Abstract: An antenna feed comprises, aligned and centered on an axis OO?, a waveguide having an inside diameter, a first end and a second end, a dielectric body having a portion inside the waveguide and a portion outside the waveguide, the outside portion comprising a section of frustoconical shape having an outside lateral surface of frustoconical shape with two ends, namely a large diameter end and a small diameter end, and a subreflector at the large diameter end of the frustoconical shape. The outside portion comprises, in addition to the frustoconical portion, a cylindrical portion whose diameter is greater than the inside diameter of the waveguide. The cylindrical portion is connected to the frustoconical portion at its small diameter end and the frustoconical outside lateral surface of the dielectric body is smooth.