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A new rumour regarding Apple and VR broke in the last day or two. In short, Apple is supposedly working on a combined AR/VR headset which will have ‘8K’ resolution per eye, be wireless, and be released in 2020.

As a HTC Vive owner, the massive leap in resolution sounds great. I love the Vive, and recommend it to early adopters (believe me, its overall user experience is still thoroughly in early adopter territory), but its resolution is without a doubt the area most in need of improvement. It has two 1080x1200 screens, one per eye, and these don’t come close to any definition of ‘Retina’ when they’re stretched to a 110° field of view.

This got me thinking, what is the threshold for a ‘Retina’ screen when we’re talking about a headset?

Pixels-per-degree

Before answering that question, let’s define a useful unit of measure: pixels-per-degree (PPD). Often, screen acuity is discussed in terms of pixels-per-inch; that is, the number of pixels that fit along an inch. While this gives an overall picture of the density of a display, it’s meaningless without considering the distance the screen is to be viewed from. The 80 PPI of a 50-inch, 4K TV sounds pitiful when compared to the iPhone X’s 458, but remember that the TV only has to hold up from ten feet away. By measuring in degrees, you can instead measure the number of pixels that occupy one degree of your field of view, and get a much better picture of how good a screen looks. Going by this measure, and assuming average viewing distances, we get a figure of 80 PPD for the iPhone X and a mighty 150 PPD for the TV.

Think about this for a moment and it makes a lot of sense; if you hold up your phone while sitting on the couch, you can probably cover up your tv entirely. In this case, each takes up the same amount of your field of view; since the 4K tv has a lot more pixels than an iPhone X, it wins the PPD race.

A ‘Retina’ headset

Given its 110° field of view (FoV), the Vive weighs in at an emphatically non-Retina 10 PPD. The Oculus Rift has a narrower FoV of 90°, but that still only gives it a PPD of 13. Even the new Vive Pro only gets to 14.5 PPD. So, to state the obvious, they’re a long way from ‘Retina’ resolution. These headsets’ screens use a 0.9:1 aspect ratio; for ease of comparison I’m going to assume the same aspect ratio in the calculations below.

Now let’s figure out what sort of resolution would be needed for a Retina AR/VR headset. Discounting the inexplicably non-Retina MacBook Air, screens on Apple’s current lineup range from 57 to 85 PPD; 57 pixels-per-degree therefore seems like a fair low-end estimate for any future products. While it's possible Apple is targeting a higher PPD, 57 is already so much higher than current offerings that I don't think it's really necessary.

A headset with the same FoV as the Vive, and the requisite 57 PPD, would need a screen resolution of around 5700x6270. One with the same FoV as the Oculus Rift would require around 4560x5130. Neither of those figures gels particularly well with the standard 8K resolution: 7680x4320. So what are the other options?

Taking the long edge of 8K as a base, a 6912x7680 screen would result in a headset with a 134° FoV at 57 PPD. Using the shorter edge, 3888x4320 would yield a 75° FoV at 57 PPD (though calling that ‘8K’ feels like cheating).

Those numbers have probably all blurred together, so here's a clearer comparison:

Possibility Resolution per eye FoV
Vive FoV 5700 x 6270 110
Oculus FoV 4560 x 5130 90
'8K' long edge 6912 x 7680 134
'8K' short edge 3888 x 4320 75

Conclusion

Coming up with these figures requires quite a few assumptions, and obviously there won't be any certainty until Apple actually announces something (or doesn't). It's interesting to see that some of the options for a Retina AR/VR experience at a similar FoV to existing headsets may indeed suggest a resolution that falls into the 8K range. Regardless of whether there's truth behind the rumour, there are some interesting takeaways on what an AR/VR headset would require if Apple wants one with a Retina screen:

The lesser ‘8K’ version doesn’t feel quite right; it would require either a fairly narrow FoV or a lower than 57 PPD resolution. That’s certainly possible, but neither option seems ideal.

The 134° FoV option at 57 PPD is a very exciting possibility; it would arguably surpass even the non-Retina to Retina leap Apple made with the iPhone 4. It would also require monstrous graphics processing, though, and I’m not sure it’d be feasible by 2020. It's also debatable whether extending that far into one's peripheral vision is really necessary, depending on the tasks this device is oriented towards. Though if Apple manage to crack a few optimisations like foveated rendering, who knows.

The option with the same FoV as the Vive, however, is a curious one. While its resolution doesn't fit with 8K in terms of horizontal or vertical pixel count, its total number of pixels would be very close to the total number of pixels on a standard 8K screen (35.7 megapixels vs 33.1 megapixels). Perhaps a phrase like 'the same number of pixels as an 8K screen' got the purple monkey dishwasher treatment as it moved along the rumour mill. This resolution would still require massive graphics processing power, but it's much more manageable than the 53 megapixels of the previous option, while still putting in a very strong showing in terms of FoV and PPD.

Sources

Retina Displays on Wikipedia
TV pixel densities.
PPD calculator