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Detection and usable measurement of an extended source depend on its surface brightness and angular extent as well as its total radiative flux. A diffuse galaxy can be missed even if its integrated flux exceeds a nominal point-source limit. Artificial-source injection over a range of sizes and profiles tests this form of survey incompleteness.

An empirical relation between the luminosity of a disk galaxy and its rotation speed. A simple virial and surface-brightness argument gives $L\propto V^4/({{\rm Y}}^{2}I)$, so changes in mass-to-light ratio or surface brightness change the slope.

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 $V(u,v)=S_{\nu }\mathrm{sinc}(\pi {\Theta }_{x}u)\mathrm{sinc}(\pi {\Theta }_{y}v)$, where $\mathrm{sinc}x=\sin x/x$. 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.