A 1920*1080 picture does not have 1920*1080 resolution.
The resolution of a 1920*1080 picture is less than its number of pixels. This is what I was trying to describe in my previous post.
A 1920*1080 picture can only resolve 1920/K * 1080/K regularly distributed elements where K is larger than 2.3 according to the Nyquist theorem.
Just do the experiment of taking an image of 1920*1080 regularly spaced holes in a back illuminated plate.
Because the number of bright spots is the same as the number of pixels, the light from each hole will fill each and every of the available pixels and the resulting image will be completely uniform, no structure will be detectable. To RESOLVE a such a distribution of holes you need black pixels between the white pixels to detect the black spaces between the holes in the plate. i.e. twice as many pixels.
Conclusion to resolve a 1920*1080 distribution or image you need a display of at least 3960*2160 pixels.
Sampling is not the same as resolution!