2.4.1 A Brief History of Mills Cross Type Antenna Arrays
B. Y. Mills initially used three aerials connected together as Michelson-type interferometers [TMGWS86] at a frequency of 101MHz to examine the galactic distribution of discrete radio sources [Mil52]. Reasonable, albeit less than originally anticipated, accuracy was achieved, with an average probable error in position of around 0.2% for strong sources and 2% for weak sources.
What is now known as Mills Cross antenna is first described in [ML53]. Mills’s goal was to construct an aerial system of high resolution but small area and low cost for investigations in radio astronomy. Mills explicitly mentions that this kind of aerial system sacrifices gain (i.e. effective area) for high resolution and low cost. This was more than acceptable because Mills’s goal was to accurately map the positions of strong radio sources.
operating at 97MHz.
Having obtained encouraging results from this first system, Mills built a 250×2+250×2 element Mills Cross type radio telescope for use at 3.5m (86MHz) [MLSS58]. Other telescopes were developed at the same time, see for example [Sha58]. Christiansen and Mathewson used a Mills Cross antenna array to scan the solar disk at a wavelength of 21cm with unprecedented detail [CM58]. The interesting thing about this particular Mills Cross antenna is the fact that Christiansen did not care about sidelobes. He designed the array in such a way that the spacing between two adjacent lobes was large enough so that no two antenna lobes could fall on the sun at the same time. Note that Christiansen only used one pencil beam at any given time. He made successive scans of the sun during the course of several days to derive the brightness distribution across the whole solar disc. He also employed phase shifters in one of the two arms of his Mills Cross antenna array to steer the fan beam generated by this arm, therefore also changing the position of the resulting pencil beam.
2.4.2 Working Principle of a Mills Cross Antenna Array The working principle of a Mills Cross antenna array is as follows.
2.4.2.1 Fan Beams
Initially, each arm of the cross is considered as a separate linear additive phased array (see section 2.3.1). Figure 2.9, panel (b) shows the idealised outline of the radiation patterns of the individual arms for the zenithal case. Each arm forms what is called a fan beam. The pointing direction of this fan beam can be influenced by appropriate phasing techniques such as the ones described in section 2.3.3. For example, if we have an arm of 32 antennas positioned half a wavelength apart from each other, and those antennas are connected to a 32 port Butler Matrix, we get 32 fan beams like the ones depicted in figure 2.3.
It is important to understand that, at this stage, the two arms of the Mills Cross are completely separate. Each arm forms fan beams of its own. If viewed from above and slightly idealised, these fan beams will be perpendicular to each other, just as the linear phased antenna arrays that were used to create them. (This is a simplified view for explanatory purposes. The fan beams are in fact cone-shaped, as can be seen in many of the 3D radiation pattern plots to follow in this and later chapters.)
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By themselves, the recordings from these fan beams are still rather useless. They cover a large solid angle, the spatial resolution (at least in one direction) is still very poor, in fact it equals the ‘resolution’ of a single antenna element. The direction of any signal recorded by such a fan beam can only be estimated in one direction, and only if no other interfering noise sources are present at the same time.
2.4.2.2 Cross-correlation, Pencil Beams
The idea that turns the Mills Cross antenna array into a high resolution array is based on cross- correlation of the signals from two perpendicular fan beams. This will extract only the signals that originate from the overlapping region of the two fan beams. A narrow pencil beam is therefore being formed for each combination of a fan beam from one arm with a fan beam from the other arm of the Mills Cross.
In case of a 32+32 antenna element Mills Cross array with a 32 port Butler Matrix for each arm, 32×32=1024 pencil beams are therefore being formed, though not all of them are physically meaningful, and even fewer perform well enough in terms of noise level and sidelobe behaviour to be suitable for further use. These issues will be discussed in more detail in subsequent chapters, primarily for one particular system, the Advanced Rio-Imaging Experiment in Scandinavia (ARIES).
Figure 2.10 is a 3D representation of the beamforming process. The two small panels on the left show an example of a fan beam formed by a linear array of antennas along the y-axis (top panel) and along the x-axis (bottom panel), respectively. The small inset in the upper right hand corner of each panel shows an idealised top-down view of several fan beams generated by the arm in question, with the shown fan beam highlighted.
The big panel on the right-hand side depicts the cross-correlation process. Two perpendicular fan beams (shaded) are cross-correlated to produce a narrow pencil beam (solid) pointing in the direction where the two fan beams intersect. Again, the diagram in the upper right-hand corner shows an idealised 2D version of this process as viewed from above. Signals from the two green fan beams are cross-correlated to derive the signal that is common to both fan beams and must therefore originate from the intersecting area, depicted by a red circle.
Figure 2.9: Original Mills Cross, taken from [ML53]. (a) Plan view of dipoles in cross arrange- ment. (b) Idealised response of the cross arrangement, plan view.
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2.4.3 Disadvantages of a Mills Cross
The following sections list well-known disadvantages of a Mills Cross antenna array when com- pared to a filled array. Note that these points don’t make a Mills Cross inferior to a filled array antenna, since superiority/inferiority always depends on the intended use of a system. Later on in this thesis we will investigate how these issues can be dealt with, and we will find that the Mills Cross still offers advantages over a filled array for use in riometry, mainly due to the by far smaller number of antenna elements required, translating into significant savings in terms of money and real estate.
2.4.3.1 High Sidelobe Levels
This section explains why the Mills Cross antenna array produces higher sidelobes than a cor- responding filled array for the untapered case. The Mills Cross forms the output signal of each pencil beam by cross-correlating the signals from two perpendicular fan beams generated by the two arms of the cross. The arms themselves are simple linear phased arrays and therefore produce a sidelobe level of around−13dB (in the untapered case).
Suppose, the received time series from the two perpendicular fan beams are called jt andkt,
respectively. Each signal has sidelobes, a source signal from the direction of the first sidelobe is therefore attenuated by−13dB in power. The signal itself, however, is therefore only attenuated by√−13dB.
The worst case happens when a source signalxtis received in the main lobe of one fan beam
and in the first sidelobe of the perpendicular fan beam. In this case the cross-correlation between the two signals will only result in a power attenuation of –6.5dB:
pt = hjt·kti (2.9)
pt = hxt·(
√
−13dB·xt)i (2.10)
pt = −6.5dB· hxtxti (2.11)
Of course, the well-established technique of tapering (see section 2.3.5) can be employed to reduce sidelobes. We will touch on sidelobe issues for the Mills Cross again in more detail in chapters 4, 9 and 10.
Christiansen [CM58] mentions that he employed different receiver bandwidths depending on the position of the observed source. He used a bandwidth of ‘several MHz’ for observations near the zenith. For observations far from the zenith (in his case the sun in midwinter), he reduced the bandwidth down to 0.3MHz. He notes that this had the effect of increasing the amplitude of noise fluctuations. Quote: “The narrowing of the bandwidth for directions away from the normal to the plane of the array is made necessary by the difference of the path length from the source to the different parts of the array. This difference in path length corresponds to a difference in phase which is not exactly the same at all frequencies in the pass band of the receiver. Hence for a given direction of the source, the bandwidth of the receiver must be kept sufficiently narrow so that phase differences over the pass band are not large enough to cause a significant deterioration in the performance of the array.”
This effect has a limiting influence on the maximum usable bandwidth although first exper- iments show this to not be a significant issue for ARIES (with a nominal bandwidth of 1MHz), therefore this effect will not be discussed further in this thesis.