# With our current technology, how large could we make a useable space-based VLBI telescope?

I am trying to find an equation that models the current technical limits that we have on creating an effective space-based VLBI telescope.

Variables that are likely relevant in the model: distance of interferometry collectors, distance of observed object, recorded wavelengths of observed object, photon intensity of observed object, resolution of observed object, recording rate of observations, transmission rate of data, phase matching of data from interferometry collectors, and precision of station-keeping of interferometry collectors.

Based upon what I've read, the last four variables seem to be the greatest challenges to our existing technology in making a space-based VLBI feasible.

What other variables, confounds would need to be included in such a model?

And if there is an existing source that already has this model, I'd welcome being pointed towards it.

• Do you want to take into account what it takes to get them off the Earth and into position? For example, fairing size and launch mass. Or can we hand-wave that and assume they just teleport to their orbits? Jul 18, 2022 at 18:09
• What should be the live time of the system? One could imagine something data when fast away from earth and transmitting data when returning. This could give a large baseline but severely reduce the usable time for observations. Jul 18, 2022 at 18:18

note: This is a partial answer providing some background on the issues. I don't think there will be a single, simple

equation that models the current technical limits that we have on creating an effective space-based VLBI telescope

but instead I'll end with an example of a "pathfinder" scenario infrared VLBI investigation.

Searching "Spektr-R" in Wikipedia and here and in Astronomy SE shows that "space-based VLBI" has already been developed, though with only one observatory in space and the other (or the rest) on Earth.

I think however that you may be asking about visible or infrared light, not radio, like for example the Very Large Telescope or VLT, or the Magdalena Ridge Optical Interferometer, except with a very long baseline.

For radio VLBI like the Event Horizon Telescope they locally digitize each radio signal at something like a GHz sample rate and record on to hard drives, then put boxes of drives on airplanes and ship them to a central location where interferometry is done months or years later by playing them back through a big computer that might be called a correlator, implementing the interference in software and adjusting the delays to get the strongest interference fringes. These delays represent the distance between telescopes around the Earth to sub-wavelength accuracy (millimeters!)

So instead of typing in precise geographic locations at millimeter levels of accuracy, they use known locations to a high but not necessarily millimeter level of accuracy (see comments below question) and then run a complicated "fringe maximization algorithm".

And/or you may be asking about multiple observatories in space. But we can look first at a proposed infrared VLBI system using an infrared space telescope. See

What they propose to do here is use an infrared laser aboard the infrared telescope to heterodyne or "beat" against the incoming infrared light inside a small bit of a nonlinear material at each "pixel" and pick up the microwaves produced by the difference in optical frequencies. This is the same down-conversion that you see in THz radio telescopes that down-convert to GHz baseband before digitizing, and in AM and FM radios, and in any wireless communications system. See

By down-converting to GHz they can digitize the signal aboard the space telescope, then transmit the digital data to Earth where the actual interferometry happens during playback, just like the EHT.

So there aren't any showstoppers to putting an optical or infrared VLBI system in space, you need a bunch of space telescopes and a bunch of radios and a bunch of pixelated nonlinear optical mixers.

But perhaps the biggest challenge is knowing the relative positions of your telescopes to fractions of a wavelength of infrared light! You can use the same "fringe maximization algorithm" but you still need to nail down their relative positions in space to perhaps sub-millimeter accuracy first, and that can be done with the same delay-doppler and VLBI techniques used currently to get positions of spacecraft in deep space or orbiting the Moon or other planets.

Alternatively if you were interested in radio VLBI you could build a bunch of telescopes like SOFIA and put them in space. You can read more about the THz radio receiving pixels at the infrared telescope's focal plane and how they are down-converted to GHz where they can be digitized in

• Why use infrared? Why not just use radio waves still? As I'm not sure what OP is after but I'm imagining "how can we best get a nice pic of Sag A* or M87* that looks a fair bit more exciting and WAY COOL than a bunch of blobby stuff with a vague suggestion of a blackhole in the middle". Maybe not as detailed as the renderings in Interstellar of course, but enough that you could actually make some of what they show in that film out, i.e. lensing effects on the accretion disc. Jul 19, 2022 at 7:26