A receptor array is considered to be a two-dimensional, spatial distribution of sensory neurons and their closely associated interneurons in a bounded area. There can be hundreds to tens of thousands of receptors. The sensory neurons are in close proximity so that their output signals can interact locally in underlying interneuronal ganglia before the processed information is sent to the CNS. Examples of large sensory arrays include the vertebrate retina, the arthropod compound eye (CE) and optic lobes (OL), the vertebrate olfactory system, and the vertebrate cochlear system. In small sensory arrays, the sensory neurons generally send their axons directly to the CNS (e.g., ampullary electroreceptors in sharks, skates, and rays), or send their axons to a small numbers of interneurons, which in turn send axons to the CNS (e.g., gravity receptors in the cockroach, Arenivaga).

This chapter describes the signal processing that occurs in the arthropod compound eyes and OL. These receptor arrays have many interesting properties, including interneuron interactions that permit enhanced optical resolution and "feature extraction" from visual objects. Some visual feature extraction operations may be associated with dynamic flight stabilization; others may have to do with finding food, or a mate, or sensing danger. Unlike higher vertebrates, where sophisticated visual information takes place in the visual cortex of the brain, insects and crustaceans appear to do most of their visual feature extraction in their OLs, which lie directly under the receptors. The OL ganglia then send the processed information to the animal's brain and ventral cord ganglia.

In this chapter, the first topic considered is the anatomy of CEs and optic ganglia. The ommatidia are the functional subunits of the receptor array of the CE. Each ommatidium consists of a dioptric apparatus (corneal lens, lens, and lightpipe-like structures) and a group of light-sensing retinula cells, arranged about a central rhabdom core like the sections of a lemon.

The ommatidia of the CE are modeled as a two-dimensional spatial sampling array. Each ommatidium is also characterized by a directional sensitivity function, which describes how effectively a point source of light is converted to a depolarizing voltage in each retinula cell as the light is flashed ON at different angles from the centerline of the ommatidium. Further mathematical treatment of CE optics develops equations to calculate intensity contrast as a black/white object is moved over an ommatidium. Intensity contrast is shown to be a measure of the resolving power of the ommatidia treated as imaging elements. A multiplicative signal processing mathematical model is offered to describe "anomalous resolution" in CE systems. The effective product of the outputs of the six retinula cells in a single ommatidium is shown to lead to improved intensity contrast over that for a single retinula cell.

To further describe the signal processing properties of the ommatidia and OLs, inhibitory signal interaction between adjacent ommatidia is next modeled. Such interaction, long known as lateral inhibition, is shown to act as a spatial frequency high-pass filter, effectively enhancing edges and boundaries in the visual object. Lateral inhibition was first observed in the CE system of the horseshoe crab, Limulus polyphemus; there is evidence for it in many other CE systems, and in vertebrate visual systems.

Finally, feature extraction operations in compound eye systems are reviewed. Feature extraction is defined as an OL neural response to a particular feature of a visual object. Examples include directionally sensitive neurons that fire when a long, contrasting object moves in a preferred direction, units that fire for a small dark object that is jittered anywhere over an eye, units that fire for dimming of general illumination (no object), etc. Feature extraction operations in insects tend to be simple, and most involve object motion. It is easy to hypothesize that the outputs of such operations are used for flight stabilization, or alerting the animal to potential danger.

While evolution has stuck arthropods with a relatively low resolution optical system (the ommatidia of the CEs), remarkably, it has allowed these animals to develop neural systems (the OLs) that make the most of the relatively low spatial input information from the retinula cells. Insects that hunt by vision (mantisses, dragonfles) have huge numbers of ommatidia (~104/eye), and the highest spatial resolution found in CE vision. Not only do dragonflies use their eyes to locate prey (e.g., mosquitos) on the wing, but they also use visual information to control their flight; they probably have the most complex CE visual systems of all the many insects and crustaceans. Not unexpectedly, very few workers have investigated dragonfly CE vision. Unlike flies and grasshoppers, these beautiful creatures are hard to catch in the wild, and very difficult to rear in captivity.

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