Binocular Summation Revisited: Beyond √2


Sometimes in the course of scouring around one finds hidden gems in unlikely sources. Such was the case for an article from the Psychological Bulletin in 2018, with the intriguing title above. It addresses binocular summation – a fancy way of saying that two eyes are better than one. But how much better? We know that two eyes confer an advantage in many aspects of binocular vision, ranging from visual acuity to stereopsis. First year Optometry students learn that when taking acuities clinically, most patients read the Snellen Chart better with both eyes open as compared to occluding the right or left eye. This is related to the boost in luminance from two channels rather than one, though it doesn’t always turn out that way. Sometimes amblyopia can cause sufficient inhibition that acuity with the amblyopic eye covered is actually better than with both eyes open together!

This article touches upon contrast sensitivity, and the opening of the abstract drew me in: “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 5 decades shows definitively that psychophysical binocular summation (the ratio of binocular to monocular contrast sensitivity) is significantly greater than the canonical value of √2.”

The body of the article begins by citing early work 50 years ago, reporting that the mean sensitivity improvement in binocular as opposed to monocular vision was a factor of √2. This means that, on average, a monocularly presented stimulus requires a contrast 1.4 times higher than the same stimulus presented binocularly in order to be equally detectable. This is consistent with a squaring nonlinearity operating before the two monocular signals are summed physiologically in the cortex. However, more recent work in the 21st century has reported substantially greater improvements, up to a factor of around 1.8, implying greater linearity.

The part of the article that really caught my eye was a two paragraph section titled What Is the Best Way to Measure Summation? As it turns out, the best way to measure summation is consistent with best practices in treating amblyopia. The authors write: “Our results here point to some guidelines for how best to estimate neural binocular summation in future studies. Patching of the unstimulated eye should be avoided if at all possible, ideally by using equipment (stereoscopes, shutter goggles or virtual reality hardware) designed for binocular presentation. If this is not possible, then placing a frosted occluder in front of the unstimulated eye will ensure that it views an uncontoured field of nearly the same mean luminance.”

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