Can VR Justify QHD and 4K Displays?

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Are we crazy for wanting QHD and 4k screens in our pockets? With rumors of Sony offering Full-HD and Quad-HD variants of the Z4 despite claiming in September that consumers can’t tell the difference, 2015 is set to be a banner year for dense displays. But as our own Emil Kako asked this past Sunday, does QHD really look much better than FHD? In most cases the science says “no,” though the other 2015 juggernaut – Virtual Reality – may beg to differ.

Optics, and Steve Jobs’ “Magic” 300 Pixels Per Inch

Before pinning down the science behind our screen density needs, let’s take a brief look at why this topic is so heated in the first place. It’s no secret that smartphone makers have long railed against the spec-sheet arms race for screen density. Apple even went so far as to base their Retina marketing campaign in 2010 on the idea that the human eye can only see so much, with Huawei and Sony echoing those sentiments as recently as last year. But with smartphone heavyweights like Samsung and LG offering qHD, and Qualcomm already pushing 4k, many consumers see lower density phones as a compromise.

To start things off, we need to unpack some jargon. Manufacturers like to bandy around numbers like 1080p (Full HD), 1440p (quad-HD), and 2160p (4k) in advertising promos, but its the relationship these numbers have with screen size that is most important. After all, it doesn’t matter that you’re looking at four thousand pixels if they’re spaced out across the entire state of Wyoming. Therefore, let’s limit our discussion to pixels per inch (PPI) – the number of RGB clusters that can be lined up along a one-inch ruler.

Now that actual density is in mind, we can get to the meat of the question: “when we look down at our phones, what’s the smallest angle our eyes can discern between two pixels before those clusters of color appear seamlessly blended together?” Physicists call this the eye’s angular resolution, which is usually ballparked around 1/60 of a degree (one arcminute), depending on things like pupil dilation, ambient light, and the color of the object being observed. This minimum angle neatly relates pixel spacing to our eye’s distance from the screen, as seen here:

Based on the relationships in trigonometry, we can express this ratio as

Tan(a/2) = opposite ÷ adjacent = (d/2) ÷ D

And solving for pixel separation, d,

d = 2 D Tan(a/2)

What do these formulas mean? In short, a smartphone held 12” away (D) and viewed under average conditions (a = 1/60 °) only needs the pixels to be 0.0035 inches apart – an astoundingly low 286.5 PPI. Screens denser than this are (scientifically) overkill, including the iPhone 4 at 326 PPI, the Galaxy S3 at 306 PPI, and certainly the modern 500+ PPI standard bearers from Samsung (Note 4) and LG (G3). So far, it seems like Steve Jobs was right when he said the magic number is around 300 pixels per inch.

Virtual Reality And Pixel Power

Asserting that 300 PPI is “good enough” may cover the average user most of the time, but it’s far from the complete picture. For example, how does the phone fare at night while pupils are dilated, or when viewed up close? In an age when Samsung, LG, and dozens of startups recommend strapping phones to heads as makeshift VR displays, these are questions that can no longer be ignored. Thankfully, the same equations used above can be employed here to gain valuable insight into the realm of the super dense.

Does this mean the current crop of phones paired with headsets like Google Cardboard, Samsung’s Gear VR, and LG’s recently announced kit aren’t ready for prime-time? Not necessarily. You might see a little pixelation or lose some detail, but the same is true of most TV setups. Besides, even the Oculus Rift has a slight “screen-door effect,” and that has not stopped Redditors from smoothing out the image with a screen protector and enjoying the immersion all the while.In other words, even my Nexus 6 shows its pixels up close, and only small qHD and 4k phones are up to the task of seamless Virtual Reality.

High density displays are unnecessary power hogs most of the time, but they’re here to stay. We might as well make the most of them by ushering in the VR wave of the future.