what is aperture synthesis and how does it work?

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what is aperture synthesis and how does it work?

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From what I understand, and hopefully if my bastardization of the explanation is wrong somehow can explain it better, without going into telescopes and satellites, imagine having multiple cameras. One camera records in regular visible light, one records in infrared, one records in low light (like night vision), one someone produces an image based on the absorbing of ambient radio signals, and another somehow produces and image based on (and this is the one that’s gonna get me crucified) sound waves. A computer collects all the imaging information of these cameras pointing at the same place to produce a super high resolution as accurate as possible image. Now this is something that they do with satellites and telescopes to get good images of things that are super far away.

It’s probably significantly more complicated than that and I apologize if it’s oversimplified to the point where it’s bordering on inaccurate

In astronomy, the best possible resolution of a telescope is dependent on its diameter, according to the [Rayleigh criterion](https://astronomy.swin.edu.au/cosmos/r/rayleigh+criterion). This criterion tells us the smallest resolvable angle (the apparent size), dependent on the diameter and the wavelength, and is roughly theta=lambda/D meaning a larger diameter gives better angular resolution while a smaller wavelength gives a better resolution. This means that getting a large diameter is important for your observations.

Another factor that can affect your observations is the signal to noise ratio, if the thing you’re trying to observe isn’t very bright when viewed in your telescope, then it may be hard to distinguish it from all the noise. In radio telescopes, the system noise of the electronics can be a big problem.

We can improve on both of these by using interferometry, which is when you take multiple wave sources and overlap them so that they interfere with each other. The resultant superimposed wave then has a “fringe visibility”, and we can use some clever maths related to the [Fourier transform](https://en.wikipedia.org/wiki/Fourier_transform) to work our way back towards what image would result in this wave pattern.

Aperture synthesis is the application of this to radio astronomy by using more than one baseline to get an actually good image (having just two stationary telescopes like in earlier discussion would result in a very “dirty” image). First you have to make sure the path difference from the light source to the different telescopes is accounted for (either digitally or physically by using extra cable length), and then you get as many baselines as you can. A baseline is essentially the number of pairs of telescopes that you could make out of the number of telescopes in the system, which can be given by the equation (1/2)N(N-1), so if you had 2 telescopes then you would have 1 baseline, 5 telescopes would have 10 baselines, 10 telescopes would be 45 baselines. If we spread these baselines out (either physically or by taking multiple observations as Earth rotates), then we can synthesis an aperture by combining all these baselines of observation.