What Qualifies as a Retina Display? [Math]

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Posted March 2, 2012 at 10:28pm by iClarified

Richard Gaywood takes a look at the math to determine how close various Apple devices are to a Retina Display and whether a 2048x1536 iPad makes the cut, in a recent TUAW article.

Gaywood notes that in the viewing angle diagram below, a, is called the angle subtended by the inter-pixel spacing, s. Whether or not a pixel can be discerned is based on the size of this angle. The size of the angle changes as you move a screen closer or further from your eye. One arcminute, or an angle of 1/60th of a degree, is considered the resolution limit of a typical human retina.

Next, Gaywood took the average viewing distances and resolutions of various Apple devices and calculated how close the subtended viewing angle was to one arcminute.

The iPhone 4 screen at a typical distance of 11" is just barely above the threshold for a Retina display. I believe this justifies my methodology. Secondly, it repeats my previous conclusion that a pixel-doubled iPad running at 2048x1536 is easily enough definition to count as a Retina display -- even at a 16" viewing distance, which is on the close side from my experimentation with an iPad and a tape measure. Similarly, that Asus tablet is a Retina display too.

It also shows that many current Mac displays are a lot closer to Retina display levels than you might have thought. The 27" iMac at a distance of 28", a 17" MacBook Pro at 26", an 11" MacBook Air at 22" -- these screens all have pixels small enough to border on invisible.

Hit the link below for a much more detailed explanation of these calculations.

What Qualifies as a Retina Display? [Math]

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Shameer - March 3, 2012 at 3:28am

They should make iPad 2 $200 cheaper for every model after 3 is released

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Ahmed Osama - March 3, 2012 at 12:32am

Regardless to the viewing distance, the Retina Display has pixel density of 336 PPI, which is only found in the iPhone 4/4S and the 4th Gen iTouch.

dancj - March 3, 2012 at 10:40am

Except for two small details. 1 - Apple get to decide what fits a term they invented. 2 - you're completely ignoring why Retina Display is called Retina Display. It makes perfect sense to take distance into account.

Adcpolo - March 4, 2012 at 2:40am

Then iPhone 3G also has retina display if viewed from 500 feet...

Ahmed Osama - March 4, 2012 at 3:05am

Well, u said it your self, they can name it as they want, because they invented it. But, when we start to compare things, we have 2 put them in the same conditions, u can't say that X passes as a Retina Display from Y distance, and Z passes from B distance, u have to compare them both in the same distance, which bring us back to the pixel density which is the real factor :) 336 pixels/inch

dancj - March 4, 2012 at 8:18am

They don't have to compare them from the same distance if they're not both generally viewed from the same distance.

Ahmed Osama - March 4, 2012 at 11:57am

Dude, it's the very basic comparing rules, when u compare 2 things, u have 2 put them in the same condition, u can't compare things in different conditions. This apply on anything on our lives. For example, u can't say that copper get hot faster than iron, while copper is in a 100 degrees environment and iron is in a 50 degrees, of course it will get hot faster, u get what I mean?

dancj - March 4, 2012 at 12:27pm

Obviously if you're measuring pixels-depth then that's true, but that's not what the Retina Display label does. That measures whether the pixels are small enough that you can't tell them apart, so obviously you have to take viewing distance into account. (as an aside, the iPhone 4/4s screen actually fails in that respect because you can still see jaggies in games without anti-aliasing)