What PPI must be used before the human eye can't distinguish each pixel

The question arose when I was discussing anti-aliasing with a friend, basically explaining the basics. He then asked why we don't just use a huge resolution to which I replied; computing power.

However I realised that I have no idea how high a PPI you'd need to be unable to perceive individual pixels (assuming say, a 2/3 foot viewing distance). Also if you were unable to distinguish individual pixels, would aliasing even be an issue any more?

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Well here's the word from Wikipedia:

The maximum angular resolution of the human eye at a distance of 1 km is typically 30 to 60 cm. This gives an angular resolution of between 0.02 to 0.03 degrees, which is roughly 0.6 arcminute per line pair, which implies a pixel spacing of 0.3 arcminute. 20/20 vision is defined as the ability to resolve two points of light separated by a visual angle of one minute of arc.[13] That's about 300 pixels per inch for a display on a device held 10 to 12 inches from the eye.

The "line pair" mentioned means a black line next to a white one, so that at that resolution you should just be able to distinguish the two. It would be interesting to see when antialiasing becomes unnecessary.

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For the first question: the resolving power of the average human is around 20 arcseconds, which means that individual pixels cannot be resolved once they appear smaller than about 0.00009 radians (say, horizontally). So assuming your screen takes approximately 0.5 radians of your field of view, which is what you get for a normal monitor viewed at a normal distance, you would need a resolution of at least 5550 pixels horizontally (multimonitor setups don't count, since they are supposed to span a larger angle in your field of view).

Given that your average 22" 1080p monitor (1920 pixels horizontally) has a PPI of 96 pixels per inch, you'd only need around 3 times that, that is, a PPI of around 300, beyond which a typical human cannot distinguish individual pixels (this appears to be more or less confirmed in this answer).

I don't know for the second question. Perhaps someone else would care to answer it in detail, but I imagine you would still need maybe double, triple that for aliasing to really disappear, as at 300 PPI you are still at the limit, where nearby pixels aren't quite yet averaged together by the sensor (i.e. human eye), they are just barely distinguishable. But that's just a guess.

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Note that the aliasing issue would exist no matter the resolution. It depends far more on the sampling grid, with a uniform rectangular grid being far worse than the blue noise sampling that the eye uses. – Dan D. Feb 11 '14 at 11:47
I would up-vote your answer, but I can't :/ I felt that stibs answer was better simply because of the wiki link. – Edward G-Jones Feb 11 '14 at 11:48
@Noodlemanny All good, his answer is more "official", I concur. I just like trying to derive things myself and then checking if it agrees with existing results (in this case they did). – Thomas Feb 11 '14 at 11:54