Lens shapes other than conic sections

[symbolipoint]

This is just a curiosity question. Are there lens shapes different than just conic sections? Any research or any found applications?

 

[Jasso]

Lenses can be in any shape, but specific shapes are more useful for specific purposes than others.

For example, check out the aspheric lens, it's described by an infinite geometric sum.

Or also check out the Fresnel lens.

 

[Andy Resnick]

The front lens used in missile guidance applications have a shape dictated by aerodynamics, not optics. "Conformal optics" was trendy for a while.