Resolution of display technologies

Written by Paul Bourke
January 2007
Introduction

The resolution of a digital display is a key component of the perceived quality. There are a number of factors that affect the resolution, such as: projector lens quality, interpixel leakage, surface properties, compression codes, geometry distortion, keystone, colour space, and so on. However one can calculate the upper quality possible by the display system by assuming a perfect system where the above have no degrading effect and considering just the pixel resolution. The figure of merit proposed is the angle a pixel subtends at the eye, convenient units for the scale of most current displays is arc seconds. This definition of resolution for some common devices is shown in the chart below, there is a bias/interest in displays the author has been involved in.

Comparison chart

Display type Projection resolution Dimensions Viewing distance Resolution
(arc seconds)
Apple 30" display 2560x1600 30 inch diagonal 600mm 86
Standard 17" display 1280x1024 17 inch diagonal 600mm 92
iPod video 320x240 2.5 inch diagonal 300mm 109
Flat screen projection (VROOM) XGA (1024x768) projector 2m wide 2m 201
Flat screen projection SXGA+ (1400x1050) projector 2m wide 2m 149
Flat screen projection HD (1920x1080) projector 2m wide 2m 109
Dome Full fisheye, XGA (1024x768) projector * Located at center 539
Dome Full fisheye, SXGA+ (1400x1050) projector * Located at center 395
Dome Truncated fisheye, SXGA+ (1400x1050) projector
75% coverage
* Located at center 292
Dome Truncated fisheye, HD (1920x1080) projector
56% coverage
* Located at center 218
Dome Spherical mirror** and HD (1920x1080) projector
Full dome coverage and 2/3 of the pixels used
* Located at center 309
Dome Spherical mirror** and HD (1920x1080) projector
80% dome coverage and 3/4 of the pixels used
* Located at center 264
Dome (planetarium) 6 projectors, each SXGA+ (1400x1050)
Assume each projector contributes 2/3 of its pixels to the final image
* Located at center 149
Dome (planetarium) 6 projectors, each HD (1920x1080)
Assume each projector contributes 2/3 of its pixels to the final image
* Located at center 126
Dome (planetarium) Full dome using two SONY 4kx2k projectors
* Located at center 103
Cylinder (AVIE) 6 projectors, each SXGA+ (1400x1050)
Assume 200 pixel edgeblend
* Located at center 178
Neptune From Earth 2.5
Mars From Earth 20

Notes

Equations

In what follows the following symbols are used.
x y are the physical linear dimensions, width and height
r is the radius
w h are the pixel dimensions, width and height
d is the viewing distance
n is the number of projectors

A small angle approximation is used, namely tan(x) = x for small values of x.

Planar display, single projector

x y
resolution = sqrt[ ------- ] / d
w h

If the pixels are square and all are used then this reduces to

x
resolution = -------
w d

Cylindrical display
Take the edge blend width in pixels into account for "w", the pixel width of each projector.

2 pi r
resolution = [ ------- ] / d
n w

If the viewer is standing in the center this reduces to

2 pi
resolution = -------
n w

Multiprojector Dome eg: planetarium
Assume each projector contributes 2/3 of its pixels to the final image.

pi r2
resolution = sqrt[ ---------------- ] / d
n (2/3) w h

If the viewer is located in the center then this reduces to

pi
resolution = sqrt[ ---------------- ]
n (2/3) w h

Dome projection with a single full fisheye

pi r2
resolution = sqrt[ ---------- ] / d
pi h / 2

For the observer at the center of the dome this reduces to

1
resolution = ----------
h / 2

Dome projection with a 3/4 truncated fisheye

pi r2
resolution = sqrt[ ---------- ] / d
pi w / 2

For the observer at the center of the dome this reduces to

1
resolution = ----------
w / 2

Dome projection using a single projector and spherical mirror

Assume p% of the pixels end up on the dome that is q% covered.

q pi r2
resolution = sqrt[ ----------- ] / d
p w h

For the observer at the center of the dome this reduces to

q pi
resolution = -----------
p w h