View source for M100 Band3 Combine 4.3

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= Overview =

This guide describes how to combine the 7m and 12m interferometric data and then how to feather the resulting image with the total power TP image. All of the data for this SV project can be found at https://almascience.nrao.edu/alma-data/science-verification. The guide has been written for data reduced in CASA 4.3.0 or later and assumes that all calibration tables (Tsys and gain tables) have been applied to the visibility weights using calwt=True. If either of these is not the case for your data, '''do not follow this guide.''' 

In order to run this guide you will need to:

* Either download the fully calibrated 7m data (i.e., M100_Band3_7m_CalibratedData.tgz) or download the uncalibrated 7m data and the relevant, standard calibration scripts available (here). An overview of the 7m data and its calibration is located at http://casaguides.nrao.edu/index.php?title=M100_Band3.

* Either download the fully calibrated 12m data (i.e. M100_Band3_12m_CalibratedData.tgz) or download the uncalibrated 12m data and the relevant, standard calibration scripts available (here). Note that this is a '''new''' calibration of the same data that were released previously, and so the data reduction path has been updated to current best practices and starts from the raw data files called ASDMs (ALMA Science Data Model). '''Do not use the previously released uncalibrated or calibrated data.''' An overview of the 12m data and its calibration is located at http://casaguides.nrao.edu/index.php?title=M100_Band3.

* Either run the [[M100_Band3_SingleDish_4.3]] guide to calibrate and image the Total Power data or download the final image (i.e. M100_TP_Image.tgz)

==Confirm your version of CASA==

This guide has been written for CASA release 4.3.0.  Please confirm your version before proceeding.
<source lang="python">
# In CASA
version = casadef.casa_version
print "You are using " + version
if (version < '4.3.0'):
    print "YOUR VERSION OF CASA IS TOO OLD FOR THIS GUIDE."
    print "PLEASE UPDATE IT BEFORE PROCEEDING."
else:
    print "Your version of CASA is appropriate for this guide."
</source>

= Combine and Image the 7m+12m Interferometric Data =


== Split off CO spectral windows (SPWs) ==

<source lang="python">
# In CASA
os.system('rm -rf m100_*m.ms.listobs')
listobs('M100_Band3_12m_CalibratedData.ms',listfile='m100_12m.ms.listobs')
listobs('M100_Band3_7m_CalibratedData.ms',listfile='m100_7m.ms.listobs')
</source>

Running the task "listobs" provides the setups used in the observations at a glance. Below are the first target scans of the 12m and 7m observations and the spectral window tables as generated by listobs; these are excerpts from the complete files obtained in each case. Notice that the six 7m data sets were taken with two slightly different correlator setups (one with four SPWs and the other with two SPWs), so the concatenated data set has six total SPWs. 

12m data:
<pre style="background-color: #fffacd;">

ObservationID = 0         ArrayID = 0
  Date        Timerange (UTC)          Scan  FldId FieldName             nRows     SpwIds   Average Interval(s)    ScanIntent
  10-Aug-2011/19:38:05.8 - 19:50:22.8    11      1 M100                      1500  [0,1,2,3]  [6.05, 6.05, 6.05, 6.05] [CALIBRATE_WVR#ON_SOURCE,OBSERVE_TARGET#ON_SOURCE]

Spectral Windows:  (4 unique spectral windows and 1 unique polarization setups)
  SpwID  Name   #Chans   Frame   Ch0(MHz)  ChanWid(kHz)  TotBW(kHz) CtrFreq(MHz) BBC Num  Corrs
  0              3840   TOPO  113726.419       488.281   1875000.0 114663.6750        1  XX  YY
  1              3840   TOPO  111851.419       488.281   1875000.0 112788.6750        2  XX  YY
  2              3840   TOPO  103663.431      -488.281   1875000.0 102726.1750        3  XX  YY
  3              3840   TOPO  101850.931      -488.281   1875000.0 100913.6750        4  XX  YY
</pre>


7m data:
<pre style="background-color: #fffacd;">

ObservationID = 0         ArrayID = 0
  Date        Timerange (UTC)          Scan  FldId FieldName             nRows     SpwIds   Average Interval(s)    ScanIntent
  17-Mar-2013/04:44:04.3 - 04:50:43.7    11      1 M100                       261  [0,1,2,3]  [10.1, 10.1, 10.1, 10.1] [OBSERVE_TARGET#ON_SOURCE]

Spectral Windows:  (6 unique spectral windows and 1 unique polarization setups)
  SpwID  Name                           #Chans   Frame   Ch0(MHz)  ChanWid(kHz)  TotBW(kHz) CtrFreq(MHz) BBC Num  Corrs
  0      ALMA_RB_03#BB_1#SW-01#FULL_RES   4080   TOPO  101945.850      -488.281   1992187.5 100950.0000        1  XX  YY
  1      ALMA_RB_03#BB_2#SW-01#FULL_RES   4080   TOPO  103761.000      -488.281   1992187.5 102765.1500        2  XX  YY
  2      ALMA_RB_03#BB_3#SW-01#FULL_RES   4080   TOPO  111811.300       488.281   1992187.5 112807.1500        3  XX  YY
  3      ALMA_RB_03#BB_4#SW-01#FULL_RES   4080   TOPO  113686.300       488.281   1992187.5 114682.1500        4  XX  YY
  4      ALMA_RB_03#BB_1#SW-01#FULL_RES   4080   TOPO  111798.250       488.281   1992187.5 112794.1000        1  XX  YY
  5      ALMA_RB_03#BB_2#SW-01#FULL_RES   4080   TOPO  113673.250       488.281   1992187.5 114669.1000        2  XX  YY
</pre>

<figure id="12m_mosaic.png">
[[Image:12m_mosaic.png|300px|thumb|right|<caption>FOV of 12m mosaic.</caption>]]
</figure>

<figure id="7m_mosaic.png">
[[Image:7m_mosaic.png|300px|thumb|right|<caption>FOV of 7m mosaic.</caption>]]
</figure>

Examination of the listobs files shows that the CO is in SPW='0' for the 12m data and in SPW='3,5' for the 7m data. There are two SPWs containing CO in the 7m data due to the slightly differing correlator setups.

Also note that the integration time per visibility (average interval parameter in listobs) is different:
6.05s for the 12m data and 10.1s for the 7m. This will be important to know later when we check the visibility weights. 

Next we split out the CO spectral windows.

<source lang="python">
# In CASA
os.system('rm -rf m100_12m_CO.ms')
split(vis='M100_Band3_12m_CalibratedData.ms',
      outputvis='m100_12m_CO.ms',spw='0',field='M100',
      datacolumn='data',keepflags=False)
os.system('rm -rf m100_7m_CO.ms')
split(vis='M100_Band3_7m_CalibratedData.ms',
      outputvis='m100_7m_CO.ms',spw='3,5',field='M100',
      datacolumn='data',keepflags=False)
</source>

Also of interest is that the 12m data has 47 fields and the 7m has 23 fields (not shown in the excerpts above). The difference in number of pointings is because the 7m antennas have a FWHP (full width half power) primary beam diameter that is 12/7 times larger than the 12m antennas. '''One easy way to see how the mosaics compare is to install the AnalysisUtils package (see [[Analysis_Utilities]] for information on how to download and import AnalysisUtils)'''. Then with AnalysisUtils you can make the following plots (look at the listobs to obtain the sourceid):

<source lang="python">
# In CASA
os.system('rm -rf *m_mosaic.png')
au.plotmosaic('m100_12m_CO.ms',sourceid='0',figfile='12m_mosaic.png')
au.plotmosaic('m100_7m_CO.ms',sourceid='0',figfile='7m_mosaic.png')
</source>

We see that the mosaics cover a common area but that the 7m mosaic is a bit larger. This means that the outer edges of the combined mosaic will be noisier than expected if they overlapped perfectly; this is just something to keep in mind. If you had the case where the mosaic coverages are dramatically different, it would be best to exclude the completely non-overlapping fields from the combination.

NOTE: At this stage one would typically do continuum subtraction (if there is any). However we already know from the individual data reductions that the 3mm continuum emission is quite weak and does not significantly contribute to a 5km/s channel, so we will forgo the the continuum subtraction step. Examples of how to do this if you are so inclined are located in various other ALMA CASAguides.

== Checking the weights and concatenating the data ==

<figure id="7m_WT.png">
[[File:12m_WT.png|200px|thumb|right|<caption> 12m weights.</caption>]]
</figure>

<figure id="12m_WT.png">
[[File:7m_WT.png|200px|thumb|right|<caption> 7m weights.</caption>]]
</figure>

When combining data with disparate properties it is very important that the relative weights of each visibility be in the correct proportion to the other data according to the radiometer equation. Formally, the
visibility weights should be proportional to 1/sigma<sup>2</sup> where sigma is the variance or rms noise of a given visibility.

Assuming that the 7m and 12m antennas have similar apperture and quantization efficiencies (a reasonable assumption since they were designed this way), the rms noise in a single channel for a single visibility is:

<math> 
\sigma_{ij}=\frac{2k}{A_{eff}} 
</math>
<math> 
\sqrt{\frac{T_{sys,i} T_{sys,j}}{\Delta\nu_{ch} t_{ij}}},
</math>

where k is Boltzmann's constant, A<sub>eff</sub> is the effective antenna area, T<sub>sys,i</sub> is the system temperature for antenna i, &Delta;&nu;<sub>ch</sub> is the channel width, and t<sub>ij</sub> is the integration time per visibility.

CASA initially scales the weights by 2&Delta;&nu;<sub>ch</sub>&Delta;t<sub>ij</sub>, and after the Tsys table applycal step of the calibration process, it further scales the weights by 1/[(Tsys(i) * Tsys(j)] as long as calwt=True. In the subsequent gain calibration table applycal step of the calibration, the weights are further scaled by a factor of [(gain(i))<sup>2</sup> * (gain(j))<sup>2</sup>]. The gains should change very little from antenna to antenna, so this scaling is effectively the average gain<sup>4</sup> (again, as long as calwt=True). In the calibration scripts for all executions of the 12m and 7m data, found (here), both applycal steps set calwt=True. To verify, we plot the weights of the 7m and 12m data and measure their ratio to be, on average, 7m/12m ~ 0.055/0.3 ~ 0.18. Note that in the plots the points are colored by SPW, so there is only one 12m CO SPW but there are two 7m CO SPWs, and that no averaging can be turned on when plotting the weights. 

<source lang="python">
# In CASA
os.system('rm -rf 7m_WT.png 12m_WT.png')
plotms(vis='m100_12m_CO.ms',yaxis='wt',xaxis='uvdist',spw='0:200',
       coloraxis='spw',plotfile='12m_WT.png')
#
plotms(vis='m100_7m_CO.ms',yaxis='wt',xaxis='uvdist',spw='0~1:200',
       coloraxis='spw',plotfile='7m_WT.png')
</source>

<figure id="combine_CO_WT.png">
[[File:combine_CO_WT.png|200px|thumb|right|<caption> 7m and 12m weights after concatenation.</caption>]]
</figure>

The two key things that are different between the 7m and 12m-array data are that the effective dish areas are different by (7/12)<sup>2</sup>, and the integration times are different by (10.1/6.05). Since the dish area and the integration time per visibility are in the denominator of the radiometer equation, and assuming the weight of an individual visibility is proportional to 1/sigma<sup>2</sup>, the ratio of the weights should be (7./12.)<sup>4</sup> x (10.1/6.05) = 0.19. This is very close to the value we measure for the ratio of the weights, particularly given that the 7m flux calibration relied on a source which changed substantially over the course of the six 7m-array observations. 

Now concatenate the two data sets and plot the concatenated weights to verify that they are as expected.

<source lang="python">
# In CASA
# Concat and scale weights
os.system('rm -rf M100_combine_CO.ms')
concat(vis=['m100_12m_CO.ms','m100_7m_CO.ms'],
       concatvis='M100_combine_CO.ms')
</source>

<source lang="python">
# In CASA
os.system('rm -rf combine_CO_WT.png')
plotms(vis='M100_combine_CO.ms',yaxis='wt',xaxis='uvdist',spw='0~2:200',
       coloraxis='spw',plotfile='combine_CO_WT.png')
</source>

Here, we create more instructive plots of the combined data to check that things are in order. (''Let each plot finish before cutting and pasting next plot. If plotms gui disappears, exit CASA and restart.'')

<figure id="M100_combine_vel.png">
[[File:M100_combine_vel.png|200px|thumb|right|<caption> Amplitude as a function of velocity.</caption>]]
</figure>

To plot amplitude as a function of uv-distance, noting that the 7m data is noisier than the 12m data:

<source lang="python">
# In CASA
os.system('rm -rf M100_combine_uvdist.png')
plotms(vis='M100_combine_CO.ms',yaxis='amp',xaxis='uvdist',spw='', avgscan=True,
       avgchannel='5000', coloraxis='spw',plotfile='M100_combine_uvdist.png') 
</source>

A fairer comparison of these data is achieved by isolating the brightest line channels in individual 12m and 7m data sets (i.e., not the concatenated data sets) and comparing only those channels in amplitude vs. uv-distance. Here the agreement is better, as it is less dominated by the scatter among the several 7m executions.

To plot the CO line as a function of velocity (this plot takes a while):

<source lang="python">
# In CASA
os.system('rm -rf M100_combine_vel.png')
plotms(vis='M100_combine_CO.ms',yaxis='amp',xaxis='velocity',spw='', avgtime='1e8',avgscan=True,coloraxis='spw',avgchannel='5',
       transform=True,freqframe='LSRK',restfreq='115.271201800GHz', plotfile='M100_combine_vel.png')
</source>

To see each spectral window independently in plotms, run the command again but remove the call to "plotfile" and add " iteraxis='spw' ".

== Image Using An Automasking Technique ==

The commands in this section perform an iterative automasking procedure down
to a user specified threshold=stop*rms where stop is typically 2-3 using the imagemode='mosaic' mode of clean.  This mode automatically calculates the correct convolution of the primary beam response of the mosaic when different antenna dish diameters are present. '''NOTE:''' even if these data had only been comprised of a single pointing of 7m and 12m-array data, the imagemode='mosaic' mode would be needed to correctly image data with different antenna sizes.

The procedure outlined below takes some care to ensure that the generated masks (i) only have values of 0 or 1; (ii) are themselves masked at the minpb level. It also removes very small masked regions that are consistent with noise bumps using a function in scipy. A typical setting is to remove mask regions that are 1/2 the beam area in pixels. This is one technique under exploration for future pipeline use.  

The commands have been split into multiple sections to aid cut and paste. Wait until the current one is done before starting next section. '''If you stop CASA and restart you will need to cut and paste again from the Define Parameters section on down'''.

When there is a long series of commands below, it is important to include the '''beginning cpaste''' and '''ending --''' in your cut and paste.

=== Define Parameters ===

Note that the parameters used here are by design the same as those used to make the stand-alone 7m-array and 12m-array images. 

<source lang="python">
# In CASA
### Initialize 
import scipy.ndimage 

### Define clean parameters
vis='M100_combine_CO.ms'
prename='M100_combine_cube'
myimage=prename+'.image'
myflux=prename+'.flux'
mymask=prename+'.mask'
myresidual=prename+'.residual'
imsize=800
cell='0.5arcsec'
minpb=0.2
restfreq='115.271201800GHz'
outframe='LSRK'
spw='0~2'
width='5km/s'
start='1400km/s'
nchan=70
robust=0.5
phasecenter='J2000 12h22m54.9 +15d49m15'
scales=[0]
smallscalebias=0.6

### Setup stopping criteria with multiplier for rms.
stop=3. 

### Minimum size multiplier for beam area for removing very small mask regions. 
pixelmin=0.5  

</source>

=== Make Initial Dirty Image and Determine Synthesized Beam area===

The dirty image is used to determine the initial peak flux density in the cube and the beam area is used to define the minimum size of masked regions in order to exclude noise bumps from the overall mask.

<source lang="python">
# In CASA
cpaste
### Make initial dirty image
os.system('rm -rf '+prename+'.* ' +prename+'_*')
clean(vis=vis,imagename=prename,
      imagermode='mosaic',ftmachine='mosaic',minpb=minpb,
      imsize=imsize,cell=cell,spw=spw,
      weighting='briggs',robust=robust,phasecenter=phasecenter,
      mode='velocity',width=width,start=start,nchan=nchan,      
      restfreq=restfreq,outframe=outframe,veltype='radio',
      mask='',
      niter=0,interactive=F)

# Determine the beam area in pixels for later removal of very small mask regions
major=imhead(imagename=myimage,mode='get',hdkey='beammajor')['value']
minor=imhead(imagename=myimage,mode='get',hdkey='beamminor')['value']
pixelsize=float(cell.split('arcsec')[0])
beamarea=(major*minor*pi/(4*log(2)))/(pixelsize**2)
print 'beamarea in pixels =', beamarea

--
</source>

=== Find properties of the dirty image ===

<source lang="python">
# In CASA
### Find the peak in the dirty cube.
myimage=prename+'.image'
bigstat=imstat(imagename=myimage)
peak= bigstat['max'][0]
print 'peak (Jy/beam) in cube = '+str(peak)
### Sets threshold of first loop, try 2-4. Subsequent loops are set thresh/2.
thresh = peak / 4.

### If True: find the rms in two line-free channels; If False:  Set rms by hand in else statement.
if True:  
    chanstat=imstat(imagename=myimage,chans='4')
    rms1= chanstat['rms'][0]
    chanstat=imstat(imagename=myimage,chans='66')
    rms2= chanstat['rms'][0]
    rms=0.5*(rms1+rms2)        
else:
    rms=0.011


print 'rms (Jy/beam) in a channel = '+str(rms)

</source>

=== Automasking Loop ===

On a reasonably fast computer the following will take a couple of hours for this spectral mosaic. For the long series of commands below it is important to include the beginning '''cpaste''' and ending '''--''' in your cut and paste.

<source lang="python">
# In CASA
cpaste
os.system('rm -rf ' + prename +'_threshmask*')
os.system('rm -rf ' + prename +'_fullmask*')
os.system('rm -rf ' + prename +'.image*')
n=-1
while (thresh >= stop*rms):   
    n=n+1
    print 'clean threshold this loop is', thresh
    threshmask = prename+'_threshmask' +str(n)
    maskim = prename+'_fullmask' +str(n)
    immath(imagename = [myresidual],
           outfile = threshmask,
           expr = 'iif(IM0 > '+str(thresh) +',1.0,0.0)',
           mask=myflux+'>'+str(minpb))
    if (n==0):
        os.system('cp -r '+threshmask+' '+maskim+'.pb')
        print 'This is the first loop'
    else:
        makemask(mode='copy',inpimage=myimage,
                 inpmask=[threshmask,mymask],
                 output=maskim)
        imsubimage(imagename=maskim, mask=myflux+'>'+str(minpb),
                   outfile=maskim+'.pb')     
    print 'Combined mask ' +maskim+' generated.'

    # Remove small masks
    os.system('cp -r '+maskim+'.pb ' +maskim+'.pb.min')
    maskfile=maskim+'.pb.min'
    ia.open(maskfile)
    mask=ia.getchunk()           
    labeled,j=scipy.ndimage.label(mask)                     
    myhistogram = scipy.ndimage.measurements.histogram(labeled,0,j+1,j+1)
    object_slices = scipy.ndimage.find_objects(labeled)
    threshold=beamarea*pixelmin
    for i in range(j):
        if myhistogram[i+1]<threshold:
            mask[object_slices[i]] = 0


    ia.putchunk(mask)
    ia.done()
    print 'Small masks removed and ' +maskim +'.pb.min generated.'

    os.system('rm -rf '+mymask+'')
    clean(vis=vis,imagename=prename,
          imagermode='mosaic',ftmachine='mosaic',minpb=minpb,
          imsize=imsize,cell=cell,spw=spw,
          weighting='briggs',robust=robust,phasecenter=phasecenter,
          mode='velocity',width=width,start=start,nchan=nchan,      
          restfreq=restfreq,outframe=outframe,veltype='radio',
          mask = maskim+'.pb.min',
          multiscale=scales,smallscalebias=smallscalebias,
          interactive = F,
          niter = 10000,
          threshold = str(thresh) +'Jy/beam')


    if thresh==stop*rms: break
    thresh = thresh/2.
    # Run a final time with stop*rms if more than a little above
    # stop*rms. Also make a back-up of next to last image
    if (thresh < stop*rms and thresh*2.>1.05*stop*rms):
        thresh=stop*rms  
        os.system('cp -r '+myimage+' '+myimage+str(n))

--
</source>

=== Notes on the Automasking procedure ===

This script is meant to be a possible stepping stone to optimal automasking -- it is by no means perfect and is certainly slower than optimal but feel free to try it with other datasets. Some notes below:

In addition to the final prename.image (prename.flux etc) this script produces and keeps each iteration of the various mask files which will allow you to explore how the masking proceeded as the threshold for masking and cleaning was lowered. The ones denoted "prename. fullmask*.pb.min" are the ones used in the clean steps themselves. At the end of the process the final "prename. fullmask*.pb.min" will also be stored in the prename.mask. Once you've verified you are happy with the masking, you may want to remove the prename.threshmask* and prename.fullmask* files, as they can be large for large cubes. 

Additionally, before running the final loop with thresh=stop*rms the script copies the .image from the preceding clean to prename.image'n' where 'n' equals the loop number of the preceding step. So in this M100 example you will see a M100_combine_cube.image and a M100_combine_cube.image2 where .image is the final image and .image2 is the next to last image. This is done for convenience in the case that thresh=stop*rms is too deep such that clean diverges, you will still be left with the clean image from the preceding loop that you can further investigate to understand why clean diverged. If all goes well with the final loop, the prename.image'n' can also be deleted. Divergence at thresh=stop*rms is often a sign that the image is "dynamic range limited" in other words the rms in channels with bright emission is significantly worse than for a line-free channel.

== Image Analysis for the 7m+12m Data ==

=== Moment Maps for 7m+12m CO (1-0) Cube ===

Start by examining the final image cube. Determine the start and stopping channels for the line emission -- this will be used in the "chans" parameter of immoments.

<source lang="python">
# In CASA
viewer('M100_combine_cube.image')
</source>

Next determine the rms noise per channel and use that to exclude pixels from the moment images. All images are shown in the gallery at the end of the following section.

<source lang="python">
# In CASA
myimage='M100_combine_cube.image'
chanstat=imstat(imagename=myimage,chans='4')
rms1= chanstat['rms'][0]
chanstat=imstat(imagename=myimage,chans='66')
rms2= chanstat['rms'][0]
rms=0.5*(rms1+rms2)
print 'rms in a channel = '+str(rms) 
</source>

Next make the moment maps. For the integrated intensity: moment 0, a 2 sigma cut often considerably improves the appearance of the image with little effect on the integrated intensity as long as emission free channels are excluded. For higher order moments it is necessary to exclude all low S/N data. Typically 5-6 sigma for the higher moments works well. We also apply further masking based on the .flux image because the edges of the combined mosaic are especially noisy because the 7m mosaic is somewhat larger than the 12m mosaic as described above (see Figures 1 & 2). 

<source lang="python">
# In CASA
os.system('rm -rf M100_combine_cube.image.mom0')
immoments(imagename = 'M100_combine_cube.image',
         moments = [0],
         axis = 'spectral',chans = '9~61',
         mask='M100_combine_cube.flux>0.3',
         includepix = [rms*2,100.],
         outfile = 'M100_combine_cube.image.mom0')

os.system('rm -rf M100_combine_cube.image.mom1')
immoments(imagename = 'M100_combine_cube.image',
         moments = [1],
         axis = 'spectral',chans = '9~61',
         mask='M100_combine_cube.flux>0.3',
         includepix = [rms*5.5,100.],
         outfile = 'M100_combine_cube.image.mom1')

</source>

Now we can make some figures showing the moment maps:

<source lang="python">
# In CASA
os.system('rm -rf M100_combine_cube.image.mom*.png')
imview (raster=[{'file': 'M100_combine_cube.image.mom0',
                 'range': [-0.3,25.],'scaling': -1.3,'colorwedge': T}],
         zoom={'blc': [190,150],'trc': [650,610]},
         out='M100_combine_cube.image.mom0.png')

imview (raster=[{'file': 'M100_combine_cube.image.mom1',
                 'range': [1440,1695],'colorwedge': T}],
         zoom={'blc': [190,150],'trc': [650,610]}, 
         out='M100_combine_cube.image.mom1.png')

</source>

If you plan to use your moment 0 image to make measurements, it needs to be primary beam corrected first. First we need to subimage the .flux cube to extract a single plane that can be used to primary beam correct the moment 0 image.

<source lang="python">
# In CASA
os.system('rm -rf M100_combine_cube.flux.1ch')
imsubimage(imagename='M100_combine_cube.flux',
           outfile='M100_combine_cube.flux.1ch',
           chans='35')
</source>

Then primary beam correct the moment 0 image. This is the version that would be used for measurements, though the uncorrected one can be useful for figures. The difference is clear in the images seen below in the following section.

<source lang="python">
# In CASA
os.system('rm -rf M100_combine_cube.image.mom0.pbcor')
immath(imagename=['M100_combine_cube.image.mom0', \
                       'M100_combine_cube.flux.1ch'],
        expr='IM0/IM1',
        outfile='M100_combine_cube.image.mom0.pbcor')
</source>

Have a look at the difference the primary beam correction makes. 

<source lang="python">
# In CASA
imview (raster=[{'file': 'M100_combine_cube.image.mom0',
                 'range': [-0.3,25.],'scaling': -1.3},
                {'file': 'M100_combine_cube.image.mom0.pbcor',
                 'range': [-0.3,25.],'scaling': -1.3}],
         zoom={'blc': [190,150],'trc': [650,610]})
</source>

With the viewer open, you can flip back and forth between the images to compare them.  Next, make a figure.

<source lang="python">
# In CASA
os.system('rm -rf M100_combine_cube.image.mom0.pbcor.png')
imview (raster=[{'file': 'M100_combine_cube.image.mom0.pbcor',
                 'range': [-0.3,25.],'scaling': -1.3,'colorwedge': T}],
         zoom={'blc': [190,150],'trc': [650,610]},
         out='M100_combine_cube.image.mom0.pbcor.png')

</source>

=== Comparison with 7m, 12m Moment Maps ===

Below the moment maps from the 7m-only and the 12m-only data are shown for comparison. The moment maps were made using clean masks drawn by hand for comparison to the automasking technique; the two appear to be qualitatively similar. The range and scaling for the 12m-only figures are the same as that used for the 7m+12m figures for ease of comparison.

As expected, the 7m+12m image shows considerably more extended emission than the 12m-only data and finer detail than the 7m-only data. For comparison, the 7m+12m synthesized beam is 3.80"x2.50", while the 12m-only beam is 3.46"x2.37" and the 7m-only beam is 12.72"x10.12".

<gallery widths=300px heights=300px>
File:12m.png | Moment 0 for 12m data alone (no primary beam correction).
File:7m_mom0.png | Moment 0 for 7m data alone (no primary beam correction).
File:combined.png | Moment 0 for 12m+7m data (no primary beam correction).
File:combine_pbcor.png | Moment 0 for 12m+7m data with primary beam correction.
</gallery>

<gallery widths=300px heights=300px>
File:12m_mom1.png | Moment 1 for 12m data alone.
File:7m_mom1.png | Moment 1 for 7m data alone.
File:combine_mom1.png | Moment 1 for 12m+7m data.
</gallery>

=== Convert 7m+12m Images to Fits Format ===

<source lang="python">
# In CASA
os.system('rm -rf *.fits')
exportfits(imagename='M100_combine_cube.image',fitsimage='M100_combine_cube.image.fits')

exportfits(imagename='M100_combine_cube.flux',fitsimage='M100_combine_cube.flux.fits')

exportfits(imagename='M100_combine_cube.image.mom0',fitsimage='M100_combine_cube.image.mom0.fits')

exportfits(imagename='M100_combine_cube.image.mom0.pbcor',fitsimage='M100_combine_cube.image.mom0.pbcor.fits')

exportfits(imagename='M100_combine_cube.image.mom1',fitsimage='M100_combine_cube.image.mom1.fits')

</source>

= Feathering the Total Power and 7m+12m Interferometric Images =

In this section the interferometric (7m+12m) image produced above is combined with the Total Power (single dish) image.
The "feather" algorithm is employed, in which the two images are combined in the spatial frequency domain, i.e.,
the low and high spatial frequency components are predominantly taken from the TP and interferometric images, respectively.

== Prepare Images for Feathering ==

Regrid the TP image to match the shape of the 7m+12m image using the task {{imregrid}}.
The TP image is resampled onto the same grid as that of the "template" 7m+12m image along the first two axes of the cube (i.e., RA and Dec; it is not necessary to regrid the velocity axis, since the axis is already common to the both images).

<source lang="python">
#In CASA
os.system('rm -rf M100TP.CO.regrid')
imregrid(imagename='M100TP.CO.cube.bl.image',
         template='M100_combined_CO.image',
         axes=[0, 1],
         output='M100TP.CO.regrid')
</source>

Now we trim the 7m+12m and (regridded) TP images, in order to exclude the regions masked by the {{clean}} task with minpb=0.2 and/or noisy edge regions in the TP image.  The {{viewer}} task can be used to determine the trimming box.  Here we use (x, y) = (219, 148) and (612, 579) [pixels] as the bottom-left and top-right corners, respectively, and set these values to the "box" parameter of the {{imsubimage}} task.

<source lang="python">
#In CASA
os.system('rm -rf M100TP.CO.regrid.subim')
imsubimage(imagename='M100TP.CO.regrid',
           outfile='M100TP.CO.regrid.subim',
           box='219,148,612,579')
os.system('rm -rf M100_combined_CO.image.subim')
imsubimage(imagename='M100_combined_CO.image',
           outfile='M100_combined_CO.image.subim',
           box='219,148,612,579')
</source>

While the 7m+12m image (before the primary-beam correction) has non-uniform primary beam response (i.e., lower response in the outskirts of the mosaic field), the TP image does not have such non-uniformity.
In order to feather the TP and 7m+12m images together, they should have the common response on the sky.
Hence we need to multiply the TP image by the 7m+12m primary beam response before proceeding.
To do this, create the subimage of the 7m+12m response,

<source lang="python">
#In CASA
os.system('rm -rf M100_combined_CO.flux.subim')
imsubimage(imagename='M100_combined_CO.flux',
           outfile='M100_combined_CO.flux.subim',
           box='219,148,612,579')
</source>

then multiply it and the TP image using the task {{immath}}.

<source lang="python">
#In CASA
os.system('rm -rf M100TP.CO.regrid.subim.depb')
immath(imagename=['M100TP.CO.regrid.subim',
                  'M100_combined_CO.flux.subim'],
       expr='IM0*IM1',
       outfile='M100TP.CO.regrid.subim.depb')
</source>

As a result, the feathered image will have the same response as that of the 7m+12m image.
The primary-beam correction can be done after the feathering process (see below).

== Feather TP Cube with 7m+12m Cube ==

Now we are ready to execute the {{feather}} task to combine the TP and 7m+12m images.

<source lang="python">
#In CASA
os.system('rm -rf M100_Feather_CO.image')
feather(imagename='M100_Feather_CO.image',
        highres='M100_combined_CO.image.subim',
        lowres='M100TP.CO.regrid.subim.depb')
</source>

The task produces the combined image in the following way:
* Convert the input images specified by the "highres" and "lowres" parameters onto the spatial frequency plane.
* Combine them on the spatial frequency plane.  The weighting is determined by the beam sizes/shapes of the input images.
* Convert it back to the image plane.
Please refer to the online help and documents for the details.

== Make Moment Maps of the Feathered Images ==

We will use the same technique as the [[#Moment_Maps_for_7m.2B12m_CO_.281-0.29_Cube|7m+12m image analysis above]] to make moment maps.

First (but optionally; this is solely for comparison to the feathered images and not needed to create the final feathered images), make moment maps for the (regridded) TP image.

<source lang="python">
#In CASA
myimage = 'M100TP.CO.regrid.subim'
chanstat = imstat(imagename=myimage,chans='4')
rms1 = chanstat['rms'][0]
chanstat = imstat(imagename=myimage,chans='66')
rms2 = chanstat['rms'][0]
rms = 0.5*(rms1+rms2)  
 
os.system('rm -rf M100TP.CO.regrid.subim.mom0')
immoments(imagename='M100TP.CO.regrid.subim',
         moments=[0],
         axis='spectral',
         chans='10~61',
         includepix=[rms*2., 50],
         outfile='M100TP.CO.regrid.subim.mom0')
 
os.system('rm -rf M100TP.CO.regrid.subim.mom1')
immoments(imagename='M100TP.CO.regrid.subim',
         moments=[1],
         axis='spectral',
         chans='10~61',
         includepix=[rms*5.5, 50],
         outfile='M100TP.CO.regrid.subim.mom1')

os.system('rm -rf M100TP.CO.regrid.subim.mom*.png')
imview(raster=[{'file': 'M100TP.CO.regrid.subim.mom0',
                'range': [0., 1080.],
                'scaling': -1.3,
                'colorwedge': T}],
       out='M100TP.CO.regrid.subim.mom0.png')
 
imview(raster=[{'file': 'M100TP.CO.regrid.subim.mom1',
                'range': [1440, 1695],
                'colorwedge': T}], 
       out='M100TP.CO.regrid.subim.mom1.png')
</source>

Then make moment maps for the feathered image.

<source lang="python">
#In CASA
myimage = 'M100_Feather_CO.image'
chanstat = imstat(imagename=myimage,chans='4')
rms1 = chanstat['rms'][0]
chanstat = imstat(imagename=myimage,chans='66')
rms2 = chanstat['rms'][0]
rms = 0.5*(rms1+rms2)  
 
os.system('rm -rf M100_Feather_CO.image.mom0')
immoments(imagename='M100_Feather_CO.image',
         moments=[0],
         axis='spectral',
         chans='10~61',
         includepix=[rms*2., 50],
         outfile='M100_Feather_CO.image.mom0')
 
os.system('rm -rf M100_Feather_CO.image.mom1')
immoments(imagename='M100_Feather_CO.image',
         moments=[1],
         axis='spectral',
         chans='10~61',
         includepix=[rms*5.5, 50],
         outfile='M100_Feather_CO.image.mom1')

os.system('rm -rf M100_Feather_CO.image.mom*.png')
imview(raster=[{'file': 'M100_Feather_CO.image.mom0',
                'range': [-0.3, 25.],
                'scaling': -1.3,
                'colorwedge': T}],
       out='M100_Feather_CO.image.mom0.png')
 
imview(raster=[{'file': 'M100_Feather_CO.image.mom1',
                'range': [1440, 1695],
                'colorwedge': T}], 
       out='M100_Feather_CO.image.mom1.png')
</source>

=== Correct the Primary Beam Response ===

Apply the primary beam response to the feathered image using the task {{immath}},

<source lang="python">
#In CASA
immath(imagename=['M100_Feather_CO.image',
                  'M100_combined_CO.flux.subim'],
       expr='IM0/IM1',
       outfile='M100_Feather_CO.image.pbcor')
</source>

and also to the moment 0 image.

<source lang="python">
#In CASA
os.system('rm -rf M100_combined_CO.flux.1ch.subim')
imsubimage(imagename='M100_combined_CO.flux.subim',
           outfile='M100_combined_CO.flux.1ch.subim',
           chans='35')

os.system('rm -rf M100_Feather_CO.image.mom0.pbcor')
immath(imagename=['M100_Feather_CO.image.mom0',
                  'M100_combined_CO.flux.1ch.subim'],
        expr='IM0/IM1',
        outfile='M100_Feather_CO.image.mom0.pbcor')
</source>

Save the primary-beam corrected moment 0 image to a PNG file.

<source lang="python">
#In CASA
os.system('rm -rf M100_Feather_CO.image.mom0.pbcor.png')
imview(raster=[{'file': 'M100_Feather_CO.image.mom0.pbcor',
                'range': [-0.3, 25.],
                'scaling': -1.3,
                'colorwedge': T}],
       out='M100_Feather_CO.image.mom0.pbcor.png')
</source>

=== Compare the Various Images ===

Now we compare all the images:

<gallery perrow=3 widths=300px heights=300px>
File:12m_pbcor.png | Primary beam corrected moment 0 for the 12m data.
File:7m_pbcor.png | Primary beam corrected moment 0 for the 7m data.
File:TP_CO_cube_Jy.regrid.subim.mom0.png | Moment 0 for the TP data.
File:combine_pbcor.png | Primary beam corrected moment 0 for 7m+12m data.
File:M100_Feather_CO.mom0.pbcor.png | Primary beam corrected moment 0 for TP+7m+12m data.
</gallery>

<gallery perrow=3 widths=300px heights=300px>
File:12m_mom1.png | Moment 1 for 12m data.
File:7m_mom1.png | Moment 1 for 7m data.
File:TP_CO_cube_Jy.regrid.subim.mom1.png | Moment 1 for the TP data.
File:combine_mom1.png | Moment 1 for 7m+12m data.
File:M100_Feather_CO.mom1.png | Moment 1 for TP+7m+12m data.
</gallery>

You can see that more extended emission is recovered by adding the TP data to the interferometric data.

For quantitative comparison, we measure the total line fluxes of the various images.
The task {{imstat}} can be used to do this.
For example, for the subimage of the 7m+12m image,

<source lang="python">
#In CASA
imstat('M100_combined_CO.image.subim')
</source>

yields the following:

<pre style="background-color: #fffacd;">
{'blc': array([0, 0, 0, 0], dtype=int32),
 'blcf': '12:23:01.170, +15.47.08.994, I, 1.14733e+11Hz',
 'flux': array([ 269.63344004]),
 'max': array([ 0.65709084]),
 'maxpos': array([172, 253,   0,  49], dtype=int32),
 'maxposf': '12:22:55.212, +15.49.15.500, I, 1.14639e+11Hz',
 'mean': array([ 0.00097561]),
 'medabsdevmed': array([ 0.00850473]),
 'median': array([ -3.25056462e-05]),
 'min': array([-0.07497632]),
 'minpos': array([260, 251,   0,  26], dtype=int32),
 'minposf': '12:22:52.163, +15.49.14.499, I, 1.14683e+11Hz',
 'npts': array([ 11914560.]),
 'quartile': array([ 0.01701281]),
 'rms': array([ 0.01756589]),
 'sigma': array([ 0.01753878]),
 'sum': array([ 11623.92616449]),
 'sumsq': array([ 3676.36438921]),
 'trc': array([393, 431,   0,  69], dtype=int32),
 'trcf': '12:22:47.554, +15.50.44.492, I, 1.146e+11Hz'}
</pre>

The 'flux' value in the result is the total flux in Jy, but the velocity channels are not taken into account.
Since the width of the velocity channels is 5 km/s, the following command gives the integrated line flux in the unit of Jy km/s.

<source lang="python">
#In CASA
imstat('M100_combined_CO.image.subim')['flux']*5.0
</source>

<pre style="background-color: #fffacd;">
array([ 1348.16720019])
</pre>

Similarly, the total line fluxes of the TP image (after multiplying the
7m+12m primary beam response), feathered image, and feathered image after the
primary-beam correction are

<source lang="python">
#In CASA
imstat('M100TP.CO.regrid.subim.depb')['flux']*5.0
imstat('M100_Feather_CO.image')['flux']*5.0
imstat('M100_Feather_CO.image.pbcor')['flux']*5.0
</source>

<pre style="background-color: #fffacd;">
array([ 2766.63524574])
array([ 2766.63528397])
array([ 3057.66449702])
</pre>

We see the followings from these values:
* The flux recovered by the 7m+12m observations is about a half of the total flux (1348/2767 = 0.487).
* The feathering process preserves the flux of the TP data.
* The flux of the primary-beam corrected feathered image is consistent with the values from the literature (2972 +/- 319 Jy km/s from the BIMA SONG; Helfer et al. 2003).

{{Checked 4.3.0}}