Measuring radio emission from air showers offers a novel way to determine properties of the primary cosmic rays such as their mass and energy. Theory predicts that relativistic time compression effects lead to a ring of amplified emission which starts to dominate the emission pattern for frequencies above ∼100∼100 MHz. In this article we present the first detailed measurements of this structure. Ring structures in the radio emission of air showers are measured with the LOFAR radio telescope in the frequency range of 110–190 MHz. These data are well described by CoREAS simulations. They clearly confirm the importance of including the index of refraction of air as a function of height. Furthermore, the presence of the Cherenkov ring offers the possibility for a geometrical measurement of the depth of shower maximum, which in turn depends on the mass of the primary particle.