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# 1920x1080 vs 1280x720 - your eye can't tell the difference

I am not sure if this is the appropriate forum for such a discussion.

That said, I have completed an analysis that relates the resolution of the human eye to HDTV. I am sure the results will startle you.

Basically, for most people, and even for some who use front projection, the difference between 1080i and 720p is essentially non-existant because the eye is not capable of telling the difference between the two. Read the attached PDF if it has you curious. All the equations are spelled out, so you can substitute in numbers for your own situation and see what the difference between the two resolutions is.

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It really depends on the size of the screen versus the viewing distance.

"Our 42 inch TV, viewed from 10 feet away, needs a resolution of appoximately 25348x14258, which equates to
361,418,121 or just over 360 million pixels, in order to be as fine as what our eye can resolve."

Not everybody watches video with a 42inch set 10 feet away.
I did.
Calculate it with a 100inch screen at 1.5x viewing distance.

Don't you enjoy IMAX size viewing perhaps?
Did you see the section that talked about the actual resolution of the human eye vs the theoretical max? That is what you should be plugging your numbers into - not the section that address the physical, optical limit of an optically perfect system. The resolution of the eye is far below that induced by the physical limitations of light.

The distance you sit from the screen relative to its size is mostly irrevelant because the angular resolution of the eye is a trigonometric and not a linear function.
I would tend to agree. The big question though, for the not-too-distant future is: what are the real differences to the naked eye between 1080p and 720p/1080i, if any? Am sure there will be many shootouts on this!
In the scenario you described, you would have a screen approximately 2.54m diagonally and you viewing distance would be about 3.81 m.

Plugging in the numbers, 1080i would require roughly a 121 inch screen before one would see pixelation.

720p would required roughly an 80 inch screen before one could start to see pixelation.

In the scenario with a 100" screen viewed at 1.5x distance, you could tell the difference between 1080i and 720p. Still, for most people, a 100" screen is far from typical. Even then, I would argue, that the difference between the two would be virtually imperceptible.
Quote:
 Originally Posted by kingstud In the scenario with a 100" screen viewed at 1.5x distance, you could tell the difference between 1080i and 720p.
Good! :)
hmm. I am assuming that the "inch screen" measurements used here are diagonals, even though most here on the forums speak in terms of width in 16x9 mode.

If this is the case, then ks is right, 100" is far from typical - it's SMALL - this is the home theatre forum - If I had the short throw pj I want I would be throwing a 120" WIDE screen with a ten foot viewing distance, and will likely be doing that with my next pj. For that matter, 10 feet wide is a good measure for HT when making arguments like this - most folks have a clear stretch of wall that size on the long end of a room, and, like the rest of us wants to fill it.

So, how does this all work on a 130"+ diagonal screen. My guess, it's going to require 1080 before the eye starts to not be able to tell.

As far as this "not being the appropriate forum" you may have that right, you may have some very good points to make for the RP folks. Of course, their viewing distance tends to be even less, so maybe not.
I am running a 133" screen at 10 foot seating distance. The problem isn't pixelization, but rather screen door, the space between the pixels. That is the main benefit to 1080. Smaller pixels ~= smaller screen door effect. I would take 720p without screendoor over 1080 with it, even though it would be small.
Warren.
Kingstud - nice analysis. It could come in handy for those debating about getting a 480p projector vs a 720p one. :)

I do think the title of your thread is a little misleading however. It implies that your eye can't differentiate between the two resolutions under any circumstance. Clearly this is not the case.
Newbie question here, but isn't the general perception of 720p vs 1080i is that 720p is better for moving images whereas 1080i is better for still pictures? If that's the case, then the whole viewing distance thing is a little exaggerated because it's like comparing apples and oranges. Dunno, still a little sleepy so my senses are a bit whacked atm
I believe that there are several numerical errors in the analysis, eg:

- Used 1 mm instead of 6 mm for pupil diameter. This under-estimates the resolving power by a factor of 6.

- The angular resolution formula gives result in radians, but the tan was taken using the argument in units of degrees (thereby over-estimating the resolving power by a factor of about 57).

By my calculations, the actual resolving power of a perfect 6 mm aperture = 180 * 1.22 * 565E-9 / 6E-3 / PI = 0.00658 degrees. This would lead to a lateral resolution at 10 feet of 0.35 mm. So, I believe kingstud's 0.03669 mm overestimates the resolving power of the eye by a factor of about 10.

It is to be expected that the resolving power of the eye does not increase proportionately with pupil diameter due to increased aberrations. However the 0.00658 degree figure is within a factor of 2.5 of the "generally accepted" figure for resolving power of the eye of 1 minute of arc (0.0167 degrees)

FWIW I tested my own visual acuity by printing out some images with and without simulated screen door and found that, for me
- pixellation disappeared at an average subtended angle of 0.029 degrees
- screen door was fully resolved at 0.035 degrees
- and screen door disappears at 0.021 degrees. More details here.

Note that these numbers make a significant difference for the number of screen widths back I have to be to get pixellation to disappear, to fully resolve screen door, & get screen door to disappear, eg:
For 800*450 I get 2.4, 2.0, & 3.1 screen widths respectively.
For 1024*576 I get 1.8, 1.5, & 2.6
For 1280*720 I get 1.5, 1.3, & 2.1
For 1920*1080 I get 1.2, 0.9, & 1.6

In other words, for typical viewing distances there is a big difference between 720p & 1080p. For me it is the difference between sitting at 2.1X (720p) or 1.6X (1080p)

Apart from that, I think kingstud presents an interesting analysis (although a real stud would have posted in the over \$3500 forum) :)

Brent
"The distance you sit from the screen relative to its size is mostly irrevelant"

Other than resolution, it's the only thing that *is* relevant, since it's what determines the subtended angle to be resolved.
Hi, Gang!

Furthermore, visual acuity clearly varies. Under some (fortunately rare) circumstances, I can see screendoor on a 1365x1024 D-ILA on an 11' screen from a 12' viewing distance (with optical anamorphic compression of the vertical axis to a 16:9 resultant image). Considering that the D-ILA fill factor is 92%, I'm therefore seeing an area that's something like 1/10th the pixel size that you're claiming is possible to see (for what it's worth, primary factors in this sensitivity are the relative brightness levels of neighboring pixels). For me, the difference between 1365x1024 and 1920x1080 is not only noticeable, it's worth a very expensive upgrade - purely from the perspective of resolution.

To emphasize my point, I'm in no way a bigot of high prices. I'm perfectly happy using \$5 zip cord for speaker wire, and in fact, am quite delighted to be able to use \$5 STP CAT5E video cables for my 1080P video connection [via a Gefen DVI/CAT-5 extender, if you're curious]. Ergo, I'm not at all a believer in the "bigger and more expensive is necessarily better" philosophy. However, at an absolute minimum, assumptions regarding visual acuity are generalities that may or may not apply to you individually.

High resolution does make a difference to some of us!

Cheers!
MarkF
the resolving angle is

tan(A) = width of pixel/distance from screen

width of pixel = width of screen / horizontal resolution

let W = width of screen
let D = distance from screen
let R = resolution

Let A be .02 degrees or .00035 radians, Kingstuds resolving power of the eye,

recognizing that for small angles in radians tan(A) = A

A * R = W / D

or more commonly D/W = 1/(A*R)
D/W = 1/(.00035 * R)

That is the viewing distance in screen widths is equal to 1 over the .00035 * resolution

so

for 855 the viewing distance is 3.35 times the screen width
1280 is 2.24x screen width
1920 is 1.5x screen with

oh and mark, 1365 is 2x so just tell yourself you can't see the SDE and it will go away, :p

This seems pretty close to Brents findings, although i would say i can sit closer to my 855x480 projector than 3.35 the screen with, but this is good enough for now

however, if kingstud had posted this in the CRT forum, he might have had a point but here in projector world, where 8 feet wide screens are the norm, you can see the need for 1920 right now

David
Quote:
 Originally Posted by kingstud The distance you sit from the screen relative to its size is mostly irrevelant because the angular resolution of the eye is a trigonometric and not a linear function.
Viewing ratio is what matters. The distance is irrelevant without the size and the size is irrelevant without the distance. All you need is the ratio (other than the resolution), like someone else said. A 42" screen from 8.4' is the same as a 420" screen from 84' as far as this goes. And the reason that the ratio is all that matters is that it is trigonometric (so the viewing ratio determines the total viewing angle).

I just did some calculations the other day. THX recommends an minimum of 36 degree viewing angle to the worst case seat in theaters and requires 26 degrees to get THX certification. If you go into a theater that was built to the 26 degree requirement instead of the recommendation, the movie is 2.35:1 (16:9 movies use less the full screen width in many commercial theaters), the front row is 10% of the total distance from the front and you pick a middle seat, then you are at about 1.2x the screen width. That is for the average seat. Some sit closer and some sit further away, but 1.2x for movies in commercial cinemas is very common. 3x the screen width is not even a choice in these theaters. If I made a mistake here hopefully somebody will correct it as I am going by memory from what I calculated and posted last week.

--Darin
Hi, PurdyD!

If I'm correctly following you, it appears that your formula determines the apparent size/angular displacement of pixels, not the size of the inter-pixel gaps. If we assume that the pixel gap spacing is uniformly distributed (horizontally and vertically, ignoring my anamorphic lens adapter), then the gaps between each of those 1365 pixels is 0.04 times the size of a pixel, and yet that's what I'm able to see under some image conditions. In that context, your formula would seem to indicate that the necessary viewing distance is just 0.08 screen widths, yet this is actually visible at times at about 1 screen distance.

Having said all that, I'm not in any way claiming to be able to see screendoor under all image conditions - only under some specific circumstances. However, the fact that this can occur at all at an order of magnitude smaller feature size than standard "perceptual limits" would tell us definitely leaves me somewhat skeptical of those standards as a universal rule! ;)

Cheers!
MarkF
Howdy!

Just for fun, I'll offer a bit of totally baseless conjecture as to how what I'm seeing might be possible at all, given the physiology of the eye. As I understand it, conventional perception limits are based on the packing density of the perceptors in the retina - the rods and cones. What this theory does not take into effect, as folks have mentioned, is eye movement. I believe that refinement of the perceptual limits of angular displacement can occur due to fine motion control of the eye. Clearly, rapid eye motion decreases perceivable resolution. However, my belief, which I suggest here without proof, is that slow eye motion, in the presence of high contrast images, can increase perceivable resolution. Part of this may be experience and training, part may simply be due to person-to-person variation.

Whatever the cause, the moral of the story for me is to believe my eyes first, and then to attempt to reconcile theory with what I can perceive. With no criticism implied, I can't help but be reminded of a hilarious post here on the forum when the president of Fox claimed a while back that the reason that they weren't broadcasting HD was that no one could see the difference between SD and HD at normal televison viewing distances, anyway. I can't remember who posted the delightful response, but it was a picture of someone with half-inch thick glasses peering blurrily out at us - ostensibly that president! :)

Have Fun!
MarkF
Quote:
 Originally Posted by kingstud Still, for most people, a 100" screen is far from typical.
I know, I know... I need to upgrade my 100" screen.. you don't have to make fun of me!... :)

(In all seriousness, it is the smallest I'd want it, viewing from 13')
"THX recommends an minimum of 36 degree viewing angle to the worst case seat in theaters and requires 26 degrees to get THX certification."

Converting that to ratios, 36 degree is about 1.5x screen width; 26 degree is 2.2x.
Quote:
 Originally Posted by Mark J. Foster Having said all that, I'm not in any way claiming to be able to see screendoor under all image conditions - only under some specific circumstances. However, the fact that this can occur at all at an order of magnitude smaller feature size than standard "perceptual limits" would tell us definitely leaves me somewhat skeptical of those standards as a universal rule! ;)
I remember reading in a book on optics that the human eye can see dark linear features such as power lines against a bright background, which fall below the resolving power of the human eye. If the eye had perfect optics, the image of the power line would be too fine to be detected by the cells in the retina. The abberations of the lens smear out and effectively enlarge the image, making it detectible to the eye. If two power lines were separated by their width at the example distance, they would not be resolvable and appear as one. The opposite example would be bright objects on a dark background, such as stars, which are not resolvable by the largest existing telescopes.
If you don't want to bother with formulas, try my calculator. It calculates everything for you automatically.
Quote:
 Originally Posted by Mark J. Foster Hi, PurdyD! Having said all that, I'm not in any way claiming to be able to see screendoor under all image conditions - only under some specific circumstances. However, the fact that this can occur at all at an order of magnitude smaller feature size than standard "perceptual limits" would tell us definitely leaves me somewhat skeptical of those standards as a universal rule! ;) Cheers! MarkF
Mark, I know nothing about eyes. If you can see it, I believe you. It might have something to do with light and dark and rods and cones. Although i have no idea what i am saying.

I also bet there is a variation in people eye sight, oh wait there is!

So i would be leary of universal rules.

Anyway, the initial post said, your eye can't tell the difference, because you need a big screen. But wait, projector forum, almost all of us have big screens! So we can!

As far as SDE, i am in denial about the whole thing, it doesn't exist. To say otherwise leads to a certain madness called upgrade fever and the affect is terminal.

Regards,

David
Quote:
 Originally Posted by rickster904 "THX recommends an minimum of 36 degree viewing angle to the worst case seat in theaters and requires 26 degrees to get THX certification." Converting that to ratios, 36 degree is about 1.5x screen width; 26 degree is 2.2x.
ok 36/1920 = .02 degrees
36/1280 =.03 degrees

sounds like another reason to get 1920x1080 projector

David
Good insights - thank you for the correction regarding my errant use of radians and degrees!

I am finding the dialogue very interesting.

As for the title of the post, that was to get you interested so you would at least click on it.

As many have pointed out, this IS the projector forum, so the analysis doesn't apply to many people here. Still, it can be used to convince people that they won't be realizing the full potential of HD if they buy a RPTV.

I am very curious about the discussion involving being able to see screen door and how motion increases/decreases the resolution of the eye. I fail to see how one could not resolve the difference between two adjacent pixels under the worst possible circumstances (static image, maximum brightness/contrast differences) but could somehow resolve the "screen door" in between.

By the way, if you want to figure out the "width" of the screen door on your projector, I suggest you find its fill ratio and do some calculations to figure out how wide one of the lines is.
Hi, KingStud!

I'd be confused if I couldn't see adjacent pixel differences but could see the screendoor, too! At that point, it'd be time to consult a shrink, not an optometrist! ;) No, that's not the situation. With a very bright image, and under some ambient light conditions, there are definitely times when my eyes can resolve sufficient detail to see not just individual pixels quite clearly (including the obvious rectangularity of their structure, as opposed to shapeless point sources), but also the gaps between those 92% fill-factor D-ILA pixels - all this at a distance of about 1.2 screen widths. My belief is that this can occur due to slow eye motion enabling the mind to in-effect "interpolate" between the images from multiple viewpoints to yield a higher resolution observation than might be considered optimal given static viewing.

Again, please note that the explanation that I'm conjecturing is nothing more than that - a guess. However, there are roughly analagous situations that might help to illuminate the situation. Let's pick an example in the audio world. As anyone here might casually tell you, you need a decent 24-bit A/D converter to get "clean" audio sampling. Not so! A lower number of bits can be used to deliver identical audio quality, as long as the sampling rate is increased. This process can in fact continue until you reach the point of reductio ad absurdum where a 1-bit ADC can yield audio that's indistinguishable from a 24-bit converter. If you will, what's occurring in this case is that the number of bits in the "sensor" can be reduced, yet still deliver identical dynamic range, by interpolating multiple "cruder" observations over time. I believe that a similar process may be occurring here!

Cheers!
MarkF
Hi, Gang!

I will point out one interesting / damning fact. The reality is that when I bought my first D-ILA ~6-7 years ago, I couldn't see screen door at all from normal viewing distances. As time has gone on, I've gotten "better" and "better" at seeing the screen door, as well as (ahem) other visual artifacts (don't ask!). If only I'd listened to PurdyD a lot earlier, perhaps I wouldn't be in the wallet-emptying process of upgrading to the HD2K now... ;)

There's little doubt that extended exposure can definitely "train" you to observe more than the average person. Astronomy buffs will certainly support this, and I'm afraid that us long-term AVSaholics can, too. Ah, the perennial upgrade bug... :o

Cheers!
MarkF
Being able to detect something is different from being able to resolve it. This is why, as rkihara pointed out, we can, for example, know a star is up in the sky (detection) but not know if it is a single star or a "binary" (paired) star (resolution).

With regard to visibility (detectability) of SDE, I think the fact that there is a regular grid pattern, not just a single black line, plays a role. So where I might not detect SDE in a small bright patch I might in a larger bright patch. The spacing of the SDE grid lines, not just the width of them seems to be important. In fact I tried a 'masked mirror" simulation experiment where I halved the spacing of the grid lines while keeping their widths constant, eg:

http://mysite.verizon.net/kiwishred/..._81percent.gif

For me, the distance for screen door visibility was reduced to about 1.3X with masked mirror compared with about 2.1X for standard (720p). More details here

In any event, from my numbers above, detectability of SDE (for me at about 0.021 degrees) is very consistent with the 1 arc-second "standard" visual acuity (0.017 degrees, or 0.020 degrees if we adopt the 1/50 degree number that Mark used in his paper). For me, I can see SDE at a closer distance than I can see pixellation (ie: the case where fill factor is 100%).

Obviously, other factors, such as overall image brightess and contrast of the grid affect SDE detectability. Contrast can be reduced by defocusing the lens or going to LCOS/D-ILA (where the "bleeding" between cells means that the lines are grey rather than black). I agree with MarkF that, on the threshold of visibility, detectability of SDE is a very transient sort of thing.

Brent
Quote:
 Originally Posted by kiwishred In fact I tried a 'masked mirror" simulation experiment where I halved the spacing of the grid lines while keeping their widths constant, eg:
This is equivalent to doubling the pixel count (both horizontally and vertically) and doubling the fill factor's difference from 100%. For example, a 960x540 panel with 90% fill factor becomes a 1920x1080 panel with 80% fill factor.

Correct?
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