A new complex offset double-reflector configuration for a wideband focal plane array (FPA) is presented which is optimized for Ka-band applications with a scan range of ±20° in the azimuth plane. This configuration is obtained by using a mathematical framework based on geometrical optics which allow us to optimize complex double-reflector FPAs with limited computational effort. The proposed reflector configuration maximizes the number of simultaneously active array elements of the phased-array feed and minimizes the required total number of array elements for this wide scan range. To realize an aperture efficiency of at least 80% at 30 GHz, our concept allows half of the antenna elements in the array to be active during scanning for a scan range of ±10° and at least a quarter of the array elements to be active for a scan range of ±20°. This is a major improvement as compared to the scanning capabilities of focal-plane arrays based on conventional single- and double-parabolic reflector configurations. In addition, the FPA configuration has been optimized for wideband optical true-time-delay beamforming which requires a linear phase distribution along the array elements. We obtained a phase linearity with rms error of 2.81° at 30 GHz. The experiments from the realized prototype demonstrate a good agreement between simulation and measurements and fully prove the required scanning performance over a ±20° scan range. The prototype demonstrates a high directivity up to 46 dBi at 30 GHz and 48 dBi at 40 GHz and reflector efficiency up to 83% at 30 GHz and 77% at 40 GHz.