Combining Mosaics and Single Dish Data

For a good discussion of the theory and practice of combining single dish and mosaic data, see the paper by Snezana Stanimirovic (ASP Conf. Series, vol 278, p 375).

One of the benefits of mosaicing is that it partially recovers spacings shorter than the shortest projected interferometer spacing. In principle, the shortest spacing present in a mosaic can be the projected interferometer spacing minus the antenna diameter, D (see the references mentioned earlier for the argument). When antennas are as closely packed as is physically possible, the minimum physical spacing will be D, and so in principle a mosaic can reduce the effective minimum spacing almost down to the zero spacing. In practise, mosaicing tends to reduce the effective minimum spacing by about D/2, rather than the theoretical D. For the ATCA observations of sources appreciable far south, the effective minimum spacing in a mosaic is about 20 m (the minimum physical interferometer spacing is 31 m).

So whereas mosaicing helps recover short spacings, there are invariably some short spacing missing. To fill these spacings, interferometer data must be augmented with single-dish data. Just as there are two approaches to mosaicing (the joint and individual approach), Miriad provides two approaches to single-dish combination - the linear and a non-linear methods, using tasks immerge and mosmem respectively. Which method produces best results is quite problem specific, and indeed it is perhaps best to try both if possible. However,

• The non-linear combination method works on the dirty mosaic produced by invert, whereas the linear method works from deconvolved images. Thus the non-linear method cannot be used with the ``individual'' mosaicing approach.
• The linear method can be more robust to the single-dish data failing to satisfy some of the assumptions of the non-linear method.
• The non-linear technique can perform better when there is emission right to the edge of the sampled region of the sky.
• The linear method assumes that the single-dish point-spread function is a gaussian. For the non-linear method, you give a ``beam'' dataset, which can be an actual measurement of the single-dish point-spread function (which can be asymmetric).

Given that combining mosaic and single-dish data can be a bit of an art, its worth doing a few checks of the result:

• The simplest check is to see that the total flux agrees with what you expect. Task histo is the simplest way of measuring the total flux in a continuum image (or plane of a spectral cube). Otherwise imstat can be used.
• The non-linear methods produce model outputs, that need to go through a restore step. Task restor will also generate residual images. You probably want to look at the residuals for both the mosaic and single-dish images, which is readily done with restor using mode=residual.

In general, to combine single dish and interferometer data, you need to image the complete region containing emission. In practise this means that sidelobes, from emission outside the region of interest, are not significant. This applies both to the single-dish and interferometric observations. Both observations should map the complete region of the emission.