NotesOnPolarization < IVOA

IVOA Web>IvoaDataModel>CharacterisationDataModel>NotesOnPolarization (2009-11-09, AnitaRichards) (raw view)
---+ Polarization

---++ IVOA Draft Note for May 2009 Interop

[[%ATTACHURL%/Note-Polarization-0.1-20090522.pdf][Note-Polarization-0.1-20090522.pdf]]

[[%ATTACHURL%/Note-Polarization-0.1-20091008.pdf][Note-Polarization-0.1-20091008.pdf]]

[[%ATTACHURL%/polarization2_amsr.xml][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 [[http://wiki.ivoa.net/internal/IVOA/InterOpMay2008DataModels/PolInterfero-DM2008.pdf][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 <nop>PolA</nop> | 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 <br/>
CTYPE3  = 'STOKES  ' <br/>
CRPIX3  =         1.000000E+00 <br/>
CRVAL3  =   1.000000000000E+00 <br/>

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 | | lin | | cir | | cir | | cir | | lin | | lin | | lin | | lin | | cir | | cir | | | | lin | | lin | |
| | I | | Q | | U | | V | | RR | | LL | | RL | | LR | | XX | | YY | | XY | | YX | | UNDEF | | POLI | | POLA | |
| | 1 | | 2 | | 3 | | 4 | | -1 | | -2 | | -3 | | -4 | | -5 | | -6 | | -7 | | -8 | | --- | | 5 | | 7 | |


-- IVOA.AnitaRichards - 16 Jun 2008
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   * [[%ATTACHURL%/Note-Polarization-0.1-20090522.pdf][Note-Polarization-0.1-20090522.pdf]]:
Topic revision: r6 - 2009-11-09 - AnitaRichards
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