Dirty Beam

The Fourier Transform of the $(u,v)$ sampling distribution in synthesis imaging

$$b' = {\mathcal F}^{-1}(S),$$ (1)

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

$$I' = {\mathcal F}^{-1}(VS) = {\mathcal F}^{-1}[V]*{\mathcal F}^{-1}[S]$$

$$= I*{\mathcal F}^{-1}(S) \equiv I*b',$$ (2)

where $*$ denotes Convolution. Here, $I'$ is the intensity which would be observed for an extended source by an antenna with response pattern $b_1$,

$$I' = b_1(\theta'')*I(\theta'').$$ (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.

See also CLEAN Algorithm, CLEAN Map, Dirty Map