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A technique based on the surface integral equation is applied for the analysis of antenna radiation in the presence of an arbitrarily shaped dielectric radome terminated by a conducting surface. The equivalence principle is used to characterize the effect of the radome on the transmitted field in terms of equivalent surface electric and magnetic currents which radiate in an unbounded medium. A set of coupled integral equations involving these currents is obtained by using the boundary conditions on the tangential components of the total fields. The adaptive integral method is applied to solve the integral equations so that electrically large radomes can be analyzed. The radiation patterns of dipole arrays with dielectric radomes of superspheroidal shape are also presented.