Some Theory

Much of the theory here has been borrowed from the memo `AT Polarisation Calibration' (AT Memo 39.3/015). See that memo for more details. A more detailed description of polarimetric interferometry can be found in Hamaker, Bregman & Sault (1996) and Sault, Hamaker & Bregman (1996) (A&AS 117, 137 and A&AS 117, 149).

Recall from Chapter 5 that *Miriad* models a feed
as having a composite gain of

where

Additionally, we have to consider the response of the feeds to polarised emission. Whether a feed is linearly or circularly polarised, its instantaneous response to a signal is a linear combination of two of the four Stokes parameters that describe the wave. In the equatorial frame of the source, ideal linear feeds respond according to

where the

These equations show immediately why it is harder to calibrate an
instrument with linear feeds, such as the ATCA, compared with an
instrument with circular feeds, such as the VLA. In the latter case,
one can make the excellent assumption that the calibrators, which are
used to determine the antenna gains, are not circularly polarised.
Thus, the *RR* and *LL* visibilities are a direct measure of *I*, for
which we have a good model (*i.e.* a point source of known flux density).
Consequently they can be used to calibrate the gains with time. On the
other hand, it is not necessarily a good assumption that a calibrator is
not linearly polarised, so that *XX* and *YY* correlations cannot always
be used as a direct measure of *I*.

In addition, for `alt-az' telescopes, the feeds rotate with respect to the equatorial frame. This causes the actual response of ideal linearly polarised feeds to vary with the angle between the ``sky'' and the feed - (which varies with time, although non-linearly), according to

So far we have assumed that the feeds are ideal. This is never the
case, and their departure from the ideal can be characterised by
leakage terms. is the leakage of the *y* component of the
electric field into the *X* feed, and is the leakage of the *x*
component of the electric field into the *Y* feed. Another way of
thinking of them is the combination of the ellipticity and error in the
position angle of the polarisation ellipses of each feed.

Incorporating these leakage terms results in fairly gory equations - see Hamaker, Bregman & Sault (1996) and Sault, Hamaker & Bregman (1996) (A&AS 117, 137 and A&AS 117, 149) for more details.

2016-06-21