# Is there a theoretical limit on telescope's resolution?

Is there a theoretical limit on what we can see with a telescope of fixed size based on Earth's orbit or the Moon, that is in Earth's region of Solar system outside the Earth's atmosphere?

Why not instead of sending probes to Pluto and Ceres, just invest efforts into building better telescopes, so to photograph the surfaces of these bodies in greater detail? I suspect that all necessary information in fact reacheds Earth's region, it is just matter of sensibility and exposure to fix it, am I right?

## 1 Answer

The absolute limit of a telescope resolution is given by diffraction. No matter how perfectly built and aligned is a telescope, you cannot resolve angles smaller than $$\theta \propto \frac{\lambda}{D}$$ where $\lambda$ is the wavelength of interest and $D$ is the diameter of the telescope. This is why a number of millimeters and radio telescope (and also some -antennas) are huge.

The first figure here shows the basic principle. Imagine that you can divide what you observe in tiny squares and consider each one as a point like source. Each one will generate a diffraction pattern when passing into the telescope and if two points are too near, you cannot distinguish between them.

Wisely you put your telescope in space: turbulence in the atmosphere degrade the signal, and the best/biggest telescopes have hard times to go below $0.5 arc seconds$

Interferometry comes to the rescue increasing $D$ from the telescope size to the distance of two (or more) telescopes (called baseline). Interferometry has been used in radio astronomy since decades. From what I hear optical interferometry is much much more complicated and as far as I know the only large scale attempt is the VLTI project.

So you could imagine to have a constellation of relatively small telescopes spread over hundred thousands or millions of kilometers. But this have the huge problem that you have to know the position and timing of every one of them with an impressive precision (my guess is that the precision in position is of the order of $\lambda$).

The other problem is light collection. If you want to see something very faint you have two options: 1)you observe for a lot of time or 2) you build a bigger telescope (6 to 40 meters in diameter). And here also the largest baseline interferometers cannot do much, as the amount of light that they collect is just the sum of the light collected by the single telescopes.

To conclude: to observe Pluto or Ceres with high enough accuracy you would need a large number of large space telescopes very far away one from the other with perfect telemetry. It's far easier and cheaper to got there to take pictures.

• Wgy VLT is not used for imaging of objects in the Solar System? – Anixx Oct 10 '14 at 13:51
• @anixx: no idea. My main guess is: political decision (also during the design phase). Then founding institutions that use the VLT are probably mostly interested in extremely faint objects (with the exclusion of rocks :D) – Francesco Montesano Oct 10 '14 at 14:05
• I have checked online and have found they made images of Ceres, but their resolution is far behind that of Hubble. – Anixx Oct 10 '14 at 14:13