A model for nonlinear stochastic behavior of the pupil

In this paper we present new experimental results that show pupillary noise to be multiplicative in a particular fashion with greatest variance in midrange and smaller variance at high and low ranges. This confirms the finding of multiplicative noise by Stanten and Stark (1966), but modifies and extends the relationship they suggested between standard deviation and mean pupil diameter. We propose a parametric model of the iris muscle which not only describes the static characteristics of pupil response to given stimuli, but also explains its random fluctuations in terms of probability density functions. We emphasize the point that the range nonlinearity is not due to decreased gain at the extrema of the pupil range, but is operational over a wide portion of the pupillary behavioral range, hence its name--"expansive range nonlinearity". We conclude that noise amplitude, which is a function of the pupil diameter, closely parallels the changes in deterministic gain. Thus pupil noise can be simply considered as cross-talk additive Gaussian noise injected into the pupil system at midbrain level.