The size of the pupils reflects directly the balance of different branches of the autonomic nervous system. This measure is inexpensive, non-invasive, and has provided invaluable insights on a wide range of mental processes, from attention to emotion and executive functions. Two outstanding limitations of current pupillometry research are the lack of consensus in the analytical approaches, which vary wildly across research groups, and the fact that, unlike other neuroimaging techniques, pupillometry lacks the dimensionality to shed light on the different sources of the observed effects. In other words, pupillometry provides an integrated readout of several distinct networks (Strauch et al., 2022), but it is unclear whether each has a specific fingerprint, stemming from its function or physiological substrate. Here we show that phasic changes in pupil size are inherently low-dimensional, with modes that are highly consistent across behavioral tasks of very different nature, suggesting that these changes occur along a pupillary manifold that is highly constrained by the underlying physiological structures. These results provide not only a unified approach to analyze pupillary data, for which we offer a toolbox (https://eblini.github.io/Pupilla/), but also the opportunity to delve deeper into the sources of the reported changes in pupil size.