Aberrations and a Lens Design Problem

In this chapter we review optical aberrations in third order geometric optics and focus on wave aberration functions. After a systematic review of aberrations, we consider a two dimensional lens design problem. The problem is the following: Given the first surface of an optical lens in two dimensions, what is the second surface such that the lens containing a liquid crystal layer between the surfaces refracts the extraordinary ray into a given fixed point? We then consider an inverse optical problem; namely, given a desired light ray trajectory, what nematic director can be imposed in order to obtain such trajectory?