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.
© 1969 Optical Society of America
Equations on this page are rendered with MathJax. Learn more.