Comparison of different theories for focusing through a plane interface

We consider the problem of light focusing by a high-aperture lens through a plane interface between two media with different refractive indices. We compare two recently published diffraction theories and a new geometrical optics description. The two diffraction approaches exhibit axial distributions with little difference. The description based on geometrical optics is shown to agree well with the diffraction optics results. Also, some implications for three-dimensional imaging are discussed.