ALMA and polarization
  =====================
  Remarks by Johan Hamaker, ASTRON, 010111


 1. Feed-configuration

        De possibility of a 'crossed-dipole' feed configuration (Weiler, A&A
1973) has been raised but generated little enthusiasm. The ASAC objects
because of its inefficiency for intensity-only observations. Hardware designers
consider it too late to consider a change as far-reaching as this. Both of
these objections might be overcome only by a very convincing case for crossing
the dipoles.


 2. Conventional polarimetric calibration

        Conventional polarimetric calibration of a (linear or circular)
homogeneous array entails three steps:

        1. Scalar selfcal of the two homogeneous subsets 'p' and 'q' of
receptors.

        2. Determination of the leakage parameters ('D terms') describing the
leakage of Stokes I into the polarized components.

        3. Determination of the phase difference 'phi' between the p and q
subsystems.

        Steps 1 and 2 are based on a linearised approximation. In this an
unpolarized calibrator is required and it is assumed that the degree of
polarization and the deviations from nominal of the feeds are 'small'. This
approximation can be avoided, though, by replacing the two steps jointly with a
matrix-based form of selfcal that is free of ad-hoc assumptions.

        In either case, step 3 is the nastiest one. A reference source with
(partly) known linear polarizationIis needed to measure the phase difference.
It can be a celestial or an artificial source. The reliability of either type
of standard is problematic, certainly in the case of ALMA.

        For linear feeds, one may also obtain phi by assuming that Stokes V is
zero for the source. I cannot judge to what extent this assumption is justified
in mm-wave polarimetry.  For circular feeds, one must know the actual direction
of linear polarization to determine phi. In this respect, circular feeds seem
to me to be more vulnerable.


 3. Do crossed dipoles help?

        The equations for crossed dipoles can be linearised in the same way as
those for parallel linear or circular feeds. However, step 1 above does require
a homogeneous system. This objection disappears when one applies a matrix
algorithm as suggested above.

        The advantage of crossed dipoles is that the matrix solution includes
phi and therefore obviates the need for a separate measurement. In considering
crossed dipoles this advantage must be balanced against the objections
mentioned. An educated guess on the likelihood of Stokes V being small at mm
frequencies would be valuable.


 4. Linear vs circular feeds

        Strong convictions exist on the superiority of either feed type for
particular types of measurement. I take no side in this, but I do want to
emphasise that all notions about the subject are based on the linearised
analysis which is incomplete. The matrix formulation that we now have puts us
in a position to re-analyse the matter from scratch and reassess the relative
merits of linear and circular feeds.


 5. Position-dependent primary-beam polarization

        The problem of 'beam squint' in the VLA is notorious. I understand that
nonetheless the present ALMA feed design accepts that this effect cannot be
avoided. I am quite convinced that the matrix formulation will help in making
this problem more tractable without demanding all feeds to be equal. (As with
the phase-difference problem, it may even help if they are not.)

        Beam squint or not, the primary beam will suffer from
position-dependent instrumental polarization that may be caused by a number of
mechanisms such as non-circular illumination and scattering off the feed
supports. Both theoretical modeling and experimental measurement of the
polarized beam are major undertakings and may actually be years away.

        It would certainly help if primary-beam polarization could be avoided
as much as possible. To what extent present feed-design efforts may be
redirected with this requirement in mind I cannot judge. Taking beam squint for
granted is in my opinion a dangerous direction to go.