Calibration

Calibration

The goal of the calibration is to estimate and correct for the instrumental gain in order to have an unbiased estimate of the true visibilities. We use a simplified version of the radio-interferometry measurement equation. The (complex) visibility $\widetilde{V}_{ijk}$ measured on the baseline from antenna $i$

$i$

to antenna $j$

$j$

at frequency channel $k$

$k$

is related to the true object visibility $V_{ij}$ by

$\displaystyle \widetilde{V}_{ijk} = g_i(t) g_j^*(t) b_{ijk}(t) V_{ij}(u_k(t),v_k(t)) + noise term$

(1)

where

$u_k(t)$

and

$v_k(t)$

are the spatial frequencies corresponding to baseline $ij$

$ij$

at time

$t$

and frequency $k$

$k$

, and we assume the object has a flat spectrum. Calibrating the data is computing the complex “calibration curves” $g_i(t)$

$g_i(t)$

and $b_{ijk}(t)$ .