A dielectric antenna with an electromagnetic feed element (2) and with a lens (3) made of a dielectric material, the feed element (2) emitting electromagnetic radiation (4) and the lens (3) being supplied with electromagnetic radiation (4) in the feed region (5), the lens (3) relaying the electromagnetic radiation (4) and radiating it with the transmission region (6). To configure these dielectric antennas such that the disadvantages of the dielectric antennas known from the prior art are at least partially avoided, first of all, the lens (3) is shaped essentially ellipsoidally at least in the transmission region (6) and the lens (3) is arranged relative to the feed element (2) such that the electromagnetic radiation (4) emitted by the lens (3) in the direction of maximum radiation (7) of the antenna has an essentially planar phase front.