# VLA Data Combination-CASA5.0.0

This tutorial was created and tested using CASA 5.0.0

## Introduction

A perfect image requires measurement of all spatial scales, which is equivalent to filling in the complete uv plane. Unfortunately, this can never be achieved with an aperture synthesis interferometer although a large number of baselines, long integration times, and multi-frequency-synthesis are all good approaches to increase the uv-coverage. One method to obtain more baselines is to observe in different array configurations and to combine the data afterwards. Deconvolution algorithms are then given good starting conditions to interpolate across the gaps in the uv-plane to achieve an improved image - an image that combines the surface brightness sensitivity of the compact baselines with the spatial resolution of the extended baselines.

The VLA can be configured into four principal array configurations, A, B, C, and D. A is the most extended and D is the most compact configuration. Consequently, A configuration data exhibits the highest spatial resolution whereas D configuration delivers the best surface brightness sensitivity and also images the largest scales of the sky brightness distribution.

In this tutorial, we will combine data from three VLA configurations (A & B & C) that were obtained in a monitoring campaign of Sgr A*, the central supermassive black hole of our Milky Way.

## Typical Observing Times

When an object is being observed by the VLA in different array configurations, on-source integration times are ideally matched to reach a common surface brightness sensitivity for all scales. Adjacent VLA configurations result in synthesized beams that differ in linear size by approximately a factor of 3. The beam areas therefore change by factors of ~10 and the more extended configuration would ideally need to have 10 times more integration time than the next compact one. This, however, is frequently not very practical and it turns out that integration times that differ by factors of ~3 are delivering data that can be combined satisfactorily as it matches the sensitivity of overlapping VLA visibilities when data are convolved to the same scales.

This rule, however, is only a guidance and any data that are being obtained from any configuration can be combined although overlapping uv-coverages are strongly recommended. Weighting will be primarily achieved during imaging by the "Briggs" scheme that allows one to adjust imaging weights between the "natural" and "uniform" extremes, i.e., between weighting by the number of visibilities that are gridded in each cell and weighting by the cells themselves.

In addition, each visibility exhibits weights that should only depend on correlator integration time, bandwidth, and system temperature (Tsys). The VLA, however, currently does apply Tsys in the online system. Visibility weights between different observations will therefore need to be adjusted as described below before they can be combined.

## The Data

In the following we will combine three different datasets from the NRAO Monitoring of the Galactic Center/G2 Cloud Encounter. We will combine S-band A, B, and C configuration data. The data were all calibrated and the science target split out.

The calibrated measurement sets can be downloaded here:
https://casa.nrao.edu/Data/EVLA/SgrA/VLA-combination-SgrA-files.tar.gz (1.4GB)


# In a Terminal
tar -xzvf VLA-combination-SgrA-files.tar.gz


This will unpack three MeasurementSets (MSs), one for each array configuration:

VLA-SgrA-Sband-Aconfig.ms

VLA-SgrA-Sband-Bconfig.ms

VLA-SgrA-Sband-Cconfig.ms


## Initial Imaging

We will inspect the data and create separate images to better understand the image parameters such as on-source integration time, resolution, and rms.

Start CASA as usual via

# In a Terminal
casa


As a first step, let's have a look at the listobs output for the different MSs. For example, the A-configuration MS has the following structure:

# In CASA
listobs(vis='VLA-SgrA-Sband-Aconfig.ms')

##########################################
listobs(vis="VLA-SgrA-Sband-Aconfig.ms",selectdata=True,spw="",field="",antenna="",
uvrange="",timerange="",correlation="",scan="",intent="",
feed="",array="",observation="",verbose=True,listfile="",
listunfl=False,cachesize=50,overwrite=False)
================================================================================
MeasurementSet Name:  /lustre/aoc/sciops/jott/casa/topicalguide/combination/test/VLA-SgrA-Sband-Aconfig.ms      MS Version 2
================================================================================
Observer: lorant sjouwerman     Project: uid://evla/pdb/11434214
Observation: EVLA
Data records: 528000       Total elapsed time = 360 seconds
Observed from   31-May-2014/09:07:57.0   to   31-May-2014/09:13:57.0 (UTC)
Compute subscan properties

ObservationID = 0         ArrayID = 0
Date        Timerange (UTC)          Scan  FldId FieldName             nRows     SpwIds   Average Interval(s)    ScanIntent
31-May-2014/09:07:57.0 - 09:13:57.0    63      0 J1745-2900              528000  [0,3,4,5,6,7,8,9,10,11,12,13,14,15]  [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] [OBSERVE_TARGET#UNSPECIFIED]
(nRows = Total number of rows per scan)
Fields: 1
ID   Code Name                RA               Decl           Epoch   SrcId      nRows
0    NONE J1745-2900          17:45:40.038300 -29.00.28.06899 J2000   0         528000
Spectral Windows:  (14 unique spectral windows and 1 unique polarization setups)
SpwID  Name           #Chans   Frame   Ch0(MHz)  ChanWid(kHz)  TotBW(kHz) CtrFreq(MHz) BBC Num  Corrs
0      EVLA_S#A0C0#80     64   TOPO    1988.000      2000.000    128000.0   2051.0000       12  RR  LL
3      EVLA_S#A0C0#83     64   TOPO    2372.000      2000.000    128000.0   2435.0000       12  RR  LL
4      EVLA_S#A0C0#84     64   TOPO    2500.000      2000.000    128000.0   2563.0000       12  RR  LL
5      EVLA_S#A0C0#85     64   TOPO    2628.000      2000.000    128000.0   2691.0000       12  RR  LL
6      EVLA_S#A0C0#86     64   TOPO    2756.000      2000.000    128000.0   2819.0000       12  RR  LL
7      EVLA_S#A0C0#87     64   TOPO    2884.000      2000.000    128000.0   2947.0000       12  RR  LL
8      EVLA_S#B0D0#88     64   TOPO    2988.000      2000.000    128000.0   3051.0000       15  RR  LL
9      EVLA_S#B0D0#89     64   TOPO    3116.000      2000.000    128000.0   3179.0000       15  RR  LL
10     EVLA_S#B0D0#90     64   TOPO    3244.000      2000.000    128000.0   3307.0000       15  RR  LL
11     EVLA_S#B0D0#91     64   TOPO    3372.000      2000.000    128000.0   3435.0000       15  RR  LL
12     EVLA_S#B0D0#92     64   TOPO    3500.000      2000.000    128000.0   3563.0000       15  RR  LL
13     EVLA_S#B0D0#93     64   TOPO    3628.000      2000.000    128000.0   3691.0000       15  RR  LL
14     EVLA_S#B0D0#94     64   TOPO    3756.000      2000.000    128000.0   3819.0000       15  RR  LL
15     EVLA_S#B0D0#95     64   TOPO    3884.000      2000.000    128000.0   3947.0000       15  RR  LL
Sources: 16
ID   Name                SpwId RestFreq(MHz)  SysVel(km/s)
0    J1745-2900          0     -              -
0    J1745-2900          1     -              -
0    J1745-2900          2     -              -
0    J1745-2900          3     -              -
0    J1745-2900          4     -              -
0    J1745-2900          5     -              -
0    J1745-2900          6     -              -
0    J1745-2900          7     -              -
0    J1745-2900          8     -              -
0    J1745-2900          9     -              -
0    J1745-2900          10    -              -
0    J1745-2900          11    -              -
0    J1745-2900          12    -              -
0    J1745-2900          13    -              -
0    J1745-2900          14    -              -
0    J1745-2900          15    -              -
Antennas: 26:
ID   Name  Station   Diam.    Long.         Lat.                Offset from array center (m)                ITRF Geocentric coordinates (m)
East         North     Elevation               x               y               z
0    ea01  N32       25.0 m   -107.37.22.0  +33.56.33.6       -441.7442     4689.9683      -16.9356 -1600781.062100 -5039347.430600  3558761.526300
1    ea02  N64       25.0 m   -107.37.58.7  +34.02.20.5      -1382.3632    15410.1417      -40.6233 -1599855.668100 -5033332.388100  3567636.626500
2    ea03  E64       25.0 m   -107.27.00.1  +33.50.06.7      15507.5911    -7263.7210       67.2006 -1587600.203200 -5050575.869700  3548885.404900
3    ea04  E24       25.0 m   -107.35.13.4  +33.53.18.1       2858.1804    -1349.1324       13.7306 -1598663.094300 -5043581.396100  3553767.023200
4    ea05  W08       25.0 m   -107.37.21.6  +33.53.53.0       -432.1181     -272.1470       -1.5057 -1601614.092200 -5042001.651900  3554652.509800
5    ea06  N56       25.0 m   -107.37.47.9  +34.00.38.4      -1105.2076    12254.3155      -34.2423 -1600128.382500 -5035104.142000  3565024.679400
6    ea07  N48       25.0 m   -107.37.38.1  +33.59.06.2       -855.2644     9405.9610      -25.9303 -1600374.875000 -5036704.207500  3562667.885900
7    ea08  N16       25.0 m   -107.37.10.9  +33.54.48.0       -155.8517     1426.6442       -9.3792 -1601061.957400 -5041175.883000  3556058.040000
8    ea09  W64       25.0 m   -107.46.20.1  +33.48.50.9     -14240.7638    -9606.2696       17.1066 -1616361.587500 -5042770.516600  3546911.446900
9    ea10  E40       25.0 m   -107.32.35.4  +33.52.16.9       6908.8305    -3240.7192       39.0202 -1595124.923100 -5045829.467200  3552210.703600
10   ea11  W24       25.0 m   -107.38.49.0  +33.53.04.0      -2673.3552    -1784.5888       10.4757 -1604008.749300 -5042135.808900  3553403.716000
11   ea12  N09       25.0 m   -107.37.07.8  +33.54.19.0        -77.4204      530.6453       -5.5755 -1601139.471200 -5041679.039700  3555316.553900
12   ea13  W56       25.0 m   -107.44.26.7  +33.49.54.6     -11333.2004    -7637.6771       15.3707 -1613255.393400 -5042613.099800  3548545.915000
13   ea14  E08       25.0 m   -107.36.48.9  +33.53.55.1        407.8298     -206.0320       -3.2196 -1600801.931000 -5042219.386500  3554706.431200
14   ea15  E56       25.0 m   -107.29.04.1  +33.50.54.9      12327.6313    -5774.7469       42.6153 -1590380.611000 -5048810.243300  3550108.432300
15   ea17  E32       25.0 m   -107.34.01.5  +33.52.50.3       4701.6413    -2209.7152       25.2066 -1597053.135800 -5044604.681200  3553058.995000
16   ea18  E72       25.0 m   -107.24.42.3  +33.49.18.0      19041.8717    -8769.2047        4.7262 -1584460.871200 -5052385.599800  3547600.000100
17   ea19  W16       25.0 m   -107.37.57.4  +33.53.33.0      -1348.7109     -890.6216        1.3005 -1602592.853600 -5042054.996800  3554140.704800
18   ea20  N40       25.0 m   -107.37.29.5  +33.57.44.4       -633.6074     6878.6018      -20.7693 -1600592.756000 -5038121.357300  3560574.853200
19   ea21  E48       25.0 m   -107.30.56.1  +33.51.38.4       9456.6097    -4431.6564       37.9341 -1592894.077600 -5047229.138200  3551221.206000
20   ea22  N24       25.0 m   -107.37.16.1  +33.55.37.7       -290.3752     2961.8594      -12.2389 -1600930.087800 -5040316.396400  3557330.387200
21   ea23  W72       25.0 m   -107.48.24.0  +33.47.41.2     -17419.4740   -11760.2758       14.9538 -1619757.312900 -5042937.664400  3545120.392300
22   ea24  W48       25.0 m   -107.42.44.3  +33.50.52.1      -8707.9403    -5861.7877       15.5282 -1610451.925800 -5042471.125800  3550021.055800
23   ea25  W32       25.0 m   -107.39.54.8  +33.52.27.2      -4359.4392    -2923.1244       11.7721 -1605808.634900 -5042230.089000  3552459.209500
24   ea26  W40       25.0 m   -107.41.13.5  +33.51.43.1      -6377.9880    -4286.7769        8.2038 -1607962.463800 -5042338.190100  3551324.947500
25   ea28  E16       25.0 m   -107.36.09.8  +33.53.40.0       1410.0378     -673.4764       -0.7821 -1599926.107500 -5042772.979700  3554319.790400
##########################################


We see that A-configuration contains only the central source, "J1745-2900", which is just a different name for Sgr A*. The on-source integration time amounts to only six minutes and the 16 spectral windows span a frequency range from 1.988 to 4.012GHz. Inspection of the other array configuration files show almost identical setups. Although the integration times between the different array configurations do not follow the 1:3:9 ratios that we discussed in the previous section, we can still combine the data without any problems. In the end, having better signal to noise on the shorter baselines can only improve the overall, combined image.

To better understand the data, let's check the uv-coverage of each of the three datasets:

# In CASA
# A-config:
plotuv(vis='VLA-SgrA-Sband-Aconfig.ms')

# In CASA
# B-config
plotuv(vis='VLA-SgrA-Sband-Bconfig.ms')

# In CASA
# C-config:
plotuv(vis='VLA-SgrA-Sband-Cconfig.ms')


The uv-coverage plots are shown in Fig. 1. The u:v aspect ratio of each uv-coverage is high as Sgr A* is a very southern source. We also see that the longest baseline in each array differs by about a factor of 3 between the three configurations, as expected from the VLA A, B, and C configurations.

 Figure 1a: UV-coverage of the A-configuration data. Figure 1b: UV-coverage of the B-configuration data. Figure 1c: UV-coverage of the C-configuration data.

The next step is to determine the image quality, the synthesized beam, and the rms of each image. To do so, the images do not have to be perfectly deconvolved as we only would like to see how the combination will improve over the individual arrays.

To keep things simple, we will use common cell sizes of 0.1 arcsec, images of 1280 pixels on each side, and we will clean 1000 iterations (see the VLA CASA imaging guide for more sophisticated imaging parameter choices):

# In CASA
# A-config:
clean(vis='VLA-SgrA-Sband-Aconfig.ms', imagename='SgrA-Aonly',field='J1745-2900',
mode='mfs',cell='0.1arcsec',imsize=[1280,1280],niter=1000,weighting='briggs',robust=0)

# In CASA
# B-config
clean(vis='VLA-SgrA-Sband-Bconfig.ms', imagename='SgrA-Bonly',field='J1745-2900',
mode='mfs',cell='0.1arcsec',imsize=[1280,1280],niter=1000,weighting='briggs',robust=0)

# In CASA
# C-config:
clean(vis='VLA-SgrA-Sband-Cconfig.ms', imagename='SgrA-Conly',field='J1745-2900',
mode='mfs',cell='0.1arcsec',imsize=[1280,1280],niter=1000,weighting='briggs',robust=0)


The clean images, shown in Fig. 2, give a first impression of the data. Note that when combining the images, we will improve on the uv-coverage and will therefore not only combine high resolution with high surface brightness sensitivity on large scales, but also expect a higher image fidelity, i.e. fewer artifacts due to better deconvolution.

 Figure 2a: Simple image of the A-configuration data. Figure 2b: Simple image of the B-configuration data. Figure 2c: Simple image of the C-configuration data.

The basic parameters of the individual images can be checked through imhead for the spatial resolution, and by determining the rms in the viewer when checking the statistics of empty areas. The central point source, Sgr A*, is variable and we see this reflected in the flux density values from the images taken in the three different configurations, which were separated in observing time by several months:

A-configuration: synthesized beam  1.44" x 0.40"; rms ~0.8mJy; peak flux density of Sgr A* 0.712 Jy/beam
B-configuration: synthesized beam  4.33" x 1.34"; rms ~0.7mJy; peak flux density of Sgr A* 0.691 Jy/beam
C-configuration: synthesized beam 11.02" x 4.20"; rms ~0.6mJy; peak flux density of Sgr A* 1.35 Jy/beam


## Removal of the variable Sgr A* point source

This step is only necessary for our case which includes a variable source. In most cases, one can skip this step.

As we have seen in the initial images, Sgr A* is a variable source. Unfortunately, this also introduces some problems for data combination as the visibilities of the different sessions will reflect the variations. Cleaning will be difficult in such a situation as flux levels at different uv points (times and baselines) are not consistent in their portion for the central point source. We will therefore remove the unresolved Sgr A* in each dataset.For those who are interested in having Sgr A* back in the image, we will later show how to re-introduce a nominal point source with a flux of 1Jy. It is perfectly fine, however, to image without the artificial source.

To start with, we create a component list for each dataset that includes only a point source at the position of Sgr A*. To do so, we first need to find out the position of the central point source. We do so by fitting a point source (2d-Gaussian function) to the A-configuration data. which has the largest angular resolution. We use imfit:

# In CASA
imfit(imagename='SgrA-Aonly.image',box='630,620,650,660')


The output of imfit is as follows:

Fit on SgrA-Aonly.image component 0
Position ---
--- ra:    17:45:40.038543 +/- 0.000059 s (0.000772 arcsec along great circle)
--- dec: -029.00.28.051472 +/- 0.004567 arcsec
--- ra:  639.9682 +/- 0.0077 pixels
--- dec: 640.1752 +/- 0.0457 pixels


So we will be using RA (J2000) =17h45m40.038543s and DEC (J2000) = -29d00'28.051472" for the central position of Sgr A*. We will use these coordinates for all three configurations , although it might be advisable to create a fit for each individually in cases where the peak may slightly shift.

The component list will be inserted as a MODEL column into the respective MS via ft. uvsub will then subtract the point source model from the CORRECTED data column. Since there's no CORRECTED column to start with, uvsub will initially copy the DATA column to the CORRECTED column. Note that an implication of this procedures is that running uvsub twice will oversubtract. So we recommend to create backup copies of the previous datasets before subtracting Sgr A*:

# In a Terminal
cp -r VLA-SgrA-Sband-Aconfig.ms VLA-SgrA-Sband-Aconfig-sub.ms
cp -r VLA-SgrA-Sband-Bconfig.ms VLA-SgrA-Sband-Bconfig-sub.ms
cp -r VLA-SgrA-Sband-Cconfig.ms VLA-SgrA-Sband-Cconfig-sub.ms


Let's start with the A-configuration data and create a component list of a point sources with a flux of 0.712 Jy at a position of RA (J2000) =17h45m40.038543s and DEC (J2000) = -29d00'28.051472" (more examples of component lists are provided in a different CASA guide):

# In CASA
cl.rename('component-SgrA-A.cl')
cl.close()


(We have used the CASA coordinate convention with colons for hms and dots for dms)

The component list is now stored in 'component-SgrA-A.cl' and we will use it to populate the MODEL column via ft:

# In CASA
ft(vis='VLA-SgrA-Sband-Aconfig-sub.ms', complist='component-SgrA-A.cl', usescratch=True)


Finally we will subtract the MODEL from the DATA/CORRECTED DATA with uvsub:

# In CASA
uvsub(vis='VLA-SgrA-Sband-Aconfig-sub.ms')


Note that to revert back to the original state, one could use clearcal to reset the MODEL column and to set CORRECTED to be identical with DATA (thus undoing the source subtraction).

Let's repeat the steps for B-configuration, now using a flux of 0.691 Jy. Although a separate fit would be even better, the subtraction also works well when using the A-configuration position:

# In CASA
cl.rename('component-SgrA-B.cl')
cl.close()
#
ft(vis='VLA-SgrA-Sband-Bconfig-sub.ms', complist='component-SgrA-B.cl', usescratch=True)
#
uvsub(vis='VLA-SgrA-Sband-Bconfig-sub.ms')


And for C-configuration we subtract a point source of 1.35 Jy:

# In CASA
cl.rename('component-SgrA-C.cl')
cl.close()
#
ft(vis='VLA-SgrA-Sband-Cconfig-sub.ms', complist='component-SgrA-C.cl', usescratch=True)
#
uvsub(vis='VLA-SgrA-Sband-Cconfig-sub.ms')


Let's image the three data sets with Sgr A* removed. We will run clean, but since the point source is removed, we only do 500 iterations for A and B configurations, and 200 iterations of the C configuration data to avoid cleaning into the noise:

# In CASA
# A-config:
clean(vis='VLA-SgrA-Sband-Aconfig-sub.ms', imagename='SgrA-Aonly-noPNT',field='J1745-2900',
mode='mfs',cell='0.1arcsec',imsize=[1280,1280],niter=500,weighting='briggs',robust=0)

# In CASA
# B-config
clean(vis='VLA-SgrA-Sband-Bconfig-sub.ms', imagename='SgrA-Bonly-noPNT',field='J1745-2900',
mode='mfs',cell='0.1arcsec',imsize=[1280,1280],niter=500,weighting='briggs',robust=0)

# In CASA
# C-config:
clean(vis='VLA-SgrA-Sband-Cconfig-sub.ms', imagename='SgrA-Conly-noPNT',field='J1745-2900',
mode='mfs',cell='0.1arcsec',imsize=[1280,1280],niter=200,weighting='briggs',robust=0)

 Figure 3a: Simple image of the A-configuration data with the central point source removed. Figure 3b: Simple image of the B-configuration data with the central point source removed. Figure 3c: Simple image of the C-configuration data with the central point source removed.

As expected, the images without the point sources as shown in Fig. 3 look similar to those in Fig. 2. but with the central point source removed. Since we cleaned a given number of iterations, some differences are visible though, in particular for C-configuration. This is expected.

## Check and Adjust the Visibility Weights

VLA weights are currently only based on channel width and correlator integration time. In the future, the VLA may use the switched power measurements to derive absolute calibrated weights. At the moment, however, the VLA weights need to be taken as being relative to each other. The relative sensitivity within an observation is measured by the gain, so weights of single, continuous observations are self-consistent. It is important, however, to adjust the weights between separate observations as they will be on different scales.

Let's have a look at the weights of the different datasets. We will plot the weights as a function of uv-distance, average over all channels in one spectral window, and will colorize by antenna:

# In CASA
# A-config:
plotms(vis='VLA-SgrA-Sband-Aconfig-sub.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')

# In CASA
# B-config
plotms(vis='VLA-SgrA-Sband-Bconfig-sub.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')

# In CASA
# C-config:
plotms(vis='VLA-SgrA-Sband-Cconfig-sub.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')


Fig. 4 shows that there are some differences. Data from configurations A and B have weights that are reasonably consistent, C-configuration data, however, seems to have consistently lower values.

 Figure 4a: A-config original weights. Figure 4b: B-config original weights. Figure 4c: C-config original weights.

The next step is to bring the weights on the same scale. There are currently two possibilities to do so.

1) Reset the weights with initweights to reflect the channel width and correlator integration time ($\displaystyle{ WEIGHT=2 \Delta \nu \Delta t }$, see the document on Data Weights in CASAdocs).

2) Calculate the weights based on the rms of the visibilities themselves, using the statwt task.

We recommend to reset the weights when there are strong sources present in the data as they will change the noise rms of the visibilities. Without strong sources, statwt should deliver better results. For this guide we will go both paths and compare the two methods.

### Option 1: Resetting the weights

As we will overwrite the WEIGHT column, we first create copies of our MSs in case we will have to revert to the original data:

# In a Terminal
cp -r VLA-SgrA-Sband-Aconfig-sub.ms VLA-SgrA-Sband-Aconfig-sub-initwt.ms
cp -r VLA-SgrA-Sband-Bconfig-sub.ms VLA-SgrA-Sband-Bconfig-sub-initwt.ms
cp -r VLA-SgrA-Sband-Cconfig-sub.ms VLA-SgrA-Sband-Cconfig-sub-initwt.ms


Now we will reset the weights with initweights. wtmode='nyq' is the default and resets the weights based on the channel width and correlator integration time (see above).

# In CASA
# A-config:
initweights(vis='VLA-SgrA-Sband-Aconfig-sub-initwt.ms',wtmode='nyq')

# In CASA
# B-config:
initweights(vis='VLA-SgrA-Sband-Bconfig-sub-initwt.ms',wtmode='nyq')

# In CASA
# C-config:
initweights(vis='VLA-SgrA-Sband-Cconfig-sub-initwt.ms',wtmode='nyq')


Let's have a look at the weight values again to see if statwt has adjusted the weights properly:

# In CASA
# A-config:
plotms(vis='VLA-SgrA-Sband-Aconfig-sub-initwt.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')

# In CASA
# B-config
plotms(vis='VLA-SgrA-Sband-Bconfig-sub-initwt.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')

# In CASA
# C-config:
plotms(vis='VLA-SgrA-Sband-Cconfig-sub-initwt.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')


 Figure 5: Weights after they were reset.

The weights are plotted in Fig. 5 for one configurations. But they are identical for all data sets, as the data were taken in the same way for all configurations with 3s correlator integration time and 2MHz channel width. According to the equation above, this amounts to a weight of 1.2e7 for all visibilities.

### Option 2: Calculating the weights based on the rms

The second option to bring all weights on the same scale involves the execution of the CASA task statwt. This task recalculates the visibility weights based on their rms. statwt is part of the VLA pipeline, which was used to calibrate the original data. This explains the similarity of the A and B configuration weights in Fig. 3. But we nevertheless will run statwt once more on all files in order to ensure proper compatibility of the data (older versions of CASA may have been used for the pipeline, and CASA underwent major changes in its definition of data weights).

statwt needs to be executed on each MS. The default setting calculates the weight based on the rms of each scan and spectral window. This setting works quite well for continuum observations. We would like to note though that for spectral line data the fitspw parameter should be set to exclude the line from the calculations. Otherwise, strong lines will be down-weighted.

As statwt will overwrite the WEIGHT column, we once more create copies of our MSs in case we will have to revert to the original data:

# In a Terminal
cp -r VLA-SgrA-Sband-Aconfig-sub.ms VLA-SgrA-Sband-Aconfig-sub-statwt.ms
cp -r VLA-SgrA-Sband-Bconfig-sub.ms VLA-SgrA-Sband-Bconfig-sub-statwt.ms
cp -r VLA-SgrA-Sband-Cconfig-sub.ms VLA-SgrA-Sband-Cconfig-sub-statwt.ms


Now, we execute statwt on the new datasets:

# In CASA
# A-config:
statwt(vis='VLA-SgrA-Sband-Aconfig-sub-statwt.ms')

# In CASA
# B-config
statwt(vis='VLA-SgrA-Sband-Bconfig-sub-statwt.ms')

# In CASA
# C-config:
statwt(vis='VLA-SgrA-Sband-Cconfig-sub-statwt.ms')


Let's have a look at the weight values again to see if statwt has adjusted the weights properly:

# In CASA
# A-config:
plotms(vis='VLA-SgrA-Sband-Aconfig-sub-statwt.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')

# In CASA
# B-config
plotms(vis='VLA-SgrA-Sband-Bconfig-sub-statwt.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')

# In CASA
# C-config:
plotms(vis='VLA-SgrA-Sband-Cconfig-sub-statwt.ms',spw='3',averagedata=True,
avgchannel='64',xaxis='uvwave',yaxis='wt',coloraxis='antenna1')


In Fig. 6 we plot the new, recalculated weights for the three configurations. The absolute scaling has indeed changed, likely due to a different weight definition that was used in earlier versions of CASA when the data were calibrated. The relative weights between A and B configurations still appear to be similar to the original, relative numbers. The C-configuration weights, however, appear to be slightly elevated relative to A and B.

 Figure 6a: A-config recalculated weights. Figure 6b: B-config recalculated weights. Figure 6c: C-config recalculated weights.

## Combined and Image All Data

We will now create a combined image of all three re-weighted datasets.

First, let's check the new uv-coverage. To do so, we need to concatenate the data with concat (alternatively, one can use virtualconcat, a task that can also concatenate multi-MSs). We concatenate both, the datasets with initialized weights as well as those with re-computed weights:

# In CASA
concat(vis=['VLA-SgrA-Sband-Aconfig-sub-initwt.ms','VLA-SgrA-Sband-Bconfig-sub-initwt.ms','VLA-SgrA-Sband-Cconfig-sub-initwt.ms'],concatvis='VLA-SgrA-Sband-initwt-combined.ms')
#
concat(vis=['VLA-SgrA-Sband-Aconfig-sub-statwt.ms','VLA-SgrA-Sband-Bconfig-sub-statwt.ms','VLA-SgrA-Sband-Cconfig-sub-statwt.ms'],concatvis='VLA-SgrA-Sband-statwt-combined.ms')


Now let's plot the uv-coverage of one of the combined MSs:

plotuv(vis='VLA-SgrA-Sband-initwt-combined.ms')


Fig. 5 shows the combined uv-coverage, which extends to A-configuration baselines but with a much higher density at the intermediate and shorter baselines contributed from B and C configurations.

 Figure 7: Combined uv-coverage.

Although concat merges all three MSs into a single one, it is actually not a required step before imaging. clean will take care of the combination when all datasets are specified as a list. By default, clean will image the data in the CORRECTED columns, i.e. it will use the portion of the MS which exhibits the replaced Sgr A* point source (if CORRECTED is not present, it will image the visibilities stored in the DATA column). Clean will also perform the spectral regridding of all datasets on the fly, in particular in mode="velocity" or mode="frequency". There's no need to run cvel/cvel2 (or mstransform) to Doppler correct the MSs beforehand.

We will now create a combined image in clean. The threshold parameter was derived by a previous run of clean on the combined MS in which we determined the rough rms noise. For our threshold, we will use the rms noise multiplied by a factor of ~2.5.

# In CASA
clean(vis=['VLA-SgrA-Sband-initwt-combined.ms'],
imagename='GC-initwt-all',field='J1745-2900',mode='mfs',cell='0.1arcsec',imsize=[1280,1280],niter=3000,
threshold='5mJy',weighting='briggs',robust=0)


And now we image the data with recalculated weights:

# In CASA
clean(vis=['VLA-SgrA-Sband-statwt-combined.ms'],
imagename='GC-statwt-all',field='J1745-2900',mode='mfs',cell='0.1arcsec',imsize=[1280,1280],niter=3000,
threshold='5mJy',weighting='briggs',robust=0)


The resulting image has a beam size of 1.58" x 0.50" (Fig. 6), very similar to the resolution of A-configuration only. This is what we want to achieve. The rms is with ~2mJy better than A-only and there are clearly many more extended spatial scales in the image. This is a pretty good combination product.

 Figure 8a: Combined image with initialized weights. Figure 8b: Combined image with recalculated weights.

In our case the image with XXXXX appears to be better than the image XXXX.

The image can still be improved. For simplicity, we did not use any interactive cleaning in the above, but we highly recommend it for producing the final images. Improvements can also be obtained, e.g., by adjusting the image weights via the Briggs robust parameter, adding a taper, or weighting the different datasets against each other (using visweightscale in concat). Wide-band imaging and multi-scale imaging will also lead to better results. We refer to the VLA CASA Imaging Guide for more details and examples.

## Inserting an artificial Point Source for Sgr A*

Finally, we will add in a point source with a canonical flux density of 1 Jy to bring back Sgr A*. To do so, we again create a component list and use ft to attach the source model. Using uvsub with reverse=True will add instead of subtract the MODEL to DATA/CORRECTED. This step can be skipped when Sgr A* is not required. When the data is going to be self-calibrated, we actually recommend not to introduce an artificial source. But for our example, we now re-introduce Sgr A*. To make life easier we copy the combined dataset:

# In a Terminal

# In CASA
cl.rename('component-SgrA.cl')
cl.close()
#
#
#
#

# In CASA
threshold='5mJy',weighting='briggs',robust=0)


And now we image the data with recalculated weights:

# In CASA
threshold='5mJy',weighting='briggs',robust=0)

 Figure 9a: Combined image with initialized weights. Figure 9b: Combined image with recalculated weights.

The image can still be improved. For simplicity, we did not use any interactive cleaning in the above, but we highly recommend it for producing the final images. Improvements can also be obtained, e.g., by adjusting the image weights via the Briggs robust parameter, adding a taper, or weighting the different datasets against each other (using visweightscale in concat). Wide-band imaging and multi-scale imaging will also lead to better results. We refer to the VLA CASA Imaging Guide for more details and examples.

## Tips for Selfcal

If the source has a bright nucleus [or bright unresolved emission generally], start with the A array data, selfcal, then add B array, selfcal again, and so on. This procedure starts with a high model flux that is increased further. If the source is mostly diffuse, then there is not much signal in the A array data, so start with the D array, selfcal, then add C array, selfcal, and so on. Each selfcal step should be phase only first with maybe two or more iterations. At the end of each selfcal step, a phase+amplitude selfcal can be attempted, before merging in the next array configuration data. After each merge the selfcal steps can be repeated.

In our case, however, the variability of Sgr A* prevents such procedures due to the variation in the source flux. Also, when we replaced Sgr A* by an artificial 1 Jy source, that source will not have phase fluctuations imprinted and cannot be used for selfcal. The only option would be to selfcal the datasets with the point source removed, then incrementally combine the data selfcal after each combination step. The introduction of the 1Jy artificial source should happen just before imaging the fully combined and selfcal'ed MS.

Last checked on CASA Version 5.0.0