View source for 3C286 Band6Pol Imaging for CASA 6.6.1

[[Category:ALMA]][[Category:Imaging]][[Category:Polarization]]

==Overview==

This portion of the '''[[3C286 Polarization]]''' CASA Guide will cover the imaging of the 
total power and polarized emission.

This guide picks up where the '''[[3C286 Band6Pol Calibration | Calibration]]''' section left off: right after running the CASA task {{split_6.6.1}} to split off the science target from the rest of the measurement set following calibration.   If you completed the Calibration section of the guide, then you can continue where you left off, with ''3c286_Band6.pol.cal.ms''.  

If you did not complete the Calibration portion of the guide, then you can instead download the file ''3C286_Band6_CalibratedData.tgz'' (the calibrated uv data) from [[3C286 Polarization#Obtaining the Data | Obtaining the Data]]'''.

Once the download has finished, unpack the file:
<source lang="bash">
# In a bash terminal outside CASA
tar -xvzf 3C286_Band6_CalibratedData.tgz
cd 3C286_Band6_CalibratedData
</source>

After that, you should have ''3c286_Band6.pol.cal.ms'' in your working directory.

{{CARTA_6.6.1}}

==Full polarization imaging of the target==

We will start by making a continuum full Stokes image of 3C286 using {{tclean_6.6.1}}. 
We first define the dataset we will use in all the following steps:

<source lang="python">
# In CASA
vis='3c286_Band6.pol.cal.ms'
</source>

Before starting the cleaning, it makes sense to check if the emission is resolved or not by plotting amplitude as a function of uv-distance.
The higher amplitudes at shorter uv-distances suggest that the source is slightly resolved.

<source lang="python">
# In CASA
plotms(vis, spw='', xaxis='uvwave', yaxis='amp', correlation='XX,YY',
       avgtime='1e8', avgchannel='1000', coloraxis='baseline')
</source>

[[File:Target_uvplot_5.4.png|300px|thumb|right|Amplitude vs. uv-distance. The source seems to be slightly resolved.]]

This plot also helps us defining the cellsize needed for the task clean.
From the plot we see that the longest baseline is 500 kilo wavelength. This means that the maximum resolution can be
approximately 1/500000*206265 arcsec = 0.4 arcsec.
We will use a '''cellsize=0.1''', to oversample the beam sufficiently. The FWHM of the primary beam of ALMA in Band 6 is about 25 arcsec, and we want to image out to at least that extent, so we will use '''imsize=250'''.

<source lang="python">
# In CASA

os.system('rm -rf 3c286.StokesIQUV*')
tclean(vis,
       imagename = '3c286.StokesIQUV',
       cell = ['0.1arcsec'],
       imsize = [250,250],
       deconvolver = 'clarkstokes',
       stokes = 'IQUV',
       interactive = True, 
       weighting = 'briggs',
       robust = 0.5,
       niter = 500,
       pbcor = True)
</source>

Specifying ''interactive=True'', the {{tclean_6.6.1}} task brings up a viewer to show the residual clean image, where clean masks can be defined. When the residuals are noise-like, the cleaning process can be finished by clicking the red X symbol. 
Please note that the cleaning will not start without any active mask (to activate a mask you need to double click inside the region).  
See [[First_Look_at_Imaging#First_Look_at_TCLEAN]] for further details on the interactive use of {{tclean_6.6.1}}.

Finally, note that we delete any previous versions of the output images before proceeding with the clean command.  This is important, because if images with the supplied root name already exist, CASA will clean those further instead of producing new output images.

After around 500 iterations, using an elliptical clean box around the central source, the residuals are already noise-like, so you can  stop the cleaning. 
To view your newly cleaned image, start CARTA. If using NRAO machines, you can open a new terminal tab, cd to the working directory, then type:

<source lang="bash">
# in terminal
carta --no_browser
</source>

Copy the output URL into a browser to view your CARTA session. Select and load:<br> ''3c286.StokesIQUV.image''

<gallery widths=250px heights=250px perrow=4 mode="packed" caption="Fig. 2: Full Polarization Image of 3c286">
File:3C286.StokesIQUV.image.I_6.6.1.png|Stokes I (total intensity)
File:3C286.StokesIQUV.image.Q_6.6.1.png|Stokes Q (linear polarization)
File:3C286.StokesIQUV.image.U_6.6.1.png|Stokes U (linear polarization)
File:3C286.StokesIQUV.image.V_6.6.1.png|Stokes V (circular polarization)
</gallery>

Now draw a box in CARTA on the I plane away from the source and use the Statistics widget to determine the rms and max. Alternatively, use {{imstat_6.6.1}} as follows:

<source lang="python">
# In CASA
calstat = imstat(imagename='3c286.StokesIQUV.image', stokes='I', box='45,45,95,95')
rms = (calstat['rms'][0])
print('>> rms in continuum image: '+str(rms))
calstat = imstat(imagename='3c286.StokesIQUV.image', stokes='I')
peak = (calstat['max'][0])
print('>> Peak in continuum image: '+str(peak))
print('>> Dynamic range in continuum image: '+str(peak/rms))
</source>

This tells us that the rms of this image is ~1.06 mJy and the peak flux density is ~299 mJy. The dynamic range (ratio between peak and rms) is ~282.

== Self-calibration ==

The quality of the image can be improved by applying self-calibration to the uv data. See [[AntennaeBand7_Imaging]] for details on this technique.

First, examine the model image we just created in CARTA:<br>''3c286.StokesIQUV.model''

<gallery widths=250px heights=240px perrow=4 mode="packed" caption="Fig. 3: Full Polarization Model Image of 3c286">
File:3C286.StokesIQUV.model.I_6.6.1.png|Stokes I
File:3C286.StokesIQUV.model.Q_6.6.1.png|Stokes Q
File:3C286.StokesIQUV.model.U_6.6.1.png|Stokes U
File:3C286.StokesIQUV.model.V_6.6.1.png|Stokes V
</gallery>

<div style="background-color: #E0FFFF; padding: 10px; font-family: 'Consolas', monospace;>
For linear feeds, I and Q are determined by parallel-hand correlations XX and YY, while U and V are determined by cross-hand correlations XY and YX. Therefore, calibrations in I also affect Q. To account for this, Q must have a reliable model before proceeding with the self-calibration of I. A low signal in Q may result in too poor of a model.
</div>

To proceed with self-calibration, first use {{tclean_6.6.1}} to read the model image and write model visibilities it into the MODEL column of the MS.

<div style="background-color: #E0FFFF; padding: 10px; font-family: 'Consolas', monospace;>
The model image must be closed in CARTA before being read by tclean.
</div>

<source lang="python">
# In CASA
tclean(vis,
       imagename = '3c286.StokesIQUV',
       cell = ['0.1arcsec'],
       imsize = [250,250],
       deconvolver = 'clarkstokes',
       stokes = 'IQUV',
       interactive = True, 
       weighting = 'briggs',
       robust = 0.5,
       niter = 0,
       calcpsf = False,
       calcres = False,
       restoration = False,
       pbcor = True,
       savemodel = 'modelcolumn')
</source>

<div style="background-color: #E0FFFF; padding: 10px; font-family: 'Consolas', monospace;>
By default, savemodel = 'none', and the MS is opened in read-only mode. Ctrl+C can then be safely used to terminate tclean as needed. With savemodel = 'modelcolumn' (or 'virtual'), the MS will be written to, and using Ctrl+C may corrupt the MS. For the stand-alone step of reading an existing model image and writing model visibilities into the MS, choose "niter = 0, calcpsf = False, calcres = False, restoration = False, savemodel = 'modelcolumn'."
</div>

Each round of self-calibration will follow the steps:
# {{gaincal_6.6.1}}: create a self-calibration gain table
# {{plotms_6.6.1}}: examine the table
# {{applycal_6.6.1}}: apply the table
# {{tclean_6.6.1}}: make a new image
# {{imstat_6.6.1}}: determine image statistics

Start with a long solution interval near the length of a target scan, and decrease with each round from there.

=== Round 1 ===

[[Image:3c286_IQUV.G1p.png|600px|thumb|right|'''Fig 4:''' Phase-only self-calibration table with solint='300s'.]]

Now create a self-calibration gain table with {{gaincal_6.6.1}}:

<source lang="python">
# In CASA
os.system('rm -rf 3c286_IQUV.G1p')
gaincal(vis,
        caltable = '3c286_IQUV.G1p',
        solint = '300s',
        refantmode = 'strict',
        refant = 'DV23',
        minblperant = 4,
        calmode = 'p',
        minsnr = 4)
</source>

The critical parameters in this setup are ''solint''' and '''calmode''.
We will force the reference antenna to remain constant with the ''refantmode='strict'.''
We want to calculate phase solutions only so we use ''calmode=p'' and we start using ''solint=300s'', which averages in time close to the target scan length.
It is usually best to start with a large solint and then go down to the integration time if the S/N of the data permits.

To check the quality of the solutions we obtained, we plot the gains for each antenna, as function of time:

<source lang="python">
# In CASA
plotms(vis='3c286_IQUV.G1p', xaxis='time', yaxis='phase', coloraxis='spw', iteraxis='antenna', gridrows=3, gridcols=2)
</source>

Now we apply those solutions to the uv data:

<source lang="python">
# In CASA
applycal(vis, gaintable='3c286_IQUV.G1p', calwt=False)
</source>

<!--
Make a copy to match the self-cal image name we will create below. This is technically only necessary if you don't specify the mask name in {{tclean_6.6.1}}, in which case an existing mask in your working directory that matches the image name will be automatically applied. If you downloaded the calibrated data, you already have this mask file named ''3c286.StokesIQUV.mask''. 

To rename the file:
<source lang="python">
# In CASA
os.system('cp -r 3c286.StokesIQUV.mask 3c286.StokesIQUV.selfcal1.mask')
</source>
-->
The mask you drew for the initial clean has been saved in your working directory as a file ''3c286.StokesIQUV.mask''. We will start with this same mask while cleaning our next image:

<source lang="python">
# In CASA
os.system('rm -rf 3c286.StokesIQUV.selfcal1*')
tclean(vis,
       imagename = '3c286.StokesIQUV.selfcal1',
       cell = ['0.1arcsec'],
       imsize = [250,250],
       deconvolver = 'clarkstokes',
       stokes = 'IQUV',
       mask = '3c286.StokesIQUV.mask',
       weighting = 'briggs',
       robust = 0.5,
       interactive = True,
       pbcor = True,
       niter = 1000,
       savemodel = 'modelcolumn')
</source>

Determine new image statistics with CARTA or {{imstat_6.6.1}}:

<source lang="python">
# In CASA
calstat = imstat(imagename='3c286.StokesIQUV.selfcal1.image', stokes='I', box='45,45,95,95')
rms = (calstat['rms'][0])
print('>> rms in continuum image: '+str(rms))
calstat = imstat(imagename='3c286.StokesIQUV.selfcal1.image', stokes='I')
peak = (calstat['max'][0])
print('>> Peak in continuum image: '+str(peak))
print('>> Dynamic range in continuum image: '+str(peak/rms))
</source>

The rms of this new image is 0.31 mJy/beam, lower than the value measured in the first image (0.9 mJy/beam).

=== Round 2 ===

We run a second self-calibration, decreasing to 30 sec the solint, apply it to the data, and image it again:

<source lang="python">
# In CASA
os.system('rm -rf 3c286_IQUV.G2p')
gaincal(vis,
        caltable = '3c286_IQUV.G2p',
        solint = '30s',
        refantmode = 'strict',
        refant = 'DV23',
        minblperant = 4,
        calmode = 'p',
        minsnr = 4)
</source>

<source lang="python">
# In CASA
plotms(vis='3c286_IQUV.G2p', xaxis='time', yaxis='phase', iteraxis='antenna', coloraxis='spw')
</source>

<source lang="python">
# In CASA
applycal(vis, gaintable='3c286_IQUV.G2p', calwt=False)
</source>

<source lang="python">
# In CASA
os.system('rm -rf 3c286.StokesIQUV.selfcal2*')
tclean(vis,
       imagename = '3c286.StokesIQUV.selfcal2',
       cell = ['0.1arcsec'],
       imsize = [250,250],
       deconvolver = 'clarkstokes',
       stokes = 'IQUV',
       mask = '3c286.StokesIQUV.mask',
       interactive = True,
       weighting = 'briggs',
       robust = 0.5,
       pbcor = True,
       niter = 1000,
       savemodel = 'modelcolumn')
</source>

You can notice when the first residual image appears that some residual central emission is evident. Continue the cleaning, by using the green continue button, until the residual image appears as much as possible noise like. 
In this example we stop the clean after 2 cycles, and we check the image statistics.

<source lang="python">
# In CASA
calstat = imstat(imagename='3c286.StokesIQUV.selfcal2.image', stokes='I', box='45,45,95,95')
rms = (calstat['rms'][0])
print('>> rms in continuum image: '+str(rms))
calstat = imstat(imagename='3c286.StokesIQUV.selfcal2.image', stokes='I')
peak = (calstat['max'][0])
print('>> Peak in continuum image: '+str(peak))
print('>> Dynamic range in continuum image: '+str(peak/rms))
</source>

The rms level in this new image is ~0.2 mJy/beam.

=== Round 3 ===

This level can be improved by a last run of self-calibration, this time solving for both amplitude and phase.

<source lang="python">
# In CASA
os.system('rm -rf 3c286_IQUV.Gap')
gaincal(vis,
        caltable = '3c286_IQUV.Gap',
        solint = '30s',
        gaintable = '3c286_IQUV.G2p',
        refant = 'DV23',
        minblperant = 4,
        refantmode = 'strict',
        calmode = 'ap',
        minsnr = 4)
</source>

<source lang="python">
# In CASA
plotms(vis='3c286_IQUV.Gap', xaxis='time', yaxis='amp', iteraxis='antenna', coloraxis='spw')
</source>

<source lang="python">
# In CASA
applycal(vis, gaintable=['3c286_IQUV.G2p','3c286_IQUV.Gap'], calwt=False)
</source>

<source lang="python">
# In CASA
os.system('rm -rf 3c286.StokesIQUV.selfcal.ap*')
tclean(vis,
       imagename = '3c286.StokesIQUV.selfcal.ap',
       cell = ['0.1arcsec'],
       imsize = [250,250],
       deconvolver = 'clarkstokes',
       stokes = 'IQUV',
       mask = '3c286.StokesIQUV.mask',
       interactive = True, 
       weighting = 'briggs',
       robust = 0.5,
       pbcor = True,
       niter = 1000,
       savemodel = 'modelcolumn')
</source>

This time the first residual map shows a new bright extended component which was completely hidden by the noise in the previous images. We add a clean box around it and proceed with the clean. After 1000 cycles we stop and check the statistics of the image:

<source lang="python">
# In CASA
calstat = imstat(imagename='3c286.StokesIQUV.selfcal.ap.image', stokes='I', box='45,45,95,95')
rms = (calstat['rms'][0])
print('>> rms in continuum image: '+str(rms))
calstat = imstat(imagename='3c286.StokesIQUV.selfcal.ap.image', stokes='I')
peak = (calstat['max'][0])
print('>> Peak in continuum image: '+str(peak))
print('>> Dynamic range in continuum image: '+str(peak/rms))
</source>

The rms is 0.11 mJy and the peak of the image is 359 mJy, leading to a dynamic range of 3291.

We can consider this result satisfying and stop the self-calibration.

== Stokes images ==

We can extract the Stokes Q, U, and V images from the selfcalibrated image, using the taks immath:

<source lang="python">
# In CASA
os.system('rm -rf 3c286.StokesI.image*')
immath(imagename='3c286.StokesIQUV.selfcal.ap.image', outfile='3c286.StokesI.image', expr='IM0', stokes='I')

os.system('rm -rf 3c286.StokesQ.image*')
immath(imagename='3c286.StokesIQUV.selfcal.ap.image', outfile='3c286.StokesQ.image', expr='IM0', stokes='Q')

os.system('rm -rf 3c286.StokesU.image*')
immath(imagename='3c286.StokesIQUV.selfcal.ap.image', outfile='3c286.StokesU.image', expr='IM0', stokes='U')

os.system('rm -rf 3c286.StokesV.image*')
immath(imagename='3c286.StokesIQUV.selfcal.ap.image', outfile='3c286.StokesV.image', expr='IM0', stokes='V')
</source>

We measure the statistic in each emage, using the task imstat:

<source lang="python">
# In CASA
I_rms=(imstat(imagename='3c286.StokesI.image', box='35,35,95,95')['rms'][0])
I_peak=(imstat(imagename='3c286.StokesI.image')['max'][0])

Q_rms=(imstat(imagename='3c286.StokesQ.image', box='35,35,95,95')['rms'][0])
Q_peak=(imstat(imagename='3c286.StokesQ.image')['max'][0])

U_rms=(imstat(imagename='3c286.StokesU.image', box='35,35,95,95')['rms'][0])
U_peak=(imstat(imagename='3c286.StokesU.image')['max'][0])

print(I_rms, I_peak, Q_rms, Q_peak, U_rms, U_peak)
</source>

The results of the measurements for the I, Q, and U images are reported in the table below.  All flux densities are reported in mJy/beam.

The results obtained from the V image are not reported in the table, since '''at this time the quality and accuracy of the circular polarization data are still undergoing verification. Results from the V image are therefore not recommended for scientific purposes at this time'''.

{| class="wikitable"
| 
| style="text-align:center;"| I
| style="text-align:center;"| Q
| style="text-align:center;"| U
|-
| rms 
| style="text-align:center;"| 0.193
| style="text-align:center;"| 0.030
| style="text-align:center;"| 0.054
|-
|Peak
|style="text-align:center;"|334 
|style="text-align:center;"|12.3
|style="text-align:center;"|53.8
|-
|Dyn range
|style="text-align:center;"|1733
|style="text-align:center;"|410
|style="text-align:center;"|996
|}

==Constructing Polarization Intensity and Angle Images==

We have now produced the images for all the four Stokes parameters: I, Q, U, and V. Stokes Q and U describe the linear polarization and V describes the circular polarization.  Specifically, Q describes the amount of linear polarization aligned with a given axis, and U describes the amount of linear polarization at a 45 deg angle to that axis.  The V parameter describes the amount of circular polarization, with the sign (positive or negative) describing the sense of the circular polarization (right- or left-hand circularly polarized).

In general, few celestial sources are expected to show circular polarization, with the notable exception of masers.  Terrestrial and satellite sources are often highly circularly polarized.  The V image is therefore often worth forming because any V emission could be indicative of unflagged RFI within the data (or problems with the calibration!).

Because the Q and U images both describe the amount of linear polarization, it is more common to work with a linear polarization intensity image, <math>P = \sqrt{Q^2 +U^2}</math>. We can also calculate the polarization position angle <math>\chi = 0.5 arctan U/Q</math>.

The relevant task is {{immath_6.6.1}}; for specific examples of polarization image processing see
[http://casa.nrao.edu/Release4.2.2/docs/userman/UserMansu323.html Polarization Manipulation].  

To form the linear polarization image, we combine the Q and U images using the mode='poli' option of {{immath_6.6.1}}.
<source lang="python">
# In CASA
os.system('rm -rf 3c286_Band6.POLI')
immath(outfile='3c286_Band6.POLI',
       mode='poli',
       imagename=['3c286.cal.StokesQ.clean.image','3c286.cal.StokesU.clean.image'],
       sigma='0.0Jy/beam')
</source>


<source lang="python">
# In CASA
calstat=imstat(imagename='3c286_Band6.POLI', region='', box='10,10,90,35')
rms=(calstat['rms'][0])
print(rms)
</source>
The measured rms is 0.050 mJy/beam.

To form the polarization position angle image we combine again the Q and U images using the mode='pola' option of {{immath_6.6.1}}.  The Q and U images can be listed in either order. 
To avoid displaying the position angle of noise, we can use the polithresh parameter to set a threshold intensity of the linear polarization above which we wish to calculate the polarization angle. An appropriate level here might be the 5σ level of the polarization image, about 0.2 mJy/beam. 

<source lang="python">
# In CASA
os.system('rm -rf 3c286_Band6.POLA')
immath(outfile='3c286_Band6.POLA',
       mode='pola',
       imagename=['3c286.cal.StokesQ.clean.image','3c286.cal.StokesU.clean.image'],
       polithresh='0.2mJy/beam')
</source>

If desired,  it is also possible to form the fractional linear polarization image, defined as P/I. 
<source lang="python">
# In CASA
os.system('rm -rf 3c286_Band6.RATIO')
immath(outfile='3c286_Band6.RATIO',
       mode='evalexpr',
       imagename=['3c286.cal.StokesI.clean.image','3c286.cal.StokesQ.clean.image','3c286.cal.StokesU.clean.image'],
       expr='sqrt((IM1^2+IM2^2)/IM0[IM0>5e-3]^2)')
</source>
Since the total intensity image can (and hopefully does) approach zero in regions free of source emission, dividing by the total intensity can produce very high pixel values in these regions.  We therefore wish to restrict our fractional polarization image to regions containing real emission, which we do by setting a threshold in the total intensity image, which in this case corresponds to five times the noise level in the Stokes I image.  The computation of the polarized intensity is specified in the previous command by 
<pre style="background-color: #fffacd;">
       expr='sqrt((IM1^2+IM2^2)/IM0[IM0>5e-3]^2)'
</pre>
with the expression in square brackets setting the threshold in IM0 (the total intensity image).  Note that IM0, IM1 and IM2 correspond to the three files listed in the ''imagename'' array, '''in that order'''.  In this case, the order in which the different images are specified is critical.

In order to have a dimensionless value for the ratio image, we now modify the keyword bunit in the header of the file:

<source lang="python">
# In CASA
imhead('3c286_Band6.RATIO', mode='put', hdkey='bunit', hdvalue='')
</source>

==Image visualization and analysis==

Now we can view these various images using CARTA.  It is instructive to display the I, P, and <math>\chi</math> images (total intensity, total linearly polarized intensity, and polarization position angle) together, to show how the polarized emission relates to the total intensity, and how the magnetic field is structured.  We can do this using CARTA.
* Begin by loading the linear polarization image in CARTA:
* Next, polarization position angle image (3c286_Band6.POLA) as a vector map.  In the CARTA panel, hit the "File" then "Append Image".  This will bring up a 'File Browser' GUI showing all images and MS in the current directory. Navigatge to your image and select the polarization position angle image (3c286_Band6.POLA).
* Select the vector overlay icon from the top of the window. Set the Data Source as the *.POLA image, set the angular source as the current image, and set the intensity source to none.  Finally click on the apply button at the bottom of the vector overlay configuration window. 
[[File:Pol_cont_vect_6.5.4.png|300px|thumb|right|Full-polarization image of 3C286]]

While we set the ''polithresh'' parameter when we created the position angle (<math>\chi</math>) image, a digression here is instructive in the use of LEL Expressions.  Had we not set this parameter, the position angle would have been derived for all pixels within the full IQUV image cube.  There is only polarized emission from a limited subset of pixels within this image.  Therefore, to avoid plotting vectors corresponding to the position angle of pure noise, we now wish to select only the regions where the polarized intensity is brighter than some threshold value.  To do this, we use an LEL (Lattice Expression Language) Expression in the 'Load Data' GUI.  For our chosen threshold of 0.2 mJy/beam (the 5 sigma level in the P image), we paste the expression 
<pre style="background-color: #fffacd;">
'3c286_Band6.POLA'['3c286_Band6.POLI'>0.001]
</pre>
into the LEL Expression box in the GUI, and click the 'Vector Map' button.  This would load the vectors only for regions where P>1 mJy/beam.

To optimize the display for ease of interpretation we click the wrench icon to open a 'Data Display Options' GUI.  This will have 3 tabs, corresponding to the three images loaded.  
We can change the image color map and transfer function, the contour levels and color, and the the vector spacing and color.

For the polarization angle vector it is also possible to add a rotation.
The polarization position angle as calculated is the electric vector position angle (EVPA).  If we are interested in the orientation of the magnetic field, then for an optically thin source the magnetic field orientation is perpendicular to the EVPA, so we must rotate the vectors by 90 degrees.  Select the vector image tab in the 'Data Display Options' GUI (labeled as the LEL expression we entered in the Load Data GUI) and enter ''90'' in the ''Extra rotation'' box.  If the vectors appear too densely packed on the image, change the spacing of the vectors by setting ''X-increment'' and ''Y-increment'' to a larger value.  

To get quantitative information from the images, we can either use the task {{imstat_6.6.1}} (we already used it above) or the 
task {{imfit_6.6.1}}. 
The task {{imstat_6.6.1}} returns the statistics in a Python dictionary, from which we can read what we need in a Python variable.  In this example we extract the peak value:
<source lang="python">
# In CASA
calstat=imstat(imagename='3c286_Band6.POLI', region='')
print(calstat)
calstat['max'][0]
</source>

The output saved in '''calstat''' is pasted below.

<pre style="background-color: #fffacd;">
{'blc': array([0, 0, 0, 0]), 
 'blcf': '13:31:09.255, +30.30.20.460, Plinear, 2.3301e+11Hz',
 'flux': array([0.14085003]),
 'max': array([0.05526536]), 'maxpos': array([125, 126,   0,   0]),
 'maxposf': '13:31:08.288, +30.30.33.060, Plinear, 2.3301e+11Hz',
 'mean': array([7.8467172e-05]),
 'medabsdevmed': array([1.71810989e-05]),
 'median': array([4.27724954e-05]),
 'min': array([7.90703183e-08]),
 'minpos': array([28, 87,  0,  0]),
 'minposf': '13:31:09.039, +30.30.29.160, Plinear, 2.3301e+11Hz',
 'npts': array([62500.]), 'q1': array([2.72247598e-05]), 'q3': array([6.23603555e-05]), 'quartile': array([3.51355957e-05]),
 'rms': array([0.00094099]), 'sigma': array([0.00093772]),
 'sum': array([4.90419825]), 'sumsq': array([0.05534188]),
 'trc': array([249, 249,   0,   0]),
 'trcf': '13:31:07.329, +30.30.45.360, Plinear, 2.3301e+11Hz'}


calstat['max'][0]=0.055265363305807114
</pre>

The task {{imfit_6.6.1}} finds one or more elliptical gaussian components on an image region.

<source lang="python">
# In CASA
fit_res=imfit(imagename='3c286_Band6.POLI', region='')
print(fit_res)
</source>

The output saved in '''fit_res''' is pasted below.

<pre style="background-color: #fffacd;">

{'converged': array([ True]),
 'deconvolved': {'component0': {'flux': {'error': array([9.44862054e-05, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]),
 'polarisation': 'Stokes',
 'unit': 'Jy',
 'value': array([0.05640328, 0.        , 0.        , 0.        ])},
 'ispoint': True, 'label': '',
 'shape': {'direction': {'error': {'latitude': {'unit': 'arcsec',
 'value': 0.00040183003218277044},
 'longitude': {'unit': 'arcsec', 'value': 0.00012498417606069957}},
 'm0': {'unit': 'rad', 'value': -2.7439276433976794},
 'm1': {'unit': 'rad', 'value': 0.532485497843355},
 'refer': 'J2000', 'type': 'direction'},
 'type': 'Point'},
 'spectrum': {'channel': 0,
 'frequency': {'m0': {'unit': 'GHz', 'value': 233.00995157526424},
 'refer': 'LSRK',
 'type': 'frequency'},
 'type': 'Constant'},
 'sum': {'unit': 'Jy/beam', 'value': 1.001404955983162}},
 'nelements': 1},
 'pixelsperarcsec': array([10., 10.]),
 'results': {'component0': {'beam': {'beamarcsec': {'major': {'unit': 'arcsec',
 'value': 0.7631725072860718},
 'minor': {'unit': 'arcsec',
 'value': 0.4026465117931366},
 'positionangle': {'unit': 'deg', 'value': 8.341339111328125}},
 'beampixels': 34.818581831598614,
 'beamster': 8.183909381307055e-12},
 'flux': {'error': array([9.44862054e-05, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]),
 'polarisation': 'Stokes',
 'unit': 'Jy',
 'value': array([0.05640328, 0.        , 0.        , 0.        ])},
 'ispoint': True,
 'label': '',
 'peak': {'error': 5.0942046375170774e-05,
 'unit': 'Jy/beam',
 'value': 0.05616799016487879},
 'pixelcoords': array([125.21729508, 125.58042049]),
 'shape': {'direction': {'error': {'latitude': {'unit': 'arcsec',
 'value': 0.00040183003218277044},
 'longitude': {'unit': 'arcsec', 'value': 0.00012498417606069957}},
 'm0': {'unit': 'rad', 'value': -2.7439276433976794},
 'm1': {'unit': 'rad', 'value': 0.532485497843355},
 'refer': 'J2000',
 'type': 'direction'},
 'majoraxis': {'unit': 'arcsec', 'value': 0.764893494058789},
 'majoraxiserror': {'unit': 'arcsec', 'value': 0.0009546133974881486},
 'minoraxis': {'unit': 'arcsec', 'value': 0.40342347102453774},
 'minoraxiserror': {'unit': 'arcsec', 'value': 0.0002658946562409573},
 'positionangle': {'unit': 'deg', 'value': 7.910498993465549},
 'positionangleerror': {'unit': 'deg', 'value': 0.03902251323677755}, 'type': 'Gaussian'},
 'spectrum': {'channel': 0, 'frequency': {'m0': {'unit': 'GHz', 'value': 233.00995157526424},
 'refer': 'LSRK', 'type': 'frequency'},
 'type': 'Constant'},
 'sum': {'unit': 'Jy/beam', 'value': 1.001404955983162}}, 'nelements': 1}}

</pre>

To extract the flux and its error, we can read them from CASA in Python variables:
<source lang="python">
# In CASA
fluxPI=fit_res['results']['component0']['flux']['value'][0]
errorPI=fit_res['results']['component0']['flux']['error'][0]
</source>

The flux measured in the fitted gaussian is 60.7 mJy with an error of 0.096 mJy.

We now use this method to estimate the fluxes in all the Stokes images:

<source lang="python">
# In CASA

# First we run imfit 
resI=imfit(imagename = '3c286.cal.StokesI.clean.image', box = '110,110,145,145')
resQ=imfit(imagename = '3c286.cal.StokesQ.clean.image', box = '110,110,145,145')
resU=imfit(imagename = '3c286.cal.StokesU.clean.image', box = '110,110,145,145')
resV=imfit(imagename = '3c286.cal.StokesV.clean.image', box = '110,110,145,145')
 
# and then we extract the flux and error values for each Stokes

fluxI=resI['results']['component0']['flux']['value'][0]
errorI=resI['results']['component0']['flux']['error'][0]

fluxQ=resQ['results']['component0']['flux']['value'][1]
errorQ=resQ['results']['component0']['flux']['error'][1]

fluxU=resU['results']['component0']['flux']['value'][2]
errorU=resU['results']['component0']['flux']['error'][2]
 
fluxV=resV['results']['component0']['flux']['value'][3]
errorV=resV['results']['component0']['flux']['error'][3]
 
</source> 

Now we use these values to compute polarization intensity, angle and ratio, and their errors:
 
<source lang="python">
# In CASA 
import math

fluxPI  = math.sqrt( fluxQ**2 + fluxU**2 )
errorPI = math.sqrt( (fluxQ*errorQ)**2 + (fluxU*errorU)**2 ) / fluxPI

fluxPImjy = 1000*fluxPI
errPImjy  = 1000*errorPI

polRatio = fluxPI / fluxI
errPRat  = polRatio * math.sqrt( (errorPI/fluxPI)**2 + (errorI/fluxI)**2 )
  
polAngle = 0.5 * math.degrees( math.atan2(fluxU,fluxQ) )
errPA    = 0.5 * math.degrees( math.sqrt( (fluxQ*errorU)**2 + (fluxU*errorQ)**2 ) / fluxPI**2 )

</source>

The results are collected in the following table:

<center>
{| class="wikitable" 
| style="text-align:center;"| 
| style="text-align:center;"| Flux 
| style="text-align:center;"| err 
|-
| style="text-align:center;"| I (mJy) 
| style="text-align:center;"| 342
| style="text-align:center;"| 0.64
|-
| style="text-align:center;"| Q (mJy)
| style="text-align:center;"| 12.8
| style="text-align:center;"| 0.054
|-
| style="text-align:center;"| U (mJy)
| style="text-align:center;"| 54.9
| style="text-align:center;"| 0.16
|-
| style="text-align:center;"| Pol int (mJy)
| style="text-align:center;"| 56.4
| style="text-align:center;"| 0.123
|-
! scope="col"| P (%)
! scope="col"| 16.4
! scope="col"| 0.46
|-
! scope="col"| χ (deg)
! scope="col"| 38.44
! scope="col"| 0.030



|}
</center>

As you can see, the polarization intensity computed from the Q and U fluxes is the same as the one extracted from the polarization image (as it should be!).

Note that '''the uncertainties quoted above are purely statistical.'''  The systematic errors will be larger, and include (but are not limited to) any net bias in the position angle of the linear feeds in the antennas, the details of different observations (at what parallactic angles, etc.), and other data quality variations (including source structure).  We conservatively estimate the position angle uncertainty to be '''± 2º'''.

And now, a quick comparison with previous results from IRAM and CARMA.

[http://adsabs.harvard.edu/abs/2012A%26A...541A.111A Agudo et al. (2012)] presented the results of single-dish millimeter measurements of 3C286 with the IRAM 30 m Telescope.
Their observations at 1 mm (229 GHz) and 3 mm (86 GHz) produced the following results: 
{| class="wikitable"
|-
| 
|style="text-align:center;"| 1 mm
|style="text-align:center;"| 3 mm
|-
|P (%)
|style="text-align:center;"|14.4 ± 1.8 
|style="text-align:center;"|13.5 ± 0.3
|-
|χ (deg)
|style="text-align:center;"|'''33.1 ± 5.7'''
|style="text-align:center;"|37.3 ± 0.8
|}

[http://arxiv.org/abs/1506.04771 Hull & Plambeck 2015 (JAI)] and CARMA Memo 64 report interferometric polarization data of 3C286 taken with CARMA at 1 mm (225 GHz). Their results are as follows:
{| class="wikitable"
|-
| 
|style="text-align:center;"| 1 mm
|-
|χ (deg)
|style="text-align:center;"|'''39.2 ± 1.0'''
|}

==Export images in fits format==

To get all images in fits format you need to use the task {{exportfits_6.6.1}}.

You can add the parameters imagename (the input image) and fitsimage (the name of the output image) one by one or you can 
run a python cycle over all the images:

<source lang="python">
# In CASA 
import glob

imagenames=glob.glob("*image") 

for name in imagenames:
    exportfits(imagename=name, fitsimage=name+'.fits')

</source>