Transduction as a limitation on compound eye function and design

A theory on the design of the compound eyes of insects adapted to bright environments is presented. The main argument is that vision in compound eyes at photopic luminances is not limited by the number of photons available from the environment, but by the finite signal: noise ratio that can be achieved by the transduction mechanism. Measurements of the signal: noise ratio in locust photoreceptors show that the $\surd $ I law (Barlow 1965) does not hold at high luminances, but that the signal: noise ratio saturates to a value of 38.5 (s.d. = 10, n = 8). Saturation implies that Weber's law holds. In the theory presented here, the physiological constraints imposed by the intrinsic noise of transduction and synaptic transfer are added to the better known limitations that the dual particle-wave nature of light impose on vision. The results are quantified by information theory. Because insect vision at high luminances is not limited by photon shot noise, the theory predicts that the resolution of the single facets should approach that set by diffraction. Thus sensitivity is sacrificed for resolution. The theory also predicts that diurnal insects should undersample by a factor of about 2. Both predictions accord with a large number of experimental observations which, until now, have defied explanation. Information theory predicts that the vertebrate eye should not undersample. This paper also shows that the faster the temporal frequency response of the photoreceptors, the greater the information capacity of the eye. Finally we show how changes in rhabdom subtense can increase the range of intensities over which the compound eye can most efficiently operate.