VII ) characterization of polarization data
bonnarel at alinda.u-strasbg.fr
bonnarel at alinda.u-strasbg.fr
Sun Nov 16 16:50:29 PST 2008
This is the end of the report of the Observation characterization Provenance
Task characterization group discussion. here the topic is
Characterization of various type of data: "Polarization data"
-----------------------------------------------------------------------------------
Step 1 FB starts with an example using the current version of charac
----------------------------------------------------------------------------------
Hi all, using an example given by Anita (see below) I built a small
charac file (with the help of camea) containing three dependent axes
with polarized flux in Stokes I, Q , U
Remarks: however the values I gave for the coverage along these axes
are just dummy ones. I need help from Anita to estimate the min/max
values on these axes and maybe sampling (Yeah these are flux axes ...)
It was not possible to create a Polarization axis. Such an axis will
require nothing else as the enumerated list of the Polarizations states
available in the data file : The four Stokes , L , R , XX, Polarization
angle, etc ...
And our schema currently doesn't allow this.
This is an addition we will have to introduce in the next version.
Anyway, it's already possible to pick up this list from the xml by an
xpath search on the ucd , checking where it starts by the string
"polarization"
This example will illustrate the capacities of Char DM to tackle
various data sets.
Please send me your comments.
--> to discuss on examples and solutions ...
URL
http://www.cv.nrao.edu/cgi-bin/postage.pl?Equinox=J2000&PolType=IQU&RA=12+30
+49.4234&Dec=%2B12+23+28.044&Size=0.25+0.25&Cells=15.0+15.0&MAPROJ=SIN&T
+ype=
application/octet-stream
Cheers
Francois
___________________________________
SIMPLE = T / file does conform to FITS standard
BITPIX = -32 / number of bits per data pixel
NAXIS = 4 / number of data axes
NAXIS1 = 61 / length of data axis 1
NAXIS2 = 61 / length of data axis 2
NAXIS3 = 3 / length of data axis 3
NAXIS4 = 1 / length of data axis 4
EXTEND = T / FITS dataset may contain extensions
COMMENT FITS (Flexible Image Transport System) format defined in Astronomy
and
COMMENT Astrophysics Supplement Series v44/p363, v44/p371, v73/p359,
v73/p365.
COMMENT Contact the NASA Science Office of Standards and Technology for
the
COMMENT FITS Definition document #100 and other FITS information.
OBJECT = 'No_Name ' / Name of object
TELESCOP= 'VLA ' / Telescope used
INSTRUME= 'L-BAND ' / Instrument/detector used
OBSERVER= 'NVSS GRP' / Astronomical observer
DATE-OBS= '1995-02-27' / Date (yyyy-mm-dd) of observations
BUNIT = 'JY/BEAM ' / Physical units of image
EPOCH = 2.000E+03 / Celestial coordiate equinox
ALTRPIX = 1.000000E+00 / Frequency alternate reference pixel
DATAMAX = 8.236951E+01 / Maximum physical value in image
DATAMIN = -1.936660E-01 / Minimum physical value in image
OBSRA = 1.880000000000E+02 / Observered Right Ascension
OBSDEC = 1.200000000000E+01 / Observered declination
CTYPE1 = 'RA---SIN' / Axis types
CTYPE2 = 'DEC--SIN'
CTYPE3 = 'STOKES '
CTYPE4 = 'FREQ '
CDELT1 = -4.166667E-03 / Axis coordinate increments
CDELT2 = 4.166667E-03
CDELT3 = 1.000000E+00
CDELT4 = 1.000000E+08
CRPIX1 = 3.100000E+01 / Axis coordinate reference pixel
CRPIX2 = 3.100000E+01
CRPIX3 = 1.000000E+00
CRPIX4 = 1.000000E+00
CROTA1 = 0.000000E+00 / Axis coordinate rotation
CROTA2 = 0.000000E+00
CROTA3 = 0.000000E+00
CROTA4 = 0.000000E+00
CRVAL1 = 1.877059308370E+02 / Axis coordinate value at CRPIXn
CRVAL2 = 1.239112333351E+01
CRVAL3 = 1.000000000000E+00
CRVAL4 = 1.400000000000E+09
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
<?xml version="1.0" encoding="UTF-8"?>
<char:characterisation
xmlns:char="http://www.ivoa.net/xml/Characterisation/Characterisation-v1.11.xsd">
<char:characterisationAxis>
<char:axisName>spatial</char:axisName>
<char:ucd>pos</char:ucd>
<char:unit>deg</char:unit>
<char:coordsystem id="TT-ICRS-TOPO"
xlin:href="ivo://STClib/CoordSys#TT-ICRS-TOPO"
xmlns:xlin="http://www.w3.org/1999/xlink"/>
<char:accuracy/>
<char:independentAxis>true</char:independentAxis>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins2>
<char:I1>61</char:I1>
<char:I2>61</char:I2>
</char:numBins2>
<char:undersamplingStatus>true</char:undersamplingStatus>
<char:regularsamplingStatus>true</char:regularsamplingStatus>
<char:coverage>
<char:location>
<char:unit>deg</char:unit>
<char:coord>
<stc:Position2D
xsi:type="stc:posVector2CoordinateType"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<stc:Name1>lon</stc:Name1>
<stc:Name2>lat</stc:Name2>
<stc:Value2 xsi:type="stc:double2Type">
<stc:C1>187.705930837</stc:C1>
<stc:C2>123.9112333351</stc:C2>
</stc:Value2>
</stc:Position2D>
</char:coord>
</char:location>
<char:bounds>
<char:unit>deg</char:unit>
<char:limits>
<char:CharBox>
<stc:Value2 xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<stc:C1>187.705930837</stc:C1>
<stc:C2>123.9112333351</stc:C2>
</stc:Value2>
<stc:Size2 xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<stc:C1>0.254</stc:C1>
<stc:C2>0.254</stc:C2>
</stc:Size2>
</char:CharBox>
</char:limits>
</char:bounds>
</char:coverage>
<char:samplingPrecision>
<char:samplingPrecisionRefVal>
<char:unit>deg</char:unit>
<char:samplingPeriod>
<stc:PixSize xsi:type="stc:double1Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">0.41666</stc:PixSize>
</char:samplingPeriod>
</char:samplingPrecisionRefVal>
</char:samplingPrecision>
</char:characterisationAxis>
<char:characterisationAxis>
<char:axisName>time</char:axisName>
<char:ucd>time</char:ucd>
<char:unit>none</char:unit>
<char:accuracy/>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins1>1</char:numBins1>
<char:coverage>
<char:location>
<char:unit>none</char:unit>
<char:coord>
<stc:Time
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd">
<stc:TimeInstant>
<stc:ISOTime xsi:type="stc:isoTimeType"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">1995-02-27T00:00:00</stc:ISOTime>
</stc:TimeInstant>
</stc:Time>
</char:coord>
</char:location>
</char:coverage>
</char:characterisationAxis>
<char:characterisationAxis>
<char:axisName>spectral</char:axisName>
<char:ucd>em</char:ucd>
<char:unit>Ghz</char:unit>
<char:accuracy/>
<char:independentAxis>true</char:independentAxis>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins1>1</char:numBins1>
<char:coverage>
<char:location>
<char:unit>Ghz</char:unit>
<char:coord>
<stc:Spectral
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd">
<stc:Value>1.4</stc:Value>
</stc:Spectral>
</char:coord>
</char:location>
</char:coverage>
</char:characterisationAxis>
<char:characterisationAxis>
<char:axisName>StokesI</char:axisName>
<char:ucd>phot.flux.density;phys.polarization.stokes.I</char:ucd>
<char:unit>jy</char:unit>
<char:coordsystem id="TT-ICRS-TOPO"
xlin:href="ivo://STClib/CoordSys#TT-ICRS-TOPO"
xmlns:xlin="http://www.w3.org/1999/xlink"/>
<char:accuracy/>
<char:independentAxis>false</char:independentAxis>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins1>10000</char:numBins1>
<char:coverage>
<char:location>
<char:unit>Jy.beam-1</char:unit>
<char:coord>
<stc:ScalarCoordinate
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd" >
<stc:Value>10.0</stc:Value>
</stc:ScalarCoordinate>
</char:coord>
</char:location>
<char:bounds>
<char:limits>
<char:CharBox>
<stc:Value xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
10.0
</stc:Value>
<stc:Size xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
20.0
</stc:Size>
</char:CharBox>
</char:limits>
</char:bounds>
</char:coverage>
</char:characterisationAxis>
<char:characterisationAxis>
<char:axisName>StokesQ</char:axisName>
<char:ucd>phot.flux.density;phys.polarization.stokes.Q</char:ucd>
<char:unit>Jy.beam-1</char:unit>
<char:accuracy/>
<char:independentAxis>false</char:independentAxis>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins1>10000</char:numBins1>
<char:coverage>
<char:location>
<char:unit>Jy.beam-1</char:unit>
<char:coord>
<stc:ScalarCoordinate
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd" >
<stc:Value>10.0</stc:Value>
</stc:ScalarCoordinate>
</char:coord>
</char:location>
<char:bounds>
<char:limits>
<char:CharBox>
<stc:Value xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
10.0
</stc:Value>
<stc:Size xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
20.0
</stc:Size>
</char:CharBox>
</char:limits>
</char:bounds>
</char:coverage>
</char:characterisationAxis>
<char:characterisationAxis>
<char:axisName>StokesU</char:axisName>
<char:ucd>phot.flux.density;phys.polarization.stokes.U</char:ucd>
<char:unit>Jy.beam-1</char:unit>
<char:accuracy/>
<char:independentAxis>false</char:independentAxis>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins1>10000</char:numBins1>
<char:coverage>
<char:location>
<char:unit>Jy.beam-1</char:unit>
<char:coord>
<stc:ScalarCoordinate
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd">
<stc:Value>10.0</stc:Value>
</stc:ScalarCoordinate>
</char:coord>
</char:location>
<char:bounds>
<char:limits>
<char:CharBox>
<stc:Value xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
10.0
</stc:Value>
<stc:Size xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
20.0
</stc:Size>
</char:CharBox>
</char:limits>
</char:bounds>
</char:coverage>
</char:characterisationAxis>
</char:characterisation>
--------------------------------------------------------------------------------
*Step 2 Anita comments
---------------------------------------------------------------------------------
Some comments:
It seems out-of-proportion to have a separate axis for each Stokes, and
how would someone who just wanted a 'normal' map, i.e. total intensity
or Stokes I manage, since people who don;t care about polarization will
not write software recognising Stokes.
> It was not possible to create a Polarization axis. Such an axis will
> require nothing else as the enumerated list of the Polarizations
> states available in the data file : The four Stokes , L , R , XX,
> Polarization angle, etc ... And our schema currently doesn't allow
> this.
I was thinking of treating the flux axis like the spatial axis, with a
unlimited number of dimensions.
I think that we do need to improve the way that CAMEA and/or the model
handles multi-dimensional axes. It would really help to know
explicitly how many dimensions an axis has, with the order.
CAMEA does not seem to display the multi-dimensional axes names, e.g. I
can see <stc:Name1>lon</stc:Name1> <stc:Name2>lat</stc:Name2> in the
xml, but I can't find this in Camea.
So, should we wait until we can upgrade the model?
> Can we estimate roughly the bounds , resolution and sampling of
> these axes ?
The units are Jy.beam-1, not jy
Bounds would be
DATAMAX = 1.967494E+01 / Maximum physical value in image
DATAMIN = -1.604240E-01 / Minimum physical value in image
from the FITS header, but that is only for Stokes I
I can get at the equivalents for Q and U but only using AIPS; in
general this is the sort of metadata that the data provider needs to
provide.
Unfortunately you can't just inherit the bounds from Stokes I because
some Stokes parameters can have genuinely negative values which are
more extreme than the lower limit for total intensity.
I'm not sure if resolution and sampling are meaningful for flux density
in noise-limited images (as distinct from photon- or count-limited); a
user might think of some multiple of the noise as the resolution in the
sense of the minimum meaningful difference, but I can't imagine any
direct use via the model and I think that it would confuse people.
The errors would be given by the data provider in the same way as for
the total intensity (often different per polarization).
Looked at from another point of view, what do I want to know about the
flux densities in the Stokes parameters in an NVSS image?
* Which polarizations are present (this is the most important!)
* What are the max and min values of flux density
* What is the noise (statistical error) and the leakage (this is usually
expressed as a percentage of the total intensity - can we handle that?
Can we allow the errors to have different units from the image?)
* If there are error maps, I'd like them (I presume that means the
variation of error across the spatial plane(s))
--------------------------------------
UCDs
I am not sure about phys.polarization. etc as it stands.
Stokes I is just total intensity so to me it seems the same as
phot.flux.density
and it would seem more logical to me to make
phot.flux.density.stokes.I etc
or phot.flux.density.polarization.stokes.I
and phot.flux.density.polarization.circular
phot.flux.polarization.angle
etc.
But I guess you have started from phys.polarization
which already exists
but it is not clear to me whether those ucds refer to flux densities or to
fractional polarization, and maybe it does not matter as long as there is
some ucd?
--------------------------------------------------------------------------------
*Step 3 Francois answers Anita
--------------------------------------------------------------------------------
-Partial Answer on UCDs
Something like phot.flux.density;phys.polarization.Stokes.I
phot.flux.density;phys.polarization.Stokes.Q
??? (combining two UCDS with the semi-column)
I guess we can find a UCD fo "relative flux" But I don't know it ...
Cheers
---------------------------------------------------------------------------------
*Step 4 Anita back to François
--------------------------------------------------------------------------------
> Thanks Anita
> -Partial Answer on UCDs
> Something like phot.flux.density;phys.polarization.Stokes.I
> phot.flux.density;phys.polarization.Stokes.Q
>
> ??? (combining two UCDS with the semi-column)
I like it!
> I guess we can find a UCD fo "relative flux" But I don't know it ...
At present there is
phys.polarization.circular
phys.polarization.linear
which to avoid ambiguity could be
phys.polarization.circular;arith.ratio
phys.polarization.linear;arith.ratio
e.g. [(Q+2 + U+2)+0.5]/I etc. (dimensionless)
and
phys.polarization.angle
as distinct from
phot.flux.density;phys.polarization.linear
which would be P = (Q+2 + U+2)+0.5 (Jy or whatever)
But I'm happy to leave it to Sebastien
--------------------------------------------------------------------------------
*Step 5 Sebastien proposal for Polarization UCds (in French)
---------------------------------------------------------------------------------
Actuellement, on a comme UCDs:
E|phys.polarization |Polarization degree (or percentage)
Q|phys.polarization.circular |Circular polarization
Q|phys.polarization.linear |Linear polarization
Q|phys.polarization.rotMeasure |Rotation measure polarization
Q|phys.polarization.stokes |Stokes polarization
Je propose de rajouter les termes
phys.polarization.stokes.I
phys.polarization.stokes.Q
phys.polarization.stokes.U
phys.polarization.stokes.V
phys.polarization.circular.L
phys.polarization.circular.R
phys.polarization.linear.X
phys.polarization.linear.Y
Est-ce qu'il faudrait un mot spécifique pour l'intensité??
On peut exprimer les termes croisés avec des combinaisons:
Correlation LR:
stat.correlation;phys.polarization.circular.L;phys.polarization.circular.R
Angle de polarisation:
pos.posAng;phys.polarization.linear
------------------------------------------------------------------------------
*Step 6 New version of the example by FB
-----------------------------------------------------------------------------
The version above allready takes into accounts some of Anita's comments
The version below contains a multifolded axis for Polarization
<?xml version="1.0" encoding="UTF-8"?>
<char:characterisation
xmlns:char="http://www.ivoa.net/xml/Characterisation/Characterisation-v1.11.xsd">
<char:characterisationAxis>
<char:axisName>spatial</char:axisName>
<char:ucd>pos</char:ucd>
<char:unit>deg</char:unit>
<char:coordsystem id="TT-ICRS-TOPO"
xlin:href="ivo://STClib/CoordSys#TT-ICRS-TOPO"
xmlns:xlin="http://www.w3.org/1999/xlink"/>
<char:accuracy/>
<char:independentAxis>true</char:independentAxis>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins2>
<char:I1>61</char:I1>
<char:I2>61</char:I2>
</char:numBins2>
<char:undersamplingStatus>true</char:undersamplingStatus>
<char:regularsamplingStatus>true</char:regularsamplingStatus>
<char:coverage>
<char:location>
<char:unit>deg</char:unit>
<char:coord>
<stc:Position2D
xsi:type="stc:posVector2CoordinateType"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<stc:Name1>lon</stc:Name1>
<stc:Name2>lat</stc:Name2>
<stc:Value2 xsi:type="stc:double2Type">
<stc:C1>187.705930837</stc:C1>
<stc:C2>123.9112333351</stc:C2>
</stc:Value2>
</stc:Position2D>
</char:coord>
</char:location>
<char:bounds>
<char:unit>deg</char:unit>
<char:limits>
<char:CharBox>
<stc:Value2 xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<stc:C1>187.705930837</stc:C1>
<stc:C2>123.9112333351</stc:C2>
</stc:Value2>
<stc:Size2 xsi:type="stc:double2Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<stc:C1>0.254</stc:C1>
<stc:C2>0.254</stc:C2>
</stc:Size2>
</char:CharBox>
</char:limits>
</char:bounds>
</char:coverage>
<char:samplingPrecision>
<char:samplingPrecisionRefVal>
<char:unit>deg</char:unit>
<char:samplingPeriod>
<stc:PixSize xsi:type="stc:double1Type"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">0.41666</stc:PixSize>
</char:samplingPeriod>
</char:samplingPrecisionRefVal>
</char:samplingPrecision>
</char:characterisationAxis>
<char:characterisationAxis>
<char:axisName>time</char:axisName>
<char:ucd>time</char:ucd>
<char:unit>none</char:unit>
<char:accuracy/>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins1>1</char:numBins1>
<char:coverage>
<char:location>
<char:unit>none</char:unit>
<char:coord>
<stc:Time
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd">
<stc:TimeInstant>
<stc:ISOTime xsi:type="stc:isoTimeType"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">1995-02-27T00:00:00</stc:ISOTime>
</stc:TimeInstant>
</stc:Time>
</char:coord>
</char:location>
</char:coverage>
</char:characterisationAxis>
<char:characterisationAxis>
<char:axisName>spectral</char:axisName>
<char:ucd>em</char:ucd>
<char:unit>Ghz</char:unit>
<char:accuracy/>
<char:independentAxis>true</char:independentAxis>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins1>1</char:numBins1>
<char:coverage>
<char:location>
<char:unit>Ghz</char:unit>
<char:coord>
<stc:Spectral
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd">
<stc:Value>1.4</stc:Value>
</stc:Spectral>
</char:coord>
</char:location>
</char:coverage>
</char:characterisationAxis>
<char:characterisationAxis>
<char:axisName>Stokes</char:axisName>
<char:ucd>phot.flux.density;phys.polarization.Stokes</char:ucd>
<char:unit>Jy.beam-1</char:unit>
<char:coordsystem id="UTC-ICRS-TOPO"
xlin:href="ivo://STClib/CoordSys#UTC-ICRS-TOPO"
xmlns:xlin="http://www.w3.org/1999/xlink"/>
<char:accuracy/>
<char:calibrationStatus>CALIBRATED</char:calibrationStatus>
<char:numBins3>
<char:I1>10000</char:I1>
<char:I2>10000</char:I2>
<char:I3>10000</char:I3>
</char:numBins3>
<char:coverage>
<char:location>
<char:unit>Jy.beam-1</char:unit>
<char:coord>
<stc:Vector3DCoordinate
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd" >
<stc:Name1>StokesI</stc:Name1>
<stc:Name2>StokesQ</stc:Name2>
<stc:Name3>StokesU</stc:Name3>
<stc:Value3>
<stc:C1>10.0</stc:C1>
<stc:C2>10.0</stc:C2>
<stc:C3>10.0</stc:C3>
</stc:Value3>
</stc:Vector3DCoordinate>
</char:coord>
</char:location>
<char:bounds>
<char:unit>Jy.beam-1</char:unit>
<char:limits>
<char:Coord3VecInterval
xsi:type="stc:coord3VecIntervalType"
xmlns:stc="http://www.ivoa.net/xml/STC/stc-v1.30.xsd"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<stc:LoLimit3Vec>
<stc:C1>10.0</stc:C1>
<stc:C2>10.0</stc:C2>
<stc:C3>10.0</stc:C3>
</stc:LoLimit3Vec>
<stc:HiLimit3Vec>
<stc:C1>20.0</stc:C1>
<stc:C2>20.0</stc:C2>
<stc:C3>20.0</stc:C3>
</stc:HiLimit3Vec>
</char:Coord3VecInterval>
</char:limits>
</char:bounds>
</char:coverage>
</char:characterisationAxis>
</char:characterisation>
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