The size of the pupil has a large effect on visual function, and pupil size depends mainly on the adapting luminance, modulated by other factors. Over the last century, a number of formulas have been proposed to describe this dependence. Here we review seven published formulas and develop a new unified formula that incorporates the effects of luminance, size of the adapting field, age of the observer, and whether one or both eyes are adapted. We provide interactive demonstrations and software implementations of the unified formula.

The discrete, sequential scanning (sampling) procedures used in electronic displays generate disturbing artifacts such as flicker, Moire-type patterns, and paradoxical motion. Application of the theory of random scanning procedures to displays can reduce these artifacts. The human retina provides an example of a system that uses randomness to avoid sampling artifacts. Though the retina performs a discrete spatial sampling of the stimulus, artifacts are not evident.