Producing MeerKAT Images with an Unlikely Algorithm
An age-old complex mathematical problem solved by an unlikely algorithm is part of the secret behind the success of the MeerKAT First Light image. The algorithm has provided the calibration solutions necessary to produce artefact-free images from the MeerKAT radio telescope, of which the first was issued recently.
The MeerKAT First Light image of the sky, which was released in July 2016 by the Minister of Science and Technology, Naledi Pandor, shows unambiguously that MeerKAT is already the best radio telescope of its kind in the Southern Hemisphere. Array Release 1 (AR1), providing 16 of an eventual 64 dishes integrated into a working telescope array, is the first significant scientific milestone achieved by MeerKAT, the radio telescope under construction in the Karoo. MeerKAT will eventually be integrated into the Square Kilometre Array (SKA).
“MeerKAT has produced a deep, artefact-free image straight off the bat – an image completely free of distortions normally seen in deep, wide-band, wide-field images. These distortions can only be removed by a special algorithm,” says Professor Oleg Smirnov, who holds the SKA SA Research Chair in Radio Astronomy Techniques and Technologies at Rhodes University, and heads the Radio Astronomy Research Group (RARG) at SKA SA.
“What we have done here is equivalent to adaptative optics used on modern optical telescopes to compensate for the deformation of the incoming wavefront by the atmosphere, except that we are doing it with mathematics and computers rather than mirrors and pistons,” says the father of the algorithm, Dr Cyril Tasse of Observatoire de Paris, who has spent two years with the RARG team before returning to France.
Smirnov explains that this would not have been possible without a collaboration between his research group and French colleagues. It took the team several years to come up with a solution to this mathematical problem. Some very innovative ideas came from Tasse while studying a calibration algorithm called StefCal.
While still a Postdoc fellow in France, he found that he could generalise StefCal’s approach to the difficult direction-dependent problem that needed to be cracked to use modern radio interferometers. He continued this work in South Africa, but the convergence of the algorithm remained a mystery. The mathematical breakthrough came when he understood that using an alternative definition of complex differentiation, was opening the gate to cracking the problem thousands or millions of times faster.
Another member of the RARG team, Dr Trienko Grobler, pointed out that this form of calculus was originally proposed by Wilhelm Wirtinger as far back as 1927. Thanks to important insights from Smirnov, the connections to the mysterious StefCal could be fully made, and suddenly a whole new family of algorithms was unveiled.
“We now have a fruitful algorithmic collaboration between SKA SA, Rhodes University and the Observatoire de Paris/ Nancay.” A highlight of this is that quite a few young South Africans have become valuable contributors to the project,” says Smirnov. These include Benjamin Hugo, Landman Bester and Simon Perkins (all SKA SA), who are rapidly turning into experts in these techniques.
The algorithm revolves around solving for direction-dependent effects. One of the most important direction-dependent effects is the primary beam, or sensitivity pattern of the antenna, which becomes important in the calibration of wide-band data, and subsequent wide-field imaging. Dealing with the primary beam is one of the aims of “third generation calibration”, or 3GC. “Thanks to this new 3GC algorithm,” says Smirnov, “we can now produce corrected images, taking primary beam effects into account.”
The reason why the artefacts appear in the first place is due to variability in the sensitivity pattern. While it may be constant from the telescope’s point of view, as the sky rotates relative to the telescope during the observation, celestial sources “see” a variable pattern, which causes distortions in the final images. Furthermore, the pattern is subtly different for every telescope of the array.
“The algorithm is so far the first and only algorithm that can take an arbitrary primary beam pattern, and produce a corrected image. This means that the algorithm can be applied to any radio telescope. So far it has also been successful with the Dutch LOFAR array, which is an SKA pathfinder, as well as with the US Jansky Very Large Array. Sphesihle Makhathini (SKA SA) has recently used it to produce a new world record image using data from the JVLA.
“Because it is so flexible, we could immediately apply it to MeerKAT,” says Tasse. “With producing images of this calibre, the numerical aspect is just as important. We have solved a mathematical problem which has now opened new possibilities, and we can produce images from data much faster. Mathematical problems that were impossible to solve before are now solvable. This is undoubtedly one of the keys that’s needed to do transformational science with modern giant radio telescopes,” says Tasse.
Smirnov and Tasse, together with the South African team (Hugo, Bester, Perkins and Makhathini), and Julien Girard (Université Paris VII, also formerly of SKA SA) have recently conducted a workshop in Ushant, France, to make rapid progress on the project. “With the full MeerKAT array soon coming online, we want to have the tools in place to make sure that artefact-free images like this are produced routinely,” says Smirnov.
Update on MeerKAT
- The integration of 32 MeerKAT antennas with single polarisation correlator was achieved in the last week of March and on target – meeting another significant milestone in the construction process.
- As of close of business on 31 March 2017, 54 pedestal/yoke assemblies have been installed and 43 dishes have been lifted at the Losberg site in the Karoo. 34 antennas have passed acceptance testing and has been handed over to SKA SA for the fitment of receivers and system level testing.