Some images produced during the MeqTree Workshop
Ionospheric patch imaging
This illustrates the problems faced by LOFAR imaging. Here we have simulated a simple thin ionospheric shell, with a one-dimensional sine wave travelling through it. The direction of the wave is fixed w.r.t. the sky. This represents a Travelling Ionopsheric Disturbance (TID).
In this simulation, 25 point sources are placed on a regular grid with a spacing of 5 arcmin. During the 8-hour observation, a TID makes it appear as though the sky is viewed from the bottom of a swimming pool, with waves travelling along the surface. This causes all sources to 'move' in different ways. It is possible to correct the data for this motion, but only for one point in the sky. Therefore, only the central source is imaged perfectly, while the (integrated) images of the others are distorted. Fortunately, these distortions can be predicted, so the sources can be largely reconstructed afterwards. However, part of their flux will be irretrievably distributed over the image, thus increasing the noise level, and thus the LOFAR sensitivity. Therefore, LOFAR images will be made as mosaicks of smaller facets, which minimizes the problem, at the cost of extra processing.
Since the waves propagate in one direction in this simulation, the error is also distributed in one direction -- as you can see, the "vertical" sources are imaged pretty much perfectly.
Some different insights may be obtained by simulating just one source -- in this case the upper-right one -- and subtracting a simulation where the ionospheric correction was "perfectly" applied. This produces a "differential" map showing the errors indtroduced into the image by one single source:
UFOs over Westerbork
This simulates a 12-hour WSRT observation of a single point source that was moving at the quite rapid rate of 0.25 arcmin/hour (i.e. 3 arcmin over the observation time). The unusual patterns are created by the shifting and rotating PSF of the WSRT.
Time/bandwidth smearing
An "educational" simulation showing the effects of time and bandwidth smearing. This is another example of a "differential" simulation. It is produced by making one simulation where the visibilities are properly averaged over their respective time/frequency bins, and a second simulation where only the visiiblities for the center points are computed. We then image the difference. The model sky here contains 9 point sources of unit flux, arranged in a cross pattern. Not surprisingly, smearing gets worse as sources get further out from the phase center.
More patch imaging
This is another "differential" simulation showing patch imaging in the presence of a very narrow primary beam. The model sky here contains 3 9-source "crosses" of unit flux. The center cross corresponds to the tracking center, the second cross is on the flank of the primary beam, and the lower-right cross is even further out in the primary beam.
We then treat each cross as a "patch", and correct it for the primary beam for the center of the patch. Not surprisingly, the error pattern looks different depending on where you are in the beam, and gets worse for sources further away from the patch center.
Per-station primary beams
Since MeqTrees can easily simulate station-dependent primary beams, it is interesting to see the difference that they make. In the example here we simulate an 30km array of 27 CLAR-type dishes. The CLAR primary beam is symmetric when looking at zenith, but broadens in the vertical direction as the dish tracks towards lower elevations. Due to the curvature of the Earth, different stations in the array will always track towards slightly different elevations. With array size being only 30km, we would expect the difference to be tiny, but a MeqTree simulation can give us an exact answer.
Here, we arranged 10 point sources in a "fan" pattern. We then made a "differential" simulation -- on the one hand, a "perfect" CLAR simulation with different beams per station, and on the other hand an "approximate" simulation where an average primary beam was used for all stations. The difference is imaged below. As you can see, the distortion gets worse further from tracking center, and is not ditributed uniformly over the sky -- in fact, for the "vertical" branch of the fan pattern there's barely any distortion at all!
The relative error is on the order of 10^-5, which would be considered "low" for today's telescopes, but unacceptable for something like the SKA.
