Methods are presented for designing and estimating the performance of artificial apposition compound eye optical sensors. Apposition compound eyes have been investigated for a wide range of applications from robotics to smart weapons. While artificial apposition compound eyes have been constructed and demonstrated, optical design issues and performance prediction for these systems have never been adequately addressed in the literature. Apposition compound eyes are a useful paradigm for applications where wide field of view is critical but high spatial resolution is not required. Natural arthropod compound eyes and their biological models are first scrutinized to give insight into designing and modeling artificial apposition compound eye optical sensors. Such sensors are shown to have comparable sensitivity to traditional single-aperture sensors for extended sources. A method for enhancing resolution over the extended-source case is demonstrated for single point sources. For the first time, the frequency response of an artificial apposition compound eye is addressed while taking into account the differences between artificial and natural ommatidia. Both a numercal integration technique for determining the contrast transfer function and a Fourier-transform modulation-transfer-function method are presented and validated with experimental results.