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.

How do KAIRA and LOFAR work? — Part 10 : Multi-beam operations

As we saw in the last web log entry in this series, digitising the signals gives some distinct benefits when it comes to adding a delay. Apart from being able to do it very precisely, you can change it quickly. However, digital data has another massive advantage.

It can be easily copied.

So, if you make a copy of your digital data, you can process each copy however you want. If you want to filter it differently (for example, to ‘listen’ at a different frequency) you can. However, you can also make a copy and apply different sets of delays to it. This means that if one copy of the data has one set of delays and another copy has a different set for the different antennas involved, then these two copies will be sensitive to different directions.

In other words the telescope will be looking in two different directions at once!

This technique of introducing delays and combining the signals to change the direction in which the telescope is sensitive is known as ‘beamforming’. And making digital copies and delaying them differently to sensitive in several directions is called ‘multiple beamforming’ (or sometimes ‘forming multiple beams’).


In the above diagram (which you can click to see a larger version), each received signal is digitised and split into two copies. The copies are fed into the different digital delay units (D1, D2, D3 & D4). Let’s say that D1 and D3 have no delay at all. The added signal from these will be sensitive to something from directly overhead. In this case, the original radio signal was coming in obliquely; it adds out-of-phase and no output is seen. On the other hand, by adding a delay to D2 (but not D4), the added signal from these will be sensitive to the oblique radio wave. It adds in phase and a strong output is seen.

Because the data is digital, you can copy and delay it as much as you want and there is no degradation of the signal. If you want to be sensitive in more directions, simply add more copies, delay units and adders. The limits are not related to the signal, but rather to issues of equipment, memory, power, space (... and ultimately the project budget).

In practice, systems like KAIRA and LOFAR are also limited by the amount of digital signal processing equipment. At the time of writing this, LOFAR is routinely operating with up to 30 or so different beams. However, some experimental observations have been carried out with over 250 beams.

How do KAIRA and LOFAR work? — Part 9 : Digital beam steering

As we saw in the last web log post on how it all works, we can adjust the cable length and thus the delay in the electrical signal to determine which directions will add in-phase (and thus be stronger) and which will add out-of-phase (and hence cancel each other out).

Although this is sometimes done by adding more cable, it doesn’t have to be. The only thing that is important is that there is the correct delay.

So, instead of using cable, we can digitise the signal and then save the data, wait a little while, and only then load them back again to feed into the adding electronics.If you are constantly taking digital data and storing them, then it is exactly the same as writing numbers into sequential memory. And if you are reading them back out at a fixed delay, then it is the effectively same thing: reading numbers from sequential memory.

As long as those data are always being written into the memory at a nice fixed rate, and are being read back out again at the same rate, all you need to do is adjust the offset between the write position and the read position and you are controlling the delay.

The limitations are that the accuracy at which you represent the incoming wave is a function of the speed at which it is being sampled. Fast memory and fast sampling requires some sophisticated electronics. There is also a limitation that the total amount of delay you can add is a function of the speed at which you are writing/reading and the total amount of memory you have.

However, with modern digital electronics, this sort of memory is relatively cheap. Additionally, changing that write-read offset (and thus the delay) can be done very quickly. As a result, you can change the signal delays, and hence the pointing direction of the entire array very quickly. To go from one side of the sky to the other takes something in the order of a millisecond.

Try doing that with a 100m radio dish!

Alternatively, you can gradually adjust the delay and move the sensitivity of the array quite slowly. This is ideal for tracking celestial sources as they appear to move slowly across the sky due to the Earth’s rotation.

However, despite the power of digital signal processing on changing the directional sensitivity of the phased array, there is another benefit as well. Stay tuned!

How do KAIRA and LOFAR work? — Part 8 : Steering a phased array

Last time, we saw that a couple of detectors can be used to collect signals and that because they will add in phase from some directions and not others, there is a certain directionality to the system.

In principle, you can ‘steer’ this system to look in different directions by tipping it, but that’s not particularly efficient. The real advantage is that without moving the antennas you can change the directionality of the overall system by changing the lengths of the cables.

Let’s consider the off-zenith case from the last part.

If we now add a bit of extra cable, these off-zenith signals now add in-phase again.

In fact, the zenith signals are the ones now out of phase when they are combined electrically. So, by adding some cable length, you can control the direction in which the array is sensitive. That is, you can steer its ‘looking direction’ around the sky without actually moving the antennas themselves.

Some phased arrays indeed use cables to adjust their pointing direction. The VHF radar in Tromsø is one such system. It is mechanically steered in the vertical direction and horizontally pointed with a phased array. By manually changing the cables, the horizontal pointing direction of the array can be altered by 15 degrees.

A view inside the feeder bridge of the VHF system
at Tromsø. (Photo courtesy Mike Rietveld)

Because this needs to be done by hand, it is not patch the cables that quickly, so these sorts of directional changes are not done too often.

Although still useful (rotating a 120×40m antenna in azimuth is tricky!) there is another technique which has recently become affordable and which makes arrays like KAIRA, LOFAR and the SKA practical.

How do KAIRA and LOFAR work? — Part 7 : Phased arrays

Finally, we're onto the phased arrays!

The phased array concept is central to the LOFAR project. Phased arrays were developed by the German physicist Karl Ferdinand Braun in 1905. During the Second World War, they were used for radars, first by the Luftwaffe and then later by the US Air Force. After the war, they were introduced into radio astronomy, in particular by Sir Martin Ryle’s group at Cambridge. These days their use is quite common and they can be found in many radio applications.

Like a regular dish, they also rely on adding signals together. But the technique is different.

In a phased array, there is not just one detector, but several. Each can receive radio waves from all directions (well, if not all, then at least a very wide range of them).

Unlike the reflecting dish, which uses the physical travel of the incoming radio waves to get them to arrive in phase when they come from a certain direction, phased arrays don’t care when the signal gets to the detector.

They delay the electrical signal, instead.

The simplest way to do this is simply by adjusting the cable length. If you consider a two-element phased array, with identical cables, then you can see that a signal coming in from overhead will be detected at the same time, travel the same distance and thus add in phase, resulting in a strong signal.



At a certain angle away from directly overhead, the arrival times will vary by half a wavelength, so the electrical signals are completely out-of-phase when they add, and thus cancel each other out.



So this simple array is sensitive to signals coming from the zenith, but not to those coming from slightly off-zenith. In other words, this phased array has sensitivity in a particular direction.

Doesn’t seem particularly useful so far, but there’s a neat trick you can then do. And we’ll reveal what it is in the next episode!

How do KAIRA and LOFAR work? — Part 6 : Squinted vision

But what if the radio signal is not coming in from directly overhead? Well, as that signal goes away from the vertical position, the result will decrease. Not only will the reflected signals miss the receiver, but they will be adding out of phase as well.

At some angles, the radio waves from different parts of the system interfere. This can result in zero signal at certain angles where the radio waves from the different parts arrive out of phase, and enhanced signal at other angles where the radio waves arrive in phase.

So if you have a set of reflectors that are carefully adjusted to give good signal addition in a particular incoming direction, and then your radio signal moves, you have to tilt the entire set of reflectors and the receiver to follow it. That is, you change the direction in which your system is most sensitive. This is the reason why radio dishes are usually made so that they can be steered.

But this presents problems: as the size of the system gets bigger, you need more and more steel for the backing structure, bigger and bigger motors and better and better controllers to cope with structural deformations at different angles, wind loading and so on.

The elevation motors on the Kiruna 32m antenna.

An azimuth motor drive and gearbox
(grey+red) on the Kiruna 32m antenna.

As a result there is a limit as to how far you can go. Thus the largest fully-steerable dishes are typically 100 metres in diameter, such as the Effelsberg Radio Telescope in Germany.

The Effelsberg 100m radio telescope, Germany

This sort of size is about the limit at which structural and cost considerations make further enlargement prohibitive. Let’s face it, a large moving steel structure is complicated, difficult to maintain and very expensive to build. But there is an alternative...

(For those of you who are patient enough to have followed this so far, we’ve now covered all the pre-amble and can get on with the interesting phased array topic later this week!)

Photographs: Derek McKay-Bukowski

How do KAIRA and LOFAR work? — Part 5 : The parabolic dish

As we saw in the last instalment, adding a reflector increases the received radio signal. And, we can continue to add more reflectors, each at the correct position and angle, to continue increasing the power of the combined radio wave.
If you do this enough, and imagine it in three dimensions, rather than two, you should understand the basic principle behind the traditional radio dish.


And, finally, for those trying to guess the faded dish photograph behind the last diagram here is view of the same structure, but from a slightly different angle.

This is the 25m dish at the Chilbolton Observatory in Hampshire, England. Next week, we’ll be considering directional sensitivity and starting to get down to the gritty detail of phased arrays!

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.

How do KAIRA and LOFAR work? — Part 2 : What is a LOFAR system?

Before we get started on the explanation, let’s take a moment to quickly describe ASTRON's LOFAR project on which KAIRA is based. The LOFAR (LOw Frequency ARray) radio telescope is a distributed system; namely, it is not all located at a single site. Instead, it is split into dozens of separate locations called “stations”. Most of these stations are in the north of the Netherlands, but there are also a few scattered further afield in Germany, France, Sweden and the United Kingdom. (KAIRA is effectively a single LOFAR station, but with some interesting features and a few special extras.)

Typically, each station has two fields containing arrays of antennas. These are referred to as the Low-Band Array (LBA) and High-Band Array (HBA). The “low” and “high” refer to the radio frequencies that these arrays are designed to receive. The LBA is optimised for the frequency range 30–80 MHz and the HBA for 120–240 MHz. The gap between the two bands is where FM radio is broadcast. It is pointless trying to listen to faint radio signals from the depths of space, when these powerful radio transmitters are nearby. Thus, LOFAR ignores this part of the radio spectrum. And, rather than designing one type of array which straddles this gap, it has been split into the two arrays, with the LBA and HBA being specifically tuned to the respective parts of the radio spectrum.

Aerials of a LOFAR Low Band Array.

Tile antennas of a LOFAR High-Band Array

Apart from the different antenna designs, the arrays are also arranged slightly differently. The LBA is made up of a scattering of spindly aerials that look like wire pyramids. The HBA comprises large flat black-plastic tiles packed sided by side. There are some good reasons for these differences, but ultimately each of them is a phased array receiving radio waves from space.

And we’ll continue with that tomorrow!

Photos: Derek McKay-Bukowski, STFC

How do KAIRA and LOFAR work? — Part 1 : Introduction

KAIRA (Kilpisjärvi Atmospheric Imaging Receiver Array) is a radio receiver system. It can measure very faint radio signals and determine very precisely which directions those signals are coming from. It uses LOFAR antennas and signal processing to accomplish this. If you ignore the details of how the data are processed and interpreted, you can safely say that antennas of LOFAR and KAIRA are doing the same sort of thing.

LOFAR (LOw Frequency ARray) is a radio telescope, designed by the Netherlands Institute for Radio Astronomy — ASTRON. Unlike the so-called traditional radio telescopes, which use large parabolic dishes, LOFAR has fields of antennas, which do not move. Instead, it uses electronics and computing to change which way the telescope is looking in the sky. With no moving parts, one is often asked how it works. The problem is that the answers often come in two extremes.

The first is that there is some glib statement that simply reiterates how the 'signals from all the antennas are combined to emulate a large telescope and that the telescope uses digital technology to change the direction that it points in the sky'.

The second is a full-blown lecture course that starts 'Consider electromagnetic radiation from direction s from a small elemental solid angle dΩ, at frequency υ, within a frequency width dυ'. From there it quickly degenerates into page after page of equations.

For the next few weeks we’ll be posting a series of articles to the KAIRA web log in addition to our regular photographs and reports. These articles will steer the middle ground between the two extremes. Of course the entire topic can be extremely complex, and there are many complications and assumptions that we’ll have to skip over to avoid getting bogged down in the detail. (For the experts out there, please indulge us these simplifications.) And yet, we intend to go into sufficient detail, step-by-step and without mathematics, to explain with words and illustrations how KAIRA and LOFAR will accomplish their amazing observations.