Theoretical limits on extreme baseline optical interferometry

I sometimes have research ideas that I think are cool, but that don’t make sense for me to pursue. I generally just make a note of them and move on. This is the sixth post in a series describing some of the ideas I’ve accumulated.

Theoretical limits on extreme baseline optical interferometry

What’s the idea?

Interferometry let’s you build a giant ‘virtual telescope’ out of lots of small telescopes. The effective baseline is the longest distance between telescopes, and the number of pixels of effective resolution is roughly the number of telescopes.

By making the wavelength smaller (e.g. going to optical) and making the baseline enormous (e.g. size of Earth’s orbit) we should be able to take images with extreme resolution. For instance, a swarm of $10^6$ spacecraft spread over $10^8\mathrm{km}$ should naively offer spatial resolution of $10^{-17}$ radians, which is enough to directly resolve people/animals over a lightyear away.

The question is: Are these naive estimates accurate? Or does something else get in the way before we can reach “count the mountains on exoplanets” territory?

Why is this interesting?

Traveling to other worlds to image them up-close is extremely hard, and will take decades at the earliest. On the other hand, at least naively it seems like extreme baseline optical interferometry can provide resolved photos of other planets and stars without requiring travel beyond the solar system. And this technology is not too far off: with photonic switches it may be possible soon to record optical signals with phase information, which is the primary hurdle at the moment.

Given this, it is worth working through whether or not there are significant limitations to extreme baseline optical interferometry before sending the field down that path (e.g. with prototypes on Earth, space-based missions, eventually giant swarms of telescopes, etc.).

How can I get started?

Brainstorm limitations to the spatial resolution! A few possibilities:

• Does diffraction by the interstellar medium place limits?
• How about gravitational lensing? Or gravitational waves?
• Errors in tracking the relative positions of the telescopes?
  • Optical interferometry is more or less what LISA does (fully analog), and there it’s crucial that the telescopes follow geodesics extremely closely. Does that matter here too?

And then, for each limitation, the question is (1) what bound does it place on resolution and (2) can it be corrected by something like adaptive optics? For instance gravitational effects ought to vary quite slowly in time and space, so it might be possible to measure the distortion in a single exposure (maybe by looking at reference objects nearby to the target) and correct for it.