The 27 antennas of the Very Large Array (VLA) in New Mexico observe the
sky simultaneously, forming a single virtual telescope with a gigantic
diameter. Credit: NRAO/AUI/NSF
Schematic illustration of an interferometer: A larger distance of two
sources in the sky leads to an increased difference in travel time
(marked red) as does a larger distance between antennae. Antennae placed
at larger distances are therefore able to resolve smaller structures,
while antennas placed closely together are more sensitive to larger
structures.© MPA
Central region of a typical radio interferometric coverage. The colours
of the individual data points indicate the observed strength of spatial
fluctuations of the flux density. © MPA
Radio telescopes observe the sky in a very indirect fashion. Sky images
in the radio frequency range therefore have to be computed using
sophisticated algorithms. Scientists at the MPI for Astrophysics have
developed a series of improvements for these algorithms, which help to
improve the telescopes' resolution considerably.
Optical telescopes produce data, which are a direct representation of
the observed object's brightness distribution, i.e. an image in the
conventional sense, which can be used for further analysis without
additional processing. In radio interferometry (i.e. the high-resolution
observation of the sky at radio frequencies), the situation is more
complicated: here one does not obtain the sky brightness at a specific
location, but rather data points indicating the amount, frequency and
direction of brightness fluctuations.
If these data points were arranged on a regular two-dimensional grid,
converting them to a normal image would be straightforward, but
unfortunately no radio telescope design exists which could produce this
arrangement. Realistic data point distributions often exhibit complex,
inhomogeneous patterns (see fig. 3). Further complications arise if the
individual antennae are not placed perfectly on a single plane, and/or
if the observed sky region is too large to be approximated by a flat
surface. In this case, additional correction terms have to be applied
during the image generation, which further increases the computational
cost.
The operation described above is called "gridding" and in practice
various different implementations exist. Some are not particularly
accurate (usually because they date back to the early times of radio
astronomy, when computational power was very limited and many
approximations and simplifications had to be made). Others provide good
accuracy, but often are not fast enough to process the huge amounts of
data produced by contemporary radio telescopes in an acceptable amount
of time.
Scientists at MPA have now used various approaches – both from both
radio astronomy itself and from unrelated scientific areas – to
implement a new version of the gridding operation. This new
implementation produces very accurate results while at the same time
consuming considerably less CPU time and computer memory.
Gridding, however, is only one of several components necessary to
produce realistic images from interferometric observations. To suppress
noise in the data and eliminate the directional changes in antenna
sensitivity, sophisticated iterative algorithms are employed.
Traditionally, very often a variant of the so-called CLEAN algorithm is
used, which is comparatively quick but does not provide an uncertainty
estimate for the resulting image. In contrast to CLEAN-based methods,
the MPA scientists developed an (admittedly significantly slower)
approach, which delivers physically motivated results including error
bars, making use of Information Field Theory and Bayesian statistics.
Three different image reconstructions of the radio galaxy Cygnus A from
VLA interferometry data. Two small regions (a bright and a dark one,
respectively), have been enlarged for easier comparison.
Top panel: naive Fourier transform without optimization.
Middle panel: reconstruction using the CLEAN algorithm. A higher
resolution is reached, but some unphysical structures are generated,
especially in the darker regions.
Bottom panel: reconstruction using Bayesian imaging and Information
Field Theory. Resolution in the bright areas is further improved, yet no
artefacts are visible in the dark areas.For a larger view of image
reconstructions B and C, please see below. © MPA; reconstruction middle image: NRAO, Klasse Richard A. Perley
Fig. 4 shows a comparison of the two methods. The observed
astrophysical source is the radio galaxy Cygnus A with a supermassive
black hole (weighing more than a billion solar masses) at its centre.
Two jets, observable at radio wavelengths, leave this centre and at some
point encounter the intergalactic medium, where they are reflected and
start to emit very brightly. The back-flows create large volumes of
radio-bright gas, which can be observed with radio interferometers like
the VLA.
The image obtained with the new algorithm exhibits significantly
better spatial resolution in the bright image regions, since the
signal-to-noise ratio in these areas is much higher. At the same time,
it does not show the pronounced structures in the darker regions from
the CLEAN results; presumably these structures are artefacts of the
CLEAN algorithm which do not correspond to real features on the sky.
The methods presented here essentially open up two new possibilities
for radio astronomy: they allow re-processing of already existing data
sets, in order to gain additional insights from the improved images. For
future observations, there may now be an option to reach the desired
image quality with shorter observation times, thanks to the improvements
in the algorithms, allowing for a higher overall number of
observations. Source: Max Planck Institute for Astrophysics
Other scientific disciplines such as medical imaging, especially
magneto-resonance tomography (MRT) employ imaging techniques that are
closely related to those in radio interferometry. It is therefore
possible that the insights gained from these developments will be
beneficial in these areas as well.
Additional information:
The two last images from Fig 4 can be enlarged separately below.
Image reconstruction with the CLEAN algorithm.
© MPA; reconstruction: NRAO, Klasse Richard A. Perley
Image reconstruction with the new algorithm developed at MPA.
© MPA
Authors
Arras, Philipp Arras
PhD student
Tel: 2034
Martin Reinecke
Scientific Staff
Enßlin, Torsten Enßlin
Scientific Staff
Tel.:2243
Original publications
1. P. Arras, R.A. Perley, H.L. Bester, R. Leike, O. Smirnov, R. Westermann, T.A. Enßlin
Comparison of classical and Bayesian imaging in radio interferometry. Cygnus A with CLEAN and resolve
A&A, Forthcoming article
Source/
DOI
2.
Philipp Arras, Martin Reinecke, Rüdiger Westermann, Torsten A. Enßlin
Efficient wide-field radio interferometry response
A&A, accepted
Source/DOI
3.Ye, H.
Accurate image reconstruction in radio interferometry
Doctoral thesis
Source/DOI
4.
Alex H. Barnett, Jeremy F. Magland, Ludvig af Klinteberg
A parallel non-uniform fast Fourier transform library based on an "exponential of semicircle" kernel
SIAM Journal on Scientific Computing, 41, 5, C479--C504, 2019
5.
Enßlin, Torsten A.
Information theory for fields
Annalen der Physik 2019, 1800127