How do KAIRA and LOFAR work? — Part 11 : Ambiguities

As we’ve seen over the past few instalments of this series, as the direction in which the radio waves approach the telescope changes, the received signals will go out of phase. This effect reduces the sensitivity of the telescope in that particular direction. Additionally, by adding a delay to the electrical signals (whether the analogue electrical signals or the digitised version) the direction in which the telescope is sensitive can be moved.

But there is a problem.

As the incoming direction changes, the signals go out of phase, and thus cancel. However, if the direction continues to change, the signals can actually start to come back in phase again. The peak of one wavefront signal comes through one receiver and adds together with the peak of a different wavefront signal that has come through the other receiver. Click on the following image to get a full-sized version and you'll see what we mean.


At first appearance this might seem like a good thing, as the telescope seems to be sensitive to several directions at once. But it is not. Instead, this leads to an ambiguity. If a signal is received, it is impossible to tell whether that source of that signal is at the ‘on axis’ direction of the telescope, or is in a region off to one side.

These directions of sensitivity that are not in the intended pointing direction of the array are referred to as ‘sidelobes’.

However, there is a way to alleviate this. This is done by adding more receivers to the array. In our example, let’s consider adding a 3rd receiver between the original two. Now, even though there may be ambiguity on the signals received by the first two receivers, the middle receiver is out of phase with the others.

The addition of additional receiving elements helps reduce the sensitivity of some of the unintended directions. This effect is sometimes referred to as ‘suppressing the sidelobes’. If we were to sketch a graph showing an approximation of the sensitivity of the system to a particular direction as we look at angles to the left and right of the primary pointing direction, it would look something like this:
Adding more and more receivers improves this even further. As more receivers are added, it will have the effect of suppressing more of the sidelobes and thus reduce the ambiguity of the telescope.

Radio bands

Throughout this web log, there are lots of references to the radio bands: UHF, VHF, VLF, etc. For example, KAIRA will receive VHF frequencies, whereas some of the EISCAT radars operate at VHF, where others work at UHF frequencies. This chart is to put them all in perspective with respect to each other.

Abbreviation	Frequency Range	Wavelength Range	Name
ELF	3 to 30 Hz	10,000 to 100,000 km	Extremely low frequency
SLF	30 to 300 Hz	1000 to 10,000 km	Super low frequency
ULF	300 to 3000 Hz	100 to 1000 km	Ultra low frequency
VLF	3 to 30 kHz	10 to 100 km	Very low frequency
LF	30 to 300 kHz	1 to 10 km	Low frequency
MF	300 to 3000 kHz	100 to 1000 m	Medium frequency
HF	3 to 30 MHz	10 to 100 m	High frequency
VHF	30 to 300 MHz	1 to 10 m	Very high frequency
UHF	300 to 3000 MHz	10 to 100 cm	Ultra high frequency
SHF	3 to 30 GHz	1 to 10 cm	Super high frequency
EHF	30 to 300 GHz	1 to 10 mm	Extremely high frequency

The two arrays of KAIRA will operate in the high and low ends of the VHF band. The KAIRA HBA will work from 120-240MHz and the KAIRA LBA will operate from 30-80 MHz. As explained earlier, there is a gap between the two, as this is where FM-radio broadcasts occur, and it is impossible to conduct delicate scientific experiments in this region of the spectrum due to such broadcasts.

Ref: http://en.wikipedia.org/wiki/ITU_Radio_Bands

How do KAIRA and LOFAR work? — Part 4 : From radio waves to electrical signals

Now let’s imagine that we have a radio receiver that converts radio waves into electrical signals. If there is a certain strength of signal, then it generates a certain electrical output. To improve the sensitivity, we can amplify the electrical output. But that can only improve things so far. As the amplifier is turned up, it amplifies not only the signal, but also any noise in the system, which limits how much this can be done. So instead, we need to somehow increase the power of the incoming radio signal.

One way to do this is to collect more signal in the first place. Let’s say we have a radio receiver, which is picking up signals from space. To get more of that signal into the radio receiver, we could take a reflector (say a sheet of metal) and bounce some signal onto the receiver. Then, we could add a second reflector and bounce in some more signal; effectively doubling the amount of radio waves that are received.



(Don't forget you can click on images and diagrams to see enlarged versions!)

This is fine, but in order for this to work well, the signals should optimally be added in phase. Because Reflector 1 is closer to the receiver than Reflector 2, the waves it is reflecting arrive at the receiver first. Because the two signals do not arrive together, they are out of phase and reduce the final result.

To get them to add “in phase”, we must somehow delay the signal from Reflector 1. The easy way to do this is to put the reflector a bit further back. That way it takes longer to get the reflector in the first place, to compensate for the fact that it has less to travel from the reflector to the receiver.



If we label the radio signal paths for a single wavefront as a, b, c and d, then for the waves to add in phase the combined length a+b must be the same as c+d. (Yes, I know, this is starting to look dangerously like equations, which I promised to avoid!)



To be continued...

How do KAIRA and LOFAR work? — Part 3 : Start with the radio waves

Phased receiver arrays like KAIRA and LOFAR work by exploiting the physical effects of constructive and destructive interference. Before we consider how they do this, we need to go back a step and consider how radio observations are made. So to start, let’s think about a radio signal, which is represented as a wave. If you have two of these signals at the same frequency (or wavelength), you can add them together. If they are lined up, then they will add together and get stronger. However, if they are not quite lined up, then they don’t always add with each other, so the result is weaker. In fact, there is an alignment where they are doing the exact opposite of each other and thus cancel each other out.


(Don't forget your can click on the images to see enlarged versions!)

This alignment of two waves (or a single wave to a reference point) is called its phase. When waves line up they are said to be “in phase” and when they are exactly mis-aligned they are said to be “out of phase”. So let’s now think about how this principle applies to a signal coming from a distant astronomical source.

Two of the challenges of astronomy are that the incoming signals from space are very weak and that in order to “see” the object under study, the observation needs to be able to make out fine detail. In other words, the telescope needs to have high sensitivity and high resolution.

Because astronomical objects are so far away, the transmitted radio waves from a star or galaxy are effectively planar when they reach us — that is, the incoming wavefront is flat and – to all intents and purposes – the signal appears to be coming from the same absolute direction no matter where you are.

As the illustration shows, the further away from the source you get, the flatter the wavefront seems. And that's over a very small distance on a computer screen. Imagine if it was coming from a radio-source deep in space.

And in the next instalment, we’ll look at how we can use the in-phase and out-of-phase properties of the radio signals.