info prev up next book cdrom email home

Dirty Beam

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

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

also called the Synthesized Beam. It is called a ``beam'' by way of analogy with the Dirty Map
$\displaystyle I'$ $\textstyle =$ $\displaystyle {\mathcal F}^{-1}(VS) = {\mathcal F}^{-1}[V]*{\mathcal F}^{-1}[S]$  
  $\textstyle =$ $\displaystyle I*{\mathcal F}^{-1}(S) \equiv I*b',$ (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'').
\end{displaymath} (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

© 1996-9 Eric W. Weisstein