Choosing a TV for yourself, your beloved, from the standpoint of science, not advertising

Hello.

The writing of this short article prompted me to argue about the choice of TV.

Now in this area - as well as in the "megapixels for cameras" - marketing bacchanalia reigns in pursuit of permissions: HD Ready has long been replaced by Full HD, and 4K and even 8K are already becoming more and more popular.

Let's see - what do we really need?

And the school geometry course and some basic knowledge from Wikipedia will help us in this.

So, according to this same Wikipedia , the naked eye of an average person is a unique device that can simultaneously view space at an angle of 130 ° -160 °, as well as distinguish elements at an angle of 1–2 ′ (about 0.02 ° –0.03 °) . Whereinfast focusing occurs at a distance of 10 cm (young people) - 50 cm (most people 50 years and older) to infinity .

It looks cool. In fact, not so simple.

Below is the field of view of the human right eye (perimeter card, numbers on the scale are angular degrees).



The orange spot is the site of projection of the blind spot of the fundus. The field of view of the eye does not have the shape of a regular circle, due to the restriction of gaze by the nose from the medial side and eyelids above and below.

If you overlay a picture of the right and left eye, then we get something like this:



Unfortunately, the human eye does not provide the same quality of vision over the entire plane in a wide angle. Yes, with two eyes we can recognize objects in a 180 ° range in front of us, but we can recognize them with three-dimensional ones only within 110 ° (to the green zone), and full-color ones in an even smaller range of about 60 ° -70 ° (to the blue zone). Yes, in some birds the field of view reaches almost 360 °, but we have what we have.

Thus we see that a person receives the most high-quality image at an angle of about 60 ° -70 ° . If you need more coverage - we are forced to "run" with our eyes through the image.

Now about the TVs. By default, consider televisions with the most popular width to height ratio of 16: 9, as well as a flat screen.



That is, it turns out that W: L = 16: 9, and D is the diagonal of the screen.

Hence, recalling the Pythagorean Theorem:



So, assuming that the resolution is:

• HD Ready has 1280x720 pixels
• Full HD is 1920x1080 pixels
• Ultra HD 4K has 3840x2160 pixels,

we get that the side of the pixel is:

• HD Ready: D / 1468.60
• Full HD: D / 2202.91
• Ultra HD 4K: D / 4,405.81

Now let's calculate the optimal distance to the screen so that the eye covers the entire image.



From the figure it is clear that



Because of the height and width of the image we have a large parameter is the width - and the eye need to cover the entire screen width entirely - calculate the optimal distance from the screen, taking into account that, as shown above, the angle of view is 70 degrees:



That is: so that the eye covers the entire screen in width, we should be at a distance no closer than about half the diagonal of the screen . At the same time, this distance should be at least 50 cm to provide comfortable focusing for people of any age. Remember this.

Now let's calculate the distance at which a person will distinguish pixels on the screen. This is the same triangle with the tangent of the angle, only R in this case is the pixel size:



That is: with a distance greater than 2873.6 pixels, the eye will not see the grain. So, taking into account the calculation of the side of the pixel above, you must be at the following minimum distance from the screen so that the picture is normal:

• HD Ready: D / 1468.60 x 2873.6 = 1.96D, i.e. two screen diagonals
• Full HD: D / 2202.91 x 2873.6 = 1.3D, i.e. about a bit less than one and a half screen diagonals
• Ultra HD 4K: D / 4405.81 x 2873.6 = 0.65D, i.e. a little more than half the screen diagonal

And now what everything was led to -

conclusions

1. You should not sit closer than 50 cm to the screen - the eye will not be able to focus normally on the image.
2. You should not sit closer than 0.63 screen diagonals - the eye will get tired, because it will have to run around the picture.
3. If you plan to watch TV at a distance greater than two screen diagonals - do not buy something cooler than HD Ready - you will not notice the difference.
4. If you plan to watch TV at a distance greater than one and a half diagonals of the screen - do not buy something cooler than Full HD - you will not notice the difference.
5. Using 4K is advisable only if you look at the screen at a distance of less than one and a half diagonals, but more than half of the diagonal. Perhaps this is some kind of computer gaming monitors or giant panels, well, or a chair that is closely standing at the TV.
6. Using a higher resolution does not make sense - you either will not see the difference with 4K, or you will be too close to the screen and the angle of view will not cover the entire plane (see paragraph 2 above). The problem can be partially solved by a curved screen - but the calculation (more complicated) shows that this gain is extremely doubtful.

And now I recommend measuring your room, the location of your favorite sofa, the diagonal of the TV and thinking: is there any point in paying more?

PS I deliberately did not discuss or mention characteristics that are difficult for me to calculate and compare.
And there are a lot of them: processing frequency, contrast, the time of changing the state of the pixel, and more - here I can get confused even in terminology. They are very important when choosing, but this is a separate issue.
Here I discuss exclusively resolution and show by simple calculation that it is especially large and it is not necessary ...
It is very possible that with other characteristics there are the same marketing traps associated with a lack of knowledge, a “word game” when new terms and technologies are invented turning out to be nonsense, etc.

PPSMany thanks to the respected nidalee for his comment : it turns out that Netflix in its VMAF image quality calculations received similar data:

The original model released when we open-sourced VMAF was based on the assumption that the viewers sit in front of a 1080p display in a living room-like environment with the viewing distance of 3x the screen height (3H). This is a setup that is generally useful for many scenarios.

Most recently, we added a new 4K VMAF model which predicts the subjective quality of video displayed on a 4K TV and viewed from a distance of 1.5H. A viewing distance of 1.5H is the maximum distance for the average viewer to appreciate the sharpness of 4K content. The 4K model is similar to the default model in the sense that both models capture quality at the critical angular frequency of 1/60 degree / pixel. However, the 4K model assumes a wider viewing angle, which affects the foveal vs peripheral vision that the subject uses.

L = 0.49D => from here, 3L = 1.47D (for Full HD); 1.5L = 0.74D (for 4K) . Which, in principle, coincides with my conclusions.