SvennoJ said:
I know what you're getting at but let me simplify it a bit. Indeed who wants to sit 8-10 ft away from a 30" screen in 2015...
THX standard specifies a 40 degree field of view for optimal visual experience. That corresponds to 1.2 times the diagonal for sitting distance with a 16:9 screen. 3ft from a 30" screen, or 6ft from a 60" screen. 1080p isn't even very nice to look at at that distance, 4K will finally full fill the THX specifications.
SMPTE standard specifies a 30 degree field of view for optimal 1080p experience. Or 1.62 times the diagonal of a 16:9 screen, hence 4ft for 30", or 8ft for 60". Very noticeable difference between 720p and 1080p.
Or to simplify your Omega factor, the number of pixels per degree you see is easier to compare: For 16:9 720p, perceived ppd = distance * 25.62 / diagonal For 16:9 1080p, perceived ppd = distance * 38.45 / diagonal
For example 1080p 50" at 5ft (60") = 46 pixels per degree (92 pixels per degree at 1ft from a 5" screen) 720p 50" at 5ft (60") = 31 pixels per degree (61 pixels per degree at 1 ft from a 5" screen)
The human eye can distinguish individual pixels upto 60 pixels per degree while people report a better smoother more detailed looking picture upto 200 pixels per degree. Makes more sense to go higher on your tv then on your phone.
Ofcourse you can be happy sitting 8 ft away from 30" 720p at 82 pixels per degree. But I rather have a more immersive experience in 2015 then a 16 degree field of view. Horizontal fov in degrees = 2 * arctan ((0.436 * diagonal) / distance)
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My intuitive observation and personal experience seem to totally agree with your math above. Given your numbers above, human eye cannot discern 1080 p on a 5 inch screen (92 pixels) but it can do with 720p (61). This is exactly what I experience.
Also your numbers again tell us that humans can easily recognize the difference between 1080p (46 pixels) and 720p (31 pixels) on a 50 inch TV at 5ft. This is also my exact experience!
In addition, this kinda proves the hypocracy of the Tech Crowd, who claim(!) that they do see a significance difference between 1080p and 720p smart hpne screens but keep downplaying the enourmous resolution gap between 720p and 1080p, while the very same crowd has been claiming CLEAR gains from 1080 to 4K.
A little bit math would also shed light on that. With your method,
1080p 50" at 5ft (60") = 46 pixels per degree (below 60 threshold)
4K (3840 x 2160P) at 5ft (60") = 92 pixels per degree (far above 60 threshold)
so 60 degrees would require 1080*60/46 =1408 so roughly speaking, a resolution like 2500*1400 would be the human vision threshold. In other words, 4K (3840 x 2160) is a bit overkill at 92 pixels per degree. BUT The tech crowd seems to disagree and tend to like the 4K. Wow, such a twisted mind! They see LITTLE use for 1080p (from 31 to 46, entirely discernible) but they are VERY ENTHUSIASTIC about 4K while 2/3 of the improvement from 46 to 92 degrees is not only wasted (indiscernible) but also less useful due to dimishing returns!