The generality of the critical spacing for crowded optotypes: From Bouma to the 21st century

It is rare to find a crowding manuscript that fails to mention "Bouma's law," the rule of thumb stating that flankers within a distance of about one half of the target eccentricity will induce crowding. Here we investigate the generality of this rule (even for just optotypes), the factors that modulate the critical spacing, and the evidence for the rule in Bouma's own data. We explore these questions by reanalyzing a variety of studies from the literature, running several new control experiments, and by utilizing a model that unifies flanked identification measurements between psychophysical paradigms. Specifically, with minimal assumptions (equivalent psychometric slopes across conditions, for example), crowded acuity can be predicted for arbitrary target sizes and flanker spacings, revealing a performance "landscape" that delineates the critical spacing. Last, we present a compact quantitative summary of the effects of different types of stimulus manipulations on optotype crowding.