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4K Resolution - The New Frontier in Home Theater & Media Rooms - Page 2

post #31 of 40
Randomoneh is right. Viewing distance isn't chosen like that. You don't move half as close to the screen when watching a DVD (instead of a BD). Rather than asking yourself "at what viewing distance does the size and resolution of my TV approach 'perfection'?", you ask yourself "at what viewing distance does the size of my TV offer the highest immersion, in spite of other limitations?". You watch from the distance that 'feels' best to you, or provides optimal 'immersion', as Randomoneh put it.

Quote:
Originally Posted by Randomoneh View Post

Warning: Spoiler! (Click to show)
No, everything is fine. Somehow I missed "vertical" resolution.
Now, there is an error with how Mr. Clark at ClarkVision calculates needed resolution and "resolution of the eye". He simply multiplies number of pixels per degree (200 for 0.3 arcmin-per-pixel) with number of degrees that print / display is occupying. Try doing that and you'll see how wrong it is. Displays and printed materials are straight and one degree of FOV might occupy 1 inch in the center of the display and 2 inches at the edge. I've made that same mistake before.
So, his example is this: "Consider a 20 x 13.3-inch print viewed at 20 inches. The Print subtends an angle of 53 x 35.3 degrees, thus requiring 53*60/.3 = 10600 x 35*60/.3 = 7000 pixels, for a total of ~74 megapixels to show detail at the limits of human visual acuity."
At 20 inches, apparent size of every pixel should be 0.3 arcminutes, that is 0.0017453292531 inches. That makes 572.957795 pixels per inch or 11459 x 7620 for whole print. Center of his image (10060 x 7000 doesn't match 200 pixels per degree / 0.3 arcminutes per pixel. His error would even higher if imaginary print occupies higher angle of viewer's field of view.
Here's number of pixels needed for some viewing angles.
Degrees of field of view / needed number of pixels:
1 = 200
5 = 1000.6097
10 = 2005.04157
15 = 3017.1764
20 = 4041.01414
25 = 5080.73843
30 = 6140.78725
35 = 7225.93252
40 = 8341.37157
45 = 9492.8346
50 = 10686.713
55 = 11930.2151
60 = 13231.5576
65 = 14600.2042
70 = 16047.1673
75 = 17585.3928
80 = 19230.2588
85 = 21000.2305
90 = 22917.73
95 = 25010.3136
100 = 27312.2871
105 = 29866.9673
110 = 32729.9105
115 = 35973.6303
120 = 39694.6728
125 = 44024.5498
130 = 49147.2306
135 = 55328.2946
140 = 62965.9458
145 = 72685.7534
150 = 85530.1329
155 = 103375.2
160 = 129972.906
165 = 174077.442
170 = 261950.853
Cotangent of 0.3 arcminutes can be used for easy calculation of needed viewing distance (in inches) or needed ppi value of display / print.
Needed viewing distance = 11459.155895344 / PPI
Needed PPI value = 11459.155895344 / distance in inches
For 7680 x 4320 displays, viewing distance = 1.29923485 x diagonal measurement. Or 2.65258238 x image height.
As for your graphs, I like them. I've made something similar before, based on 0.3 arcminute per pixel value, too.

I like your attention to details.
I think your chart looks very professional, much more advanced than mine! smile.gif

Yes, to calculate the number of dots needed on a piece of paper (I will use the words "pixels" and "screen"), you follow the same procedure as I did for 16:9 screens. Only this time you know the height and width of the screen beforehand, so you won't have to bother with the Pythagorean theorem and aspect ratios.

First, you calculate the desired pixel pitch, of the pixel which is the very closest to your eyes, based on the viewing distance. Then, you go on to calculate the target PPI (pixels per inch) or target resolution from that. The only problem I can see is that, on the diagonal pixel pitch will be wider (due to the Pythagorean theorem). Again, it's an approximation.

I only used Dr. Clark's sources, not his calculations, so I haven't really looked at them. But, I can make my own:

To calculate the desired pixel pitch p when viewed from distance y:
Code:
p = y * tan( 0.3 arcminutes )

Example: The desired pixel pitch when viewed from a distance of 20 inches:
( 20 in ) * tan( 0.3 arcminutes ) = 44.3313631 microns

From this, the desired PPI can be calculated:
Code:
ppi = ( 1 in ) / ( y * tan( 0.3 arcminutes ) )

Which is the same as:
Code:
((( y ) * tan( 0.3 arcminutes ))^(-1))*(1 in)

Example: The desired PPI when viewed from a distance of 20 inches:
((( 20 in ) * tan( 0.3 arcminutes ))^(-1))*(1 in) = 572.958

That is very close to the standard 600 DPI resolution of printers at home.

To calculate the desired resolution r for a specific length (dimension) w of screen, replace "1 in" with w:
Code:
r = w / ( y * tan( 0.3 arcminutes ) )

Example: The 13.3 inches from a distance of 20 inches in Clark's example:
( 13.3 in ) / ( ( 20 in ) * tan( 0.3 arcminutes ) ) = 7620.34

Now, you asked, what if we only know the field of view the paper or screen occupies?

Well, the FoV really only lets you calculate the size of the sceen, so you can replace the screen size with that calculation in the above formula.

If the screen occupies an angle of q when centered, perpendicular to your line of vision, and viewed from distance y, its length is:
Code:
2 * tan( q / 2 ) * y

Example: The length of a screen occupying 35.3 degrees when viewed from 20 inches:
(2 * tan( 35.3 degrees / 2 ) * 20 in) in inches = 12.7271772 inches

Now we can just merge the two formulae into one:
Code:
( 2 * tan( q / 2 ) * y ) / ( y * tan( 0.3 arcminutes ) )

And simplify:
Code:
2 * tan( q / 2 ) / tan( 0.3 arcminutes )

Example: Pixels needed to approach theoretical "perfection" on a screen occupying 35.3 degrees:
2 * tan( (35.3 degrees) / 2 ) / tan( 0.3 arcminutes ) = 7292.14

Hope that helps.
Edited by MisterMuppet - 8/7/12 at 11:08am
post #32 of 40
Really making this harder - Why 4K TVs are stupid (still).
post #33 of 40
This is pretty funny as the vast majority of people can't even tell the diff between HD and SD when viewed on similar widescreen sets. I was at CES a few years ago and Samsung had two sets side by side with identical programming, one in 720P and the other in 1080P and none of the experts walking by could tell the diff., to me it wasn't close but it told me a lot about what people really saw if they didn't know what to look for on the screen.
post #34 of 40
Quote:
Originally Posted by HughScot View Post

This is pretty funny as the vast majority of people can't even tell the diff between HD and SD when viewed on similar widescreen sets. I was at CES a few years ago and Samsung had two sets side by side with identical programming, one in 720P and the other in 1080P and none of the experts walking by could tell the diff., to me it wasn't close but it told me a lot about what people really saw if they didn't know what to look for on the screen.
Well, you'll understand if I tell you I have more belief in scientific study that deals with much wider range of [angular] resolutions than anecdotal evidence.
post #35 of 40
You Folks are missing a point. With 8k, or 4k, or even 1080p, you can see exactly what you want to see. What if you knew someone on the TV screen, and it was in 8k or 4k? You could then zoom in on that face in the crowd. With lower resolutions, you will get poorer results.

The display will then take on new markets, not just movies anymore. Professionals could use the features to show off their projects. Law enforcement could zoom in on a suspect. Outer space will be more visible. Whole new markets could develop that we can't yet imagine. I am looking forward to that day. Have a good day.
post #36 of 40
Quote:
Originally Posted by RobertR View Post


The math in this statement doesn't make sense. 3940/2160 is 1.78, exactly the same as 16/9. 4096/2160 is 1.90, which does NOT "match the 16:9 ratio of modern television screens".

4096x2160 is the resolution for professtional 4K which is used in 4K Digital Cinema. 3840x2160 (Quad HD) will be the consumer version.

It's the same with HD. Digital Cinema uses 2048x1080 while consumer HD is 1920x1080.
post #37 of 40
Quote:
Originally Posted by Lee Stewart View Post

4096x2160 is the resolution for professtional 4K which is used in 4K Digital Cinema. 3840x2160 (Quad HD) will be the consumer version.
It's the same with HD. Digital Cinema uses 2048x1080 while consumer HD is 1920x1080.
Why the difference? Isn't there a benefit from having a resolution that is power of 2 (2^12 in case of 4096 and 2^13 in case of 8192)?
post #38 of 40
Quote:
Originally Posted by Randomoneh View Post

Why the difference? Isn't there a benefit from having a resolution that is power of 2 (2^12 in case of 4096 and 2^13 in case of 8192)?

I believe it has to do with the chips that digital cinema projectors use. Not 100% sure though.
post #39 of 40
I am all for new technology like 4K but if you dont have a huge screen to see the difference then whats the point? I believe to really enjoy the 4K experience you are going to need a really big HDTV or a projection system. Full HD 1080p is more then good enough for me right now.
post #40 of 40
Indeed! I shall see real advantage shall be in 70 plus screens where people have to sit close , needing much pixel density
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