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A three-dimensional ray tracing technique for internally reflected rays is developed and applied to compute the radiation pattern of an integrated lens antenna architecture with a twin arc-slot printed feed. The feed is represented in simulation by equivalent currents computed by the method of moments. The simulated results are compared against measurements at 30.2 GHz, including the case of an offset feed, in which internal reflections lead to pattern contributions of up to 20 dB that cannot be predicted by first-order physical optics (PO) techniques described in prior work. The twin arc-slot design reduces undesired sensitivity in diagonal lateral directions with respect to a comparable rectangular slot feed. Low-directivity feed model basis functions are shown to reduce discretization noise in the simulated patterns with respect to an array factor model. A frequency sweep analysis is introduced to test the sensitivity of individual sidelobes to the fabrication tolerances of the dielectric lens.