Renewal theory is applied to a particle-counter model of visual discrimination in order to determine the effects of neural-impulse scaling and dead time on the detection of increment thresholds. Let the ratio of absorbed photons to neural spikes (scaling factor) be denoted by r and the dead time by τ. We show that the particle counter is equivalent to one with dead time τ* = τ/r and scaling factor r* = 1. Further, if τ = 0, the particle counter does not exhibit the Weber-Fechner behavior for high background luminances as predicted by Barlow. These are asymptotic results, valid for large observation times. For more general observation times, the performance of a particle-counter mechanism with r=2 and τ=0 is evaluated for different types of starting procedures.
EUGENE A. TRABKA, "Effect of Scaling Optic-Nerve Impulses on Increment Thresholds," J. Opt. Soc. Am. 59, 345-348 (1969)