# Exoplanet surface detail: Limitations on size of space telescope array

How big could an array of space telescopes acting as an interferometer be ?

How big would it have to be to resolve exoplanet surface detail the size of Iceland at a distance of 100 light years ?

Well, with current or immediate-future technology, let's use LISA as an example of the largest baseline achievable at $5\times 10^6$ km. Then the diffraction limit says $\theta \sim \frac{\lambda}{D}$, where $\theta$ is angular resolution, in this case ($10^7$ cm)/($10^{20}$ cm)=$10^{-13}$ radians. At optical wavelengths, the LISA-type detector would have resolution of $10^{-16}$, so yes, in principle, this seems possible.

The biggest problem I think I am ignoring is flux: there wouldn't be enough photons coming from exo-Iceland to do proper interferometry, and then there is also the problem of contrast: what is the difference in flux between land and sea features, aside from contrast with host star.

With current radio telescopes, a much-quoted factoid is that you could read the date on a dime on the moon, but in practice you never could because it doesn't emit in the radio, and certainly not with that contrast in signal.

• Not sure if this is right about LISA. That is a gravity wave detector. It is not configured as an optical telescope, so it is not clear whether it could function as one in the way you suggest. I acknowledge that its parameters are suggestive, but is there more behind your example? Nov 17 '20 at 15:06

Iceland (the country) is about 250 km across. It would subtend an angle of about $$2.5 \times 10^{-13}$$ radians from 100 light years.

Taking a simple angular resolution criterion of $$\lambda/D$$, where $$\lambda$$ is the wavelength of observation and $$D$$ is the diameter of your array, then if working at optical wavelengths ($$\lambda = 500$$nm) then $$D>2000$$ km. So basically you could construct such an array on the Earth.

An Earthbound optical interferometer of this size would not work because you would not be able to get it phase-locked because of the (time-varying) difference in atmospheric conditions above each telescope and the lack of technology to record the data at high enough speeds and subsequently do off-line correlation and phase closure locking of the signals (as is done with radio interferometers with intercontinental baselines).

Could you put something in space? Yes, eventually. But the technology to establish metrology of a fraction of an optical wavelength on baselines of 2000 km has only been achieved in ground-based gravitational wave detectors.

There is probably more promise in working at microwave (mm) wavelengths. Here the data can be recorded sufficiently quickly that the signals can be correlated after the fact. If you have three receivers then you can use phase closure techniques even if the exact position of the receivers is not known. This is already done across baselines the size of the Earth - for example the Event Horizon Telescope project, that works at wavelengths of 1.3mm.

If you could launch free-flying mm-wave telescopes and record the data at a sufficient rate and with sufficiently stable pointing, then making an array of size $$\sim 5\times 10^6$$ km ought to do the trick (that is if Iceland emits mm-waves).