Following the initial calibration, your next task is a little more enjoyable; namely, making some images. With the ATCA you always get spectral information (unless you throw it away; see § 6) around your central observing frequency, allowing the possibility of multi-frequency synthesis (i.e., putting all the channels in the band in their correct places in the (u,v) plane and making one image) for continuum data. In addition, the temporal frequency agility of the ATCA enables observations with a number of widely spaced frequencies in the one broad band, so that again the (u,v) coverage can be improved.
New algorithms and tasks have been developed by Bob Sault to take advantage of these features (see the MIRIAD User's Guide and Bob's ATNF technical memorandum). However, this code resides in MIRIAD\ where you must work if you wish to make the most of your ATCA data in this regard. The algorithms in AIPS remain fairly basic; the biggest drawback in AIPS (but not MIRIAD) is that it cannot cope with a source brightness that changes substantially between the frequencies to be combined; i.e., a non-zero spectral index. Be aware of this, as it limits the usefulness of the multi-frequency synthesis procedure.
I will discuss a variety of different ways to image ATCA data. These will include multi-frequency synthesis and spectral-line imaging. No matter which of these you actually plan to do, you should read the first sub-section on how to image just one channel at one frequency, as it contains some technical discussion that is required background for all ensuing sub-sections.
The imaging tasks in AIPS are MX, UVMAP, and HORUS. UVMAP\ functions only on single-IF single-source files in XY sort order (XY order means that the data are put in order of increasing u and v). MX also only functions on single-source files, although it does IF selection and can take a TB sorted file for input. This is quite an advantage as the sorting procedure is very expensive on computer resources. Imaging TB sorted data directly does limit the size of the image, but there should be no problem for most applications. HORUS functions on both multi- and single-source files in either TB or XY order and has IF selection. Both HORUS and MX can do multi-frequency synthesis imaging including gridding multiple IFs together.
There is a vast body of literature discussing the digital 2-D Fourier transformation of visibility data into images, and I will not replicate much of it here. Excellent references are the NRAO workshops on imaging. The basic concept to grasp is that the Fourier Transform of the visibilities (called the dirty image) is the sky brightness (multiplied by the primary beam response of one telescope of the array) convolved by the point-spread function of the synthesis array (called the dirty beam). The better your (u,v) coverage, the more your dirty beam approaches a delta function which is what you would get with complete u,v) coverage.
The first major step is referred to as gridding. This procedure
interpolates the irregularly sampled (in u and v) visibilities onto
a regular grid so that the data can be fast Fourier transformed. You
could do a direct Fourier transform on the ungridded visibilities if you
wished, but that would be computationally prohibitive for any but the
smallest problems. Gridding is done by convolving the visibilities with
a function that is just a few grid cells wide, and then resampling the
convolved function at the centre of grid cells. The width of a grid
cell (in u say) in wavelengths is 
, where
is the pixel size in radians in the image, and N is the
number of pixels.
The next step is the FFT, which produces a dirty image. However, because the visibilities were convolved by some function in the gridding procedure, the convolution theorem indicates that the effect on the image is to multiply it by the Fourier transform of the convolving function. Therefore, the `grid correction' is made, which divides the dirty image by the Fourier transform of the convolving function. As well as the dirty image, the dirty beam is computed. This is achieved by replacing the gridded visibilities by a point source of unit amplitude at the phase centre and re-computing the grid corrected image. Thus, the dirty beam is just the Fourier transform of the sampling function of the (u,v) plane.
Note that the units of the dirty beam are not terribly useful. They are Janskys per dirty beam area. However, since the integral of the dirty beam (and dirty image) is zero, this does not mean much. The only real meaning is that an isolated point source of flux density S Jy will appear in the dirty image as a dirty beam shape with amplitude S. An extended source of total flux density S Jy will appear in the dirty image convolved with the dirty beam, but the integral won't in general be S Jy.
It is always a good idea, when you first image a field, to examine the entire primary beam FWHM (or more) on the sky. That is, you should find out what sources your data are responding to. If you have a high resolution observation, this may require you to initially lower the resolution (called ``tapering''; see below) so that you can image the full primary beam in a modest sized (1024 by 1024 pixels) image. Note that the ATCA telescope primary beam (as distinct from the synthesised dirty beam) has quite high sidelobes, and you can find that the array is responding to very distant bright sources.
Your dirty image generally requires some form of image reconstruction (deconvolution) to remove the effects of the dirty beam's sidelobes. This might be achieved with CLEAN or maximum entropy and will be discussed in § 16. Of course, if you have no signal in your image (e.g. a detection experiment that failed to detect anything) then there is no point deconvolving the noise.