Deconvolution implicitly interpolates values for un-sampled u,v spacings. In most cases `CLEAN' does this interpolation reasonably well. However, in the case of short spacings the poor interpolation is sometimes rather more noticeable since very extended objects have much more power at the short spacings. The error is nearly always an underestimation and is manifested as a ``bowl'' of negative surface-brightness in which the source rests. In such a case, introducing an estimate of the zero-spacing flux density into the visibility data before forming the dirty image can help considerably. The appropriate value of this flux density would be that measured by a single element of the array. In practice, however, single array elements rarely have sufficient sensitivity or stability to provide this estimate accurately. Values estimated from surveys made with larger, more sensitive, and more directive elements are therefore frequently substituted. Choosing the weight for the zero-spacing flux density is difficult; the best estimate seems to be simply the number of unfilled cells around the origin of the gridded u,v plane. However, the results obtained are fairly insensitive to the value used provided that the `CLEAN' deconvolution goes deep enough.
The `CLEAN' windows or boxes offer a way to constrain the shape of the visibility function V(u,v) near the zero spacing u=v=0. For this reason, careful choice of `CLEAN' windows may also minimize problems associated with the short spacings.
After `CLEAN'ing, the emission should be, but is not guaranteed to be, distributed sensibly over the `CLEAN' image. Failure of the interpolation is indicated by the presence of a ``pedestal'' of surface brightness within the `CLEAN' box upon which the source rests. Such a pedestal all over the image can be caused by insufficient `CLEAN'ing; one can experiment by simply increasing .
Ultimately, of course, it may be necessary to measure the appropriate short-spacing data!
1996 November 4