What Qualifies as a Retina Display? [Math]
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.