The earliest treatments of electromagnetic focusing problems are due to Ignatowsky (1919, 1920), who derived formulae for the electric and magnetic field vectors in the image region of an aplanatic system and also of a paraboloid. Richards and Wolf (1959) rederived the basic formulae of Ignatowsky (1919) for an aplanatic system and made important deductions about the polarisation, the energy density and the energy flow in the focal region. A new aspect of electromagnetic focusing is considered in a recent paper by Ling and Lee (1984), who treat the case in which the aperture and the focal point are in two different dielectric media. Their study is motivated by the use of focused microwave energy for localised heating of embedded cancerous tumours, a treatment commonly known as hyperthermia. This chapter examines the structure of the image field in a rotationally symmetric optical system, following largely the analysis of Richards and Wolf.