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A lot of awesome optics projects like hacking cameras and projectors become possible with CAD lens modelling software1, if we can also easily prototype the lenses we design.
What are some materials and additive or subtractive 3D fabrication strategies that can make a clear lens with strong refraction and the ability to be polished?
1 Here is a helpful list of 37 different lens design & simulation programs.
I interpret your question to read, that you want to directly manufacture the lens through an additive process.
My experience with this recently is that it basically isn't possible (practically anyway). Even injection molding lenses of good quality is quite an art. There is a reason that optical-quality glass lenses are so expensive.
More specifically, we tried to make a custom LED focusing lens using stereo-lithography in a range of PC, PE, PTFE, and (even!) PVC-type plastics. In all cases we had trouble achieving sufficient optical clarity, uniform density, and dimensional accuracy. Granted, we were making a small lens (about 11mm diameter), but it was suspended across an integrated holder (causing a lot of the same problems you'll face if you try to fabricate just a lens in isolation).
I know this has been a bit of a hand-wavy response, but hopefully it's at least a little helpful. If anyone else has any better experiences with this, I'd love to hear about it.
One thing to watch out for is that many of the additive or extrusion-based 3D printers will leave small gaps between the beads of plastic that they lay down. Even if you polish the surface, the interior will be very poor optically.
You may want to look at Selective Laser Sintering (SLS) to create a finished product that is more uniformly solid.
3D printing a refractive lens is possible using "printoptical technology" by LUXeXceL. It was developed for making perfectly smooth surfaces. With this technology there is no need for post-processing (grinding, polishing / coloring, etc.).
