<Center> **Screen displays are getting at a point of having higher and higher amount of pixels while size remain constant. This can be seen in our phones, TVs, and computers. But at what point is enough?**
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> [Source 1](https://pixabay.com/en/eye-green-eye-close-up-macro-girl-1132531/) - [Source 2](https://pixabay.com/en/mobile-phone-smartphone-tablet-572865/)
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## The eyes
> Scheme of the eye - [by Rhcastilhos & Jmarchn, CC BY-SA 3.0](https://commons.wikimedia.org/wiki/File:Schematic_diagram_of_the_human_eye_en.svg)
Our natural optical instrument and provider of one of the 5 basic sensations.
You may know that light bounces off objects, travels to receptors in the eye, and *somehow* they make the image to be processed in the brain. But have you wondered how does it work?
We are interested in the maximal resolution of the eye, so we are going to focus on the **visual acuity** rather than in contrast or luminosity differences.
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## Our Retina
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> Cones Mosaic & fovea in the retina. Each dot is a receptor - [by Mark Fairchild](http://rit-mcsl.org/fairchild/WhyIsColor/images/ConeMosaics.jpg), [CC BY-SA 3.0](https://commons.wikimedia.org/wiki/File:ConeMosaics.jpg)
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We have in our retinas some light sensitive cells which are of two kinds:
-) [*Rods*](https://en.wikipedia.org/wiki/Rod_cell) are the cells responsible for *black & white*.
-) [*Cones*](https://en.wikipedia.org/wiki/Cone_cell) are the cells responsible for *color reception*. These cones can be of three types, for the [3 RGB colors](https://en.wikipedia.org/wiki/RGB_color_model).
We see sharpener in a zone of higher density of cells called *fovea*.
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> All layers of Retina - [by Henry Gray](https://en.wikipedia.org/wiki/Henry_Gray), [Public Domain](https://commons.wikimedia.org/wiki/File:Gray881.png)
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These cells are connected by other neural cells in series up to 10 layers!
Funnily enough, these layers are inverted. Meaning they are facing the outside of the eye and not to the inside.
But also, there is one *blind spot*. You don't notice it's there because our brain fills the gaps.
The reason of its existance?
Well, the vessels that nourish and the nerves that carry the information have to enter and leave somewhere!
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## Visual Acuity & the Math behind it
> [Source](https://pixabay.com/en/glasses-reading-glasses-spectacles-1246611/)
Now that we know how the eye is organised and its basic parts, we can start to understand how it works.
Remember the *Cones Mosaic* before? That is the representation in a daily basis, when the eye is stimulated constantly by seeing the objects surrouding it.
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> [Source](https://pixabay.com/en/hex-hexagonal-abstract-modern-675576/)
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But to simplify it, look at the right. Imagine that the 3 yellow hexagons are the only rods sending nerve impulses (and others are **off**).
This means that there is an object (or more) in the distance detected by the eye, but we cannot specify what it is as it looks too small.
However as it approaches the viewer, more rods fire and more detail can be acquired.
We are interested in the amount of rods (resolution) that can be resolved by the eye, which means, the minimum distance that two objects need to have to be picked up by the eye to be separate.
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> Visual angle scheme - [by Ojosepa, CC BY 3.0](https://commons.wikimedia.org/wiki/File:EyeOpticsV400y.jpg)
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For the eye, **2 objects are seen as separate** if the rods firing for them have at least **1 rod not firing** in between. Something like this: ⚫️⚪️⚫️
where blacks are rods firing & the white is a rod not firing.
The angle that both firing rods create is called the *minimum angle of resolution* or *MAR*. In the image, it would be the angle created by *a* & *b* or also angle *V*.
This angle is of about 25 [arcseconds](https://en.wikipedia.org/wiki/Minute_and_second_of_arc) in average and can be used in the equation above. Introducing our variables, looks like this:
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V = 0.00694444444 degrees (25 arcsec)
D = distance from our screen (in meters)
S = distance between pixels in the screen (m) or also called [Dot Pitch](https://www.techopedia.com/definition/2697/dot-pitch)
## Screen and Distances
> [Source](https://pixabay.com/en/chairs-conference-room-furniture-2181951/)
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We have seen the Retina, how it works, and the calculations behind it. So now it comes the time for the calculation & analysis!
For that, we will use the rearranged equation on the right.
For screen displays we need to compare our results with the [Dot Pitch](https://www.techopedia.com/definition/2697/dot-pitch) which is the distance between two pixels in a certain display. Parameters used for its calculation are the vertical & horizontal resolution, and the size of the display.
There are tools online that can help you calculate the Dot Pitch. I used for instance [this one](https://www.omnicalculator.com/other/pixels-per-inch) from omnicalculator.com
### Smartphone screen
> [Source](https://pixabay.com/en/smartphone-white-silver-gray-1957740/)
The average distance from your eyes to the phone is about [36 centimeters](https://www.news-medical.net/news/20110713/Study-evaluates-viewing-distance-and-font-size-in-smart-phone-users.aspx). Which if we put in our equations gives us that the Dot Pitch is **S = 0.0436 milimiters**. Which means that it is the limit of Dot Pitch for our vision.
Now, time to compare for different sizes!
+ For a 5" screen at 1440p (2560x1440) resolution will be roughly the limit.
More pixels wouldn't be beneficial as your sight wouldn't be able to notice it.
**S = 0.0432 milimeters**
+ On the other hand, if you increase the screen size to tablet-size (8") the resolution limit at same distance would be around 2160p. (3840x2160).
**S = 0.0461 milimeters**
+ Finally, for smaller phones (3.5") the resolution has to decrease. And it does substantially, as it will need to go down to around 900p (1600x900).
**S = 0.0484 milimeters**
### TVs
> [Source](https://pixabay.com/en/lion-image-7-55-inch-2210947/)
This one is a bit easier as there are more people interested in it. There is even a Wikipedia page dedicated to it named [Optimum HDTV viewing distance](https://en.wikipedia.org/wiki/Optimum_HDTV_viewing_distance). However, I still want to run my calculations.
According to [Bernard Lechnner](https://hdguru.com/lechner-distance-the-number-you-need-to-know-before-buying-an-hdtv/21/), a TV engineer, the median distance between a user and the TV is about 2.7432 meters (9 feet).
With this value, we calculate again using the equation depicted above and we get that the Dot Pitch limit is **S = 0.332 milimiters**.
Now, time for comparisons:
+ For a small 30", the resolution limit is around 1080p (1920x1080).
**S = 0.346 milimeters**
+ For a standard 40", the resolution limit would be around 1440p (2560x1440).
**S = 0.346 milimeters**
+ Finally for a big 65", the resolution limit would be around 4k (3840x2160)
**S = 0.375 milimeters**
### Monitors
> [Source](https://pixabay.com/en/laptop-computer-technology-monitor-3190194/)
Unfortunately I couldn't find any online so I measured my normal use distances while working or in University and got 62cm average. One more time we run the calculations at average monitor distance and we get that the Dot Pitch limit is **S = 0.0751**.
One more round of comparisons!
+ For a 11.6" small monitor (like small laptops), the limit resolution would be 1800p! (3200x1800)
**S = 0.0803 milimeters**
+ For a 15.6" monitor (a laptop's monitor), the limit resolution would be around 2160p or 4K! (3840x2160).
**S = 0.09 milimeters**
+ Finally for a big monitor (24") the limit resolution would be around 8K! (7680x4320)
**S = 0.0692 milimeters**
## Conclusion
> [Source](https://pixabay.com/en/balloon-comic-popart-communication-3203197/)
We went together on how the science of the eye & the Math necessary to give the numbers to fool your vision. Bear in mind that it was all done with the assumption of having an average distance, in a healthy person. And depending on case to case it may vary.
I really thought that higher resolutions in phones was an absolute non-sense until I did the calculations myself. It really checks out. That is why every time there is a new phone in display at a store, the screen it looks so detailed. They are getting better at fooling our vision.
For TVs I actually expected the sizes matching their resolutions, so not much to say. Maybe we will be stuck at 4K displays forever, as we would not be able to see the improvement unless we buy an exagerated 100" TV.
Finally, laptop displays really got me impressed. I didn't think that for my own laptop (15.6", 1080p) the resolution needed to fool my eyes was much higher. And for high-end laptops it is just a ridiculously high resolution at 8K.
You can always do your calculations using the tangent formula. And you can also check with tools like the [PPI Calculator](https://www.omnicalculator.com/other/pixels-per-inch) from omnicalculator.com or with [Retina Calculator](https://designcompaniesranked.com/resources/is-this-retina/) by designcompaniesranked.com.
## Image Sourcing
The images have their Sources in their respective footnotes.
Most are CC0. Others give the credit to their authors, acknowledging their copyright status & giving a link to the source found.
The only images not sourced are from the representation of the calculations, which I myself made on my image editing software and then uploaded.
## References
- [Visual Acuity](https://www.ncbi.nlm.nih.gov/books/NBK11509/) - *Webvision: The Organization of the Retina and Visual System* by Kolb H, Fernandez E, Nelson R, & editors; Salt Lake City (UT): University of Utah Health Sciences Center; 1995-
- [Visual Acuity (2)](http://webvision.med.utah.edu/book/part-viii-gabac-receptors/visual-acuity/) - by Michael Kalloniatis and Charles Luu for *Webvision*
- [Visual angle is the critical variable mediating gain-related effects in manual control](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2366211/) - by David. E. Vaillancourt at Departments of Movement Sciences, Bioengineering, and Neurology, University of Illinois at Chicago.
Pamela. S. Haibach and Karl. M. Newell for the Department of Kinesiology, The Pennsylvania State University, University Park, PA, USA
- *Guyton and Hall textbook of medical physiology*, 10th Edition; Hall, J. E., & Guyton, A. C.
- [Study evaluates viewing distance and font size in smart phone users](https://www.news-medical.net/news/20110713/Study-evaluates-viewing-distance-and-font-size-in-smart-phone-users.aspx) - by Optometry and Vision Science for news-medical.net
- [Lechner Distance: The number you need to know before buying an HDTV](https://hdguru.com/lechner-distance-the-number-you-need-to-know-before-buying-an-hdtv/21/) - by Greg Tarr for hdguru.com
+Bernard Lechner for its statistical anaylisis of median and average distance of TVs in the U.S.
- [PPI Calculator](https://www.omnicalculator.com/other/pixels-per-inch) - by omnicalculator.com
- [DPI & Retina Calculator](https://designcompaniesranked.com/resources/is-this-retina/) - by designcompaniesranked.com
## Closing
Recently I got a [defective pixel](https://en.wikipedia.org/wiki/Defective_pixel) on my screen and by chance I figured out at what distance disappears from my vision. This thing only made me search deeper into the topic to find different optimal ranges for sizes of and their optimal resolutions.
By the way, my screen is a 1080p 40" & the pixel disappeared from my vision at around 2 m.
I hope you have found it interesting and helpful for the optimal use of your screen. Although maybe is most useful for gamers!
This post is dedicated to my father as he is a really enthusiastic person with screen displays.
As always
This is @deholt signing off!
hiveblocks