# "What do your elf eyes see" - what are the limits of sharp eyes?

I am thinking about how I could write a particularly sharp-sighted people and I'm wondering about the practicalities of this. How far might they realistically be able to see sharply ( assuming a world like our own ) before other physical factors get in the way? Would very sharp distance sight have any effects on their ability to see close-up or other aspects of perception? I'm interested in how this might affect modern humans and also what might be required for a human-like species to develop super-good vision if they were able to dispense with any physiological restrictions that limit us.

• This may be relevant youtube.com/watch?v=Rk2izv-c_ts Mar 5 '15 at 12:18
• While diffraction will be the limit for a single eye pupil, you could imagine 'holographic eyes' that resolve diffraction patterns instead of just light intensity. The brain 'back-end' would be immensely more complex too, and the limit would be in brightness, amount of light from distant objects reaching the retina.
– SF.
Mar 5 '15 at 13:05
• Could Legolas actually see that far? on physics.SE Mar 5 '15 at 13:43
• How far could Legolas see? on scifi.SE Mar 5 '15 at 13:44
• Many birds have extraordinary eye sight, so if you are concerned about the 'realism', such sharp sightedness is biologically possible. You might investigate the resolution of eagles' eyes to get an idea of what is possible. Mar 5 '15 at 16:48

Assuming perfect optics and perfectly high receptor density on the retina, and taking the wavelength range as a given (visible light), what determines the achievable resolution is just one quantity: The size of the eye (more exactly, the size of the pupil). Ever wondered why astronomers build ever-bigger telescopes? That is the answer.

The resolution of an instrument (and the eye is nothing but a biological instrument) is given by $$\theta = 1.220\frac{\lambda}{D}$$ where $\theta$ is the angular resolution (for the small values relevant in optics, you can approximate it as distance between two points over distance to the points), $\lambda$ is the wavelength (for visible light, between $400\,\rm nm$ and $750\,\rm nm$) and $D$ is the diameter of the pupil (for the human eye, the largest occurring size is $9\,\rm mm$), so assuming normal-sized eyes, the angular resolution is at best $10^{-4}$ for blue light, that is, you would be able to distinguish two points one meter apart at ten kilometers distance. For red light, the optimal resolution would be half as large.

A typical dot mask size for computer screens is 0.025mm; Someone with "limit vision" would therefore see the individual pixels of a computer screen from 2.5 meters distance, at least for the blue pixels (for the red pixels, he'd have to go to about half that distance).

Of course that's assuming that the pupil size is not enlarged. Hypothetical humans who grew twice as large eyes (or just twice-as-large pupils) would of course also see twice as well.

Also note that the main limitation in our actual eyes is generally not the optics, but the receptor density in our eyes. For example, while the theoretical resolution is best for blue light, the actual eye has lowest resolution there, since the blue receptor density is lowest. That's also why many early home computers used blue backgrounds: The pixels — which were much larger than today — could simply not be that well resolved for blue, so the background looked smoother.

According to this Wikipedia article the perfect human eye has an angular resolution of 50 CPD, which if I understand the definition of CPD correctly, corresponds to an angular resolution of $3.5\cdot 10^{-4}$. So the human eye is about a factor 3.5 from the theoretical optimum.

According to this: http://www.livescience.com/18658-humans-eagle-vision.html
If humans had eyesight as good as an eagle, we'd be able to pick out a single ant on a blade of grass from the top of a 10 story building. That's something like 20/5 vision. Being able to pick out a human from several miles seems pretty easy.
Also according to that source, it wouldn't effect your close up vision.

My brother has 20/15 vision, and he's told me that he can pick out individual pixels on a computer screen pretty easily, so with 20/5 vision you'd have to get used to that being kind of a problem, and everything looking pixelated... I wonder if you'd end up getting computer glasses to correct your vision down a little to make watching tv more enjoyable.

One cool thing they mention at the end of the article is that laser surgery may soon develop to the point where you could go in and get eyesight between 20/10 and 20/8.

• I don't think computer pixels would be a problem - you would train yourself not to "see" them the same way we read words instead of letters. It might be annoying at first, but I'm pretty sure that would go away very, very quickly. Oct 31 '16 at 18:22
• @Ghotir It probably would. I know if I think about it I can see the pixels on my relatively close computer screen, but if I am paying attention to what's actually on the screen it all just blends together. I imagine that it would be the same for people with better than normal vision. Oct 31 '16 at 21:04