# Arecibo: Advantages of Giant Dish?

I'm sure all of you have heard about the recent events at the Arecibo observatory, and the controversial decision to close the facility. I've also heard that Arecibo is the second largest single aperture radio observatory in the world (outside of FAST in China).

However, I've also heard that it's possible to array dishes in order to achieve much better performance than from a single dish, as in facilities like the Very Large Array and the proposed Square Kilometer Array. To me, this seems like a rather desirable solution, as it would be easier to build and to point than a single giant telescope.

My question is, what are the drawbacks of doing this compared to having a true giant dish like Arecibo?

PS: I know that Arecibo can also do radar astronomy. But I guess my question extends to that as well. Could an array of radio telescopes be modified to do similar astronomy, and would this be better/worse than with a single dish?

• Better fit for astronomy stack exchange? astronomy.stackexchange.com – Organic Marble Nov 21 '20 at 21:27
• I've posted an answer that explains why this is not off-topic here. I don't know where this is best asked or better answered, but it probably shouldn't be insta-closed here. – uhoh Nov 22 '20 at 0:20
• @uhoh there is a severe lack of close votes on this question atm. Insta- or otherwise! – Organic Marble Nov 22 '20 at 0:25
• @OrganicMarble comments are written to be read in the future rather than the past, and to be read by anybody and everybody stopping by, I've seen severl "it has some astronomy in it so can't be on-topic here" close-vote cascades ne avalanches in the past, and there are several meta questions documenting these. So this is meant to be preemptive and preventative rather than responsive. – uhoh Nov 22 '20 at 0:29
• @uhoh wait till I fire up my Time Machine. – Organic Marble Nov 22 '20 at 1:00

## 3 Answers

Radar Astronomy of solar system objects is actively pursued using FAST, Goldstone 70 m dish, Greenbank and until now Arecibo (some in receive mode only) in order to explore asteroids as they pass near Earth and hopefully don't hit us. They've even been used to find a dead spacecraft in orbit round the moon via passive radar reflection!

So this is on-topic here, as well as in Astronomy SE.

I'm no expert but I'll add some thoughts and will welcome counterargumens.

### Receive signal to noise ratio

One large dish has one front-end receiver at temperature $$T$$ that generates 1 $$k_B T \Delta f$$ of noise equivalent power or NEP. If instead there were 100 dishes of 0.1 big-dish-diameter each, the received power would be the same but the NEP would be either 10 or 100 times larger. I think it's 10 times larger only, because we need to add amplitudes first then square for coherent interferometry, but I could be wrong.

Multiple dishes allow for a much tighter beam (receive or transmit) so it may offset NEP in some cases.

### Gain

Keeping the total areas equal, the one big dish and the 100 dishes of 0.1 big-dish-diameter will have the same receive gain for a given frequency, assuming they have simple receive horns optimized for a diffraction-limited response for the dish they're on. When there are feed horn arrays it gets more complicated1.

The total power received from a given direction to which an array is pointed and phased accordingly is basically the total area of all dishes, assuming they're all steerable as most arrays are.

However for a single fixed dish there are two problems.

1. obliquity or cosine theta, since rays coming in at an angle see a reduced cross section, which of course goes to zero at 90 degrees.
2. reduced aperture in order to cover more sky in order to reduce aberrations (e.g. spherical!) The "S" in FAST is for spherical. "Although the reflector diameter is 500 metres (1,600 ft), only a circle of 300 m diameter is used (held in the correct parabolic shape and "illuminated" by the receiver) at any one time"

### Resolution and beam structure

Interestingly, things are a little different for transmit, and this one of several reasons why deep space ground stations build truly giant single dishes on truly giant steerable platforms instead of lots of smaller dishes properly phased.

While a hard aperture dish will have a roughly Airy disk beam pattern. For the amplitude as a function of angle:

$$E(\theta) = E_0 \frac{2 J_1(k a \sin(\theta))}{k a \sin(\theta)}$$

note: I need to take a break for a bit, will finish this as soon as I can have coffee, breakfast, and then normalize this correctly.

Presumably we can have a (properly phased) radio transmitter with the same power in one big dish or 100 smaller dishes, since for a ground station on the ground there is plenty of power.

However, a sparse array of transmitting dishes will always generate a complex radiation pattern. In addition to the broad envelope produced by the $$\lambda/D_{dish}$$ of each dish, the much higher resolution of the total array $$\lambda/D_{array}$$ will really be a complex pattern of tiny spots. If we look at ALMA or even precursors like Meerkat, we see that they try to "mix it up" with a sort of random spiral pattern, rather than a regular array. Why? Because this partially alleviates the problem of the complex fine structure in the beam pattern.

This issue may not be as important for transmitting to a spacecraft in deep space, but it was very important when targeting a dead spacecraft near the Moon (an obviously much larger reflector, though of a different doppler shift).

A single big dish and its cleaner spatial beam pattern is also important for imaging planets using radar. Using delay-doppler one can image a rotating planet's surface even if it is unresolved by the dish, because each latitude will execute a different doppler profile as it first moves towards us then away from us. However, there's no way using Doppler to differentiate the two hemispheres because for axial tilts near perpendicular it's only the absolute value of latitude that matters. Astronomers use the beam pattern of a single large dish to alternate between preferential illumination of one hemisphere, then the other to generate hemisphere contrast, then do a lot of computing.

With the messy fine structure of an array, this might be easier or might be much harder, depending on the size and distance of the object and the specifics of the array.

For further reading on issues of signals, see answers to:

1 Some dishes, and sometimes even arrays of dishes are equipped with focal plane arrays of feed horns that can themselves participate in interferometric imaging:

• Two questions: (a) Isn't "receive-only radar astronomy" a contradiction in terms? Or do some projects rely on a single transmitter and multiple receivers? (b) Didn't FAST have precision issues... have these been resolved? – Mark Morgan Lloyd Nov 22 '20 at 13:15
• @MarkMorganLloyd Good questions! (a) the first question linked under the first paragraph is an example of one dish transmitting and the other receiving; I think Green Bank has no transmitter at all. Why was the 100m Green Bank dish needed together with DSN's 70m Goldstone dish to detect Chandrayaan-1 in lunar orbit? – uhoh Dec 1 '20 at 22:28
• @MarkMorganLloyd (b) That is an excellent question and I don't know the answer, so I think you should go ahead and post it as a new question. It's a pretty challenging project with all those independently moveable sections so I wouldn't be surprised if there were some startup hiccups and in-the-field design upgrades. Actually "Has anything like this been tried before?" is also an interesting question worth asking! – uhoh Dec 1 '20 at 22:30
• @MarkMorganLloyd at least FAST doesn't look like this! – uhoh Dec 2 '20 at 0:52
• Thanks very much for that, you've just saved me some effort. Reports of the collapse elsewhere appeared to be based on a photo published on Twitter which looked very much as though it had been edited: before-and-after photos from the same location but with the towers truncated and the cables completely vanished t.co/jWuAwtUc1s – Mark Morgan Lloyd Dec 2 '20 at 8:49

It's not a one-size-fits-all situation:

1. Resolving power. This is based on the diameter of the collector and greatly favors a multiple dish approach as the distance between the dishes counts--two dishes on opposite sides of the planet have the same resolving power as one dish the size of the planet.

2. Signal gathering power. This is based on the surface area of the collector and was Arecibo's real strength. To match Arecibo's ability to see faint signals would require a lot of lesser dishes.

Note that the multiple-dish approach adds an awful lot of headaches compared to the single-dish route. I don't remember the accuracy required but it's a small fraction of the signal frequency. This is needed both spatially (knowing exactly where the equipment is) and temporally. This is why it's normally only done in the radio band--while in theory you could do the same thing with optical telescopes I've only heard of it being done when the mirrors are all part of one structure.

Sensitivity: in an ideal world, you need to increase the number of nodes in an array by 2 orders of magnitude to increase sensitivity by 1 order of magnitude. Absolute best case, you need 100 dishes to equal the sensitivity of a dish with 10 times the diameter. The real world isn't ideal, so actual performance will be less than this.

Interference: sparse arrays can't fully distinguish radiation coming from different points in their field of view. A bright source in a side lobe can interfere with observations in the area of interest.

Cost: the more nodes in your array, the more more components to maintain and upgrade. A separate receiver and amplifier for each dish, mechanisms to aim the dish, power and signal runs for each node, etc. The equipment to process all the signals and make the array function as a single instrument is also not cheap. You can reduce costs by using a very sparse array, but that has tradeoffs as described above.

Transmitting through a distributed array is actually much more difficult. You can record the received waveform and work out the relative phase, any skew in the timebases, etc while crunching the numbers later. When transmitting, the actual transmissions from each node have to be precisely synchronized with the others in real time, to within a fraction of a wave period of the signal being transmitted. And of course the amount of power you must handle is much higher...approaches suitable for small signals won't scale to kilowatts to megawatts of transmit power.

Also, much of the power transmitted through a sparse array will go into side lobes. If you move the modes apart to increase the array's resolution and make the main beam narrower, it doesn't make the beam any brighter, it just redirects more transmit power into side lobes. The main benefit of arrays, of being able to spread the nodes out and use a very sparse array to improve resolution, largely doesn't apply to transmission.