The mutual coherence function (also called the visibility function) for an unresolved and unpolarized source, measured by an interferometer array can be modeled as a product of antenna based complex gains. These complex gains can be derived from the measured visibility function using the standard algorithm, which we call antsol. antsol forms the central engine of most amplitude and phase calibration schemes used for radio interferometric data. (The earliest published reference for an algorithm for antsol of which we are aware is Thompson & D'Addario (1982)).
Usually antenna feeds measure the components of the incident radiation along two orthogonal polarization states by two separate feeds. The signals from the two feeds travel through essentially independent paths till the correlator. However, due to mechanical imperfections in the feed or imperfections in the electronics, the two signals can leak into each other at various points in the signal chain.
At the correlator, signals from all the antennas are multiplied with each other and the results averaged to produce the visibilities. The signals of same polarization are multiplied to produce the co-polar visibilities while the signals of orthogonal polarizations are multiplied to produce the cross-polar visibilities. The co-polar and cross-polar visibilities can be used to compute the full Stokes visibility function. Antenna based instrumental polarization and polarization leakage can be derived from the full Stokes coherence function for a source of known structure (usually an unresolved source) (Hamaker et al.1996; Sault et al.1996, henceforth HBS).
The correlator used for the Giant Metrewave Radio Telescope (GMRT) by
default computes the co-polar visibilities using the Indian
mode of the VLBA Multiplier and Accumulator (MAC) chip. Here we
describe a method, which we call leaky antsol, for the computation of
the leakages using only the co-polar visibility function
for an unpolarized source. Following the notation used by HBS, we
label the two orthogonal polarizations by 
and 
to remind us
that the formulation is independent of the precise orthogonal pair of
polarization states chosen.
Section 7.2 describes the motivation which led to this analysis. For orientation, Section 7.3 starts with the problem of solving for the usual complex antenna based gains and sets up an iterative scheme for the solution. The problem of simultaneously solving for the complex antenna gains and leakages is then posed in Section 7.3.1 and a similar iterative scheme is set up. Section 7.3.2 presents the results of the simulations done to test the scheme. Section 7.4.1 presents some results using the GMRT at 150 MHz. Also, we were fortunate to have the L-band feeds of one of the GMRT antennas converted from linear to circular polarization. We observed 3C147 in this mode where all baselines with this special antenna measured the correlation between nominally linear and circular polarization. Results of this experiment demonstrate that the leakage solutions are indeed giving information about the polarization properties of the feeds. These results and their interpretation on the Poincaré sphere are presented in section 7.4.2. Section 7.5 gives the interpretation of the leakage solutions and discusses closure errors due to polarization leakage using the Poincaré sphere.