Multiplication noise in the human visual system at threshold: 2. Probit estimation of parameters

Abstract

A mathematical technique is described that relates detection model parameters to stimulus magnitude and experimental probability of detection. The normalizing transform is used to make the response statistics approximately Gaussian. Conventional probit analysis is then applied. From measurements at M stimulus levels, a system of M equations is solved and estimates of M unknown parameters of the detection model are obtained. The technique is applied to a threshold vision model based on additive and multiplicative Poisson noise. Results are obtained for the parameter estimates for individual subjects, and for the standard deviation of the estimates, for various values of the stimulus energy and number of trials. A frequency-of-seeing experiment is performed using a point-source stimulus that randomly assumes 3 energy levels with 200 trials per level. With a central efficiency of 50%, the estimated ocular quantum efficiency for our four subjects lies between 12% and 23%, the average dark count at the retina lies between 8 and 36 counts, and the threshold count for our (low false-report rate) data lies between 11 and 32. The theoretical results reduce to those obtained by Barlow (J. Physiol. London 160, 155-168, 1962), in the absence of dark light and multiplication noise.