The `CLEAN' restoring beam is used to suppress high spatial frequencies that which are poorly estimated by the `CLEAN' algorithm. There are two competing opinions on this in the radio astronomy community: some object that it is purely ad hoc and is undesirable--in the sense that the equivalent predicted visibilities do not then agree with those observed. Others defend it as a way of recognizing the inherent resolution limit. In practice, re-convolving with a `CLEAN' beam seems to be necessary to produce astrophysically reasonable images.
The most common way to choose the `CLEAN' beam is to fit an elliptical Gaussian to the main lobe of the dirty beam. This choice is a compromise between resolution and apparent image quality, however, and either larger or smaller beams may be appropriate in some cases. If one is prepared to tolerate a decrease in the apparent quality of the `CLEAN' image, and if both the signal-to-noise ratio and the u,v coverage are good, then a smaller `CLEAN' beam can be justified.
Various attempts have been made to improve the choice of the `CLEAN' beam. The dirty beam, truncated outside the first zero-crossing, is appropriate in some applications since it lacks the extended wings of a Gaussian, but we emphasize that, after convolution with such a beam, just as in the case of a Gaussian clean beam, the `CLEAN' image does not agree satisfactorily with the original visibilities. An ideal `CLEAN' beam might be defined as a function obeying three constraints:
Constraint (1) is usually the first to be relaxed, and then only positivity of the transform is necessary. It may be that in typical applications `CLEAN' performs so poorly that these constraints do not allow an astrophysically plausible `CLEAN' image, however such a topic is probably worth further consideration.
An important consequence of choosing the `CLEAN' beam poorly is that the units of the convolved `CLEAN' components may not agree with the units of the residuals. The units of a dirty image are poorly defined, but can be called ``Jy per dirty beam area'' because an isolated point source of flux density S Jy will appear in the dirty image as a dirty beam shape with amplitude S Jy per dirty beam area. An extended source of total flux density S Jy will be seen in the dirty image convolved with the dirty beam, but the integral will not, in general, be S Jy. However, convolved `CLEAN' components do have sensible units of Jy per `CLEAN' beam, which can be converted to Jy per unit area since the equivalent area of the `CLEAN' beam is usually well-defined. If `CLEAN' is run to convergence, the integral of the `CLEAN' image will often be a good estimate of the flux density of an extended object, failing only if the u,v coverage fails to sample the true peak visibility of the source adequately on the shortest spacings. If convergence is not attained, then both flux density and noise estimates obtained from the `CLEAN' image can be significantly in error.
1996 November 4