This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis\nof a single reflector antenna by simultaneously imposing Snell�s Law and Conservation of Energy in a tube of rays, yielding a\nsecond-order nonlinear partial differential equation of Monge-Ampere type, which can be solved as a boundary value problem.\nThe investigation explores the interpolating properties of confocal quadrics to locally represent the shaped reflector surface. It\nallows the partial derivatives involved in the formulation to be analytically expressed. To illustrate the method, two examples of\noffset single reflectors shaped to radiate a Gaussian power density within a super elliptical contoured beam are presented.The results\nare validated by Physical Optics analysis with equivalent edge currents.
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