Essentially there are 3 approaches to lens surface design:
1. Traditional --- spherical lens surfaces, where every surface is a portion of a spherical surface (circular radius to all points)
2. Aspheric --- where some lens surfaces employ a conic, parabolic or other non-circular surface --- for these surfaces the deviation from a true sphere is measured in wavelengths of light, and the deviation generally is noticeable only in the outer 10-20% of the lens’s optical clear aperture. One aspheric surface (when used properly) will typically provide the same aberration correction as 1-2 spherical surfaces. In other words, you can get the equivalent optical performance with fewer parts when an aspheric is used. However aspheres are more than twice as hard to make as spherical surfaces.
3. Freeform --- Freeform optics are a modification of aspheric surfaces. Instead of applying a specific mathematical form to the aspheric surface (e.g. parabola), you let the last 10-20% of the optical clear aperture vary as required in order to insure all the optical rays meet at the focal point. This generally creates a generic shape that follows no common mathematical formula (e.g. conic).
So the freeform optic will only give a slight improvement over an aspheric optic, which in turn only replaces 1-2 surfaces in an all-spherical lens design. If you are making exotic optics, this is a great tool. But the fabrication costs are probably orders of magnitude different.
Also notice that the article only addresses a single lens element, not a more useful/complex lens design with multiple elements.
I’ll hang on to my current lenses for a while.