Binocular summation revisited: beyond √2

Our ability to detect faint images is better with two eyes than with one, but how great is this improvement? A meta-analysis of 65 studies published across more than five decades shows definitively that psychophysical binocular summation (the ratio of binocular to monocular contrast sensitivity) is significantly greater than the canonical value of √2. Several methodological factors were also found to affect summation estimates. Binocular summation was significantly affected by both the spatial and temporal frequency of the stimulus, and stimulus speed (the ratio of temporal to spatial frequency) systematically predicts summation levels, with slow speeds (high spatial and low temporal frequencies) producing the strongest summation. We furthermore show that empirical summation estimates are affected by the ratio of monocular sensitivities, which varies across individuals, and is abnormal in visual disorders such as amblyopia. A simple modeling framework is presented to interpret the results of summation experiments. In combination with the empirical results, this model suggests that there is no single value for binocular summation, but instead that summation ratios depend on methodological factors that influence the strength of a nonlinearity occurring early in the visual pathway, before binocular combination of signals. Best practice methodological guidelines are proposed for obtaining accurate estimates of neural summation in future studies, including those involving patient groups with impaired binocular vision.