Some optimal tapers are shown in fig.9-10 and in fig.3 (see the previous section). In order to provide a wide range of distances, the amplitude at the antenna edge should be considerable (see fig.9). The phase inversion of this high-amplitude step changes the beam angular size greatly. On the other hand, in order to have a high value for the collection efficiency, it was necessary use Gaussian-like tapers with low amplitude at the antenna edge (see fig. 10). This helps to explain the following fact: if the value of the parameter r0 is fixed, the higher the collection efficiency, the narrower the range of allowable distances (see fig.8 and compare fig. 3, 9, and 10). Transmitted Power Maximization Let us discuss a more complex problem now. Assume that the desirable range of distance changes allowed is narrower than the maximum distance changes for the assumed values of r0 and of the collection efficiency r/. In this case it is possible to optimize other system characteristics by an appropriate choice of the illumination taper. In this section the maximization of power transmitted is discussed. Assume that the antenna radius and the peak power density at the antenna are fixed. In this case the maximization of the power transmitted is equal to the antenna power coefficient:
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