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The clean component list may be searched on an arbitrarily fine spatial grid without too much physical sense as the interferometer has a finite spatial resolution. The convolution by the clean beam thus reintroduces the finite resolution of the observation, an information which is missing from the list of clean components alone. This step is often called a posteriori regularization.
The shape (principally its size) of the clean beam used in the restoration step plays an important role. The clean beam is usually a fit of the main lobe (i.e. the inner part) of the dirty beam. This ensures that 1) the flux density estimation will be correct and 2) the addition of the residual map to the convolved list of clean component makes sense (i.e. the unit of the clean and residual maps approximately matches).
The final addition of the residual map plays a double role. First, it is a first order correction to insufficient deconvolution. Second, it enables noise estimate on the cleaned image since the residual image should be essentially noise when the deconvolution has converged.
Some odd dirty beams may lead to incorrect flux measurements. For example, if the dirty beam has a very narrow central peak superimposed on a rather broad plateau, the volume of the Gaussian fitted to the central peak does not match that of the dirty beam, and the flux scale will be incorrect. Data-reweighting is required to cure these peculiar situations, and this always implies a loss of sensitivity.
Super-resolution is the fact of restoring with a clean beam size smaller that the fit of the main lobe of the dirty beam. The underlying idea is to get a bit finer spatial resolution. However, it is a bad practice because it breaks the flux estimation and the usefulness of the addition of the residual maps. It is better to use robust weighting to emphasize the largest measured spatial frequencies.