Display resolution

Written by Paul Bourke
March 2014

The following will present the relative resolution of different displays. A relatively straight forward exercise but as a frequently asked question it warrants some consideration. The first thing to realise is the perceived resolution is not just about the technical resolution of the display or projector. It also depends on the size of the display and the distance of the viewer. The best measure of the perceived resolution is the angle a pixel subtends at the eye, so for a device with a certain number of pixels the perceived resolution increases as the device becomes smaller or as the viewer get closer. In what follows it will be assumed the pixels are square, the vast majority of the cases these days, this allows us to only consider the horizontal angle a pixel subtends at the eye, the vertical angle will be the same. It should be noted that the discussion here assumes a perfect device displaying content with independent pixels, this is rarely the case (see later for degrading effects).

If N is the number of horizontal pixels, W the physical width of the display or projected image, and D the distance the viewer is from the display, then the angle A in radians of a single pixel subtended at the eye is simply

A = W / (N D)

The following table gives some representative subtended angles for commonly encountered display panels or projected images.

Description
Angle a pixel subtends
at the eye (degrees)
Occulus kit V2, 440 pixels per inch panel viewed from 4cm. 0.16
30 inch display (660mm wide) with 2560 pixels viewed from 400mm. 0.07
VGA (1024x768) projector at 3m wide at 5m viewing distance, typical PPT presentation system. 0.067
iPhone 4 (326 pixels per inch) viewed from 200mm. 0.065
400mm wide HD (1920x1080) computer display viewed from 400mm. 0.06
iPad retina display (264 pixels per inch) viewed from 300mm 0.036
Typical tiled display, 46inch (1m wide) HD panels viewed from 2m. 0.03
2m wide HD (1920x1080) home cinema viewed from 5m. 0.02
Typical home LCD, 42inch (910mm) HD panel viewed from 4m. 0.018
2m wide 4K projector viewed from 5m. 0.01
Digital 4K iMAX on a 10m screen viewed from 25m. 0.01

What might ask what the resolving power of the human eye is, there is not one definition. 20/20 vision is defined as the ability to resolve two points of light separated by a visual angle of 0.016 degrees. Alternatively the maximum angular resolution of the human eye at a distance of 1 km is typically 30 to 60cm, this gives an angular resolution of between 0.02 to 0.03 degrees.

It should be noted that the above considerations relate to the idealised situation, in reality the actual perceived resolution of a digital image presentation can be less. Some factors reducing the effective resolution are listed below.

  • The lens quality of a projector based display.

  • The screen door effect around pixels of a display panel or projector.

  • Lossy compression of the digital movies being presented, most notably compression such as mpg, H264, and similar. To a lesser extent lossy compression of image formats such as jpeg.

  • For projected images the projection surface can degrade the image quality. Similarly for panels the layers of transparent glass/plexiglass in front of the raw pixels diffuse/scatter some light.

Angles marked on a figure from PQM: A New Quantitative Tool for Evaluating Display Design Options. Software, Electronics, and Mechanical Systems Laboratory 3M Optical Systems Division Jennifer F. Schumacher, John Van Derlofske, Brian Stankiewicz, Dave Lamb, Art Lathrop.

Planetariums domes

One might extend this to planetariums although in this case the true resolution is influenced by other things. In what follows it will be assumed that the rated dome projection is real where in fact it is not, for example the use of the words "4K" and "8k" to refer to dome resolution have no meaning in reality but are purely marketing terms. This is due to the following factors.

  • How much edge blending is there? Any edge blending can drastically reduce the resolution across the blend, especially as components drift.

  • Planetariums with multiple projectors have image warping (geometry correction) occurring so pixels are no longer independent.

  • There are lenses on the projectors with blurring and chromatic error effects increasing towards the rim of the lens, especially so for wide angle or fisheye lenses.

  • As mentioned before most, if not all, movie playback in planetariums is done using very lossy codecs, such as mpeg and its variants. As such there is significant degradation occurring that again removes any pixel independence, indeed adds even nastier long range effects.

In the following table it is assumed that the observer is in the center of the dome and located at the spring line (the ideal viewing position). For viewers off center the angle a pixel subtends at the eye increases for the most distant side of the dome and decreases for the close side. Note that in the scenario discussed here the radius of the dome is not a factor, on a larger dome the pixels are larger but further away so the perceived resolution remains the same.

Description
Angle a pixel subtends
at the eye (degrees)
4K planetarium
0.06
8K planetarium
0.03