The point source sensitivity is well adapted to unresolved sources because it directly delivers the estimation of the flux of these sources. For extended sources, the point source sensitivity is expressed in unit of Jy/Beam that is difficult to understand because it depends on the synthesized beam resolution in a non-trivial way. When a source is resolved (extended compared to the expected synthesized beam), it is much easier to think in temperature brightness. We thus convert back to a brightness temperature scale, but we now do it at the synthesized beam resolution.
After calibration (including the calibration of the atmospheric
decorrelation), imaging, and deconvolution (including a potential phase
self-calibration), an interferometer mimick the observation by a telescope
of angular resolution equal to the synthesized beam. However, the notion of
effective collecting surface is ambiguous in this case. In order to
generalize Eq. 5 to the final product of an
interferometer, we use the fact that the solid angle resolution
of a telescope of effective collecting surface
is by definition
linked to the observing wavelength (
) through
![]() |
(11) |
Combining Eq. 10, 13,
and 14, we yield