= Visibility of a uniform rectangular source
{title2=$V=S_\nu\operatorname{sinc}(\pi\Theta_xu)\operatorname{sinc}(\pi\Theta_yv)$}
With constant <surface brightness> over a centred angular rectangle of widths $\Theta_x,\Theta_y$, and a nearly uniform <primary beam> over that rectangle, the <Fourier transform> separates into two one-dimensional integrals. The result is $V(u,v)=S_\nu\operatorname{sinc}(\pi\Theta_xu)\operatorname{sinc}(\pi\Theta_yv)$, where $\operatorname{sinc}x=\sin x/x$. The zero-spacing value is the integrated <spectral flux density>, while the first axial null is at $|u|=1/\Theta_x$. Long baselines therefore do not measure the total flux of a resolved rectangle.
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