<p>Partial answer pre-coffee:</p>
<p>Your first link <a href="https://arxiv.org/abs/1909.01408" rel="nofollow noreferrer">Extremely long baseline interferometry with Origins Space Telescope</a> is indeed very interesting!</p>
<blockquote>
<p>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.</p>
</blockquote>
<h3>So, What (the heck) is HERO's interferometry possibility? (heterodyning, digitizing, analysis later)</h3>
<p>As discussed in my question</p>
<ul>
<li><a href="https://astronomy.stackexchange.com/q/36633/7982">Has optical interferometry been done at radio frequency using heterodyning with a laser in a nonlinear material?</a></li>
</ul>
<p>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 &quot;beat&quot; and generate a lower frequency in the radio spectrum that you can digitize.</p>
<p>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 <a href="https://en.wikipedia.org/wiki/Intermediate_frequency#Uses" rel="nofollow noreferrer">455 kHz</a> 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 <em>digitize the radio-frequency electronic heterodyne signals produced in each pixel</em>.</p>
<p>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.</p>
<ul>
<li><a href="https://astronomy.stackexchange.com/q/20082/7982">How does the Event Horizon Telescope implement the interferometry?</a></li>
</ul>
<p>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. <em>It's certainly not easy</em> but they feel it is possible.</p>
<ul>
<li>See <a href="https://physics.stackexchange.com/a/630432/83380">this answer to <em>Precise Event Horizon Telescope locations?</em></a> which discusses the fringe maximization algorithm. Yes it will be incrementally harder but I think it will be the same basic idea, modified for spacecraft trajectories rather than items bound to a rotating Earth.</li>
</ul>
<p>This would be the basis of an excellent new question!</p>
<p>from <a href="https://twitter.com/MIT_CSAIL/status/1116007460039483392/photo/1" rel="nofollow noreferrer">tweet</a> (click for larger, from <a href="https://astronomy.stackexchange.com/a/32731/7982">here</a>):</p>
<p><a href="https://i.sstatic.net/4ugoo.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/4ugoom.jpg" alt="enter image description here" /></a></p>
<h3>So how do they get such high resolution?</h3>
<p>With a baseline of 1.5 million kilometers and a wavelength of say 15 microns, that's a ratio of 1×10<sup>14</sup>! That corresponds to an angular resolution of 2 nanoarcseconds.</p>
<blockquote>
<p>...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?</p>
</blockquote>
<p>Well maybe not so ridiculous since</p>
<ul>
<li>what's talked about here is an &quot;upscope&quot; 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 &quot;<a href="https://en.wikipedia.org/wiki/Australian_Square_Kilometre_Array_Pathfinder" rel="nofollow noreferrer">pathfinder</a>&quot; for VLBI optical's future using heterodyne down-conversion in space</li>
<li>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.</li>
<li>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.</li>
</ul>
<h3><strong>Q:</strong> &quot;Each of these should be within 0.5-1 billion in cost, but they would bring immense benefits. So what’s the catch?&quot;</h3>
<p><strong>A:</strong> It's that &quot;0.5-1 billion in cost&quot; of course! If you can do a significant fraction of something first as an add-on or &quot;upscope&quot; 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!</p>
<h3><strong>Q:</strong> &quot;What is stopping Event Horizon Telescope the size of the Earth’s orbit?&quot;</h3>
<p><strong>A:</strong> 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)</p>

CC BY-SA 4.0
2022-06-29T20:33:21.680Z
That fringe algorithm is even trickier when your telescopes are in orbit, with clocks that are experiencing changing time dilation due to variations in velocity & gravity. I guess it's similar to the problem of synching GPS clocks, but GPS sats aren't trying to log interferometry data. ;)
PM 2Ring
CC BY-SA 4.0
2022-06-29T21:22:57.740Z
@PM2Ring actually satellites that use radar or lasers to map planets surfaces and gravity fields to unbelievable precision have to do it too. The reason I keep emphasizing heterodyning and recording is to point out that all of those corrections can be implemented or at least refined years later during data analysis in a self-consistent way. While tricky for newcomers, the algorithms for implementing GR corrections for constellations of spacecraft [are a half-century old](https://en.wikipedia.org/wiki/Global_Positioning_System#Development).
uhoh
CC BY-SA 4.0
2022-06-29T21:24:48.627Z
@PM2Ring see [Earth’s gravity from space](https://link.springer.com/article/10.1007/s12210-020-00889-8) and [GRAIL](https://en.wikipedia.org/wiki/GRAIL) and [GRACE and GRACE-FO](https://en.wikipedia.org/wiki/GRACE_and_GRACE-FO) and [Gravity Field and Steady-State Ocean Circulation Explorer (GOCE)](https://en.wikipedia.org/wiki/Gravity_Field_and_Steady-State_Ocean_Circulation_Explorer)
uhoh
CC BY-SA 4.0
2022-06-29T22:44:36.950Z
Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/137420/discussion-between-pm-2ring-and-uhoh).
PM 2Ring
CC BY-SA 4.0
2022-06-28T22:48:20.073Z
2022-06-28T22:48:20.073Z
uhoh
<p>Adding to Uhoh's answer, while having telescopes very far part helps with angular resolution, its the total telescope area that determines the total flux you can detect. So having a few small telescopes very far apart will give you good resolution, but you will only be able to look at bright objects. To view dim objects you would need larger telescopes (which then get even more expensive to build).</p>
<p>Thus there is then a trade off then between whether you want high resolution or the ability to view dim objects. Different people (competing for the same funding) will want different things.</p>

CC BY-SA 4.0
2022-06-29T21:13:08.343Z
You make a very good and important point! It's a lot easier to make a say 30 meter diameter microwave reflector unfold in space with an order millimeter surface error than a 30 meter optical reflector unfold in space to a surface error of order microns!
uhoh
CC BY-SA 4.0
2022-06-29T09:05:57.907Z
2022-06-29T09:05:57.907Z
Rob
<p>There is a <a href="https://arxiv.org/abs/1909.01408" rel="nofollow noreferrer">proposal</a> to include a radio sensor in a telescope going to the Sun-Earth L2, getting 120x improvement in angular resolution to EHT. Knowing nothing about interferometry, 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?</p>
<p>The proposal estimates the following requirements in terms of positional errors:</p>
<ul>
<li>Position error &lt; 600 m</li>
<li>Velocity error &lt; 2 mm/s</li>
<li>Acceleration error &lt; <span class="math-container">$10^{-9}$</span> m/s²</li>
</ul>
<p>I found a <a href="https://link.springer.com/article/10.1007/s40295-021-00290-z" rel="nofollow noreferrer">paper</a> which <em>seems</em> to say that (p. 3) through the Deep Space Network, we can already get 1-3m position error and 0.1 mm/s velocity error. Alternatively if that causes a bandwidth problem you could use alternatives outlined there (pulsars for example give a few km precision). In any case wouldn’t it be perfectly straightforward to scale EHT’s own <a href="https://physics.stackexchange.com/questions/473320/precise-event-horizon-telescope-locations">‘fringe maximization algorithm’</a> to the Solar System scale? It seems that we already have all the tech to make it work.</p>
<p>Each of these should be within 0.5-1 billion in cost, but they would bring <em>immense</em> benefits. So what’s the catch?</p>

CC BY-SA 4.0
2022-06-28T17:58:26.077Z
Throw at it enough money and it's no issue... if you look at budgets, a billion € or $ is surprisingly large share of an annual science budget in astronomy.
planetmaker
<telescope><space-telescope><interferometry><event-horizon-telescope>
What is stopping Event Horizon Telescope the size of the Earth’s orbit?
Ahmbak
# What is stopping Event Horizon Telescope the size of the Earth’s orbit?

(Asked by: username_0 on 2022-06-28)

There is a [proposal](https://arxiv.org/abs/1909.01408) to include a radio sensor in a telescope going to the Sun-Earth L2, getting 120x improvement in angular resolution to EHT. Knowing nothing about interferometry, 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?

The proposal estimates the following requirements in terms of positional errors:

* Position error < 600 m
* Velocity error < 2 mm/s
* Acceleration error < $10^{-9}$ m/s²

I found a [paper](https://link.springer.com/article/10.1007/s40295-021-00290-z) which *seems* to say that (p. 3) through the Deep Space Network, we can already get 1-3m position error and 0.1 mm/s velocity error. Alternatively if that causes a bandwidth problem you could use alternatives outlined there (pulsars for example give a few km precision). In any case wouldn’t it be perfectly straightforward to scale EHT’s own [‘fringe maximization algorithm’](https://physics.stackexchange.com/questions/473320/precise-event-horizon-telescope-locations) to the Solar System scale? It seems that we already have all the tech to make it work.

Each of these should be within 0.5-1 billion in cost, but they would bring *immense* benefits. So what’s the catch?

**Tags:** telescope, space-telescope, interferometry, event-horizon-telescope
> **Comments:**
> **username_1**: Throw at it enough money and it's no issue... if you look at budgets, a billion € or $ is surprisingly large share of an annual science budget in astronomy.  

---

## 2 answers

### Answer by username_2 on 2022-06-28. Score: 3 | Accepted answer

Partial answer pre-coffee:

Your first link [Extremely long baseline interferometry with Origins Space Telescope](https://arxiv.org/abs/1909.01408) 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

* [Has optical interferometry been done at radio frequency using heterodyning with a laser in a nonlinear material?](https://astronomy.stackexchange.com/q/36633/7982)

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](https://en.wikipedia.org/wiki/Intermediate_frequency#Uses) 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.

* [How does the Event Horizon Telescope implement the interferometry?](https://astronomy.stackexchange.com/q/20082/7982)

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.

* See [this answer to *Precise Event Horizon Telescope locations?*](https://physics.stackexchange.com/a/630432/83380) which discusses the fringe maximization algorithm. Yes it will be incrementally harder but I think it will be the same basic idea, modified for spacecraft trajectories rather than items bound to a rotating Earth.

This would be the basis of an excellent new question!

from [tweet](https://twitter.com/MIT_CSAIL/status/1116007460039483392/photo/1) (click for larger, from [here](https://astronomy.stackexchange.com/a/32731/7982)):

[![enter image description here](https://i.sstatic.net/4ugoom.jpg)](https://i.sstatic.net/4ugoo.jpg)

### 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](https://en.wikipedia.org/wiki/Australian_Square_Kilometre_Array_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)

> **Comments:**
> **username_3**: That fringe algorithm is even trickier when your telescopes are in orbit, with clocks that are experiencing changing time dilation due to variations in velocity & gravity. I guess it's similar to the problem of synching GPS clocks, but GPS sats aren't trying to log interferometry data. ;)  
> **username_2**: @PM2Ring actually satellites that use radar or lasers to map planets surfaces and gravity fields to unbelievable precision have to do it too. The reason I keep emphasizing heterodyning and recording is to point out that all of those corrections can be implemented or at least refined years later during data analysis in a self-consistent way. While tricky for newcomers, the algorithms for implementing GR corrections for constellations of spacecraft [are a half-century old](https://en.wikipedia.org/wiki/Global_Positioning_System#Development).  
> **username_2**: @PM2Ring see [Earth’s gravity from space](https://link.springer.com/article/10.1007/s12210-020-00889-8) and [GRAIL](https://en.wikipedia.org/wiki/GRAIL) and [GRACE and GRACE-FO](https://en.wikipedia.org/wiki/GRACE_and_GRACE-FO) and [Gravity Field and Steady-State Ocean Circulation Explorer (GOCE)](https://en.wikipedia.org/wiki/Gravity_Field_and_Steady-State_Ocean_Circulation_Explorer)  
> **username_3**: Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/137420/discussion-between-pm-2ring-and-uhoh).  

---

### Answer by username_4 on 2022-06-29. Score: 3

Adding to Uhoh's answer, while having telescopes very far part helps with angular resolution, its the total telescope area that determines the total flux you can detect. So having a few small telescopes very far apart will give you good resolution, but you will only be able to look at bright objects. To view dim objects you would need larger telescopes (which then get even more expensive to build).

Thus there is then a trade off then between whether you want high resolution or the ability to view dim objects. Different people (competing for the same funding) will want different things.

> **Comments:**
> **username_2**: You make a very good and important point! It's a lot easier to make a say 30 meter diameter microwave reflector unfold in space with an order millimeter surface error than a 30 meter optical reflector unfold in space to a surface error of order microns!  

---

