Polarimetry Example

Stokes parameters are the most common method for storing and analysis of polarimetric data. Here is an illustrative example of how they might be stored using the $<$NDF$>$ structure, taking the approach that the $I$ data is the principal data array, and is therefore stored at the top-level of the structure. The $Q$, $U$ and $V$-parameter data are $<$NDF$>$ structures called, respectively, [STOKES_Q], [STOKES_U] and [STOKES_V], and located within a polarimetry extension.

The obvious alternative approach would be simply to add to the [DATA_ARRAY] an extra dimension so that the different Stokes parameters could all be stored in a single data array. Thus, for example, the four Stokes pictures from a 512$\times$512 imaging polarimeter would be stored as different planes of a 4$\times$512$\times$512 data cube. Though superficially more elegant than using separate arrays for each Stokes parameter, such an approach would introduce the danger of invalid processing, because the Stokes parameters are intrinsically different from each other; they cannot be combined (for example adding a $Q$ pixel value to its $V$ value would be meaningless) whereas analogous arithmetic between values in the spatial time and wavelength/energy dimensions (for example rebinning) would, of course, be valid.

Table: Example Polarimetry extension.

Component Name	TYPE	Brief Description
[STOKES_Q]	$<$NDF$>$	Stokes $Q$ data objects
[STOKES_U]	$<$NDF$>$	Stokes $U$ data objects
[STOKES_V]	$<$NDF$>$	Stokes $V$ data objects

Table: A polarimetry example using the $<$NDF$>$

Component Name	TYPE	Brief Description
[TITLE]	$<$_CHAR$>$	title of $<$NDF$>$
[DATA_ARRAY]	$<$various$>$	Stokes $I$ data array
[LABEL]	$<$_CHAR$>$	label describing the data array
[UNITS]	$<$_CHAR$>$	units of the data array
[VARIANCE]	$<$s_array$>$	variance of the data array
[QUALITY]	$<$various$>$	quality of the data array
[AXIS(NAXIS)]	$<$AXIS$>$	axis values, labels, units and errors
		applicable to all Stokes parameters
[HISTORY]	$<$HISTORY$>$	history structure
[MORE]	$<$EXT$>$	extension structure
[.POLARIMETRY]	$<$EXT$>$	polarimetry extension

Usually, the different Stokes parameters will have the same axis information and, using the structure above, specialist polarimetry applications will be able to exploit this fact. However, general-purpose applications will not be able to do so, because of the rule on ``tree-walking''. To obtain other than default axis data using a general-purpose application, say displaying [STOKES_Q.DATA_ARRAY], the axis information must be duplicated in the [STOKES_Q] structure; alternatively, application should have a parameter which specifies where the axis information is to be found. If the default is taken, the application should look for the $<$AXIS$>$ structure in the normal place, i.e. within [STOKES_Q.]