Would "layered" radio interferometry work?

Question

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.

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?

Answer 1

Absolutely this can work as can be seen in The Murchison Widefield Array or MWA in Western Australia. This is essentially exactly how it works. You definitely do loose information (the first stage of combining antennas significantly reduces the field of view, and the number of interferometric baselines you get is reduced).

From this page:

Frequency Range            70-300 MHz
Number of Receptors        2048 dual-polarization dipoles
Number of antenna tiles    128
Number of baselines        8128

There are 32 receptors per tile (2 polarizations for $4x4=16$ elements), and $N = 128$ tiles. The number of baselines is $N(N-1)/2 = 8128$.

The advantages is a reduction in the data rates, so reduced digital processing. Note the first stage would be treated as beam forming - you cannot do interferometry between the first stage and somehow do interferometry between the results. Ie the first stage is summing the voltages (with appropriate phase corrections) and the second stage would be interferometry.

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One of the tiles making up the 32T, a prototype instrument for the Murchison Widefield Array (source)

An MWA antenna consists of a four by four regular grid of dual-polarisation dipole elements arranged on a 4m x 4m steel mesh ground plane. Each antenna (with its 16 dipoles) is known as a "tile". Signals from each dipole pass through a low noise amplifier (LNA) and are combined in an analogue beamformer to produce tile beams on the sky. Beamformers sit next to the tiles in the field. The radio frequency (RF) signals from the tile-beams are transmitted to a receiver, each receiver being able to process the signals from a group of eight tiles. Receivers therefore sit in the field, close to groups of eight tiles; cables between receivers and beamformers carry data, power and control signals. Power for the receivers is provided from a central generator.

Answer 2

update: See @Chris' cool answer about MWA for something thad does work!

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In principle, would this work?

I can't say "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?

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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).

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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?