3.3. Planning for good Polarization Calibration

When observing in any of the continuum modes the cross hand
products (RL and LR) are produced automatically by the correlator for
each IF.  Typical "impurities" of the feeds are about 5% for the
center of most VLA bands and degrade toward the band edges and 
away from the pointing center in the image plane.  Without
any polarization calibration an unpolarized source will appear to be
polarized at the ~1% level.  Furthermore, without calibration of the
R-L phase difference, the polarization angle is undetermined.
Fortunately it is not difficult to obtain a reasonably good
polarization calibration under most circumstances.  With a modest
investment of time spent on calibrators and a little effort the
instrumental polarization can be reduced to less than 0.1%.

3.3.1. Determining the Leakage Terms (aka D-terms)}

The best way to determine the leakage terms (which produce the
instrumental polarization), is to observe an unresolved source over a
wide range in parallactic angle.  The polarization of the calibrator
will appear to rotate in the sky with parallactic angle while the
instrumental contribution stays constant.  The AIPS task PCAL uses
this behavior to simultaneously solve for the source polarization
properties and the leakage terms.  The usual recommendation is for 5
or more observations covering 100 degrees or more of parallactic angle
in roughly uniform steps.  Strong and compact calibrators (code "P")
sources are preferred, although often a reasonably good solution can
be obtained from a weaker calibrator observed many times throughout a
run for gain and phase calibration.  More than one source can be used
in the solution provided all sources are unresolved.  Algorithms have also
been developed in AIPS recently (for VLBI polarization calibration)
that allow the use of a single resolved calibrator.  In planning an
observing run it may be useful to consult the parallactic angle
diagram below:

The leakage terms are also known to be time-variable (Holdaway,
Carilli & Owen 1992, VLA test memo #163) and software has been
developed in AIPS++ to contend with this variability.

A single observation of a strong unpolarized source (or a source with well
known polarization properties) can be used to determine the leakage
terms.  As an example, 3C84 is strong, unpolarized and unresolved for
most VLA frequencies and configurations, so that a single scan on
3C84 may be sufficient.  The leakage terms are also fairly constant
over weeks to months, so that measurements from one observing run can
be passed to another made using the same frequencies and bandwidths
and observed in the same configuration.  The leakage terms are carried
entirely in the antenna table, so to transfer them one merely copies
the antenna table.

3.3.2. Calibrating the absolute polarization angles:

Calibration of the absolute polarization angle (or R-L phase
difference) can be accomplished with a single observation of a
polarized source having a known polarization angle (the true R-L phase
difference will be twice the source polarization angle). The best
source for these purposes is 3C286, which is also a primary flux
density calibrator.  If 3C286 can't be reached then 3C138 will work in
most circumstances.  Some information is known about 3C48 and 3C147 as
well.  All observations of polarization angles summarized below are
tied to 3C286 which is assumed to have a Faraday Rotation Measure of 0
rad m$^{-2}$.

                        1995.2 Polarization Measurements
Source    R-L Phase difference (degrees) / Fractional Polarization (%)
           20cm        6cm      3.7cm        2cm      1.3cm      0.7cm
  3C48   N/A  0.5  -148  4.1  -132  5.3  -135  7.0  -145  7.6  -166  9.2
 3C138   -18  7.9   -22 11.1   -22 11.9   -24 10.8   -30 10.6   -23 11.6
 3C147   N/A <0.1   N/A <0.1   -57  0.8   110  3.1   145  4.2   180  5.2  
 3C286    66  9.4    66 11.0    66 11.7    66 12.0    66 12.0    66 12.5

                        1999.2 Polarization Measurements
Source    R-L Phase difference (degrees) / Fractional Polarization (%)
           20cm        6cm      3.7cm        2cm      1.3cm      0.7cm
  3C48   -60  0.4  -148  4.1  -138  5.6  -134  7.0  -146  8.2  -172  8.8
 3C138   -15  8.0   -20 11.4   -22 11.7   -24 11.7   -30 11.6   -28 12.2
 3C147   N/A <0.1    16  0.4   -54  0.7   109  2.9   147  4.5   170  6.5  
 3C286    66  9.4    66 11.2    66 11.6    66 12.1    66 12.4    66 13.3
No ionospheric correction has been made to these data, and fluctuations
in the ionospheric Faraday rotation, especially approaching the solar
maximum in 1999, could cause an error in the above determinations by
10 degrees or more at 20cm.  As 3C48 is only weakly polarized at 20cm,
it should not be used at this frequency.  If it must be used (e.g. no
suitable calibrator was observed) then the polarization angle given at
epoch 1999.2 can be used.  3C48 may also be undesirable at 22 and 43
GHz where it is weak and variable.  At 90cm all the above sources are
unpolarized.  Some pulsars, however, are strongly polarized and we are
invesigating using these along with good ionospheric models and data
to obtain polarization calibration at 90cm.  Contact Rick Perley
(rperley@nrao.edu) for further information.

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