Wednesday, February 18, 2009

More HD musings

Still looking at John Lewis as my purchaser of choice, although with the doom and gloom the price might drop; probably as soon as I buy it. However one of the little side-quests involved the actual physical size of the television in that a) will it fit where I want it, and b) could I go up to the 37" version? Answers being yes and no respectively it still left one other point - optimal viewing distance or to put it bluntly how far away should I be from the TV?

Okay some reports put it such that the TV occupies an arc of 30° others that the minimum distance should be an arc of 26° with a maximum of 36°, however looking closer all these figures are based on cinema screens which not only don't use pixels but have a different screen ratio too. Besides it seems they can't even make up their minds isn't their something a little more scientific about?

Yes there is and it's called visual acuity, a measure of the smallest thing the human eye can distinguish. It appears that the human eye (20:20) has an acuity of 1/60°, it's measured in degrees for the obvious reason that we can see smaller things close-to that we wouldn't see far away. Let me give an example of what this means.

If I print of a sheet of paper with a black and white chequerboard pattern with each square being 1mm in size and stand a 20:20 sighted person 3.5m away they should be able to see that the page is made up of individual squares; move them 7m away and they'll see a grey sheet of paper as the squares appear to merge together.

So for televisions I want a distance that allows me to perceive each pixel (otherwise what's the point of having HD?) without being so close that each pixel start to dominate the picture. In other words I want a distance where each pixel perfectly fits my 1/60° view (Although of course my vision isn't 20:20 it's still a good estimate).

At this point I knock out a quick calculator that gives me the distance dependant on screen diagonal, however while useful this isn't practical. I can change the size of my television, what I can't do is easily change the size of my room and thus the distance I sit; I need to reverse the calculation.

So just for fun with a 21" SD television the optimum distance is 82", which is amusing as it's pretty much bang on to what I've already got. So what HD television do I need to sit at the same distance. Well if I bought a 720 pixel screen I'd need a 35", for a 1080 I'd need a 53"; why? Because the pixels are smaller on a 35" 1080 than they would be on a 35" 720, so for the pixels to be the same size I need a bigger screen.

So taking into account that when I play games I or those with me can often sit closer, a 32" 1080 with a distance of 50" is about right, If the space was available a 37" might have been better, but it turns out not to be a major difference (8") so that's that.

For those interested the equations needed are as follows:

For a 4:3 screen width is root(diagonal^2/25)*4 each pixel being 1/704th of that which then needs to be divided by two and then tan (1/120) to give the viewing distance

For a 16:9 screen the width is root(diagonal^2/337)*16 each pixel being either 1/1280th or 1/1920th depending on 720 or 1080 screen and then divide by 2 then tan (1/120) to give the viewing distance.

Oh and yes of course it works with height too as the pixels are, or should be, square - just change 4 to 3 or 16 to 9 and divide by 525, 720, or 1080.

Obviously to start with the viewing distance just reverse the equations or you could just post the distance or diagonal here and I'll do it for you :-)

4 comments:

Anonymous said...

"Okay some reports put it such that the TV occupies an arc of 30° others that the minimum distance should be an arc of 26° with a maximum of 36°"

Sorry to nitpick, but that's the wrong way around. The minimum viewing distance makes the TV subtend the maximum arc, and vice-versa.

You calculate a distance based on pixel size, but that's only half the story. The research on cinema screen sizes pays more attention to the comfort of the eye's field of view: how large can you make the screen before the viewer starts flicking his head back and forth like a spectator at a tennis match? As you correctly say, his is much less of a consideration for smaller TV screens, but it's much more important for cinema screens, and that's why the literature on the subject is more extensive than some simple trig.

Also, when choosing or siting your TV, you don't want it so you can see every pixel: you want it so you can't see the individual pixels, but of course you get the most benefit when you only just can't see the pixels. The distance you calculate represents how close you can get to the screen before it starts to look blocky. But for some people, having the screen subtend more of their field of view (making it a more immersive experience) is more important than it looking smooth, so they might buy a larger screen than this caculation suggests.

FlipC said...

Feel free to nitpick I had the figures in front of me and the 26° was larger than the 36° and I still mixed them up.

As for cinema screens, yes once you start going above a certain size the important factor is that the whole screen fits reasonably well within the field of view. As you say this is less a consideration for smaller screens, otherwise we'd only be sitting a foot away from them.

That was one of my points, that the figures quoted are all based on cinemas with large screens and are simply being applied to televisions with no real basis that I can see other than "these are the only figures we've got", as such I wanted a more 'objective' measure.

I also expected a touch of common sense in that stating that the distance you should be sitting at is 82" away I wouldn't expect people to get out tape measures. What I expected was people to say "I've got a distance of X between me and where I want the television, so how roughly how big should it be?".

To put it another way using the 30/26/36 degree calculation for a 21" 4:3 I should be sitting at 31"/36"/26" which for the maximum distance and 1/60th° gives me a distinguishable feature at 0.3mm for a pixel size of 0.6mm; I think I prefer my measurement ;-)

Okay as you say some people want a full immersive experience a cinema type view and for that yep you'd need a much bigger television. I have no problem with that if said people remember that cinema is generally light projected through film and thus has a much greater resolution than the television has to offer.

Me I get disorientated with such big screens, then again on my trip to Merry Hell one of the main entrances is floored with alternating black rubber and metal strips and that does my head in too.

Don B said...

Sorry for the late response to this blog - my DSL connection was down from 12 Feb until yesterday 11 Mar (but at least my speed has gone up from 120bps to 289bps), hence no comments from me on WFA or here on The Mad Ranter
*****
"Still looking at John Lewis as my purchaser of choice".

We have just bought a new HD/Freesat TV from John Lewis at Solihull. Their comments were that the ideal viewing distance from the screen should be about 3 times the size of the screen. So with a 32inch screen the viewer should be about 96inches away from the screen.

FlipC said...

Hey Don glad your connection's back - ouch a month with broadband who the hell was your provider?

Anyway yeah I've come across the 3x the size and it has as much scientific basis as the 30 degree calculation and doesn't take into consideration whether you're watching a 1080 or 720 or even an SD television. As Dan implies field of view plays a part and I think this is where the 3x rule comes from.

But hey for all that it's still a good approximation, but the best method would still be going to see it and finding your own comfort zone. Of course next to impossible at most stores as they line up all the TVs in aisles except for the monsters and you can't get more than three feet away from them without backing into the other row.

So anyway which TV did you go for and how is it looking?