Signal decorrelation

$J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{sd}}$ characterizes the antenna hardware, i.e. it assumes perfect atmospheric conditions or the use of autocorrelations, as in single-dish measurements. In interferometric mode, the phase of the turbulent atmosphere above each antenna of a given baseline has a random part that causes an additional “attenuation” of the amplitude of the correlation. A point source of 1 Jy flux will appear as a source of $\eta_\ensuremath{\mathrm{atm}}$ Jy flux (with $\ensuremath{\eta_\ensuremath{\mathrm{atm}}}\le 1.0$), if we only use the $J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{sd}}$ factor. This is called atmospheric decorrelation and it depends on the weather during the observations.

However, the last calibration step of interferometric data is to measure a point source of known flux to deduce the actual conversion factor, $J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}$, taking into account the atmospheric decorrelation that happens during the observations. By definition of $\eta_\ensuremath{\mathrm{atm}}$, we yield

$\displaystyle \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}...
...m{ant}}^\ensuremath{\mathrm{sd}}}}{\ensuremath{\eta_\ensuremath{\mathrm{atm}}}}$   and$\displaystyle \quad
\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}} \ge \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{sd}}}.$ (8)

It can be shown that $\eta_\ensuremath{\mathrm{atm}}$ is related to the atmospheric rms phase noise ( $\phi_\ensuremath{\mathrm{rms}}$) through

$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{atm}}}{} = e^{-\frac{\ensuremath{\phi_\ensuremath{\mathrm{rms}}}^2}{2}} \le 1.0.$ (9)