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Extensive air showers, induced by high energy cosmic rays impinging on theEarth's atmosphere, produce radio emission that is measured with the LOFARradio telescope. As the emission comes from a finite distance of a fewkilometers, the incident wavefront is non-planar. A spherical, conical orhyperbolic shape of the wavefront has been proposed, but measurements ofindividual air showers have been inconclusive so far. For a selectedhigh-quality sample of 161 measured extensive air showers, we havereconstructed the wavefront by measuring pulse arrival times to sub-nanosecondprecision in 200 to 350 individual antennas. For each measured air shower, wehave fitted a conical, spherical, and hyperboloid shape to the arrival times.The fit quality and a likelihood analysis show that a hyperboloid is the bestparametrization. Using a non-planar wavefront shape gives an improved angularresolution, when reconstructing the shower arrival direction. Furthermore, adependence of the wavefront shape on the shower geometry can be seen. Thissuggests that it will be possible to use a wavefront shape analysis to get anadditional handle on the atmospheric depth of the shower maximum, which issensitive to the mass of the primary particle.

The shape of the radio wavefront of extensive air showers as measured with LOFAR