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Searching the environment in a fast and efficient manner is a critical capability for humans and many other animals. Normally, multiple fixations are used to identify and localize targets. However, in the special case of covert search the target must be identified and localized within a single fixation. Here we present a theory of covert search that takes into account the statistical variation in background images, the falloff in resolution and sampling with retinal eccentricity, the increase in intrinsic location uncertainty with retinal eccentricity, and the prior probability of target presence and target location in the image. The computational steps of the theory are as follows. First, the effective prior probability distribution on target location is computed from the prior and the intrinsic location uncertainty. Second, the effective amplitude of the target (also dependent on retinal eccentricity) is computed and the target (if present) is …