National Center for Radio Astrophysics (NCRA), Pune, India 411007

This paper presents an algorithm for solving antenna based
polarization leakage in a radio interferometer using co-polar
observations of unpolarized sources. If ignored, polarization leakage
manifests itself as closure errors in parallel hand (co-polar)
visibilities. Many working radio telescopes offer observational
advantages for observations in non-polar mode (e.g., higher frequency
resolution, lower integration time, etc.). Many observations are
therefore done in non-polar mode and the computation of antenna based
leakage gains in co-polar visibilities is scientifically useful for
debugging and calibrating the instrument. Also, this is a useful
option to use when one cannot or does not want to put in the
additional measurement effort to determine the leakage term by means
of cross-polar measurements. We also present results from test data
taken with the Giant Meterwave Radio Telescope (GMRT) and discuss the
degeneracy in the solutions and the equivalence of the leakage induced
closure phase and the Pancharatnam phase of optics.

where and are two orthogonal polarization states (R and L or X and Y), the antenna complex gain for the -channel of antenna , the leakage of

is the independent baseline based noise. Usually this represents the noise in after the correlation operation plus the antenna based noise. therefore is a measure of the

In the presence of significant s (compared to
), ignoring the second term in Equation 2
will be equivalent to a system with * apparent* increased closure
noise (
instead of just
). * Hence, polarization leakage manifests as
increased closure errors*. This has also been pointed out by Rogers
(1983) in the context of VLBA observations, and extensive study by
Massi & Aaron (1997) for EVN shows that imaging quality is limited by
these errors.

3. Solution Degeneracy, Simulations and the GMRT Experiment

However, an obvious degeneracy is rotation of all the 's by a common phase factor and the s by an, in general different, phase factor, does not affect the left hand side of Equation 2. We also have the freedom to choose a suitable basis in polarization space (see Bhatnagar & Nityananda 2001 for details). We choose this basis in such a way that the sum of the absolute squares of all the leakage terms is minimized. Carrying out the maximization of by the method of Lagrange multipliers, subject to a constant , we obtain the condition that (implying that the leakage coefficients be orthogonal to the gains) and can be incorporated by first choosing an overall phase for the 's so that is real. Then, carry out a rotation in the plane by an angle satisfying . Results of such a transform on simulated data are shown in Figure 1. The absolute frame of reference in which s are measured, also remain undetermined since the source is unpolarized. However this degeneracy is same as that in the phase of s and is not important for correcting the data.

Bhatnagar, S. & Nityananda, R. 2001, A&A, 375, 344-350

Massi, M. & Aaron, S. 1997, EVN Tech. Memo, N75

Pancharatnam, S. 1956, S. Proc. Indian Aad. Sci., A44, 247

Rogers, A. E. E. 1983, VLB Array Memo No. 253

- ... Bhatnagar,
^{1} - Now at the National Radio Astronomy Observatory (NRAO), Socorro, NM 87801, Email: sbhatnag@aoc.nrao.edu
- ... Urvashi
^{2} - Birla Institute of Technology & Science (BITS), Pilani, India and now the department of Computer Science and Engineering, UCSD, CA 92093. Email: uraovenk@cs.ucsd.edu
- ... Nityananda
^{3} - Email: rajaram@ncra.tifr.res.in

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