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This paper examines the performance of dual-linear sinuous antennas on silicon extended hemispherical silicon dielectric lenses. A theoretical impedance of 106 Ω is identified based on the analysis of an ideal self-complementary structure, and this result compares well with simulations and measurements. The radiation properties of a linearly polarized sinuous antenna are simulated using Method of Moments software coupled to a GO/PO code, and also agree well with measurements. The results indicate that the sinuous antenna is an excellent wideband planar feed for a silicon lens, with cross-polarization levels below -17 dB, and polarization variations of ±5° over two octaves in frequency. The application areas are millimeter-wave, wideband, dual-polarized radio-astronomy receivers.