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Consider a sky containing only isolated point sources. In
the dirty map, each appears as a copy of the dirty beam, centred on the
source position and scaled by its strength. However, the maxima in the map
do not strictly correspond to the source positions, because each maximum
is corrupted by the sidelobes of the others, which could shift it and
alter its strength. The least corrupted, and most corrupting, source is
the strongest. Why not take the largest local maximum of the dirty map as
a good indicator of its location and strength? And why not subtract a
dirty beam of the appropriate strength to remove to a great extent the bad
effects of this strongest source on the others?
The new maximum after the subtraction now has a similar role. At every
stage, one
writes down the co-ordinates and strengths of the point sources one is
postulating to explain the dirty map. If all goes well, then at some stage
nothing (or rather just the inevitable instrumental noise) would be left
behind. We would have a collection of point sources, the so called CLEAN
components, which when convolved with the dirty beam give the dirty map.
One could exhibit this collection of point sources as the solution to the
deconvolution problem, but this would be arrogant, since one has only
finite resolution. As a final gesture of modesty, one replaces each point
source by (say) a gaussian, a so called ``CLEAN" beam, and asserts that the
sky brightness, convolved with this beam, has been found.
This strategy, which seems so reasonable today, was a real breakthrough in
1974 when proposed by J. Högbom. Suddenly, one did not have to live with
sidelobes caused by incomplete coverage. In fact, the planning for
new telescopes like the VLA must have taken this into account- one was no
longer afraid of holes.
Next: The Behaviour of CLEAN
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