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Possible solution to the wide-field imaging problem

There are in fact a number of different possible approaches to solving the wide-field imaging problem. These are reviewed by Cornwell and Perley. Here we give a brief account:

• 3D transform - after a 3D transform of the visibilities from a non-planar array is performed, the image can be recovered only after a 3-D deconvolution is performed. This technique suffers from the fact that it is very expensive computationally (Cornwell and Perley).

• Faceting the image plane - the image plane can be considered as small tangential facets to the Celestial sphere. The size of the facets are chosen such that the PSF is invariant over the each facet. Each facet has one PSF associated with it. In an iterative fashion, CLEAN is used on each facet down to some limit (the minor cycle), and then the components found are subtracted from the visibilities (via Fourier transform), and a re-computation of the residual images is made (the major cycle).

  Calculation of the facet planes can be handled in two ways:

  1. By phasing the visibility data appropriately, the dirty image and PSF are made for each facet and the above process is applied to the facets. At the end of processing, the final CLEANed images have to be transformed to a single common plane.

  2. By phasing the visibility data and reprojecting the uv coordinates appropriately, the dirty image and PSF are made for each facet onto a common tangent plane, and the above process is applied to the facets. No final reprojection is required.