You don't need 1080p

Ok, I admit that I stole this week’s blog post from myself, but I’m still getting questions on this, so here it is. I’m also posting older Gearworks and Hook Me Up articles over the coming weeks so we have a better catalog of helpful articles that had been in the mag but hadn’t been posted here.

Viewing Distance vs. Resolution

Or, how I learned to stop worrying and love 720p.

Resolution starts (and ends) with the eye. If you're one of the lucky few with 20/20 vision (corrected or not), your eye can discern one-sixtieth of a degree of arc at 20 feet. Translated to inches, this means that, at 20 feet, your eye can discern objects roughly 0.067 inches wide, as long as there's enough of a contrast difference between the object and the background. This refers only to black-and-white info; your eye doesn't resolve color nearly as well as black-and-white. Also, eyes and contrast are a whole other GearWorks that I'll get to eventually. Lastly, we're going to stick with width for simplicity, although this discussion obviously applies to both width and height. Most people sit about 10 feet from their TVs. At this distance (and everything else being equal), your eye can resolve objects that are 0.033 inches wide.

Talk TV, Smart Guy
The average 42-inch-diagonal, 1,280-by-720 plasma or LCD display has pixels that are roughly 0.029 inches wide. (Of course, each model has different inter-pixel spacing, but, for now, we'll assume they don't.) If the same size display had a resolution of 1,920 by 1,080, the pixels would be 0.019 inches wide. As you can see, in a 42-inch display at a distance of 10 feet, your eye can't discern the resolution available even with 720p. Even more resolution is "wasted" at 1,920 by 1,080.

Now, assuming that you're not going to move your couch but you want a bigger TV, how does this work with a 50-inch set? The pixels in a 1,280-by-720 display are 0.034 inches wide, which is almost exactly what your eye can discern at 10 feet. A 1,920-by-1,080 display has 0.023-inch-wide pixels, smaller than your eye can resolve. A 1,920-by-1,080 display would have to measure more than 70 inches diagonally before you start testing your eyes' limits on the display's resolution (at least at 10 feet). Scan lines are the pixels of the CRT world and, in this case, function similarly. The pixels in some displays are not square, in which case you'll also need to check pixel height.

Hold Up, Math Whiz
That isn't the whole story. High resolution, in and of itself, isn't why the the move was made to HD. Ideally, a screen should fill 30 degrees of your field of view for so-called "optimum viewer enjoyment." This is why kids sit so close to the TV, and movies in the theater were more fun than your old TV. By making the screens wider and letting you sit closer (thanks to the higher resolution), the average TV's field of view went from 11 degrees (in most cases) with NTSC to 33 degrees with an ideal HDTV. Rarely is everything ideal, though. The "3x picture height" rule that's tossed about as the ideal seating distance for HDTV (compared with 7x for NTSC) doesn't take into account that displays and high-definition material aren't perfect (and, until recently, none were really 1,920 by 1,080). Just because you can match or exceed your eye/pixel resolution doesn't mean that the material you're watching has anything close to that level of detail. Video noise, artifacts, and poor-quality low-resolution sources (NTSC cable/satellite feeds) are all too noticeable at close distances.

To split the difference between NTSC and HDTV, I recommend a 5x seating distance as a starting point (even at a loss of field of view). At 5x, your eye can almost exactly resolve 720p, regardless of screen size. Since the original writing, we put this math to the test, with intersting results. You can read that article here.

So, Can I Buy a Cheap TV?
Just because your eye can't resolve the additional resolution doesn't mean that you shouldn't get a higher-resolution set; it just means that you don't necessarily have to. From where most people sit, you don't need 1080p in a 37-42 inch TV. It's arguable that you do in a 50-inch set. The key, then, is moving your seating. If you're sitting more than 5x the picture height away from your TV, then you probably don't need 1080p. If you can move closer, you should get the highest resolution display you can, sit close enough that you can't see the pixels, and enjoy your huge screen.

The Math
(Screen Diagonal x 0.87) / Horizontal Resolution = Pixel Width
(Screen Diagonal x 0.49) / Vertical Resolution = Pixel Height
At a distance of 10 feet, the eye can resolve 1/120 of a degree of arc, which translates to a width of 0.033 inches.

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COMMENTS
Aron's picture

That's neat to know that the ideal viewing angle -- if you aren't resolution-limited--is 30 degrees. Even with my old non-HD 48", I liked to sit within about 3 screen heights. So perhaps that's why (or maybe it's the kid in me). With regard to the limit at which you can tell the diff. between 1080 and 720, I will point out two things: (1) 20/20 is not "perfect" vision; I think it's merely the limit beyond which correction is not indicated. Many individuals (including myself) have vision that is 20/15 or 20/13. (2) I understand the arguments about the resolution limit of the human eye; but just because you're just at the point where you can't resolve two individual spots, does that mean that an entire field of spots (at that separation) will look no different from a uniform (non-spotted) field of equivalent density? I.e., is the two-spot resolution figure the right statistic for evaluating the perceptibility of resolution changes in pictures? I'd need to see some controlled studies before accepting that.

Geoffrey Morrison's picture

We did a follow up to test the math, with some interesting results. The link is in the article. Shortly after the original article was published, Panasonic released a study of their own with nearly identical results to the math here.

Aron's picture

Just read the link. Looks like you're on the right track: you're trying to eliminate as many variables as possible, to isolate the comparison to resolution alone. Here's an alternate approach you might consider: You'll need an HD-DVD player, a 1080p display, and (two of) the best scaler you can find. Then compare Case I and Case II: Case I: output 1080i from the HD-DVD to one of the scalers, then output 1080p from this scaler to the display. Case II: Output 1080i from the HD-DVD to the first scaler; then output 540p from this first scaler to the second scaler; finally output 1080p from the second scaler to the display. Thus in Cases I and II you are feeding the display with 1080 and 540 lines of resolution, respectively. Yes, in Case II the signal is rescaled twice; but by doing "integral" scaling with good scalers, you may be introducing less variation than w/ your approach of using two different display models (w/ the attendant unavoidable differences in circuitry, calibration, and pixel struture).

John 's picture

Well there you have it. An intellegent discussion that shows the limits of our eyesight has been reached. Thanks

Justin's picture

I just read the review on the new Sony SXRD A2000 and it wasn't exactly a rave. I don't understand how the Grand Wega RPTV recieved a better overall rating a year and a half ago than this tv even though it has a 720p resolution compared to this tv which has a 1080p. I have looked at both tvs and for an aditional 300-500 dollars the new one blows the grand wega out of the water. In comparison to last years xbr it is a step down but the review has scared me off slightly. I thought this tv would be the one to replace my old Non-HD tv but your objection to lack of detail has left me a bit puzzled. Please help ease my mind.

Al's picture

Very nice explanation. A couple of questions:- Suppose I buy a 720p set now and in 2 years when blue ray DVD players are cheap, I get one of those. Can I feed the 1080p signal from the player to the 720p TV and see a nice clean picture? Will I need a scalar of sorts? Or will the DVD player output a 720p signal?- Which 720p TVs now are capable of processing a 1080p signal correctly for viewing - if any?Thanks very much

Aron's picture

To John: Well, perhaps the limit of our eyesight with respect to spatial resolution - unless, like me, you like to sit quite close to the screen. But don't forget about gray-scale and color resolution. In these areas, I don't believe displays can meet the abilities of the human eye. Also, at 24 fps, we haven't reached the limit of our eyes' temporal resolution. Not to mention the noise that is often present from displays and sources. And I think you understand this all intuitively. After all, if TV displays and sources were perfect, with one eye closed (thus removing our binocular vision), we wouldn't be able to distinguish between what's on a display and what we see looking through a window. Yet of course even the best displayed video doesn't yet come close to real life. So there's still a long way to go before we get to the point where improvements in performance can no longer effect a noticeable difference in picture quality.

Michael's picture

Refreshing to read someone who understands visual acuity. From experience, color, contrast, and resolution, in that order, will determine perception of quality. Note that resolution is last. That should offer further explaination to those folks who are confused about how a 720 display can look better than a 1080 display.

david's picture

It's worth remembering that resolution is different in the vertical and horizontal directions. In principle, assuming a monochrome CRT, the horizontal direction is continuously varying in brightness whereas the vertical direction is sampled by the line structure. This means that the max spacial frequency vertically is limited at best to half that of the line structure. Therefore, the resolution horizontally is better than vertically. I realise the pixel structure of modern display devices upsets horizontal as well as vertical definition, because it imposes sampling on both, but it is worth remembering the basic limitations of a line-scanned system.

Richard's picture

Note; the static image resolution test that found that the Sony A2000 displayed less than the full potential of a 1080p source has been resolved by Sony since some time during the August 2006 build. A free fix from Sony on a memory stick that can be inserted in the rear USB input is available for sets built prior to the fix. Sony claims that it not a real issue in that it is only a limit in displaying the static test image and is not a limit on real program material (which is 1080i/60 in any case. That is what Sony say's. There is a simple recalibration one can perform in the service menue to fix this without the USB memory card from Sony. People on the calibration/user blogs don't report that they see a resolution issue on these early sets before or after the "fix."RichardRichard.

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