Optical designs for non-scanning, imaging optical system with fields of view exceeding 2p steradians are presented. These optical designs are derived from arthropod visual systems that represents the results of millions of years of evolutionary optical system optimization. Superposition compound eyes, which are the basis for these designs, have evolved on nocturnal insects and deep-water crustaceans. Both of these optically challenging environments are similar to signal poor applications such as missile approach warning where the entire environment of a sensor's platform must be continuously searched for approaching threats. Manmade optical sensor based on superposition compound eyes offer the advantage of no moving parts, no off-axis optical aberrations, no 'dead zones' due to scanning, and a field of view that is limited only by the obscuration of the platform the sensor resides upon. In theory, the maximum field of view of a superposition sensor is 4p steradians, all of which is imaged onto a single image surface. Presented in this paper are designs for manmade versions of these versatile, naturally occurring optical sensors and the results of ray-tracing simulations demonstrating their imaging qualities.