Conclusions and Outlook

In this last chapter, we provide a brief summary of the previous chapters. We then enumerate a number of open directions where this research could lead to, starting from determining a more general Snell’s Law and then revisiting the challenges of absolute instruments. Moreover, we suggest a way to ease the restrictions of an absolute instrument by considering what we call nearly absolute instruments, where instead of no aberrations being present, one allows for a small amount of wave aberrations. Related to this and the associated wave aberration function, we consider the optical transfer function as a measure of the image quality of an optical system. Here we make interesting connections between the very concrete optical transfer function and harmonic analysis techniques related to oscillatory integrals. We also say a few words about incorporating topological objects into this geometric optics analysis, such as skyrmions, hopfions, and heliknotons. Finally, we provide some directions related to helical media (especially, cholesteric liquid crystals) and detail a short conclusion.