Horseshoe crabs use vision to find mates. They can reliably detect objects resembling potential mates under a variety of lighting conditions. To understand how they achieve this remarkable performance, we constructed a cell based realistic model of the lateral eye to compute the ensembles of optic nerve activity ("neural images") it transmits to the brain. The neural images reveal a robust encocding of mate-like objects that move underwater during the day. The neural images are much less clear at night, even though the eyes undergo large circadian increases of sensitivity that nearly compensate for the millionfold decreasein underwater lighting after sundown. At night the neurral images are noisy, dominated by bursts of nerve impulses from random photon events that occur at low nighttime levels of illumination. Deciphering the eye's input to the brain begins at the first synaptic level with lowpass temporal and spatial filtering. Both neural filtering mechanisms improve the signal-to-noise properties of the eye's input, yielding clearer neural images of potential mates, especiallyat night. Insights about visual processing by the relatively simple visual system of Limulus may aid in the designof robotic sensors for the marine environment.