The behaviour of the mosaicing algorithm towards deconvolution artifacts and/or
instrumental effects can be studied by the means of simulations of the whole
mosaicing process. The models presented below were computed with several synthetic
sky brightness distributions. uv coverage of real observations were used
(4-antennas CD configuration of a source of declination
). No
noise has been added to the simulations shown in the figures, so that pure
instrumental effects can directly be seen.
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Stripes
A well-known instability of the CLEAN algorithm is the formation of stripes during
the deconvolution of extended structures. After the dirty beam has been subtracted
from the peak of a broad feature, the negative sidelobes of the beam are showing up
as positive peaks. The next iterations of the algorithm will then identify these
artificial peaks as CLEAN components. A regular separation between the CLEAN components is thereby introduced and the resulting map shows ripples or stripes.
[Steer et al 1984] presented an enhancement of CLEAN (command SDI in MAPPING)
which prevents such coherent errors: the CLEAN components are identified and
removed in groups. As mosaics are precisely observed to map extended sources, the
formation of stripes can a priori be expected. Indeed, the algorithm described
in the previous paragraph presents this instability. Fig. 15.2 shows
an example of the formation of such ripples. To make them appear so clearly, an
unrealistic loop gain (
) was used. But the algorithm of [Steer et al 1984],
adapted to the mosaics, does not result in these stripes, even with the same loop
gain. It seems thus to be a very efficient solution to get rid of this problem, if
it should occur. Note however that more realistic simulations, including noise and
deconvolved with normal loop gain, do not show stripes formation. This kind of
artifacts seems thus not to play a significant role in the image quality, for the
noise and contrast range of typical Plateau de Bure observations. In practice, they are never
observed.
Short spacings
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The missing short spacings have potentially strong effects on the reconstructed brightness distributions in a mosaic. In each field, the most extended structures are filtered out, which thus introduces a lack of information on an intermediate scale as compared to the size of the mosaic. As a consequence, a very extended emission can be split into several pieces, each one having roughly the size of the primary beam. This effect can be very well seen on the simulation presented in Fig. 15.3. Should this problem occur, the only way to get rid of it is to add the short spacings information (deduced typically from single-dish observations) to the data set. Note however that the effects of the missing short-spacings on the reconstructed mosaic strongly depend on the actual uv coverage of the observations, as well as on the size and morphology of the source: the artifacts can be small or negligible if the observed emission is confined into reasonably small regions. From this point of view, the example shown in Fig. 15.3 represents the worst case.
In any case, CLEAN is known to be not optimal to deconvolve smooth, extended structures. In order to partially alleviate this problem and the effects of the missing short-spacings, [Wakker & Schwartz 1988] proposed an enhanced algorithm, the so-called multi-resolution CLEAN: deconvolutions are performed at low- and high-resolution, and the results are combined to reconstruct an image which then accounts for the extended structures much better than in the case of a classical CLEAN deconvolution. As already quoted before, this algorithm cannot be applied to a mosaic, because it relies on a linear measurement equation. A multi-resolution CLEAN adapted to mosaics has however been developed ([Gueth 1997]) and is currently implemented in MAPPING. This method will not be described here.
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Pointing errors
Pointing errors during the observations can of course strongly affect the images
obtained by mosaicing. The rms of the pointing errors of the antennas of the Plateau de Bure interferometer is about 3''. By comparison, the primary beam size at 230 GHz is (Table 15.1). The pointing errors are difficult to model
precisely: they are different for each antenna, random errors as well as slow drifts
occur, the amplitude calibration partially corrects them, etc. A complete simulation
should therefore introduce pointing errors during the calculation of each
visibility. For typical Plateau de Bure observations, such a detailed modeling is probably not
necessary, as the final image quality is dominated by deconvolution artifacts. To
get a first guess of the influence of pointing errors, less realistic simulations
were thus performed, in which each field is shifted as a whole by a (random)
quantity. Such a systematic effect most probably maximizes the distortions
introduced in the images. (Note that for a single field, the source would simply be
observed at a shifted position in such a simulation. For a mosaic, the artifacts are
different, as each individual field has a different, random pointing error.
See [Cornwell 1987] for a simplified analysis in terms of visibilities.)
Figure 15.4 presents typical reconstructed mosaics for different
rms of the pointing errors of the Plateau de Bure antennas. Obviously, the larger the pointing
error, the worse the image quality. With a pointing error rms of 3'', reasonably
correct mosaics can be reconstructed even at 230 GHz. Clearly, care to the pointing
accuracy has however to be exercised when mosaicing at the highest frequencies.