and while searching for a good cross-section technical drawing of one I came across some interesting work from Adam Donovan from 2007 that is in many ways similar to explorations I'm making now.

I'm mainly interested in creating light modifiers for use in a Maxwell environment, so it doesn't matter to me what the lens looks like, only what kind of beam it throws.

The main advantage of a Fresnel lens is that it is thin and lightweight compared to a bulky, heavy plano-convex lens of equivalent power. [glass Nd = 1.51]

In CG I don't care about bulkiness or weight, so I opted to dispense with the Fresnel lens and use its plano-convex equivalent.

I used a portion of a sphere for a lens, and found the focal point by trial and error. A sphere doesn't have perfect focus, but a little spherical aberration is acceptable to me in a light source.

UPDATE

Changed my mind. I simulated a Fresnel lens after all.