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

^*For the dome and cylindrical environments the resolution is independent of the size of the display assuming the observer is at the central sweet spot. As the dimensions of the surface get larger the observer gets further away.
For the multiple projector domes it is assumed that 2/3 of the display area of each projector contributes to the final image. This does depend on the aspect ratio of the projectors being used but is the upper limit for standard geometry corrected and edge blended frames.
^**The spherical mirror projection does not result in equal size pixels across the dome and it is possible to vary the dome coverage from the same as a truncated fisheye to 100%. Some parts of the dome will be higher resolution, others lower.

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

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