[fitsbits] Representation of polarimetry data in WCS

[Mark Calabretta]

On Wed 2006/04/26 09:24:16 MST, Marshall Perrin wrote
in a message to: fitsbits at nrao.edu

>WCS Paper I defines a 'STOKES' axis convention for storing  
>polarimetric data, which uses a series of integers to denote the  
>various Stokes parameters and/or other forms of polarimetry data. WCS  

This is one of the "conventional" axes, others are COMPLEX and CUBEFACE,
and in future we may also have RGB, CMYK, HSB and maybe others.  These
axes do not form a proper image axis because pixel values are not
interpolable along them.  In effect they are simply a way of aggregating
a number of images into one cube.  The images are independent but
closely related, each contributes the element of a vector or similar
entity and each has the same WCS on the other axes.  In other words,
conventional axes are essentially just a way of storing vector-valued
pixels; as with ordinary vectors the elements (images) must be given in
a predefined sequence.

Conventional axes are very simple-minded, there is limited flexibility
in the way they are sequenced; reversal is possible via negative
CDELTia, regular skips by setting |CDELTia| > 1, or subsetting (via
NAXISia), e.g. STOKES implicitly assumes that no more than four
polarizations will be given and in the set sequence.  For example, you
could have I and V (CDELTia = 3), or V and I (CDELTia = -3) but not
I, U, and V.  However, sequences disallowed by these simple rules are
not likely to be meaningful.

Implicit in this is that the data must be organized to match the defined
sequence.  This is akin to requiring that vector elements be ordered.

>Paper III says that the CTYPEn keyword for a -TAB axis should follow  
>the 4-3 format, using the 4-letter axis type.  So then the proper  
>value to use is 'STOK-TAB', correct?

'STOK' is not formally recognized, nor any combination of it with a
non-linear algorithm code.  It should be clear from above why this is
so and why there are restrictions on CRPIXia, CDELTia, CRVALia, and
particularly PCi_ja for conventional axes.

>(P = sqrt(Q^2+U^2+V^2). Is there any convention on an integer code to  
>denote that with?

Not currently, nor for linear combinations.

Mark Calabretta
ATNF