on 9.5), and it is possible to synthesize an aperture with a planar array. There is a significant benefit to this approach. The aperture fields are determined by the waveguide horn fields, which are constrained by boundary conditions and are usually monotonic functions. This constraint does not exist with the array, SO a much larger range of radiation patterns can be produced. Optimum patterns with most of the energy radiated into the main beam and very low sidelobes can be designed. Adaptive Arrays In a previous section it was shown that the radiation pattern of an aperture antenna is the spatial Fourier transform of the aperture distribution. Antenna radiation patterns can Chapter 9 Antennas therefore, in principle, be synthesized by control of the aperture excitation. If the aperture excitation can also be varied electronically, an adaptable radiation pattern is available. Elec- tronic beam steering or null steering (to minimize interference) can therefore be provided. There are limitations on beamwidth imposed by the aperture size, as the Fourier transform relationship implies. In practice it is very difficult to implement control of the excitation of a continuous aperture. An array antenna allows far more control by using a number of individual antenna elements grouped together to form a sampled aperture. The array ele- ments themselves might not be much more expensive than a continuous aperture antenna, such as a reflector, but in general the control devices are a significant cost penalty. This has to be traded off against the various advantages of an array antenna system. Because an array is a sampled aperture, there are limitations on the spacing of the array elements. A typical spacing is on the order of 2/2 (this will be explained in a later section), and SO fairly small antennas are required as elements. Dipoles, monopoles, slots, patches, and open-ended waveguides can all be used. The theory given here will be for a linear array of identical, equispaced elements. This is the simplest case and is also 