Sizing up screens - #32

Well, its better than sizing up other things... ahem. Dan Rutter answers the question of the mega-super-screen TV: How many dots, and do the inches really count?

It's a question that has mystified humankind for all of history:
What TV (that costs less than a new car) should you get, in order to enjoy image quality as good as you get from your PC monitor? Like, 1600x1200?
(OK, actually this is a question that Ben Mansill asked me. But let's get on with it anyway, shall we?)
Regrettably Ben, there is no such TV.
Non-high-definition TVs have a hard time resolving even 640x480 pixels. Some more expensive CRT TVs can manage a vaguely plausible 800x600 - more horizontal, less vertical, for 16:9 widescreen sets.
The reason for this is that the distance you view a TV from means it doesn't need super resolution. Over there on the other side of the lounge room, your eyes can't resolve much better than 640x480, unless the room's pretty tiny or the screen's pretty vast.
Figuring out what you can actually see at a particular distance and with a particular screen size is tricky.
The screen size and distance part of the equation is simple maths - move it twice as far away and the screen has to be twice as big for the same possible apparent detail, duh - but there are lots of other variables. Your personal visual acuity, of course, but also the nature of the target - contrast, brightness and so on.
This is where I handwave everything but visual acuity, because the other variables involve Nasty Calculations.
It's a general rule of thumb that 300 dots per inch (DPI) is all you need for something to look perfect under fairly close inspection (30cm away) by a person with 20/20 vision.
If you take 300 DPI at 30cm to be your gold standard for resolution, then 150 DPI at 60cm is acceptable, and so on.
I think 1.5 metres would be about the minimum viewing distance for a lounge room TV. Two or three metres is more common.
At 1.5 metres, 60 DPI would be adequate. At two, three and four metres you'd be talking 45, 30 and 22.5 DPI.
If we wave our hands a bit more and assume that paper DPIs are directly transferable to monitor DPIs, then our next helpful factoid is that the standard rule-of-thumb computer monitor DPI is 72. Nothing but small, super-high-res laptop LCD panels is going to manage more than 100 DPI.
CRTs can be told to display very high resolutions, but they don't really have fine enough phosphor dots to do a whole lot more than 72 DPI. A 19 inch monitor with a 36cm horizontal dimension will be running out of phosphor dots above 1280x960, and 1280 pixels across 36 centimetres is 90 DPI.
Now, this is a computer monitor, with a dot pitch (distance, diagonally, from any phosphor to its nearest identically coloured neighbours) of about 0.23mm.
TV manufacturers seldom even quote dot pitches for their sets, but you can bet on a mainstream $700-ish 68cm set not being significantly finer than 0.7mm. If it's got a nice bright aperture grille tube, its effective dot pitch is likely to be even worse. The highest quality TV CRTs manage around 0.4mm.
A 0.7mm-pitch 68cm TV has a 27 inch viewable diagonal, 1.5 times bigger than the 18 inches of a 19 inch monitor (TVs, unlike CRT monitors, don't generally rip you off by one inch under their quoted diagonal size), but 640x480 will be the approximate limit of its resolving power.
640x480 on that TV would look as good as anything can look to you, resolution-wise at least, at a distance of three metres. Move the screen closer and keep it the same size and you could use more resolution; move it away and keep it the same size and you could get away with even lower resolution. Though you probably wouldn't want to, for other reasons; good-sized TVs with really low-res tubes are often cheap and nasty crap.
And then, there's the bleeding Kell factor.
Interlaced video - which is what you get from every normal, non-progressive-scan TV - has lower vertical resolution than you'd expect. Interlace itself eats some detail, and so do filtering measures taken to reduce interlace flicker. All of this is collectively known as the "Kell factor" - see http://members.aol.com/ajaynejr/kell.htm . The Kell factor is part of why 1080i HDTV (1080 horizontal lines, interlaced) looks worse than 720p (720 lines, progressive scan).
So what's the take-home message?
If your CRT TV's a regular decent quality consumer model without flat square DSP enhanced progressive comb filtered dual overhead induction intercoolers, then its diagonal size multiplied by about four or five tells you how close you can sit to it and not need any more screen resolution.
If the set's a fancier high-end model with 0.4mm-ish dot pitch, then you can probably sit about 2.5 to three times the set's diagonal size away from it before you start seeing the grain, as it were.
1600x1200, though, ain't gonna happen with any normal TV. Even terrifyingly expensive plasma panel displays don't approach that resolution; they're not expected to be viewed from close enough that they'd need to.
You can get 1600x1200 from a "UXGA" video projector, though. One of those can currently be yours for not a lot more than $US20,000.
So you'd better start saving, Ben.