Looking for video explaining how correlators work in aperture synthesis

[Gfamily]

I'd love to prepare a talk for my local astro society about how aperture synthesis works - in particular how the correlator works to bring signals together from separate radio telescopes and combines them to produce the 2d image. 

I have found this Youtube video of how the Murchison Widefield Array does it, but it has a 'black box' approach so doesn't explain what's going on.

Is anyone aware of any good explanations - preferably including animations to show the way that getting the correlation right allows the image to be produced? 

Realistically, I think this is probably a subject that's too involved for a non-technical audience, but it would be interesting to see if there is anything out there that would help to explain it. 

Anyone aware of anything? 

[vlaiv]

Best thing that I can think of would be to show them wave simulations, to first get them to understand why there is resolution limit depending on size of aperture.

Such simulations explain Airy disk pattern nicely.

Here is nice one that can be modified to show phenomena.

http://www.falstad.com/ripple/

Parabolic mirror and focus spot are indicated. Parabolic mirror was stretched to bring out focal point further. (just choose parabolic mirror 2 setup as base).

Same setup showing how tilted wave front produces focused spot away from optical axis:
(I changed wave source at the top - moved one point defining it down to tilt it a bit)

This one has lower frequency wave, and clearly shows that interference creates larger Airy disk spot:
(frequency control is to the right of display area)

Once they understand how image is formed in terms of wavefronts, reflection and interference at focal plane, then you can "split" the mirror into two parts to show that it works that way as well - maybe just add central obstruction to show the effect like this:
(I selected Add / Wall menu item and just defined it's position)

Next you have to explain that wave does not need to go in straight lines and you can use wave guides to bring waves to the same point - and they will interfere. Simulation also shows how wave guides operate and you can actually create some setup to simulate that. It is just explaining that interference depends on distance - when wave is split into two and both "parts" travel the same distance - they undergo constructive interference. If they are half a wavelength out of phase - they undergo destructive interference. All effects in telescopes are due to this - constructive interference at focal point (for perpendicular wave front, or away from mid point on focal plane for tilted wavefront) and consecutive Airy pattern rings.

Once you bring two waves (same wavefront) from two different telescopes and make sure they are aligned properly you can detect signal where it constructively interferes and not in places where it destructively interferes. Shifting the phase between two (or more) parts of wavefront "scans" left / right / up / down and creates 2d image - same as measuring at different places on focal plane, due to different distance traveled by wave parts, tilted waves will interfere differently.

Hope this both makes sense and also can be useful for you to capture video, or maybe even show the simulation in real time and explain things.

Btw, there are bunch of parameters that you can change in this simulation and play around to create different scenarios.

 

[Gfamily]

On my phone, so unable to 'play' now; but thanks, that looks good. 

[JRWASTRO]

Hi Gfamily,

I had a look at the video and what it shows is that those chaps are doing their processing in the frequency domain.

You may process a signal in what ever domain you choose.

Time domain is what we are all used to. We talk about the frequency domain (audio 20Hz - 20kHz) but most people are used to time domain processing.

The same signal may also be represented in the frequency domain by taking the FFT.  Now what the video shows is that the signal from each antenna is converted to the frequency by the discreet Fourier transform ( the algorithm is called the Fast Fourier Transform (FFT). The FFT is a transform (it has an inverse) Notice those guys multiplied the FFT's of the signals from the individual aerials OK. I do not think they just multiplied the signals what they would have have done is multiplied the signal (FFT) from one antenna by the complex conjugate of the signal from the other antenna this quantity (X(F) x X*(F) ) may be averaged and you are now looking at an animal called the power spectral density ... the auto PSD and Cross PSD .... you are looking at many correlators  in the frequency domain!!

Jeremy