A dielectric antenna (1) having at least one supply element (2) and at least one lens (3) formed of a dielectric material. The dielectric antenna makes it possible to measure the surface of a medium with an essentially consistent measuring accuracy in that the lens (3) has an outer component (4) and an inner component (5). The outer component (4) has a radiating surface (6) that is spherical and an inner surface (7) that is spherical, and the inner component (5) has a contact surface (8) that spherical. Furthermore, the antenna is usable as part of a fill level sensor operating on the radar principle.