Introduction

A Radio interferometer samples the spatial coherence function of the radiation field as a function of the baseline (projected antenna separation measured in the units of wavelength). These measurements, called the Complex Visibilities ($V_{ij}$) can then be Fourier inverted under suitable assumptions to make the raw map of the corresponding radiation field. However, the observed visibilities ( $V_{ij}^{obs}$) as measured by the interferometer needs to be calibrated to recover the true visibilities ( $V_{ij}^{true}$). In the absence of any systematic baseline based offsets true visibilities are related to observed ones as

$$V_{ij}^{obs}(t)=g_{ij}(t)~V_{ij}^{true}(t) + n_{ij}$$ (1)

where $g_{ij}$ and $n_{ij}$ are the baseline based complex gains and noise respectively. A very straightforward way to recover the true visibilities would be to look at a standard calibrater and determine the $g_{ij}$s i.e. baseline-based calibration. For various reasons antenna-based calibration is preferred over this method(see section 7.5 of reference 1).

In the antenna-based calibration scheme, $g_{ij}(t)$ is modeled as the product of two antenna-based complex gains:

$$g_{ij}(t)=g_i(t)~g_j(t)=a_i(t)~a_j(t)~e^{i(\phi_i(t)-\phi_j(t))}$$ (2)

where $a_i(t)$ is the antenna based amplitude correction and $\phi_i(t)$ is the antenna based phase correction. These are traditionally determined from observations of an unresolved source. However at low frequencies many of the VLA calibrators show extended emission. Hence, they are not usable as the phase-calibrater in the usual scheme of calibration (see references 1 and 2). This imposes a limit on the uvrange¹ that can be used to compute the antenna based complex gains. Consequently, not all antennas can be calibrated using a resolved source. For the predominantly low frequency interferometers like the GMRT (Fig. 1), there is a serious dearth of phase calibrators since a significant fraction of the VLA calibrators are resolved at GMRT resolutions. The limit on the maximum baseline can however be relaxed if the structure of the source is known. Rest of the document describes a method of getting the source structure, starting from a point-source model and the corresponding uv(range)-limit.

Figure: The figure shows all the 30 antennas of the GMRT with 14 of them clustered in the Central square and rest along the Western, Southern and Eastern arms.