[fitswcs] Polarization codes

[Mark Calabretta]

On Tue 2008/03/11 18:26:15 -0000, Paddy Leahy wrote
in a message to: fitswcs at nrao.edu

>I propose that we extend the existing list to include all the meaningful 
>non-linear combinations of I,Q,U,V. I may be naive, but it seems to me 
>that there are only a small number of such non-linear combinations of 
>interest. I think the following thirteen items are a complete list:

Dear Paddy,

The conventional axes, STOKES, COMPLEX, CUBEFACE (and potentially RGB,
CMYK, etc.) have been defined to allow closely related images to be
aggregated into one data structure.  However, they do not form a proper
image axis since it doesn't make sense to interpolate either coordinates
or pixel values along such axes.

The traditional use of the STOKES axis reflects the fact that radio
correlators typically measure either two or four polarizations and it
is natural to want to store them together in a single array, e.g. for
polarization calibration or to form the products that you're interested
in here.  (Vector-valued pixels would be more appropriate but FITS
doesn't provide them; this is the next best thing and is essentially
equivalent in terms of data storage).

At a practical level, the STOKES axis is only useful because of the way
the values have been chosen; they reflect the very limited ways that
polarizations are measured at the telescope or that Stokes values are
derived from them.  For example, the ATCA measures either (XX,YY), or
(XX,YY,XY,YX) and, with STOKES codes (-5,-6) or (-5,-6,-7,-8), these
are representable via CRPIX, CDELT, and CRVAL.  If, perversely, you had
(I,XX,RL) with STOKES codes of (1,-5,-3), then that would not be
representable because the codes are not equi-spaced.

Thus, in the general case, defining extra STOKES codes won't help you to
aggregate derivative polarization products into one array, and if you're
not interested in aggregation then it's not really the way to do it.
The proper way would be to define a keyword that describes what the
pixel values measure (not strictly a WCS issue), potentially it would
be useful for more than just polarizations.  Currently there is nothing
more than BUNIT (or roll your own) - clearly a gap that needs filling.

Regards,
Mark Calabretta
ATNF