Very Large Array - What's the limit?

[Cikomyr2]

I am currently reading The Commonwealth Saga from Hamilton. The Inciting Incident of the first book is the discovery that a specie has erected a Dyson Sphere (or a Dyson Sphere-like barrier) around a star within a few seconds. Since the Commonwealth of Mankind is spread across multiple light-years, it was known that the Dyson Sphere would be erected between two specific time point (a 6 year period, specifically, based on the distance difference between two colonies and the event, and the fact that one of the colony still saw the star in question).

Now, in the book, they act as if the only really methodology of investigation is sending a ship (a challenge since the Commonwealth has been built with Wormhole tech). Adventure ensures, it's a fun book.

However, I remember a Schlock Mercenary comic strip where one of the main character deploys for fun 200 missile drones over a 200 million kilometer diameter to transform it into a Very Large Array.

And it got me thinking.

What are the effective limitation on a Very Large Array? Like, is it theoretically possible to see details on a planet that is effectively 1,000 light years away? Like, could you deploy millions and millions of drones that covers the size of the Solar System (287 Billion kilometers) to observe and spy on another planet, in another solar system?

[Palanan]

A VLA is typically used for observing at radio wavelengths, so the question is whether your target world would be emitting in the radio portion of the spectrum with a strong enough contrast between regions to resolve surface details.

We can detect planets several thousand lightyears away with specialized satellites, observing in visible light, but that mainly tells us presence/absence and basic data about the orbit, just estimates for distance and orbital period.

If you’re observing a system a thousand lightyears away in the radio spectrum, you’ll probably need a baseline greater than the solar system. If you’re already capable of FTL travel between stars, then it should be possible to seed a series of receivers across several thousand AU—but that’s a lot of effort when you already have FTL-capable ships, so it may well be simpler just to send a ship to the target world.

Also keep in mind that even if you set up a VLA with a thousand-AU baseline, you’re still observing a target that’s a thousand lightyears away, which means the information you receive will be a thousand years out of date. Photons in the radio spectrum are still photons, which means they’re limited to traveling at the speed of light.

So by definition, if your target is a thousand lightyears away, it takes a thousand years for the photons to travel the intervening distance, and your observations will reflect conditions on the target world a thousand years ago. That may not be ideal for purposes of up-to-date intel.

[factotum]

I don't think you need a VLA to detect if a star *literally stops shining*, though...

[Cikomyr2]

Also keep in mind that even if you set up a VLA with a thousand-AU baseline, you’re still observing a target that’s a thousand lightyears away, which means the information you receive will be a thousand years out of date. Photons in the radio spectrum are still photons, which means they’re limited to traveling at the speed of light.

So by definition, if your target is a thousand lightyears away, it takes a thousand years for the photons to travel the intervening distance, and your observations will reflect conditions on the target world a thousand years ago. That may not be ideal for purposes of up-to-date intel.

Well, yhea. the point is to investigate the event of enwrapping a star. With a wormhole based interstellar society, you can set up the Large Array where the upcoming wrapping event is only 2 years away, and then observe closely how the whole events unfolded. The point being is to use the "light-recording" of these long-past events to investigate.

So, the speed of light limitation is not an actual limitation in my scenario; it's a feature. What I was wondering is the limitation you referred to: you need contrast in the EM field to be perceptible by the VLA? So it's not behaving like a camera?

I don't think you need a VLA to detect if a star *literally stops shining*, though...

that's not the point.

[Fat Rooster]

The limit is that you need to know the position of each of your array elements with a precision measured in the order of the wavelength you are working at. Mirrors (and lenses, but slightly more confusing with them) essentially work by making the light path length between the source of the light and your receiver 'equal' no matter where on the mirror it hits, so all these paths constructively interfere. This means that if a segment is out of position by a quarter wavelength it will actually lower your signal. If you change the angle of the source the light paths will be different lengths, and will sum to something near zero.
Phased arrays basically work the same, except that instead of making the paths actually the same to force constructive interference we artificially introduce a delay, and combine the signals in electronics.

Basically, for optical light, you need to coordinate time to the 10s of femtoseconds and position to the hundreds of nanometers. Doing this on solar system scales is going to be hard, but may be possible by using distant stars as reference points.

You can think of a mirror telescope as a phased array with the delay of each mirror segment encoded in how far it is from your receiver pixel. If you think of it as each mirror segment re-emiting all light it receives in a hemisphere (rather than a ray), and then consider how each segment's emitted light interferes with the rest's, you find that there is a single direction where the signals constructively interfere, which is why mirrors reflect preserving direction scattering light.

Sorry if that is a little hard to follow, hard to describe without pictures.

[Cikomyr2]

The limit is that you need to know the position of each of your array elements with a precision measured in the order of the wavelength you are working at. Mirrors (and lenses, but slightly more confusing with them) essentially work by making the light path length between the source of the light and your receiver 'equal' no matter where on the mirror it hits, so all these paths constructively interfere. This means that if a segment is out of position by a quarter wavelength it will actually lower your signal. If you change the angle of the source the light paths will be different lengths, and will sum to something near zero.
Phased arrays basically work the same, except that instead of making the paths actually the same to force constructive interference we artificially introduce a delay, and combine the signals in electronics.

Basically, for optical light, you need to coordinate time to the 10s of femtoseconds and position to the hundreds of nanometers. Doing this on solar system scales is going to be hard, but may be possible by using distant stars as reference points.

You can think of a mirror telescope as a phased array with the delay of each mirror segment encoded in how far it is from your receiver pixel. If you think of it as each mirror segment re-emiting all light it receives in a hemisphere (rather than a ray), and then consider how each segment's emitted light interferes with the rest's, you find that there is a single direction where the signals constructively interfere, which is why mirrors reflect preserving direction scattering light.

Sorry if that is a little hard to follow, hard to describe without pictures.

It is hard to follow, but it's also extremely interesting. So I think what you are saying is that the problem is one of positioning coordination for the entire array. I suspect millions of drones over the entire solar system would require one *hell* of a CnC software. If all of them have to perfectly align on the target.

Thank you, I didn't realized how delicate the VLA has to be.

[Radar]

It is hard to follow, but it's also extremely interesting. So I think what you are saying is that the problem is one of positioning coordination for the entire array. I suspect millions of drones over the entire solar system would require one *hell* of a CnC software. If all of them have to perfectly align on the target.

Thank you, I didn't realized how delicate the VLA has to be.

And that is only part of the whole problem as there is something far more trivial and at the same time more difficult to deal with. The signal you get will not be clean as the space between you and the observed star system is not exactly empty. Even worse, it is not filled uniformly, so the passing light will be scattered in unpredictable ways. If you want such a high resolution that femtosecond delays and nanometer scale displacement are affecting your readings, it might simply be impossible.

I know that for example we have good algorithm to clean atmosphere fluctuation from images made with Earth-based telescopes, but this is about random noise, which is far easier to filter in comparison to some thin, unknown dust clouds between you and the target. Also, the resolution we expect from the telescopes is far lower than what is needed for the VLA. And I did not even include the general relativity effects, which are easy to predict for masses in the solar system, but far less so for - let's say - some gravity waves crossing the light beam going in your direction.

Bottom line is, there are a lot of effects summing up to the fact that even with best possible equipment, you will still get a blurry, distorted picture.

[Fat Rooster]

It is hard to follow, but it's also extremely interesting. So I think what you are saying is that the problem is one of positioning coordination for the entire array. I suspect millions of drones over the entire solar system would require one *hell* of a CnC software. If all of them have to perfectly align on the target.

Thank you, I didn't realized how delicate the VLA has to be.

They don't need to be anywhere specific, you just need to know exactly how long light takes to reach each sensor from the source with a precision of the order of 1/frequency. For light this is absurdly fast, but there are optical tricks that can let us manage it. For radio waves we can just do it with electronics. A good 'telescope' with detectors this sensitive would be able to use tricks to understand it's own configuration with the necessary precision, if you had the computing power. You basically look at a few known objects that are small, bright, and changing, and find the setup that can see them.

I'll try again on helping you understand how it works.
Consider if you had objects that flashed periodically (very fast flashes very occasionally), and a pixel that required three flash readings to trigger. The pixel is connected to three sensors, and you care about a particular object, but you want to filter out all as many other object flashes as possible. First lets consider if your sensors right beside each other. In this case any flash will trigger all the sensors, so your pixel will light up whenever anything flashes. You cannot resolve anything. Now lets consider if your sensors are very far away from each other. Light does not reach the sensors simultaneously, so in order to make sure our object of interest triggers the pixel we need to put appropriate delays on two of the sensors so that the readings reach the pixel simultaneously. A flash happens, all three readings get to the pixel at the same time, so the pixel triggers.
Now think about what happens if a different object flashes. The light will not reach the sensors at times related to the delays, so the readings will get to the pixel at different times. The pixel will not trigger, as it will not get all 3 flash readings at the same time. Our setup is now able to resolve our target object relative to other objects.
Arrays (and at a basic level all imaging) take this trick to the extreme, and operate at the waveform level. Line up your timings correctly and the readings on your point of interest will constructively interfere, while everywhere else they will cancel. Further apart means sources closer to your point of interest will differ in timing more, so you can resolve more detail. In order for this to work though you need to be able to line up your waveforms. This is related to the frequency and the wavelength of the light we are concerned about.

Is that any clearer? (Probably still not 'clear' )

[Cikomyr2]

They don't need to be anywhere specific, you just need to know exactly how long light takes to reach each sensor from the source with a precision of the order of 1/frequency. For light this is absurdly fast, but there are optical tricks that can let us manage it. For radio waves we can just do it with electronics. A good 'telescope' with detectors this sensitive would be able to use tricks to understand it's own configuration with the necessary precision, if you had the computing power. You basically look at a few known objects that are small, bright, and changing, and find the setup that can see them.

I'll try again on helping you understand how it works.
Consider if you had objects that flashed periodically (very fast flashes very occasionally), and a pixel that required three flash readings to trigger. The pixel is connected to three sensors, and you care about a particular object, but you want to filter out all as many other object flashes as possible. First lets consider if your sensors right beside each other. In this case any flash will trigger all the sensors, so your pixel will light up whenever anything flashes. You cannot resolve anything. Now lets consider if your sensors are very far away from each other. Light does not reach the sensors simultaneously, so in order to make sure our object of interest triggers the pixel we need to put appropriate delays on two of the sensors so that the readings reach the pixel simultaneously. A flash happens, all three readings get to the pixel at the same time, so the pixel triggers.
Now think about what happens if a different object flashes. The light will not reach the sensors at times related to the delays, so the readings will get to the pixel at different times. The pixel will not trigger, as it will not get all 3 flash readings at the same time. Our setup is now able to resolve our target object relative to other objects.
Arrays (and at a basic level all imaging) take this trick to the extreme, and operate at the waveform level. Line up your timings correctly and the readings on your point of interest will constructively interfere, while everywhere else they will cancel. Further apart means sources closer to your point of interest will differ in timing more, so you can resolve more detail. In order for this to work though you need to be able to line up your waveforms. This is related to the frequency and the wavelength of the light we are concerned about.

Is that any clearer? (Probably still not 'clear' )

Let's just say I will have to re-read that a few times to make sure I understand. But I am happy to.