14.4.1 Synthesized aperture

Let  $\mathcal{H}$ be the Fourier domain: $\mathcal{H}=(-\Delta u/2, \Delta u/2)^2$. In Fourier synthesis, the frequency coverage to be synthesized is a centro-symmetric region  $\mathcal{H}_s \subset \mathcal{H}$ (see Fig. 14.4).

CLEAN and WIPE share a common objective, that of the image to be reconstructed. This image, $\Phi_{\! s}$, is defined so that its Fourier transform is quadratically negligible outside  $\mathcal{H}_s$. More explicitly, $\Phi_{\! s}$is defined by the convolution relation:

$$\Phi_{\! s} = \Theta_s \star \Phi_{\! o}.$$ (14.7)

The ``synthetic beam'' $\Theta _s$ is a function resulting from the choice of  $\mathcal{H}_s$: the well-known clean beam in CLEAN, the neat beam in WIPE.