How binocular overlap impacts horizontal field of view

In a previous post, we discussed binocular overlap which increases overall horizontal (and diagonal) field of view. HMD manufacturers sometimes create partially overlapped systems (e.g. overlap less than 100%) to increase the overall horizontal field of view.

For example, imagine an eyepiece that provides a 90 degree horizontal field of view that subtends from 45° to the left to 45° to the right. If both left and right eyepieces point at the same angle, the overall horizontal field of view of the goggles is also from 45° to the left to 45° to the right, so a total of 90 degrees. When both eyepieces cover the same angles, as in this example, we call this 100% overlap.

But now lets assume that the left eyepiece is rotated a bit to the left so that it subtends from 50° to the left and 40° to the right. The monocular field of view is unchanged at 90°. If the right eye is symmetrically moved, it now covers from 40° to the left to 50° to the right. In this case, the binocular (overall) horizontal field of view is 100°, so a bit larger than in the 100% case, and the overlap is 80° (40° to the left to 40° to the right) or 80/90=88.8%

The following tables provide a useful reference to see how to percent of binocular overlap impacts the horizontal (and thus also the diagonal) field of view. We provide two tables, one for displays with a 16:9 aspect ratio (such as 2560×1440 or 1920×1080) and the other for 9:10 aspect ratio (such as the 1080×1200 display in the HTC VIVE). Click on them to see a larger version.

For instance, if we look at the 16:9 table we can read through an example of a 90° diagonal field of view, which would translate into 82.1° horizontal and 52.2° vertical if the entire screen was visible. Going down the table we can see that at 100% overlap, the binocular horizontal field of view remains the same, e.g. 82.1° and the diagonal also remains the same. However, if we chose 80% binocular overlap, the binocular horizontal field of view grows to 98.6°, vertical stays the same and diagonal grows to 103.2°

For those interested, the exact math is below:

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