@@ -102,9 +102,18 @@ For processing LOFAR data, we use an IBM BlueGene/P (BG/P) supercomputer. The LO
\caption{LOFAR antennas}
\end{figure}
In this paper, we will present the LOFAR \emph{beam former}: a collection of software pipelines that allow the LOFAR telescope to be aimed at hundreds of directions simultaneously. This feat is made possible by LOFAR's unique design and the resources offered by the BG/P. Traditional radio telescopes are aimed by focussing their dishes on a source, resulting in a sharp but narrow field-of-view per dish. The LOFAR antennas are omnidirectional, and do not have to be moved or rotated. A station is focussed on a source by taking advantage of the fact that the speed of electromagnetic waves is finite, causing an electromagnetic wave to arrive at different antennas at different times (see Figure \ref{fig:delay}). A process called \emph{delay compensation} counters the differences in arrival times by delaying the signals from different antennas such that they are synchronised with respect to the observed source. The synchronised signals from all antennas are accumulated (by the station \emph{beam former}) and sent to the BG/P. The resulting \emph{station beam} has a wide field-of-view around the source. It contains samples for both the X and the Y polarisations as 16-bit complex integers, resulting in 3.1~Gb/s of data per station.
In this paper, we will present the LOFAR \emph{beam former}: a collection of software pipelines that allow the LOFAR telescope to be aimed at hundreds of directions simultaneously. This feat is made possible by LOFAR's unique design. % and the resources offered by the BG/P. The
Traditional radio telescopes are aimed by focussing their dishes on a source, resulting in a sharp but narrow field-of-view per dish. The LOFAR antennas are omnidirectional, and do not have to be moved or rotated. A station is focussed on a source by taking advantage of the fact that the speed of electromagnetic waves is finite, causing an electromagnetic wave to arrive at different antennas at different times (see Figure \ref{fig:delay}). A process called \emph{delay compensation} counters the differences in arrival times by delaying the signals from different antennas such that they are synchronised with respect to the observed source. The synchronised signals from all antennas are accumulated (by the station \emph{beam former}) and sent to the BG/P. The resulting \emph{station beam} has a wide field-of-view around the source.
The BG/P, which receives the signals from all stations, again performs delay compensation and beam forming, this time in software. The BG/P beam former can focus on sources anywhere in the fields of view of the station beams, creating \emph{tied-array beams} (beams). An example is shown in Figure \ref{fig:pencilbeams}, in which station beams (represented by an ellipse) contains several tied-array beams (represented by hexagons). The actual width of the station beams, as well as the width of the tied-array beams, depends on the number as well as the locations of the stations used. Hundreds of tied-array beams are typically needed to fully cover the field of view of a station beam. Different tied-array beams are created by adding the signals from the individual stations using different delays, which depend on the relative positions of the stations and the relative direction of the tied-array beam with respect to the station beam. The BG/P applies delay compensation in two steps. First, coarse-grain compensation is performed by shifting the samples from different stations with respect to each other. Then, for each tied-array beam, the remaining sub-sample delays are compensated for by shifting the phases of the signals. The phase of each sample is changed through a complex multiplication with a precomputed weight. Tied-array beams are thus a linear combination of the (shifted) signals from the stations.
% Tied array beam uitleggen!
%It contains samples for both the X and the Y polarisations as 16-bit complex integers, resulting in 3.1~Gb/s of data per station.
%The BG/P, which receives the signals from all stations, again performs delay compensation and beam forming, this time in software. The BG/P beam former can focus on sources anywhere in the fields of view of the station beams, creating \emph{tied-array beams} (beams). An example is shown in Figure \ref{fig:pencilbeams}, in which station beams (represented by an ellipse) contains several tied-array beams (represented by hexagons). The actual width of the station beams, as well as the width of the tied-array beams, depends on the number as well as the locations of the stations used. Hundreds of tied-array beams are typically needed to fully cover the field of view of a station beam. Different tied-array beams are created by adding the signals from the individual stations using different delays, which depend on the relative positions of the stations and the relative direction of the tied-array beam with respect to the station beam. The BG/P applies delay compensation in two steps. First, coarse-grain compensation is performed by shifting the samples from different stations with respect to each other. Then, for each tied-array beam, the remaining sub-sample delays are compensated for by shifting the phases of the signals. The phase of each sample is changed through a complex multiplication with a precomputed weight. Tied-array beams are thus a linear combination of the (shifted) signals from the stations.
\comment{
TODO ideeen:
- psets prevent global scheduling across psets, data has to be routed through i/o nodes
}
Our beam former supports several pipelines: \emph{XY polarisations}, \emph{Stokes IQUV}, and \emph{Stokes I}. The XY polarisations pipeline outputs the raw tied-array beams, which consist of two 3.1~Gb/s streams of 32-bit complex floating points numbers (floats), one stream for each polarisation. The Stokes IQUV pipeline applies a domain transformation to each sample of the raw tied-array beams, which is useful for polarisation-related studies. The four Stokes parameters, calculated through $I = X\overline{X}+ Y\overline{Y}$, $Q = X\overline{X}- Y\overline{Y}$, $U =2\mathrm{Re}(X\overline{Y})$, $V =2\mathrm{Im}(X\overline{Y})$, with each parameter being a 32-bit float, resulting in four 1.5~Gb/s streams. The Stokes I pipeline calculates only the first Stokes parameter, which represents the signal strength in both polarisations. The Stokes I pipeline supports temporal integration to trade time resolution for a reduced bandwidth per beam, allowing more beams to be created.
