# How accurately could we theoretically see into far space?

Travels to different galaxies are strongly limited by the speed of light. Unless we find a way to travel through space with some wormholes, we will never reach planets in another galaxy.

But what about seeing them? Is there such a theoretical limit on the maximum "zoom" or "sharpness" of a picture? Or, in theory, it would be possible to build a telescope so strong, that it would allow us to see surface of a planet in another galaxy?

The spatial resolution of a telescope is going to be limited in what it can resolve by something called the diffraction limit. Basically, light can only be focused so much by a lens given its initial starting size and the focal length of the lens. Its useful to think about this in terms of angular resolution for the case of telescopes, and the minimum resolvable angle can be derived to be:

$$\Delta\theta = 1.220 \frac{\lambda}{D}$$

where $\lambda$ is the wavelength of the light that you are measuring and $D$ is the diameter of the lens aperture that you are using.

Now, in theory, the only thing that you need to do is make a very large telescope in order to resolve smaller features, if you can collect light for long enough and maintain your pointing accuracy. However, given the extremely small angular size of planets in another galaxy, I think that maintaining this pointing accuracy would be an extreme technical challenge (basically, if there is any jitter in the direction that you are pointing, you are going to get a blurry image for features on the order of the angular jitter). I'd be interested to see if just random thermal fluctuations would be enough to ruin the pointing accuracy.

Something that people do to increase their resolving power beyond that of just a single large telescope, which can be impractical, is to build telescopic arrays like the VLA in New Mexico. This increases the effective size of your telescope to that of the size of the array, allowing for higher resolution.

There is another big problem with ultra-small luminosities: due to the small initial light + 1/r² decrease, it might be that only a few photons per hour sent by your target planet reach the diameter of Earth (better be in your telescope ! ). At very small luminosity you have to remind that light is not continuous and made of photons. And way before the extreme case of "one photon arriving in a while", you will suffer the randomness of photons, in time, location, color, yielding noise. Ok you could make ultra-long pause, but with the problem of everything moving during that time.

Moreover, the rest of the sky is also sending photons, comprising the interstellar medium between you and the target (who will win ?).

Worse: your own instrument is also sending photons (due to heat) and electrons (noise due to circuits). We use ultra-cooling systems to reduce them, but they are there, so for ultra-faded light they compete, and at long pauses they multiply...