The Binocular Advantage

It is generally acknowledged, and empirical experiments confirm, that when using two eyes, our threshold of detection of faint objects is approximately 1.4 times as good as with one eye.2 This is a consequence of what is called binocular summation,3 which is itself probably a result of at least two different phenomena:

• Statistical summation. For objects of a low threshold of visibility, there is a greater probability that photons from the object will be detected by at least one of two detectors (in this case, eyes) than by a single detector. If the probability of detection in one detector is just over 0.5, then the probability of detection in both is indeed approximately 1.4 times greater. For example, for a detection probability of 0.6 in one detector, the probability of detection in one of two identical detectors is given by:

P(Both) = P(Right) OR P(Left) - (P(Right) AND P(Left)) = 0.6 + 0.6 - (0.6 x 0.6) = 0.84 0.84/0.6 = 1.4

• Physiological summation. This is essentially an improvement of signal-to-noise ratio (SNR). The signals from each eye are added, but the random neural noise is partially canceled. If the noise is random, the resulting improvement in SNR will be V2, or approximately 1.4.

The consequence of binocular summation is that, with two eyes, we experience an improvement in both acuity of vision and in contrast. This is apparent when we have our eyes tested by an optometrist, where we notice that the eye chart is easier to read with both eyes than with one eye alone. It is easy to demonstrate this with binoculars: find an object that you can only just detect, or a double star that you can only just split, with both eyes, then cap each objective in turn. You may even notice it while reading this page! However, this is only true for well-corrected vision; if the image in one eye is sufficiently degraded, then the consequence is that binocular vision is degraded to below the performance for the good eye. This obviously has implications for when we use binoculars.

Another bonus of using two eyes is stereopsis. Although astronomical objects are obviously far too distant for them to be seen with true stereoscopic vision, when we use both eyes, there is an illusion of stereoscopic vision that enhances the aesthetic attributes of many objects. I find this effect particularly apparent with rich open clusters, especially when there are stars of obviously different colors.

Lastly, when you observe with two eyes one eye sees the small part of the field of the other eye that is obliterated by the blind spot, the location on the retina where the optic nerve enters the eye. In this sense, the binocular can be said to give a more complete view than single-eye observing.

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