[fitsbits] Stokes parameters coordinate system

[Eric Greisen]

On 3/2/20 2:09 PM, Thompson, William T. (GSFC-671.0)[ADNET SYSTEMS INC] 
via fitsbits wrote:
> Folks:
> 
> WCS Paper I describes a convention for Stokes parameters.  I’ve been 
> asked how to best represent the coordinate system that these Stokes 
> parameters are expressed in, specifically the Q and U parameters.  Is 
> there a standard practice of how this should be done?  It appears that 
> some space-based instruments define Q and U relative to instrument 
> (pixel) coordinates.  However, the comment was made that this is not 
> really practical for a ground-based alt-az telescope due to field 
> rotation.  Another possible way to encode the Stokes parameters would be 
> relative to the real-world coordinates of the data.
> 
> Suppose that one had a three dimensional cube with the following axis 
> definitions:
> 
> CTYPE1 = ‘RA---TAN’
> 
> CTYPE2 = ‘DEC--TAN’
> 
> CTYPE3 = ‘Stokes’
> 
> And that the PC matrix had cross terms between axes 1 and 2, i.e. image 
> rotation.  Is there a convention for how the Q and U values should be 
> interpreted?  For example, if Q/I=1, would you interpret that as 
> polarization aligned along the first pixel direction, or along the RA 
> direction as defined by the PC rotation matrix?
> 
> Is there a better way to distinguish between these cases other than 
> putting a comment into the header?
> 
> Thank you,
> 
> Bill Thompson

I have looked up the definition in Wikipedia and in Thompson, Moran, and 
Swenson.  They appear to differ seriously.  I take the latter (which 
cites numerous fundamental references) to be correct.  Q/I = 1 occurs 
when the electric vector is pointed at the north celestial pole and Q/I 
= -1 when it is directed in the right ascension direction.  This is said 
to be the IAU definition and FITS is an IAU standard.  Thus, use of 
other coordinates such as galactic should not affect the Stokes 
definition.  (Note that Thompson et al is a bit confusing in that they 
use x as the axis to the North.)

Eric Greisen