Rogers (1983) pointed out that non ideal feed polarizations of the individual antennas of a radio interferometer can result into closure errors in the co-polar visibilities. In this chapter we described and demonstrated a method to measure the polarization leakage of individual antennas using the nominally co-polar visibilities for an unpolarized calibrator. This method can therefore be used as a useful tool for studying the polarization purity of the antennas of radio interferometers from the observations of unpolarized calibrators. However, since only unpolarized calibrators are used, the actual solution for the leakage parameters is subject to a degeneracy. This degeneracy does not affect the correction of the visibilities and can be used to remove the closure errors due to polarization leakage. Massi et al. (1997) have shown that such polarization leakage induced closure errors in the data from the EVN is the dominant effect of instrumental polarization. For the EVN, this effect can be seen as a reduction in the dynamic range of the images. Our method can be used for such data to remove these closure errors for unpolarized sources.
The general elliptic state of the polarization of radiation can be represented by a point on the Poincaré sphere. The phase difference between three coherent sources of radiation but with different states of polarization goes by the name of Pancharatanam or geometric phase in the optics literature. We interpret the co-polar visibilities with polarization leakages on the Poincaré sphere and show that the polarization induced closure phase errors in radio interferometers is same as the Pancharatanam phase of optics. The antenna based leakages also map to points on the Poincaré sphere and the ambiguity in the solution can be understood as a rigid rotation of the Poincaré sphere, which leaves the leakage solutions unchanged relative to each other.