Pupillary dilation as a measure of attention: a quantitative system analysis

Abstract

It has long been known that the pupil dilates as a consequence of attentional effort. But the function that relates attentional input to pupillary output has never been the subject of quantitative analysis. We present a system analysis of the pupillary response to attentional input. Attentional input is modeled as a string ofattentional pulses. We show that the system is linear; the effects of input pulses on the pupillary response are additive. The impulse response has essentially a gamma distribution with two free parameters. These parameters are estimated; they are fairly constant over tasks and subjects. The paper presents a method of estimating the string of attentional input pulses, given some average pupillary output. The method involves the technique of deconvolution; it can be implemented with a public-domain software package, Pupil.

We are grateful to C. C. A. M. Gielen and two anonymous reviewers for extensive comments on an earlier version of this paper. We thank Frans Pijnenborgh for carrying out the experiments. We also wish to thank P. C. M. Molenaar, A. S. Gilbert, and G. J. M. Baeten for help in solving the deconvolution problem. Johan M. Thijssen and Marinus H. M. Cuypers kindly helped us with the luminance and illuminance measurements. Finally, we want to thank the Technical Group of the Max Planck Institute for Psycholinguistics for their support during the experiments.