# How should the eyes be arranged that can see microscopic objects?

The phenomenon of "microscopic vision" (mainly according to NS Leskov's story "Lefty") is an amazing visual acuity, for example, some grinders are able to see gaps up to 0.0005 mm, while ordinary people are only up to 0.1 mm ... The artist distinguishes between changes equal to 1 / 60-1 / 150 of the size of the depicted object.

And so, how should the eyes of my genetically modified person be changed so that he can distinguish very small objects ?, up to unicellular organisms, which are known to vary in shape and size, ranging from 0.3 microns.

Note: I should probably divide this topic into two parts, depending on the development of microscopic vision: first, where this ability should not interfere with seeing objects in the distance at today's level, and where this ability is a priority, due to which it can overlap other visual abilities.

• How large is the specific microorganism which you want to see? For example, a large Paramecium is about 330 µm (0.3 mm), which is confortably within the range of normal vision. Oct 31, 2020 at 14:40
• How large (or how small) is the smallest detail which you need to see? (And you are missing the "to ..." part after "ranging from".) Oct 31, 2020 at 14:54
• The smaller the better, but it would be good if the acceptable limit began with the size of blood cells (erythrocytes) or other cells of the human body. Oct 31, 2020 at 15:06
• How much macro scale vison are you willing to give up?
– John
Feb 16, 2021 at 15:39
• You do realise that the eye itself is made up of cells? Including the cornea?The major problem with being able to see individual cells is that your eye could not see past its own cells. For all we know, our eyes do have the resolution to see finer than 0.01 mm objects, but the brain edits them out just for sight to be useful Feb 17, 2021 at 8:09

## 2 Answers

They can see UV, although...

If they are to see details of size $$0.3 \ {\mu m}$$ while holding an object close to their face (let's say $$15 \ cm$$ away), they require an angular resolution of $$\theta_c=2 \times10^{-6} \ \text{rad}$$. Smaller $$\theta$$ means better resolution. The diffraction-limited resolution of a a circular aperture (like an eye) is

$$\theta=1.22 \frac{\lambda}{D}$$

Where $$\lambda$$ is the wavelength of light being imaged, and $$D$$ is the aperture diameter. Plugging in the values $$\lambda=550\ nm$$ (wavelength for which humans have the highest sensitivity) and $$D=8\ mm$$ (optimistic estimate for a dilated human pupil, ie. at night), we find

$$\theta_0 = 8 \times 10^{-5} \ \text{rad}$$

Which we can vaguely think of as the 'theoretical diffraction limit' for unaided vision. Using $$D=3\ mm$$ (human pupil during daytime), we find the 'textbook' answer of $$\theta_0=30 \times 10^{-5} \ \text{rad}$$.

To achieve $$\theta_c=2 \times10^{-6} \text{rad}$$, using the same light, $$\lambda=550 \ nm$$, your people would require eyes of diameter $$D=34 \ cm$$, which is impractical. Keeping $$D=8\ mm$$, we find $$\lambda= 20 \ nm$$, which is within the far ultraviolet (UV) part of the spectrum. Thus they can achieve the resolution if their eyes are sensitive to the appropriate part of the UV spectrum.

Some animals have cone cells that are sensitive to UV , although not as far into UV as your people would need. Perhaps when they need to look at something small they shine a UV lamp on it in an otherwise dark room. They would also see the world differently if they are also sensitive to near UV: you can get a feel for that by searching "UV film photography".

... They might not want to

Far UV is harmful: it's used to sterilize things. I think this is where most of the 'genetically modified hand-waving' must be. Their eyes can't block out the UV, but also should be able to survive it. Maybe the cells in their eyes have modifications allowing rapid repair after exposure to UV.

There is an interesting correlation here that you might want to explore: The more dangerous the light: the better the resolution. UV with a lower wavelength is less harmful, but allows a worse angular resolution: in the much less dangerous near-UV, $$\lambda \sim 300 \ nm$$ we have $$\theta=4 \times 10^{-5} \text{rad}$$: that's enough to make out a $$6 \ \mu m$$ feature (such as a white blood cell) at $$15 \ cm$$.

Edit: What if they hold the objects closer than $$15 \ cm$$?

By pure chance, $$15 \ cm$$ from the face turns out to be close to the near point of adult human visual accommodation. Apparently, children can focus on objects at about $$6.5\ cm$$, let's say your people can focus on objects at $$5 \ cm$$. This leads to $$\theta_c=6 \times10^{-6} \ \text{rad}$$, and a corresponding wavelength of $$\lambda= 40 \ nm$$, still in the far UV.

• What are the limitations for placing the object closer to the eye? How about viewing objects at 2cm, or even at 5mm? There is absolutely no motivation for a supermicroscopic vision eye to have a field of view wide enough (or the focus needed) to view anything at a real distance. Feb 16, 2021 at 21:28
• @PcMan Good point, thank you! I hadn't considered this before, but it turns out that it doesn't change the numbers that much.
– Sal
Feb 16, 2021 at 21:58
• The question I wonder about is - your "theoretical diffraction limit" of 300 µrad suggests the possibility to see down to about 5 µm size objects with no extremely exotic eyes. However, real humans obviously can't do this. What would have to be different about the eye to reach this limit, and is such a thing biologically prohibited for other reasons (e.g. like how small you can make a photoreceptor)? Sep 22, 2021 at 0:23

# Do it like the Keck:

Astronomers have a similar issue to you, in that they want high angular resolution but struggle to make large mirrors. Instead, the Keck uses 2 reasonably sized mirrors and cross references them for much greater angular resolution.

If you're willing to handwave superhuman image-processing ability, you may be able to reach an effective 30cm eye diameter by fusing the visual data from 2 (or more) eyes spaced 30-40cm apart, which as per Sal's answer gives the resolving power you want. If you combine it with the suggestion to see into near-UV, you can relax this requirement even more.

• You mean interferometry? Which would require not primarily processing but to have both eyes rigidly fixed and mirrors in the skull. Or fiber optics. Sep 21, 2021 at 12:54
• Not exactly interferometry - I believe the Keck uses some clever algorithm to blend the 2 images. Phase determination might be part of it, but that's possible based on only the image (and some extra criteria, like how the intensity changes when moving closer or farther) Sep 22, 2021 at 3:57