Dirty Beam

The Fourier Transform of the sampling distribution in synthesis imaging

 (1)

also called the Synthesized Beam. It is called a beam'' by way of analogy with the Dirty Map
 (2)

where denotes Convolution. Here, is the intensity which would be observed for an extended source by an antenna with response pattern ,
 (3)

The dirty beam is often a complicated function. In order to avoid introducing any high spatial frequency features when CLEANing, an elliptical Gaussian is usually fit to the dirty beam, producing a CLEAN Beam which is Convolved with the final iteration.