We are facing lots of screens and displays today starting with computer monitors, TVs and smart phones and ending with more sophisticated virtual reality (VR) displays like Oculus Rift. Most of them already use high resolution displays. For instance, Ultra HD 4k displays are becoming more and more available. But what does this mean and is this enough or too much? There are many tests and debates running about proper screen resolution when you have good picture quality and not wasting money for numbers only. This is not what are we are going to discuss. Everyone has to find their own optimal solution. Why not to do this rationally instead of chasing numbers.

Fig. 1 Screen door effect

From practical side, resolution alone doesn’t have significant meaning when choosing screen. You could take other two parameters in account – distance from screen and screen size. All those parameters goes along with human visual acuity – the smallest thing he can spot. When you go to the eye inspection you are given character chart where you need to point the smallest symbols you can see. The number next to that line represent your visual acuity. For healthy people the parameter is 6/6 (20/20 in feet) what means that eye is able normally to discern 1.75 mm objects from 6 meters. Wiki has great explanation of acuity parameters. The best recorded acuity was 6/3. For a simplicity we are going to use decimal scale where 6/6 acuity is expressed as 1.0 value where 0.1 would mean top line of acuity test chart.

Fig. 2 Visual acuity test chart (source)

We can understand standard visual acuity 6/6 (or 20/20) as ability to discern two points per single arc minute angle (as you may know – one arc minute is 1/60 of degree). To make things simple we need to relate screen resolution, distance from screen and screen size to viewing angle and then we can have a convenient way of finding best resolution for your needs.

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Fig. 3 Pixel size compared to visual acuity 1.0

**Example 1:** Take your standard 23” Full HD (1920 x 1080) monitor screen. You are sitting about 70 centimeters from it. Simplified screen height and width would be 29 X 51 cm. First thing we need to do is to calculate viewing angle of monitor. For this we need to find arctangent of half screen width and distance ratio: a = 2*arctan(14.5/70) = 24 degrees. Now we can calculate how many pixels we get for a one arc minute angle: p = 1080 / 24 / 60 = 0.75. So we get less than one pixel when we need at least single pixel. Seeing this we can make an assumption that 4K (2160) monitor would make a difference leaving us with 1.5 pixel per arc minute.

**Example 2:** Now let’s move to TV. Take same Full HD TV 1080p resolution 32” screen. The height of screen is about 50 cm and we sit 3 meters away from TV. By applying same calculus we get viewing angle 9.5 degrees. And for one minute arc we get around 1.9 pixels. So we get more than enough from Full HD TV and you don’t need Ultra HD TV unless you are sitting 1 meter away from it.

**Example 3:** Smart phones. Let’s take LG L90 smart phone which comes with 4.7” 540×960 screen. We take width as 6.7 cm and we look at it from 25 cm distance. The viewing angle we get is 15 degrees. Then we can calculate pixels per arc min which is 540 / 15 / 60 = 0.6. This is not enough to get great experience. Take Full HD display and we get 1.2 pixels per arc min for normal visual acuity. I’d say you don’t need more than Full HD display (1920×1080) for your smart phone and the higher is just wasting phone resources and your money.

**Example 4: **Last example I would like to discuss is Oculus Rift 2 display. This is where things get interesting. Its resolution per eye is 1920 x 1080. Their declared field of view is 100 degrees. So we can directly calculate the number of pixels for single arc minute: 1080 / 100/ 60 = 0.18. We would need like 6 times more resolution (16k with smallest axial resolution of 6480) to get clear picture in virtual environment. Even 4K display will not be able to produce natural feel. This is where small displays with very high resolution will come handy. I can imagine the data stream these glasses will have to deal with.

Feel free to comment and share your thoughts.