Some Theory and Preparing the Single-Dish Data

Both the linear and non-linear methods require a mosaic and a single-dish image as inputs. Miriad has not tasks to form images from single-dish data. Thus you must use another package to generate the single-dish image, which you will then import into Miriad (presumably via FITS - see Section 8.2). Further massaging might then be needed within Miriad to prepare the single-dish image for the combination process. The steps needed are as follows:
  1. Coordinate grids: The coordinate systems of the single-dish and mosaic image must be identical. That is the image size, pixel increment, equinox, projection geometry, etc, must be the same. Often, the regrid task can achieve this reasonably painlessly. Given an input image and a template image, regrid resamples (by interpolation) the input onto the grid of the template. In doing so, it correctly handles different projection geometries, equatorial/galactic coordinate conversion, equinox conversion and different velocity definitions.

    Note you should not regrid the mosaiced image. In regridding, the information that describes the mosaicing process is lost, which will make life difficult for you.

    Typical inputs to regrid would be

    REGRID Input single dish image.
    tin=lmc.mosaic The mosaic giving the coordinate system
      that we want to regrid to.
    out=lmc.sd_regrid The output, regridded, single-dish image.

    For interpolation to produce a faithful output, the grid of the input cannot be too coarse - the number of pixels across the single-dish beam should be at least 3. Although this is usually readily satisfied on the spatial axes, spectral line users should be more wary: the number of channels across the spectral axis response function is usually very small. In addition, whereas the spatial resolution of the single dish will be poorer than the mosaic, this is not necessarily true for the spectral axis. So, in addition to regridding, some spectral smearing might need to be performed to reduce the spectral resolution of the single-dish image to that of the mosaic. Unfortunately, Miriad is poorly equipped to solve these problems; these issues are left as a difficult exercise for the user.

  2. Flux scale calibration: The single-dish and mosaic images both should have flux units of Jy/beam. Although appropriate calibration during the observations is obviously the best method to ensuring that the flux scales of the mosaic and single-dish images are the same, this is not always achieved. The flux scales of two images, that are nominally in the same units, can differ by a modest, but appreciable, amount.

    A common approach to estimating flux calibration factor is to compare the single-dish and mosaic images in that annulus of spatial frequencies where both are sensitive. For example, a Parkes observation will sample spatial frequencies from 0 to near 64 meters, and a ATCA mosaic (assuming the shortest ATCA spacing is observed) will be sensitive from about 20 meters upwards. As the reliability of the data near the extremes is suspect, spatial frequencies from 25 to 40 meters should be modestly reliably represented in both an ATCA mosaic and a Parkes image. Comparing in the overlap annulus works very well when there is a simple source which is well represented in this region (e.g. a dominant point source).

    The tasks to perform the linear and non-linear combination both have parameters for setting and deducing the flux calibration factor.

  3. Point-spread function: In principle, knowing the point-spread function (the ``beam'') of the single-dish image is just as important as it is for the mosaic. It is best to `map' this at the time of the single-dish observations and to account for any change in the beam that is caused by the single-dish imaging process.

    While it is possible to imagine algorithms that could deduce the beamwidth based on the spatial frequency overlap between the single-dish and mosaic data, in practise this is not possible (the overlap region is not wide nor is the data reliable enough). In estimating beamwidth parameters, the beamwidth and flux calibration factor are highly coupled; an error in the beamwidth has much the same effect in the overlap region as an error in the flux scale. Thus you cannot determine the beamwidth and flux scale simultaneously.

    The linear combination method assumes the single-dish point-spread function is a gaussian form, whereas the non-linear method takes a image dataset as the point-spread function (the point-spread function need not be symmetric). If a point-spread function is not readily available for the non-linear method, a gaussian dataset can be produced.

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