Polarization

IVOA Draft Note for May 2009 Interop

Note-Polarization-0.1-20090522.pdf

Note-Polarization-0.1-20091008.pdf

xml description of an NVSS cube primarily constructed by Francois Bonnarel

Some considerations for including Polarization in the Characterisation Data Model.

Astronomical Polarization

Polarization is essentially a set of Observables which are forms or derivative of Flux Density. If no polarization is specified this usually implies total intensity. There are a number of conventions for the order of polarization products etc. but unfortunately these differ between observatories. The examples etc. concentrate on the radio regime, other examples needed if data are available to the VO.

Registry/top level description

This could simply specify:

Polarization state: one or more of
- Total intensity
- Undefined
- Linear
- Circular
- Other (covering rotation measure (RM) maps, etc.)

Polarization axis

A single data set can have one or more polarizations which could be represented as a polarization axis.

If the polarization axis is present, the model should specify:
- Number of polarizations present
- Ordered list of labels e.g.
  - A data cube or image in a single, e.g. LL polarization
  - NVSS image cube with polarization axis with Stokes I Q U
  - A set of related images in P, chi etc.
  - Visibility data with an axis with correlations LL RR LR RL
  - A set of spectra, consisting of pairs of LCP and RCP
  - A rotation meaasure image
A number of labels are in common use, with a few synonyms, some of which are listed below.
If there are multiple polarizations present, each plane on the polarization axis can inherit the first plane properties but they can be replaced if necessary:
- Spatial and spectral location, bounds usually the same
- Sensitivity, dynamic range etc. can differ
- First plane may not be total intensity
- Some properties may not make sense for pol. angle chi

Calibration status etc.

A useful level of generalisation could include the following terms. Note that these should be available even for total intensity data, since its fidelity may be affected by polarization calibration.

Parallactic angle correction performed
Leakage correction performed
- Systematic and statistical errors
Polarization angle corrected
- Systematic and statistical errors
Method used to estimate errors in advanced products e.g. Ricean bias for RM images.
Considerations for IR and shorter wavelength data...
Pointers to external/supporting data, history, observatory pipeline used...

Supporting material

See talk at 2008 May interop (Trieste) for some illustrations and use cases.

Term	Common symbol	Description
Stokes parameters	I Q U V	total intensity, linear, linear, circular
Linear polarization angle	usually chi or PA or PolA	1/2 Arctan(U,Q) (anticlockwise from North)
Linearly polarized intensity	P	Sqrt(Q^2 + U^2)
Elliptically polarized intensity	M	Sqrt(Q^2 + U^2 + V^2)
Circularly polarized intensity	abs(V)	Absolute value of V
Fractional Q	q	Q/I
Fractional U	u	U/I
Fractional V	v	V/I
Fractional linear polarization	p	Sqrt(Q^2 + U^2) / I
Fractional elliptical polarization	m	Sqrt(Q^2 + U^2 + V^2) / I
Fractional circular polarization	v	abs(V) / I
Circular feeds	LCP, RCP (or L, R or LL, RR or LHC, RHC) and LR, RL	Left, right circular polarization, cross hands
Linear feeds	X, Y or XX, YY and XY, YX	Linear polarization NB relation to Q and U is instrument specific!

FITS code numbering

The numerical values will appear as the CRVAL etc. for the appropriate axis in the FITS header, for example, an NVSS IQU cube will have

NAXIS3 = 3 / length of data axis 3
CTYPE3 = 'STOKES '
CRPIX3 = 1.000000E+00
CRVAL3 = 1.000000000000E+00

The top line in the table below indicates whether the code corresponds to total intensity (tot), Linear (lin) or circular (cir) polarization e.g. for the purpose of ucd construction.

tot

lin

cir