Question: The video [“How Far Can Legolas See?”](https://www.youtube.com/watch?v=Rk2izv-c_ts) by MinutePhysics recently went viral. The video states that although Legolas would in principle be able to count $105$ horsemen $24\text{ km}$ away, he shouldn't have been able to tell that their leader was very tall.

![enter image description here](https://i.stack.imgur.com/ZpHOj.jpg)

I understand that the main goal of MinutePhysics is mostly educational, and for that reason it assumes a simplified model for seeing. But if we consider a more detailed model for vision, it appears to me that even with human-size eyeballs and [pupils](http://en.wikipedia.org/wiki/Pupil)$^\dagger$, one might actually be able to (in principle) distinguish smaller angles than the well known [angular resolution](http://en.wikipedia.org/wiki/Angular_resolution):
$$\theta \approx 1.22 \frac \lambda D$$

So here's my question—using the facts that:

* Elves have two eyes (which might be useful as in e.g. the [Very Large Array](https://en.wikipedia.org/wiki/Very_Large_Array)).
* Eyes can dynamically move and change the size of their pupils.

And assuming that:

* Legolas could do intensive image processing.
* The density of [photoreceptor cells](http://en.wikipedia.org/wiki/Photoreceptor_cell) in Legolas's [retina](http://en.wikipedia.org/wiki/Retina) is not a limiting factor here.
* Elves are pretty much limited to visible light just as humans are.
* They had the cleanest air possible on Earth on that day.

How well could Legolas see those horsemen?

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$^\dagger$ I'm not sure if this is an accurate description of elves in Tolkien's fantasy

Answer: 
Deconvolution can work but it only works well in case of point sources [as e.g. pointed out here](http://www.goedoc.uni-goettingen.de/goescholar/bitstream/handle/1/9858/aa2320-04.pdf?sequence=1). The principle is simple; the blurring due to the finite aperture is a known mathematical mapping that maps a hypothetically infinite resolution image to one with finite resolution. Given the blurred image, you can then attempt to invert this mapping. The blurred image of a point source that should have affected only one pixel if the image were completely unblurred, is called the point spread function. The mapping to the blurred image is competely defined by the point spread function. There are various algorithms that are able to deblur an image to some approximation, e.g. [Richardson–Lucy deconvolution](https://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution) or [Wiener filter method](https://en.wikipedia.org/wiki/Wiener_deconvolution).

In practice you can't deconvolve an image perfectly, because this involves divding the Fourier transform of the blurred image by the Fourier transform of the point spread function, and the latter will tend to zero at large wavenumbers. This means that you will end up amplifying the noise at high wavenumbers and it is precisely at the high wavenumbers that the small scale details are present. So, the resolution you can obtain will ultimately be limited by the noise.
There is also a geometric limitation for seeing that far. I have [Q&A'ed](https://math.stackexchange.com/questions/902017/how-far-can-one-see-over-the-ocean) it on mathematics.SE. If standing on level ground, Legolas would have been able to see only 4.8km far due to the planet's curvature (assuming that Middle Earth is on a planet resembling ours). To see that far, he would have to have climbed a hill or tree of about 50m height.