tl;dr - Is splitting up the process of interferometry as shown in the diagram possible, and if so, is it more efficient and/or easier than traditional methods?

I have been doing some research into radio interferometry, and I had a question about it - I know that we can combine the signals from multiple telescopes into one "image" using interferometry, but what if I was able to do that multiple times?

Let me describe this a bit better. Say I have nine dishes. I arrange three of them in an equilateral triangle, and then I do the same with the other 6, and then, I arrange those three groups of three into a larger equilateral triangle. Then, I combine the signals from each three of the telescopes, and then I combine the three resulting signals. Here's a diagram that might help - the blue dishes are the "telescopes", and the red and green boxes are the "processors" or where the signals would be interfered.

enter image description here

In principle, would this work? And, in the context of radio astronomy, would it be easier to combine or interfere only three signals rather than nine?


In principle, would this work?

I can't say for sure that "no, in principle it could never work" but the combination in the layers loses information than it would almost certainly decrease image quality somewhat.

Is it more efficient and/or easier than traditional methods?

It depends what "more efficient" means. If the performance of your array is worse by a factor X but you saved a fraction of the money Y, is this a "more efficient" way to do science?

In an imaging optical telescope (or any imaging system including eyes) every pixel is illuminated simultaneously and directly by all areas of the aperture. From a given point in the distance a telescope will (try to) preserve the phase of all paths reaching the pixel so that the resulting intensity corresponds to the incoming power. This allows the system to obtain the best resolution.

Once you perform the interference and measure the resulting intensity, you lose the phase information forever (in conventional systems).

In the same way, in a radio telescope array usually all signals from all elements are combined together in a device called a "correlator" which in modern radio astronomy is a digital computer. Each pixel in the final image is calculated from correlations of every possible pair of elements in the array.

For example, from Alma Observatory's Correlator page:

The ALMA Main Array Correlator

To make images from millimetric wavelengths joined by multiple antennas, we need an absolutely colossal amount of computer power. Signals from each antenna pair – there are 1225 possible pairs alone in the main array of antennas (50)- should be mathematically compared billions of times per second. You would need millions of laptop computers to perform the number of operations that ALMA carries out every second! This need resulted in the construction of one of the fastest supercomputers in the world, the ALMA Correlator.

The Correlator, installed in the AOS Technical Building at an altitude of 5,000 meters above sea level, is the last component in the cosmic wavelength collection process. It is a very large data processing system, composed of four quadrants, each of which can process data from up to 504 antenna pairs. The complete Correlator has 2,912 printed circuits, 5,200 interface wires and over 20 million welding points. The Correlator is made up of Tunable Filter Bank (TFB) cards. The distribution requires four TFBs for data that arrives from a single antenna. These cards have been developed and optimized by the Bordeaux University in France.

Note that:

$$1225 = \frac{50 \times 49}{2}.$$

Again, once you perform correlation, you lose the phase information.

If you did that in each branch of your diagram, you would never be able to do the subsequent correlations properly because you'd lose phase information along the way, and could therefore no longer perform correlation of every possible pair.

There may still be some lossy algorithms that allow you to do some reduced amount of imaging the way that you propose, but the point of building such a large and expensive array would be to get the maximum amount of information.

So in reality the signal from each element is heterodyned with a local oscillator (How does ALMA produce stable, mutually coherent ~THz local oscillators for all of their dishes?) to a baseband of a few GHz, digitized (Why are the ALMA receivers' ADCs only 3-bits?) and then sent along a digital fiber optic cable to the main correlator computer building, with the original phase information from each dish still intact (albeit in digital form).

Important Caveat: However, in your diagram you could imagine that each of the green elements in the top layer is a "patch" of reflector on one dish, and the combination boxes in red (middle layer) is the collecting feed horn of one dish. So phase information from within the aperture of a single dish is indeed lost forever.

In that sense yes, it does work, and the resolution of an array is limited by the distances that separate the centers of each of the dishes, and not by the size of the dishes.

To help think more about that, see How do ASKAP's focal plane phased array feeds interact with the entire array phasing?

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  • $\begingroup$ Of the three currently linked question, only one has any answers posted, and for that one no answer has yet to be accepted. $\endgroup$ – uhoh Jan 1 at 22:24
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    $\begingroup$ @Calc-You-Later that sentence is not incorrect, but doing that would not let you generate a final radio image of the same quality (less=easier). It would be more efficient in terms of money alone if you build a cheaper system, but you will lose performance. If you need or want that lost performance, then it would not be more efficient because zero results divided by lots of money spent is zero efficiency. It's possible that you might be better off hurting your results by using fewer dishes than hurting your results by using localized pre-processing, at least that's my understanding. $\endgroup$ – uhoh Jan 2 at 0:05
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    $\begingroup$ @Calc-You-Later However, if your preprocessing boxes are local correlators and you pass along not only the raw data and its phase information, but also some of the local correlation results by increasing the bandwidth of the interconnects, that might work, but it's not any cheaper and may be more expensive. It would be basically moving some processors from the central correlators out towards the edges; you don't save anything and you introduce more complexity and more long-distance high-bandwidth connections. $\endgroup$ – uhoh Jan 2 at 0:07
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    $\begingroup$ This is all very helpful and makes sense - thank you for the responses! I'll take those factors into account $\endgroup$ – Calc-You-Later Jan 2 at 0:09
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    $\begingroup$ Ah, understood - I'll wait for other answers. $\endgroup$ – Calc-You-Later Jan 2 at 0:13

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