Originally posted by Pål Jensen Linear resolution is meaningless as images are not one-dimensional.
The ability to resolve detail is determined by whether or not you can distinguish a feature from something directly adjacent to it. This means that the only thing that matters for resolving power is the linear separation between one detail and any other detail, i.e. one dimension.
For instance, the ability to resolve two lines parallel to each other, the only thing that matters is the perpendicular axis between them. Lines of pixels along the parallel axis are useless because they are along the lines, and do not separate them. If you want to clearly resolve lines that are twice as thin, you need to double the
linear resolution, which is four times the pixels (assuming square pixels). This applies to individual pixels as well, lines are just easier to visualize (you can think of pixels as very short lines running in a direction perpendicular to the axis between it and the pixel you are comparing it to). The only thing you need to distinguish one pixel from any other pixel is the line of pixels between them. Pixels in any other direction are not necessary.
There is a reason why print quality is given in DPI (dots per inch) or PPI (pixels per inch), and why astronomers state the resolving power of their telecopses in terms of
angular resolution, which are all single dimensional units. This is why you cannot believe that marketing nonsense that 4K UHD (3840x2160) is "four times clearer" than 1080p. 4K will only resolve twice as finely spaced details as 1080p, with four times the total pixels.