[fitswcs] Polarization codes

[Mark Calabretta]

On Thu 2008/03/13 15:44:55 -0000, Paddy Leahy wrote
in a message to: Mark Calabretta <mcalabre at atnf.csiro.au>
and copied to: fitswcs at nrao.edu

Dear Paddy,

>Jy/beam and brightness temperature are both ways of specifying the same 
>quantity, viz. brightness, intensity or whatever you want to call it.

They may differ by a constant factor, but still they differ.

>One question you should always ask about any brightness measurement is the 
>polarization it represents. The existing STOKES codes are incomplete here 
>at least in the sense that they omit |V|, Sqrt(Q^2 + U^2) and Sqrt(Q^2 
>+ U^2 + V^2) all of which have dimensions of brightness, and one of which 
>is frequently written to FITS files (with STOKES code  5).

...and it should be mentioned (for the lurkers) that (I,Q,U,V) themselves
are not measured directly in practice, but calculated from either
(RR,LL,RL,LR) or (XX,YY,XY,YX).

In your original 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             ---

the ones arrowed are those that I agree could have new STOKES codes
(I'm not sure what you have in mind for "undefined").  Admitting
these will increase the likelihood that a STOKES axis of length > 2
will be unrepresentable (as I discussed initially), but I guess that's
too bad.

The rest trespass into the area of what is measured, e.g. linear
polarization angle is the measurement for which BUNIT must be an
angular measure. 

>In short 1) *any* dataset derived from measurements of EM radiation, 
>astronomical or otherwise, requires the polarization to be specified at 
>least implicitly.

No argument there, as previously discussed, that is how the STOKES codes
are currently used.

>2) The polarization specification is not an option in a list which 
>includes quantities like "optical depth" and "brightness" but is always 
>required in addition (even when the polarization product is something like 
>position angle).

I agree with the first part (which is the same as your first point), but
not with the comment about position angle since that is the measurement,
e.g. how would you combine it with brightness, spectral index, or
anything else?

>3) The existing "STOKES" codes are inadequate to do the job but could 
>easily be extended to cope.

I agree with extra codes for the four quantities indicated above.  As
for the others, since the proposal is to define standard or quasi-
standard usage, I am trying to preclude usage that I don't think is a
good idea in the longer term.

>Obviously any extension of the standard would require some new coding for 
>full implementation. So far I haven't come across a reader than chokes on 
>the non-standard codes written by AIPS.

Coding BTYPE may be slightly more difficult than coding extra STOKES
codes but clearly it would be effort well spent.

>provide a complete list (and a short one), even in the astronomical arena 
>it would be hard to argue that any such list of types would be complete...
>let alone for more general FITS usage (grain yield per hectare??).

It never would be complete, but in many instances BTYPE would only be of
interest in labelling graphs - like CTYPE used to be and often still is.
A basic set could be defined initially and new ones registered in a
central repository, like that of keywords, at a later time.

>So let's not hold up a simple fix for the lack of a theory of 
>everything...

It's only one little keyword - and, looking on the bright side, the
requirement for it to take at least seven years to get anything ratified
in FITS has now been dispensed with!

Regards, Mark