Feature Pages: 4K Displays –Can you see the difference?

4K Displays – Usage in Digital Signage

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As 4K displays become more commonplace, they are starting to be used in digital signage and industrial applications. The question many developers are asking though is can the human eye actually see the difference between a 4K display and a 1080p display they are starting to replace.

While this sounds like an easy question, it does not have a completely clear-cut answer. To come to a conclusion, we have to consider the quality of eyesight of the viewer along with both the size of the display and the viewing distance between the viewer and the display.
In order to answer whether a 4K display is going to look any better than a lower resolution display, we need to determine the pixel pitch (the distance between the pixels) of the display and compare it to what the viewer is actually capable of seeing.
To do this, we only need a bit of math and four pieces of information:

The size of the display
The resolution of the display
Your visual acuity (20/20, 20/15, etc.)
The distance between the viewer and the display (viewing distance)

While the math is not difficult, here is an easy to use Google Spreadsheet to solve the equations. In this spreadsheet entering the relevant information will give the pixel pitch of the display and the pixel pitch capable of being seen. With this, it is possible to determine if the viewer is physically capable of seeing the difference in using a 4K display or if a lower cost, lower resolution display can be used instead.

Determining The Pixel Pitch of a Display

The first task that needs to accomplished is to determine the pixel pitch (or the distance between pixels) of the display being considered. The manufacturer will usually provide this information as part of the display specification, but if this is not the case, it is possible to determine the pixel pitch based on the resolution and physical screen size.
There are many different ways to calculate the pixel pitch, but the usual method is to first determine the diagonal resolution of the display and then relate that to the physical screen size. To find the diagonal resolution, we can use the Pythagorean Theorem (a²+b²=c²).

In this case, the formula to determine the diagonal is:

$diagonal=\sqrt{width^{2}+height^{2}}$

For a 4K screen, the calculation would be $\sqrt{3840^{2}+2160^{2}}$ , which results in a diagonal resolution close to 4406. With this, it is possible to find the PPI (pixels per inch) of the display by determining the ratio between it and the physical screen size in inches (which is the diagonal measurement of the screen):

$PPI =\frac{diagonalresolution}{screensize}$

For a 31.5 inch display we would use the calculation $4406/31.5$ , which results in a PPI of about 140. To get the pixel pitch in mm, we can also convert to millimeters at the same time with the formula:

$pixel pitch(mm)=\frac{25.4}{PPI}$

For our example 31.5" screen that has a PPI of 140, this translates to a pixel pitch of about 0.182mm.

What Resolution Can the Human Eye See?

Asking what resolution the human eye can see is misleading, as the human eye does not see a fixed resolution. Human vision is measured based on angular resolution. This is how far apart two objects need to be, for them to be resolved at a certain distance. In terms that we are familiar with, this looks like:

We already know the pixel pitch of the display, so now we need to determine the pixel pitch it is possible to resolve based on the distance from the display. To do this, we first need to determine the angular resolution based on visual acuity.
For a person with 20/20 vision (using the Snellen chart) angular resolution works out to be one arc minute which is about .017° or .000296706 radians. However, since not everyone has exactly 20/20 vision, it is possible to determine the angular resolution for any visual acuity (20/10, 20/40, etc.) with the very simply formula:

$arcminutes=\frac{1}{first number/second number}$

So a person with 20/10 vision would use the calculation: $1/(20/10)$ which gives a result of 0.5 arc minutes. We now need to convert this into radians and since there are about 0.000290888 radians in an arc minute we need to use the formula:

$radians=0.000290888*arcminutes$

For a person with 20/10 vision (or 0.5 arc minutes), this translates to 0.000145444 radians. With the angular resolution in radians, we can then determine the pixel pitch it is possible to see at a set distance. To do this, we need to use part of SOHCAHTOA:

$\tan(angle)=\frac{opposite}{adjacent}$

In order to properly apply this formula, we need to actually use only half of the angular resolution (in order to keep the viewing distance and pixel pitch at a right angle) then multiply the result by two to get the full pixel pitch. Taking this into account, we can re-arrange this formula into:

$PixelPitch(in)=2*d*\tan\frac{a}{2}$

d = distance to screen (inches); a = angular resolution (radians)

This is still in inches, so if we wanted to convert to a pixel pitch in mm we simply need to multiply by 25.4 since there are 25.4 millimeters in an inch:

$PixelPitch(mm)=25.4*(2*d*\tan\frac{a}{2})$

d = distance to screen (inches); a = angular resolution (radians)

With this formula, a person with 20/20 vision looking at a display 24 inches from their eyes would use the calculation:

$25.4*(2*24*\tan\frac{.000290888}{2})$

This works out to a pixel pitch of about 0.177mm. If we would rather think in terms of PPI (pixels per inch), we simply need to take the inverse and convert back to inches by multiplying by 25.4:

$PPI=\frac{25.4}{Pixel Pitch(mm)}$

In our example, this works out to about 144 PPI. In other words, a person with 20/20 vision looking at display 24” away would ideally want a display that has a pixel pitch of less than 0.177 mm (or more than 144 PPI).
To be able to easily check multiple resolutions and display sizes, use the Google Spreadsheet that has all of the math automated.

Conclusion

Below is a chart showing the ideal maximum size of a display for different resolutions based on visual acuity:

Ideal maximum display size for 24" viewing distance	20/30	20/20	20/15	20/10
1080p (1920x1080)	23"	15"	11.5"	7.5"
2K (2560x1440)	30.5"	20"	15.5"	10"
4K (3840x2160)	46"	30.5"	23"	15.5"
5K (5120x2880)	61.5"	41"	31"	20.5"

At a viewing distance of 24”, it is possible to start making out individual pixels with a 1080p display. Above a 20” display it should be possibleto see a difference by moving to 4K resolution.

The average acuity for a healthy adult under the age of 60 or 70 is actually closer to between 20/13 and 20/17 (source 1 and 2). So a typical visual acuity would be around 20/15 at which point the need for a higher resolution is even greater.

Ideal maximum display size for 24" viewing distance	20/30	20/20	20/15	20/10
1080p (1920x1080)	21"	14"	10.5"	7"
2K (2560x1440)	28"	18.5"	14"	9"
4K (3840x2160)	42"	28"	21"	14"
5K (5120x2880)	57"	37.5"	28"	18.5"

Both of these charts are generalisations, so use the Google Spreadsheet to experiment with different display sizes, distances and visual acuity.

These calculations indicate there is a benefit to having a 4K display when the viewer is close. With typical digital poster size ranging between 40” and 46”, the answer is very clear. With just 20/20 vision, it should be able to see the difference on any display larger than 20” in size and the difference becomes greater and greater as the size inceases.