Partial answer pre-coffee:
Your first link Extremely long baseline interferometry with Origins Space Telescope is indeed very interesting!
Operating 1.5 million km from Earth at the Sun-Earth L2 Lagrange point, the Origins Space Telescope equipped with a slightly modified version of its HERO heterodyne instrument could function as a uniquely valuable node in a VLBI network. The unprecedented angular resolution resulting from the combination of Origins with existing ground-based millimeter/submillimeter telescope arrays would increase the number of spatially resolvable black holes by a factor of a million, permit the study of these black holes across all of cosmic history, and enable new tests of general relativity by unveiling the photon ring substructure in the nearest black holes.
So, What (the heck) is HERO's interferometry possibility? (heterodyning, digitizing, analysis later)
As discussed in my question
if you shine single frequency light (in this case the light is in the far IR) onto a nonlinear crystal that's also receiving light from a telescope they will heterodyne or "beat" and generate a lower frequency in the radio spectrum that you can digitize.
That's the key to one way to do optical interferometry at long baselines; you convert the optical signals (even 50 microns is 6 THz) to a low enough frequency (few GHz range, for example ALMA's baseband for digitization is 0 to 2 GHz) by heterodyning, just like the old AM radios converted 540 kHz up to 1700 kHz to a constant 455 kHz via a nonlinear mixer, HERO will shine IR light of constant frequency on to a set of nonlinear pixels receiving infrared light from the infrared telescope, and digitize the radio-frequency electronic heterodyne signals produced in each pixel.
That means you can record the data digitally and sent it home later, just like how each dish of the Event Horizon Telescope recorded their digitized streams to hard drive and then put those drives on an airplane bound for a central location where interferometry could be done offline months or years later.
You have to know where exactly the telescope is relative to the other telescopes presumably closer to Earth in order to do interferometry, to an accuracy of a fraction of the initial wavelength of say 50 microns(!) but the point is that once you digitize the data you have plenty of time to figure that out offline based on calibrations from other sources, auxiliary timing data of continuous signals between the telescopes and other things like ballistic trajectory integration. It's certainly not easy but they feel it is possible.
This would be the basis of an excellent new question!
from tweet (click for larger, from here):
So how do they get such high resolution?
With a baseline of 1.5 million kilometers and a wavelength of say 15 microns, that's a ratio of 1×1014! That corresponds to an angular resolution of 2 nanoarcseconds.
...it seems pretty ridiculous that you can achieve that much by a very small antenna positioned far away enough. This begs a question: why can’t we similarly park a few similarly capable antenna at Sun-Earth L3/4/5 and get orders of magnitude further improvement?
Well maybe not so ridiculous since
- what's talked about here is an "upscope" or tweak on the technology of the Origin Space Telescope that's already going up there for other reasons and would presumably already be funded for those reasons. In that case though you'd have to use ground stations below Earth's atmosphere to implement interferometry. Think of it as like a "pathfinder" for VLBI optical's future using heterodyne down-conversion in space
- There are plenty of objects with signals strong enough that a 6 meter aperture can capture enough power for a low temperature cooled focal plane array at both optical and radio frequencies. By receiving optical frequencies and heterodyning them down to digitize-able radio frequency, we get the diffraction limited performance associated with the micron wavelength and 6 meters, rather than millimeter wavelength and 6 meters.
- In the infrared (and optical) there are also plenty of strong and narrow emission line sources that can be explored for very accurate radial velocity measurements together with the incredible spatial resolution provided by microns at millions of kilometers.
Q: "Each of these should be within 0.5-1 billion in cost, but they would bring immense benefits. So what’s the catch?"
A: It's that "0.5-1 billion in cost" of course! If you can do a significant fraction of something first as an add-on or "upscope" of a separately funded effort first, you bloody well do it first if you want to demonstrate that you are serious about the full project!
Q: "What is stopping Event Horizon Telescope the size of the Earth’s orbit?"
A: Ditto (i.e. nothing, but do this first please because you learn a lot by testing and demonstrating the same technologies necessary for that to work)