1 - The quantum efficiency of vision

Summary

Attempts to understand the quantum efficiency of vision have resulted in three distinct measures of efficiency. This chapter shows how they fit together, and presents some new measurements. We will show that the idea of equivalent input noise and a simplifying assumption called ‘contrast invariance’ allow the observer's overall quantum efficiency (as defined by Barlow, 1962a) to be factored into two components: transduction efficiency (called ‘quantum efficiency of the eye’ by Rose, 1948) and calculation efficiency (called ‘central efficiency’ by Barlow, 1977).

When light is absorbed by matter, it is absorbed discontinuously, in discrete quanta. Furthermore, it is absorbed randomly; the light intensity determines only the probability of absorption of a quantum of light, a photon (Einstein, 1905). This poses a fundamental limit to vision; the photon statistics of the retinal image impose an upper limit to the reliability of any decision based on that retinal image. An observer's overall quantum efficiency F is the smallest fraction of the corneal quanta (i.e. quanta sent into the eye) consistent with the level of the observer's performance (Barlow, 1958b, 1962a). (This is closely analogous to Fisher's (1925) definition of the efficiency of a statistic.) Surprisingly, the overall quantum efficiency of vision is very variable, and much smaller than best estimates of the fraction of photons absorbed by the photoreceptors in the retina.

At all reasonable luminances the fraction of corneal photons that excite photoreceptors is almost certainly quite constant. Barlow (1977) concluded that for rods it must be in the range 11% to 33% (for 507 nm light). This is independent of the size and duration of the signal, and independent of the background luminance, up to extremely high luminances.