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We present an antenna engineering approach to significantly improve off-axis detection properties of terahertz focal plane arrays (FPAs) behind an extended-hemispherical lens. In particular, antennas in the off-axis pixels in a large FPA were redesigned to exhibit tilted receiving patterns. The new antenna structure corrects for beam distortions in off-axis sensors due to the small lens size. Specifically, this approach is well suited for monolithic antenna structures integrated with high-sensitivity heterostructure backward diodes. Although the approach is demonstrated for 100- and 500-GHz FPAs, the presented technique is equally applicable to other planar antenna topologies and sensor materials that operate well into the terahertz regime. In addition, standard RF impedance-matching techniques were used to improve responsivity performance of the diode-coupled FPAs. The beam-correction techniques allow for a factor-of-5 larger size FPA for a fixed lens size. We also note that a tradeoff between Gaussicity and directivity becomes necessary for larger lenses. Thus, increasing the size of the FPA, without resorting to increasing the lens size, enables improved coupling efficiencies (Gaussicity) as well as better pixel resolution (directivity).