Next generation sub-mm imaging instruments require kilo-pixel focal plane arrays filled with background limited detectors. Microwave kinetic inductance detectors (MKIDs) are a state-of-the-art detector for future instruments due to their inherent multiplexing capabilities. An MKID consists of a superconducting resonator coupled to a feed-line that is used for readout. In the device presented here radiation coupling is achieved by coupling the MKID directly to a planar antenna. The antenna is placed in the focus of an extended hemispherical lens to increase the filling factor and to match efficiently to fore optics. In this paper, we present the design and the optical performance of MKIDs optimized for operation in a 100-GHz band around 850GHz. We have measured the coupling efficiency, frequency response, and beam patterns and compare those results to simulated performance. We obtain an excellent agreement between the measured and simulated beam pattern, frequency response, and absolute coupling efficiency between a thermal calibration source and the power absorbed in the detector. Additionally, we demonstrate that antenna coupled MKIDs offer background limited radiation detection down to 100 aW of power absorbed in the detector.
