[fitswcs] Polarization codes

[Paddy Leahy]

Dear All,
 	I was surprised to find recently that the current FITS WCS 
conventions do not appear to provide an unambiguous (i.e. machine- 
interpretable) way of specifying such routine polarization products as 
polarization angle and fractional polarization. I'm not sure if this 
mailing list is the right place to raise the issue but since the current 
"Stokes" codes were defined in WCS paper I it seems a good place to start.

Reminder: on the current definition (WCS Paper I, Table 7), the official 
stokes parameters I, Q, U, V are assigned STOKES 1,2,3,4, while various 
products such as RR through XY (which are linear combinations of I,Q,U,V) 
are assigned STOKES -8 through -1.

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:

Linear polarization angle          1/2 Arctan(U,Q)
Linearly polarized intensity       Sqrt(Q^2 + U^2)
Elliptically polarized intensity   Sqrt(Q^2 + U^2 + V^2)
Unpolarised intensity              I - Sqrt(Q^2 + U^2 + V^2)
Circularly polarized intensity     |V|
Fractional Q                       Q/I
Fractional U                       U/I
Fractional V                       V/I
Fractional linear polarization     Sqrt(Q^2 + U^2) / I
Fractional elliptical polarization Sqrt(Q^2 + U^2 + V^2) / I
Fractional circular polarization   |V| / I
Fractional unpolarized emission    1 - Sqrt(Q^2 + U^2 + V^2) / I
undefined polarization             ---

Some of these (e.g. |V| and |V|/I) may not be needed but are included 
to ensure this issue will not have to be re-visited in the future.

Thhe most useful of these are assigned "STOKES" codes by AIPS, viz:

5 => Linearly polarized intensity (pace "Going AIPS" p.5-6 which says
                                    "Percent polarization" in error)
6 => Fractional polarization
7 => Polarization position angle

AIPS also uses STOKES 0 => beam, 8 => Spectral index and 9 => Optical 
depth, but these seem inappropriate definitions (all of these may in 
general need polarization labels as well). These codes are written to FITS 
headers by AIPS.

"Once FITS always FITS" would require that we avoid using codes 0, 8, 9 
and either adopt the existing AIPS usage for codes 5,6,7 (if not rendered 
ambiguous by the usage of oteher fits writers) or choose new unambiguous 
codes (e.g. starting at 10 or 100) for the above set of eleven.

What do people think, and what is the best way of going about (eventually) 
getting a formal ruling?

regards,
 		Paddy Leahy

======================================================
Dr J. P. Leahy, Jodrell Bank Centre for Astrophysics,
Current address: Osservatorio Astronomico di Trieste
INAF, Via GB Tiepolo 11, 34143 Trieste, Italy
Tel.+39 040 3199160 Fax +39 040 309418