300 PPI is not the limit , why we can go all the way to 952 ppi (or more)

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"It turns out there’s a magic number right around 300 pixels per inch, that when you hold something around 10 to 12 inches away from your eyes,
is the limit of the human retina to differentiate the pixels."

That's what Steve Jobs said when he introduced the Retina Display brand back in 2010.

And that made a lot of people think that any resolution above ~300PPI in a smartphone display is just an overkill and a waste of GPU and memory since the human eye will not be able to resolve the extra pixels anyway.

But is the limit to human vision is really 300 PPI ?!

Math time

According to a modern studies[1] Human eye can resolve 77 cycles per degree, and you need a minimum of 2 pixels to define a cycle, so you need 77*2=154 pixel per a degree of vision

To calculate how may degrees a display take, we will use the following formula

Eyeopticsv400y_medium

via upload.wikimedia.org

A typical smartphone in normal use will be held 12 inches away from eye, so each 1 inch of display hold in a 12 inch distance will take 2*arctan(1/(2*12))*(180/pi)=4.77 degree of your vision, multiply that by 154 pixel/degree the we calculated above and you will get 4.77*154= 735 pixel per inch.

So wee need 735 PPI for a phone used from 12 inch away , not the 300 PPI Steve Jobs told us.

And this 735 PPI turns to 881 PPI if we change the viewing distance to 10 inch.

If you don't trust my numbers, Cult of Mac have also calculated that you need much much more than 300 PPI to get full advantage of the human vision.

There numbers is even higher than mine because they used 200 pixel per degree ((1/0.3)*60) based on a different study while i used 154 pixel per degree .

Here is what Cult of Mac think a True "Retina displays" should be vs what Apple claim to be :

Appleretinavstrueretina_medium

Cult of Mac also point out to a discovery made by Japan’s NHK Science & Technology Research Laboratories back in 2010 that the smaller the pixels, the more real an on-screen object seemed to the person viewing it, even if they didn't have perfect vision. In fact, this effect is so profound on individuals that it eventually reaches a point where you have pixels small enough that on screen objects are completely indistinguishable from real objects.

Science has spoken,

Smartphones with displays that have higher than 300 pixels per inch is not an overkill.

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via st.gsmarena.com

So Putting a 1080p display in a 5" device like the new HTC J butterfly is not as a crazy as it sound , in fact I expect high-end devices with 4.x inch to adopt the 1080 x 1920 resolution by 2013/2014.

Science_medium

via imgs.xkcd.com

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[1] Curcio, C.A., Sloan, K.R., Kalina, R.E. & Hendrickson, A.E., Human photoreceptor topography. Journal of Comparative Neurology 292, 497-523, 1990.