Binocular summation revisited: beyond /2

Daniel Baker, Freya Lygo, Timothy S Meese, Mark A Georgeson

Research output: Contribution to journalArticlepeer-review


Our ability to detect faint images is better with two eyes than with one, but how great is this improvement? A metaanalysis 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 Ö2. 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.
Original languageEnglish
Pages (from-to)1186-1199
JournalPsychological Bulletin
Issue number11
Early online date13 Aug 2018
Publication statusPublished - Oct 2018

Bibliographical note

This article has been published under the terms of the Creative Commons
Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Copyright for this article is retained by the author(s). Author(s) grant(s) the American Psychological Association the exclusive right to publish the article and identify itself as the original publisher.

Funding: Engineering and Physical Sciences Research Council Grants
GR/S74515/01 and EP/H000038/1, and Biotechnology and Biological Sciences Research Council Grant BBH00159X1, Wellcome Trust (Grant 105624).


  • binocular summation, meta-analysis, psychophysics, contrast, spatiotemporal frequency


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