We present the microoptical adaption of the natural superposition compound eye, which is termed "Gabor superlens". Enabled by state-of-the-art microoptics technology, this well known principle has been adapted for ultra-compact imaging systems for the first time. By numerical ray tracing optimization, and by adding diaphragm layers and a field lens array, the optical performance of the Gabor superlens is potentially comparable to miniaturized conventional lens modules, such as currently integrated in mobile phones. However, in contrast to those, the Gabor superlens is fabricated using a standard microlens array technology with low sag heights and small diameter microlenses. Hence, there is no need for complex diamond turning for the generation of the master structures. This results in a simple and well controllable lens manufacturing process with the potential to high yield.