and the antenna electric field is zero for ra>RT. Although the Fourier Bessel transform is analogous to the Fourier transform in its treatment of antenna and ground fields, the integral in Eq. 17 cannot be solved analytically for many aperture field distributions. Let us consider two field distributions: a uniform illumination (which can readily be solved) and a 10 dB Gaussian taper as used in the SPS reference system. The aperture distribution is a critical parameter when considering rectenna collection efficiency and sidelobe levels, but is a minor factor in determining grating lobe peaks and antenna attitude constraints. To illustrate this point, consider first a uniform antenna distribution, by letting Ea^ be a constant in Eq. 17 to provide an electric field at the ground This uniform antenna pattern has a relatively narrow mainbeam and low sidelobe peaks as shown in Fig. 6. The power density on the ground is proportional to the electric field squared and may be written
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