January 2007

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.

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) projectorFull dome coverage and 2/3 of the pixels used |
^{*} |
Located at center | 309 |

Dome |
Spherical mirror^{**} and HD (1920x1080) projector80% 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.

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**

resolution = sqrt[ | ------- | ] / d |

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

resolution = | ------- |

**Cylindrical display**

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

resolution = [ | ------- | ] / d |

If the viewer is standing in the center this reduces to

resolution = | ------- | |

**Multiprojector Dome eg: planetarium**

Assume each projector contributes 2/3 of its pixels to the final image.

^{2} |
||

resolution = sqrt[ | ---------------- | ] / d |

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

resolution = sqrt[ | ---------------- | ] |

**Dome projection with a single full fisheye**

^{2} |
||

resolution = sqrt[ | ---------- | ] / d |

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

resolution = | ---------- | |

**Dome projection with a 3/4 truncated fisheye**

^{2} |
||

resolution = sqrt[ | ---------- | ] / d |

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

resolution = | ---------- | |

**Dome projection using a single projector and spherical mirror**

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

^{2} |
||

resolution = sqrt[ | ----------- | ] / d |

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

resolution = | ----------- | |