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A high-frequency method for the three-dimensional analysis of integrated dielectric lens antennas is presented. This method consists on improving the physical optics (PO) currents on the lens surface by modifying, via suitable transition functions, the spreading factor of those rays from the source point which arrive at the lens-air interface close to the critical angle of incidence. Invoking the locality principle of the high-frequency phenomena, the method uses the rigorous canonical solution of the semi-infinite dielectric space locally tangent at the lens surface. A uniform asymptotic evaluation of this canonical solution is provided with the introduction of a new transition function for the TM case. The present formulation provides significant correction from the PO currents of an elliptical lens, with a consequent improvement of the radiation pattern prediction, testified by comparisons with results from a full-wave analysis.