Minimal smooth lenses for perfect imaging of two wavefronts.

The problem of designing a lens for perfectly imaging two incident wavefronts into two respective refracted wavefronts is considered. In particular, the problem of deriving a unique such lens of prescribed smoothness is analyzed. Building upon an idea by Benitez and Minano et al., we propose a method for constructing such twice-differentiable lenses and derive equations for computing them. The theoretical considerations are supplemented by a few examples.