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A technique is developed for estimating the scattering effects of a homogeneous half space that contains strongly conducting patches on its surface. The technique directly relates the radiative behavior of the scattered field to that of the field sources acting alone. In particular, the method can be used to relate the performance of an antenna over a perfectly conducting plane to its performance over a finite ground screen. Unlike some previous attempts at this problem, the present approach does not rely upon an impedance boundary condition or upon a physical optics approximation to screen currents.