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 $i$ to antenna $j$ at frequency channel $k$ is related to the true object visibility $V_{ij}$ by

$$\widetilde{V}_{ijk} = g_i(t) g_j^*(t) b_{ijk}(t) V_{ij}(u_k(t),v_k(t)) + noise term$$ (1)

where $u_k(t)$ and $v_k(t)$ are the spatial frequencies corresponding to baseline $ij$ at time $t$ and frequency $k$ , and we assume the object has a flat spectrum. Calibrating the data is computing the complex ``calibration curves'' $g_i(t)$ and $b_{ijk}(t)$ .