aperture, d is the aperture diameter of a conical horn λ is the wavelength, eA is a dimensionless parameter between 0 and 1 called the aperture efficiency, The aperture efficiency ranges from 0.4 to 0.8 in practical horn antennas. For optimum pyramidal horns, eA = 0.511., while for optimum conical horns eA = 0.522. So an approximate figure of 0.5 is often used. The aperture efficiency increases with the length of the horn, and for aperture-limited horns is approximately unity. Horn-reflector antenna A type of antenna that combines a horn with a parabolic reflector is known as a Hogg-horn, or horn-reflector antenna, invented by Alfred C. Beck and Harald T. Friis in 1941 and further developed by David C. Hogg at Bell labs in 1961. It is also referred to as the "sugar scoop" due to its characteristic shape. It consists of a horn antenna with a reflector mounted in the mouth of the horn at a 45 degree angle so the radiated beam is at right angles to the horn axis. The reflector is a segment of a parabolic reflector, and the focus of the reflector is at the apex of the horn, so the device is equivalent to a parabolic antenna fed off-axis. The advantage of this design over a standard parabolic antenna is that the horn shields the antenna from radiation coming from angles outside the main beam axis, so its radiation pattern has very small sidelobes. Also, the aperture isn't partially obstructed by the feed and its supports, as with ordinary front-fed parabolic dishes, allowing it to achieve aperture efficiencies of 70% as opposed to 55–60% for front-fed dishes. The disadvantage is that it is far larger and heavier for a given aperture area than a parabolic dish, and must be mounted on a cumbersome turntable to be fully steerable. This design was used for a few radio telescopes and communication satellite ground antennas during the 1960s. Its largest use, however, was as fixed antennas for microwave relay links in the AT&T Long Lines microwave network. Since the 1970s this design has been superseded by shrouded parabolic dish antennas, which can achieve equally good sidelobe performance with a lighter more compact construction. Probably the most photographed and well-known example is the Holmdel Horn Antenna at Bell Labs in Holmdel, New Jersey, with which Arno Penzias and Robert Wilson discovered cosmic microwave background radiation in 1965, for