Protoplanetary Disk Simulation - VLA-CASA5.3.0: Difference between revisions

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The following tutorial shows how to adopt typical parameters for simulating Karl G. Jansky VLA data. We will use the same image as the ALMA tutorial [https://casaguides.nrao.edu/index.php/Protoplanetary_Disk_Simulation_(CASA_5.1) "Protoplanetary Disk Simulation"]. Follow [https://casa.nrao.edu/Data/EVLA/simulation/ppdisk672_GHz_50pc.fits this link to obtain the protoplanetary disk model image]. Model images are in units of Jy/pixel. Other simulation options, e.g. using component lists, or how to use the toolkit are explained in the [https://casaguides.nrao.edu/index.php/Simulating_Observations_in_CASA_5.1 Simulations in CASA] section of the CASAguides.


VLA version: under construction!!!
In Fig. 1 we show the model that we will use for this simulation tutorial.


{|
|[[Image:VLAsim-ppdiskmodel.png|400px|thumb|left|'''Fig. 1:''' Model image of a protoplanetary disk with units of Jy/pixel that we use for this simulation guide.]]
|}
The ALMA version of the tutorial shows a way on how to derive the center of the image. We will use their results and specify direction='J2000 18h00m00.031s -22d59m59.6s' for all of our simulations. The image center can also be determined with the CASA viewer. Given that the VLA primary beams at the VLA frequencies are much larger than the image, the precise pointing direction center is less important. 
We will use the {{simobserve}} and {{simanalyze}} tasks similar to the ALMA tutorials (in particular the plotted image sequence). As the model is specified for 672GHz so we will adapt it to work at VLA frequencies.
Note that {{simobserve}} has a few limitations. E.g. it cannot simulate different spectral windows. If this is desired, one needs to set up the simulation for each spw separately, and then use {{concat}} to merge all MeasurementSets. {{simobserve}} also has no option to add pointing errors to the simulated data. All VLA configurations and the VLA receiver temperatures are, however, accessible in {{simobserve}}.
===Q-band, 128MHz bandwidth, noiseless image, 1h integration time, A-configuration, no deconvolution===
Let's start with a simulation at Q-band at 44GHz, with a bandwidth of 128MHz. We will use the VLA A-configuration as it provides the resolution that is needed for the disk to be well resolved. To start with we do not apply any noise to the data:
<source lang="python">
# In CASA
simobserve(project='psimvla1', skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel', incenter='44GHz', inwidth='128MHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='', graphics='both', overwrite=True)
</source>
'''project:''' The name of our project is ''psimalma1''
'''skymodel:''' The input model image in Jy/pixel units. We adjust the peak to a lower <math>3\times10^{-5}</math>Jy/pixel value with the ''inbright'' parameter, as expected at a lower frequency. We also overwrite the fits header to assume that the model is valid for 44GHz with ''incenter'' and the bandwidth to 128MHz with ''inwidth''
'''setpointings:''' will allow {{simobserve}} to derive the pointing positions by its own algorithm. Given that the primary beam at Q-band is about 1arcminutes (see the VLA [[https://science.nrao.edu/facilities/vla/docs/manuals/oss/performance/fov observational status summary]], and the size of the model is less than an arcsecond, a single pointing will be more than enough.
'''integration:''' To avoid time smearing, we follow the guidance for data rates in the [https://science.nrao.edu/facilities/vla/docs/manuals/oss/performance/tim-res OSS] and assume 2s per visibility integration.
'''direction:''' the center of the map. For a single pointing this is equivalent to the pointing center.
'''obsmode:''' ''int'' is used for interferometric data such as VLA observations.
'''antennalist:''' the VLA configuration antenna position file. The files are available in CASA via 'vla.x.cfg'  where 'x' is the name of the array configuration. Here 'vla.a.cfg' is the VLA A configuration (the python command  ''os.getenv("CASAPATH").split()[0]+"/data/alma/simmos/" shows the directory that contains all configurations that are packaged in CASA)
'''hourangle:''' is used to simulate observations at a specific hour angle. We use 'transit' for culmination. 
'''totaltime:''' This is the time on source.
'''thermalnoise:''' We leave this parameter empty for this noise-less simulation.
'''graphics:''' 'both' will show graphics on the screen and save them as png files in the project directory.
'''overwrite:''' ''True'' will overwrite previous results: be careful when running multiple setups as the files may have different names and only the files with the same names will be overwritten. 
The output of the simulation is shown in Figs. 2 and 3. The first image is the sky coverage which shows clearly that the primary beam exceeds the size of the model image by far.  The other ouputs are explained in the caption of Fig. 3.
{|
|[[Image:VLAsim-psim1-sky.png|400px|thumb|left|'''Fig. 2:''' Sky Coverage. ]]
|[[Image:VLAsim-psim1-obs.png|600px|thumb|left|'''Fig. 3:''' Output of {{simobserve}}. '''Upper left:'''  Elevation vs time of the modeled source (blue). The vertical green line marks the transit time and the red bar is the time span of the simulated observations. '''Upper right:''' The VLA antenna positions in units of meters to the central VLA reference point. '''Lower left:''' The uv-coverage of the simulations (note that they do not account for the bandwidth). '''Lower right:''' the psf of the observation with fitted Gaussian major and minor beam sizes. ]]
|}
The task {{simanalyze}} can now process the newly created MeasurementSet and image the data:
<source lang="python">
# In CASA
simanalyze(project='psimvla1', image=True, vis='psimvla1.vla.a.ms',  imsize=[192, 192], interactive=False, niter=0, weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
</source>
'''project:''' The project name, same as in our call for {{simobserve}}.
'''image:''' ''True'' will image the visibilities with the following sub-parameters.
'''vis:''' The input MeasurementSet. Note that {{simobserve}}'s notation is to use the project name appended by the antenna configuration file name.
'''imsize:''' the number of pixels for the image dimensions. We use 192 for each axis. By default {{simobserve}} will use the pixel size of the model image as the ''cell'' size for each pixel (3.11 milli-arcseconds in our case). 
'''interactive:''' If set to ''True'', the cleaning will be interactive to allow the step by step setting of clean boxes and clean depths (see the [[https://casaguides.nrao.edu/index.php/VLA_CASA_Imaging VLA imaging topical guide]]). We will turn this feature off. 
'''niter:''' number of clean iterations. We start with a dirty map and set ''niter=0''.
'''weighting:''' (cf. [https://casa.nrao.edu/casadocs/latest/synthesis-imaging/data-weighting Image weighting schemes]. We will use ''briggs'' which defaults to a ''robust = 0.5''.
'''pbcor:''' If set to ''True'' the image will be primary beam corrected. In our case of a very large primary beam (see Fig. 1), primary beam correction will introduce very small corrections, so we turn it off. 
'''stokes:''' The Stokes polarization to be produced, we want Stokes I.
'''analyze:''' When set to ''True'' {{simobserve}} will perform basic analysis of the produced images and produce hard copies of the following displays.
'''showuv:''' We set this to ''False'' as we already show the uv-coverage in the {simobserve}} output (Fig. 3).
'''showpsf:''' Although we already have a plot of that in Fig. 3, we show it here again to have the comparison to the other plots.
'''showconvolved:''' produces a plot of the model convolved with the synthesized clean beam.
'''showclean:''' shows the deconvolved image (in our case we do not perform deconvolution, but show the plot anyways to be consistent with subsequent runs).
'''showresidual:''' a plot of the residual image after deconvolution.
'''showdifference:''' displays the difference between output cleaned image and input model sky image convolved with output clean beam, i.e. it shows remaining clean artefacts.
'''showfidelity:''' a fidelity image, as defined by <math>\frac{I}{|I-T|}</math> where <math>I</math> is the observed image and <math>T</math> the sky model, see the {{simanalyze}} CASAdoc help.
The resulting plots of our first simulation are shown in Fig. 4. Since this is a dirty image only (niter=0), the image and residual are the same dirty image. SInce we also did not turn on any thermal noise, the image corruptions are all due to the incomplete uv-coverage of our observations.
{|
|[[Image:VLAsim-psim1-ana.png|600px|thumb|left|'''Fig. 4:''' Simulated Images for noise-less Q-band observations. '''Upper left:''' the psf of the observations with the clean beam parameters. '''Upper center:''' the Sky model. '''Upper right:''' The sky model convolved with the clean beam. '''Bottom left:''' the simulated image. '''Bottom center:''' the residual image from deconvolution. '''Bottom right:''' the fidelity image (note that a bug in CASAS shows two color wedges for this plot; the inner one is the correct one to use).]]
|}
===Q-band, 128MHz bandwidth, noiseless image, 1h integration time, A-configuration, cleaned ===
As a second step we will deconvolve this data set. This could be done with inside the same project, but for a cleaner separation of our use cases, we will create a new MS with {{simobserve}} with a modified call of {{simanalyze}}:
<source lang="python">
# In CASA
simobserve(project='psimvla2', skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel', incenter='44GHz', inwidth='128MHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='', graphics='both', overwrite=True)
simanalyze(project='psimvla2', image=True, vis='psimvla2.vla.a.ms',  imsize=[192, 192], interactive=False, niter=1000, threshold='1e-4Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
</source>
The only difference to the earlier call of {{simobserve}} is our setting of ''niter=1000, threshold='1e-4Jy' '' which corresponds to a maximum number of 1000 clean iterations and a clean threshold of 0.1mJy. The threshold was chosen based on the previous image to be a few times above the rms of the image. The residual image is now flatter as expected and the bulk of the sidelobes disappear.
{|
|[[Image:VLAsim-psim2-ana.png|600px|thumb|left|'''Fig. 5:''' Same as Figure 4, this time, however, with a cleaned image.]]
|}
===Q-band, 128MHz bandwidth, 4mm pwv, 1h integration time, A-configuration===
We now add a precipitable water vapor of 4mm and a ground temperature for spillover of 270K. This can be achieved by the ''user_pwr'' and ''t_ground'' parameters. {{simobserve}} only adds thermal noise due to the sky brightness, but not phase noise due to pwv variations across the array. The ''sm.settrop'' tool can be used for the more sophisticated troposhperic models. A description is given in [https://casaguides.nrao.edu/index.php/Corrupting_Simulated_Data_(Simulator_Tool) Corrupting Simulated Data].
<source lang="python">
# In CASA
simobserve(project='psimvla3', skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel', incenter='44GHz', inwidth='128MHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)
</source>
The simobserve output will be identical to Fig. 2 and 3 since we do not change any of the displayed parameters. Now let's analyze the MS:
<source lang="python">
# In CASA
simanalyze(project='psimvla3', image=True, vis='psimvla3.vla.a.noisy.ms', imsize=[192, 192], interactive=False, niter=1000, threshold='4e-4Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
</source>
Note that we adjusted the cleaning threshold to account for the higher noise. The results are displayed in Fig. 6. The noise is dominating the image now, which is expected.
{|
|[[Image:VLAsim-psim3-ana.png|600px|thumb|left|'''Fig. 6:''' Output of {{simanalyze}} after injecting noise.]]
|}
==== Comparison with the VLA Exposure Calculator ====
We can compare the simulation to the predicted VLA sensitivity via the [http://go.nrao.edu/ect VLA Exposure Calculator Tool (ECT)]  ([http://go.nrao.edu/ect Description]). Using winter observing conditions (for good pwv), a medium elevation (cf. Fig.  3), 128MHz bandwidth at a frequency of 44GHz, the ECT predicts a beam size of 0.067" and which is very close to our simulations (cf. Fig. 3 and 6). The ECT output is shown in Fig. 7.
{|
|[[Image:VLAsim-etc.png|400px|thumb|left|'''Fig. 7:''' Exposure Calculation for 4mm pwr, 128MHz bandwidth]]
|}
The rms provided in Fig. 6 is over the entire image and includes the source. It is therefore not representative to the thermal noise. To obtain a better noise figure, we produce an image with the same parameters as {{simanalyze}}, but with a larger image size directly via {{tclean}}. Since the briggs parameter in {{simanalyze}} defaults to robust=0.5, we will use the same value here:
<source lang="python">
# In CASA
tclean(vis='psimvla3/psimvla3.vla.a.noisy.ms', imagename='psim3-bigimage', imsize=[640, 640], cell='3.11e-3arcsec',  specmode='mfs',  gridder= 'standard', deconvolver='hogbom', weighting='briggs', robust=0.5, niter=1000, threshold='4e-4Jy') 
</source>
opening the image in the {{viewer}}
<source lang="python">
# In CASA
viewer('psim3-bigimage.image')
</source>
and measuring the noise statistics away from the source (Fig. 8), gives a value of about 7e-5Jy/beam which is a very good agreement with the predicted noise figure of 6.9e-5 Jy/beam.
{|
|[[Image:VLAsim-tcleanbig.png|600px|thumb|left|'''Fig. 8:''' Larger image of the simulation given in Fig. 6, measuring the rms noise in the purple rectangle regions away from the emission. A few low-level sidelobes are still present, however. ]]
|}
===Q-band, 8GHz bandwidth, 4mm pwv, 1h integration time, A-configuration===
To compensate for noise, we will extend our bandwidth from 128MHz to 8GHz. At this time, {{simobserve}} has no chanelization so the simulation will not have the better uv-coverage that is obtained in multi-frequency imaging. Consecutive simulations with different spectral windows, and combined MSs, however, can achieve that and we will show how to obtain a multi-channel MS shortly. For large bandwidths, one needs to be careful to not introduce [[https://science.nrao.edu/facilities/vla/docs/manuals/oss2016A/performance/fov/bw-smearing bandwidth smearing]]. Our source is at the center of the image and bandwidth smearing will be minimal.
<source lang="python">
# In CASA
simobserve(project='psimvla4',  skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel', incenter='44GHz', inwidth='8GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)
</source>


CASA <253>: inp
The {{simobserve}} output again is identical with Fig. 3.  
----------> inp()
#  simobserve :: visibility simulation task
project            =  'psimvla'        #  root prefix for output file names
skymodel            = 'ppdisk43_GHz_50pc.fits' #  model image to observe
    inbright      =        ''        #  scale surface brightness of brightest pixel e.g. "1.2Jy/pixel"
    indirection    =        ''        #  set new direction e.g. "J2000 19h00m00 -40d00m00"
    incell        =        ''        #  set new cell/pixel size e.g. "0.1arcsec"
    incenter      =        ''        #  set new frequency of center channel e.g. "89GHz" (required even for 2D model)
    inwidth        =    '8GHz'        #  set new channel width e.g. "10MHz" (required even for 2D model)


complist            =         ''       #  componentlist to observe
<source lang="python">
setpointings        =       True
# In CASA
    integration    =       '3s'       # integration (sampling) time
simanalyze(project='psimvla4', image=True, vis='psimvla4.vla.a.noisy.ms', imsize=[192, 192], interactive=False, niter=10000, threshold='5e-5Jy', weighting='briggs', pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
    direction      = 'J2000 18h00m00.031s -22d59m59.6s' #  "J2000 19h00m00 -40d00m00" or "" to center on model
</source>
    mapsize        = '0.76arcsec'     # angular size of map or "" to cover model
    maptype        =   'square'       #  hexagonal, square (raster), ALMA, etc
    pointingspacing =         ''       #  spacing in between pointings or "0.25PB" or "" for ALMA default INT=lambda/D/sqrt(3), SD=lambda/D/3


obsmode            =      'int'        #  observation mode to simulate [int(interferometer)|sd(singledish)|""(none)]
The image (Fig. 9) is clearly better defined, as expected from a broader bandwidth. We also decreased the cleaning threshold to 0.05mJy and added a few more iterations to allow to reach this threshold.  
    antennalist    = 'vla.a.cfg'      #  interferometer antenna position file
    refdate        = '2014/05/21'      #  date of observation - not critical unless concatting simulations
    hourangle      =  'transit'        #  hour angle of observation center e.g. "-3:00:00", "5h", "-4.5" (a number without units will be interpreted as
                                        #  hours), or "transit"
    totaltime      =  '12000s'        #  total time of observation or number of repetitions
    caldirection  =        ''        #  pt source calibrator [experimental]
    calflux        =      '1Jy'


outframe            =    'LSRK'        #  spectral frame of MS to create
{|
thermalnoise        = 'tsys-atm'        #  add thermal noise: [tsys-atm|tsys-manual|""]
|[[Image:VLAsim-psim4-ana.png|600px|thumb|left|'''Fig. 9:''' Imaging with 8GHz bandwidth.]]
    user_pwv      =          4        #  Precipitable Water Vapor in mm
|}
    t_ground      =      270.0        #  ambient temperature
    seed          =      11111        #  random number seed


leakage            =        0.0        #  cross polarization (interferometer only)
graphics            =    'both'        #  display graphics at each stage to [screen|file|both|none]
verbose            =      False
overwrite          =      True        #  overwrite files starting with $project


<!--


===
==== Comparison with the VLA Exposure Calculator ====


CASA <255>: inp
We compare again the simulation to the predicted VLA sensitivity via the [http://go.nrao.edu/ect VLA Exposure Calculator Tool (ETC)]  ([http://go.nrao.edu/ect Description]). Using the same conditions and parameters as above, except for 8GHz bandwidth, the ECT predicts a rms of 10.7<math>\mu Jy</math> (Fig. 10):
----------> inp()
#  simanalyze :: image and analyze measurement sets created with simobserve
project            =  'psimvla'        #  root prefix for output file names
image              =      True        #  (re)image $project.*.ms to $project.image
    vis            = 'psimvla.vla.a.noisy.ms' #  Measurement Set(s) to image
    modelimage    = 'ppdisk43_GHz_50pc.fits' #  lower resolution prior image to use in clean e.g. existing total power image
    imsize        = [192, 192]       # output image size in pixels (x,y) or 0 to match model
    imdirection    =        ''        #  set output image direction, (otherwise center on the model)
    cell          =        ''        #  cell size with units e.g. "10arcsec" or "" to equal model
    interactive    =      False        #  interactive clean?  (make sure to set niter>0 also)
    niter          =          1        #  maximum number of iterations (0 for dirty image)
    threshold      =  '1e-7Jy'        #  flux level (+units) to stop cleaning
    weighting      =  'uniform'        #  weighting to apply to visibilities. briggs will use robust=0.5
    mask          =        []        #  Cleanbox(es), mask image(s), region(s), or a level
    outertaper    =        []        #  uv-taper on outer baselines in uv-plane
    pbcor          =      True        #  correct the output of synthesis images for primary beam response?
    stokes        =        'I'        #  Stokes params to image
    featherimage  =        ''        #  image (e.g. total power) to feather with new image


analyze            =      True        #  (only first 6 selected outputs will be displayed)
{|
    showuv        =      False        #  display uv coverage
|[[Image:VLAsim-etc8GHz.png|400px|thumb|left|'''Fig. 10''': Exposure time calculation for 4mm pwr, 8GHz bandwidth]]
    showpsf        =      True        #  display synthesized (dirty) beam (ignored in single dish simulation)
|}
    showmodel      =      True        #  display sky model at original resolution
    showconvolved  =      True        #  display sky model convolved with output clean beam
    showclean      =      True        #  display the synthesized image
    showresidual  =      True        #  display the clean residual image (ignored in single dish simulation)
    showdifference =      True        #  display difference between output cleaned image and input model sky image convolved with output clean beam
    showfidelity  =      True        #  display fidelity (see help)


graphics            =    'both'        #  display graphics at each stage to [screen|file|both|none]
Note that the VLA exposure calculator switched to 3bit observing to accommodate the large bandwidth. The simulator, however, assumes 8bit samplers, which provide about 15% better sensitivity than VLA 3bit correlations (For a discussion, see the [https://science.nrao.edu/facilities/vla/docs/manuals/oss/performance/vla-samplers VLA Samplers] page).
verbose            =      True
overwrite          =      True        #  overwrite files starting with $project
dryrun              =      False        #  only print information [experimental; only for interfermetric data]
logfile            =        ''


Similar to the case of 128MHz bandwidth, we produce a larger image to be able to measure the image rms in a signal-free region:


<source lang="python">
# In CASA
tclean(vis='psimvla4/psimvla4.vla.a.noisy.ms', imagename='psim4-bigimage', imsize=[640, 640], cell='3.11e-3arcsec',  specmode='mfs',  gridder= 'standard', deconvolver='hogbom', weighting='briggs', robust=0.5, niter=10000, threshold='5e-5Jy') 
</source>


opening the image in the {{viewer}}
<source lang="python">
# In CASA
viewer('psim4-bigimage.image')
</source>


[[Protoplanetary Disk Simulation - VLA]]
and measuring the noise statistics away from the source (Fig. 11), gives a value of about 1.3e-5Jy/beam which is in reasonable agreement with the exposure calculator prediction. The regions where we measured the noise still contains some residual sidelobe structure and deeper cleaning, especially with a clean mask would improve the noise figure further, bringing it even closer to the predicted value.


[[Category: Simulations]]
{|
|[[Image:VLAsim-tcleanbig8GHz.png|600px|thumb|left|'''Fig. 11:''' Larger Image of the 8GHz simulation in Fig. 9, measuring the rms noise in the purple rectangle regions away from the emission.]]
|}
-->


* '''This is an advanced simulation tutorial.  New users are recommended to begin with reading the [http://casa.nrao.edu/casadocs/latest/ CASA Docs] documentation pages on [http://casa.nrao.edu/casadocs/latest/simulation/ "Simulations"].'''
==== Multi-Term-Multi-Frequency Synthesis Imaging ====
* '''This guide is applicable to CASA version 5.1. 
* '''To create a script of the Python code on this page see [[Extracting scripts from these tutorials]].'''


== Data ==
In reality, the 8GHz bandwidth is not confined to a single channel but to many channels. This results in a spread out uv-coverage as it depends on the projected baselines expressed in number of wavelengths. Combining the channels in a multi-frequency synthesis (mfs), therefore does not only increase the sensitivity, but also the image fidelity. This leads to a better defined psf. Channelization and mfs imaging are also reducing bandwidth smearing effects.


For this CASA Guide we will use a protoplanetary disk model from S. Wolf.  Get the data [https://casa.nrao.edu/Data/EVLA/simulation/ppdisk35_GHz_50pc.fits here]. Note that this is a modified image from the  [http://casaguides.nrao.edu/index.php?title=Sim_Inputs ALMA Simulation Inputs], where we changed the center frequency 35GHz and the bandwidth to 128MHz. '
As mentioned above, {{simobserve}}, naturally, does not channelize the visibilities when the input image is not chanelized.  


== Script with Explanation ==
In the following, we will channelize the MS and, to show the procedure, we will also apply a spectral index of <math>S\propto\nu^{-1.5}</math> at the same time.


Set '''simobserve''' as the current task and reset all parameters.
To start with, we need to produce a multi-channel model image. The following script converts our current model image from fits to the CASA image format with {{importfits}}.
We then create 64 planes, apply the spectral index, and fix the headers accordingly to bring them into consecutive frequency order.  Each channel is specified to a width of 128MHz (real VLA data would have typical channel widths of 2MHz). Finally, our individual planes are combined into a cube with the '''ia.imageconcat''' tool method.  


<source lang="python">
<source lang="python">
# In CASA
# In CASA
default("simobserve")
importfits(fitsimage="ppdisk672_GHz_50pc.fits", imagename="ppdisk_Q_50pc.im")
stats=imstat(imagename='ppdisk_Q_50pc.im')
maximum=stats['max'][0]
ratio=3e-5/maximum
for x in range (0, 64):
    y=40+x*0.128
    immath(imagename="ppdisk_Q_50pc.im", mode='evalexpr', expr="IM0*"+str(ratio)+"*(("+str(y)+"/40)^-1.5)", outfile="ppdisk_Q_50pc_spx_"+str(x)+".im")
    imhead(imagename="ppdisk_Q_50pc_spx_"+str(x)+".im", mode="put", hdkey="crval4", hdvalue=str(y)+"GHz")
    imhead(imagename="ppdisk_Q_50pc_spx_"+str(x)+".im", mode="put", hdkey="cdelt4", hdvalue="128MHz")
 
comb=ia.imageconcat(outfile="ppdisk-combined_spx.im", infiles="ppdisk_Q_50pc_spx*.im",  axis=3, relax=True, tempclose=False, reorder=True, overwrite=True)
comb.close()
</source>
</source>


Using this model cube in {{simobserve}} will produce the channelized visibilities:


Let's call our project "psimvla".  This defines the root prefix for any output files from {{simobserve}}.
<source lang="python">
<source lang="python">
project = "psimvla"
# In CASA
simobserve(project='psimvla4mfs',  skymodel='ppdisk-combined_spx.im',  setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='none', overwrite=True)
</source>
</source>
 
 
Review the image coordinate system using task {{imhead}}.
The graphical output of {{simobserve}} and {{simanalyze}} would treat such data as a data cube rather than a multi-channel continuum data set. So we will produce our own graphics and imaging.
 
Let's first have a look at the new uvcoverage, each channel is displayed in a different color in Fig. 10 (note that the graphical output of {{simobserve}}  


<source lang="python">
<source lang="python">
# This reports image header parameters in the Log Messages window
# In CASA
imhead("ppdisk43_GHz_50pc.fits")
plotms(vis='psimvla4mfs/psimvla4mfs.vla.a.noisy.ms', xaxis='Uwave', yaxis='Vwave',coloraxis='channel')
</source>
</source>
 
{|
|[[Image:VLAsim-uvcovermfs.png|400px|thumb|left|'''Fig. 10:''' uv-coverage of chanelized visibilities.]]
|}


This confirms that the data are set at 43GHz center frequency with a bandwidth of 128MHz. Note that the reference coordinate of the image is at pixel (0,0), i.e. in a corner of the image, not the center. In [[https://casaguides.nrao.edu/index.php?title=Protoplanetary_Disk_Simulation_(CASA_5.1)]] a method is provided on how to derive the image centers through the toolkit. Using that method, or inspecting the image with the viewer shows that the image center is at RA=18h00m00.031s, DEC=-22d59m59.6s.
{{simanalyze}} would assume that these data are to be imaged as a cube. Our aim, however, is to create a continuum image with the mfs technique, and, to recover the spectral index, we will use the Multi-term Taylor expansion in frequency (mtmfs, see [https://casa.nrao.edu/casadocs/latest/synthesis-imaging/deconvolution-algorithms CASAdocs Deconvolution Algorithms]). We will use nterms=2 to derive the spectral index. The spectral index map, however, is fairly sensitive to the scales in the image. A regular Hogbom clean based on point sources, typically creates maps with too steep spectral indices when applied to extended emission. To avoid this effect, we therefore use the multi-scale algorithm with a range of scales: 


We'll set '''skymodel''' to the FITS file downloaded, above, and leave all '''skymodel''' subparameters at their default values.  {{simobserve}} will create CASA image <tt>psimvla.skymodel</tt>.
<source lang="python">
<source lang="python">
skymodel = "ppdisk43_GHz_50pc.fits"
# In CASA
</source>
tclean(vis='psimvla4mfs/psimvla4mfs.vla.a.noisy.ms', imagename='psimvla4mfs/8GHzmfs', imsize=[192, 192], cell='3.11e-3arcsec', specmode='mfs', gridder='standard', deconvolver='mtmfs', nterms=2, scales=[0,2,4,8,13,20,40],  niter=1000, threshold='2e-4Jy', weighting='briggs', robust=0.5)
</source>
We will specify the sky position for the center of the observation and set the map size to the size of the model image.  The image is very small compared to the VLA primary beam at 35GHz () Since the model image is 2/3 arcseconds across, we should only need one pointing.  In this case, '''pointingspacing''' and '''maptype''' can be left at their default values.
As before, we are not attempting primary beam corrections as the image is very small compared to the primary beam (cf. Fig. 2).   
 
<!--


Let's also do a cube:
<source lang="python">
<source lang="python">
setpointings      = True
# In CASA
direction          = "J2000 18h00m00.031s -22d59m59.6s"
tclean(vis='psimvla4mfs/psimvla4mfs.vla.a.noisy.ms', imagename='psimvla4mfs/8GHzmfs_cube', imsize=[192, 192], cell='3.11e-3arcsec', specmode='cube', gridder='standard', deconvolver='hogbom', niter=1000, threshold='2e-4Jy', weighting='briggs', robust=0.5)
mapsize            = "0.76arcsec"
</source>
</source>  


We do want to simulate an interferometric observation, so we set '''obsmode''' accordingly.  We'll set '''totaltime''' to a 20-minute snapshot observation.
and we will use {{spxfit}} to calculate the spectral index from the cube for comparison. First, however, we need to smooth to a common beam across all frequencies, the parameter ''kernel="commonbeam"'' smoothes the entire cube to the lowest resolution in the cube (typically the channel with the lowest frequency):


<source lang="python">
<source lang="python">
obsmode            = "int"
# In CASA
totaltime          = "1200s"
imsmooth(imagename='psimvla4mfs/8GHzmfs_cube.image', kernel='commonbeam', outfile='psimvla4mfs/8GHzmfs_cube.image.common')
 
spxfit(imagename='psimvla4mfs/8GHzmfs_cube.image.common', spxest=[1.5,-1.5], multifit=True, spxsol='psimvla4mfs/8GHzmfs_cube.image.common.spx', spxerr='psimvla4mfs/8GHzmfs_cube.image.common.spxerr')
</source>
</source>


We want to use the appropriate antenna configuration for the desired angular resolution. Configuration 20, <tt>alma.out20.cfg</tt>, is the largest "compact" configuration. A list of configuration files available in CASA 4.1 is available [[Antenna_Configurations_Models_in_CASA| here]].
The ''multifit'' parameter will attempt to fit a spectral index to each individual pixel and ''spxest'' provides initial parameters for the fits. The task will write out a "_1" file that is the first parameter of the fitted polynomial, which is the spectral index ("filename_0" is the scaling offset).  
 
 
'''Note, that for both, {{tclean}} with ''mtmfs'' and {{spxfit}} reliable results are only obtained for high signal-to-noise regions.'''
 
-->  
 
The images can be displayed with the viewer, note that the image itself is now called ''psimvla4mfs/8GHzmfs.image.tt0'' (Fig. 11) and the spectral index map: ''psimvla4mfs/8GHzmfs.alpha'' (Fig. 12). In Fig. 12 we also show the contours of the image on the spectral index map, to check for the signal-to-noise at each position.
 
{|
|[[Image:VLAsim-psim4mfstclean.png|400px|thumb|left|'''Fig. 11:''' The image of Fig. 9 but using multi-frequency-synthesis (mfs) imaging. ]]
|[[Image:VLAsim-psim4mfstcleanalpha.png|500px|thumb|left|'''Fig. 12:''' The spectral index map with image contours overlaid.]]
|}
 
As seen in Fig. 11, this method should produce a somewhat better fidelity than the non-mfs image shown in Fig. 9, although a direct comparison is difficult given the spectral index that we introduced. The spectral index map itself (Fig. 12), unfortunately, is dominated by noise, even at the brightest regions, due to the pwv that we assumed. This results in a relatively unreliable spectral index map overall, although the values scatter around the spectral index of -1.5 that we inserted earlier.
 
===Q-band, 8GHz bandwidth, 4mm pwv, 4h integration time, A-configuration===
 
Let's improve the depth of the observations even further by going to 4h on-source integration, via '' totaltime='14400s' ''.  


<source lang="python">
<source lang="python">
antennalist       = "vla.a.cfg"
# In CASA
simobserve(project='psimvla5',  skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel',  incenter='44GHz', inwidth='8GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='14400s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)
</source>
</source>


We do not want to simulate observations with thermal noise in this example, so we set:
Fig. 13 shows a better uv-coverage (lower left image) and the 4h observation is also marked by a wider red bar in the top left image. This also improved the shape of the psf.
 
{|
|[[Image:VLAsim-psim5-obs.png|600px|thumb|left|'''Fig. 13:''' Output of {{simobserve}} with 8GHz bandwidth of 4h of on-source observing time. ]]
|}
 
<source lang="python">
<source lang="python">
thermalnoise = ''
# In CASA
simanalyze(project='psimvla5', image=True, vis='psimvla5.vla.a.noisy.ms',  imsize=[192, 192], interactive=False, niter=1000, threshold='2e-5Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
</source>
</source>


Now run simobserve.
Given the expected deeper image we reduced the cleaning threshold to 0.02mJy, and the result is shown in Fig. 14.  The image now is an almost perfect representation of the true sky model convolved with the clean beam.
 
{|
|[[Image:VLAsim-psim5-ana.png|600px|thumb|left|'''Fig. 14:''' Images after increasing the integration time to 4h.]]
|}
 
 
==== Comparison with the VLA Exposure Calculator ====
 
We compare again the simulation to the predicted VLA sensitivity via the [http://go.nrao.edu/ect VLA Exposure Calculator Tool (ETC)]  ([http://go.nrao.edu/ect Description]). Using 8GHz bandwidth 4h on-source, and a low elevation due to the longer observations, the ECT predicts a rms of 7.1<math>\mu Jy</math> (Fig. 15):
 
{|
|[[Image:VLAsim-etc8GHz4h.png|400px|thumb|left|'''Fig. 15''': Exposure time calculation for 4mm pwr, 8GHz bandwidth]]
|}
 
Note that the VLA exposure calculator switched to 3bit observing to accommodate the large bandwidth. The simulator, however, assumes 8bit samplers, which provide about 15% better sensitivity than VLA 3bit correlations (For a discussion, see the [https://science.nrao.edu/facilities/vla/docs/manuals/oss/performance/vla-samplers VLA Samplers] page).
 
Similar to the case of 128MHz bandwidth 1h case, we produce a larger image to be able to measure the image rms in a signal-free region:


<source lang="python">
<source lang="python">
simobserve()
# In CASA
tclean(vis='psimvla5/psimvla5.vla.a.noisy.ms', imagename='psim5-bigimage', imsize=[640, 640], cell='3.11e-3arcsec',  specmode='mfs',  gridder= 'standard', deconvolver='hogbom', weighting='briggs', robust=0.5, niter=10000, threshold='5e-5Jy')
</source>
</source>


Now that we've simulated the visibility measurements, we want to generate an image from the simulated data.  '''simanalyze''' makes this easy.  We begin by setting '''project''' to the same prefix used in simobserve and setting '''image''' to True.
opening the image in the {{viewer}}


<source lang="python">
<source lang="python">
default ("simanalyze")
# In CASA
project = "psimvla"
viewer('psim5-bigimage.image')
image = True
</source>
</source>


We set '''modelimage''' to use the input FITS image when cleaning the simulated visibilities. We set the image size to 192 pixels square.
and measuring the noise statistics away from the source (Fig. 16), gives a value of about 7mJy/beam which is in reasonable agreement with the exposure calculator prediction. 
<!--
The regions where we measured the noise still contains some residual sidelobe structure and deeper cleaning, especially with a clean mask would improve the noise figure further, bringing it even closer to the predicted value.
-->
{|
|[[Image:VLAsim-tcleanbig8GHz4h.png|600px|thumb|left|'''Fig. 16:''' Larger Image of the 8GHz simulation in Fig. 14, measuring the rms noise in the purple rectangle regions away from the emission.]]
|}
 
 
 
 
<!--
===Q-band, 8GHz bandwidth, 18mm pwv, 1h integration time, A-configuration===
 
We will now go back to 1h integration, but assume worse conditions of the VLA site with a precipitable water vapor of 18mm.  


<source lang="python">
<source lang="python">
modelimage = "ppdisk43_GHz_50pc.fits"
# In CASA
vis = project + ".vla.a.ms"
simobserve(project='psimvla6',  skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel',  incenter='44GHz', inwidth='8GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=18, t_ground=270.0, graphics='both', overwrite=True)
imsize = [192, 192]  
</source>
</source>


Specify the number of iterations for cleaning, with proper threshold and weighting.
<source lang="python">
# In CASA
simanalyze(project='psimvla6', image=True, vis='psimvla6.vla.a.noisy.ms', imsize=[192, 192], interactive=False, niter=1000, threshold='2e-4Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
</source>
 
We see that the resulting image is almost identical to the pwv of 4mm (Fig. 7), with almost identical noise figures. The observations seem to be very little affected by the variations in the VLA site pwv. Note that the simulations do not include pointing errors due to stronger winds.
 
{|
|[[Image:VLAsim-psim6-ana.png|600px|thumb|left|Fig. 10: Assuming less than ideal weather conditions with pwv of 18mm.]]
|}
 
-->
 
===Q-band, 8GHz bandwidth, 4mm pwv, 1h integration time, C-configuration===
 
Our last Q-band simulation will use a precipitable water vapor of 4mm again, but to we will now simulate the observations with the VLA C-configuration (specified with the ''antennalist'' parameter).  


<source lang="python">
<source lang="python">
niter = 10000
# In CASA
threshold = "1e-7Jy"
simobserve(project='psimvla6',  skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel',  incenter='44GHz', inwidth='8GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.c.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)
weighting = "natural"   
</source>
</source>


We'd like to calculate a difference and fidelity image, but we don't need to see the uv coverage.
As expected, the uv-coverage decreases by a factor of about 10 and and the synthesize beam increases by the same factor, as seen in Fig. 17.
 
{|
|[[Image:VLAsim-psim6-obs.png|600px|thumb|left|'''Fig. 17:''' Output of {{simobserve}} using the C-configuration. ]]
|}


<source lang="python">
<source lang="python">
analyze = True
# In CASA
showuv = False
simanalyze(project='psimvla6', image=True, vis='psimvla6.vla.c.noisy.ms',  imsize=[1728, 1728], interactive=False, niter=1000, threshold='1e-4Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
showresidual = True
showconvolved = True
</source>
</source>


Plot both to the screen and PNG files with lots of messages.
Note that the output filenames will now change and reflect C-configuration in their names. The resulting images are displayed in Fig. 18, where the images now look like a point source with the degraded resolution. The surface brightness sensitivity of the observations, however, increase and we can clean to a lower threshold of 0.1mJy.  {{simobserve}} automatically detected that the beam is massively oversampled and that a larger image size will provide a better field of view.
 
{|
|[[Image:VLAsim-psim6-ana.png|600px|thumb|left|'''Fig. 18:''' C-configuration results.]]
|}
 
To combine data of two different array configurations, we refer to the [https://casaguides.nrao.edu/index.php/VLA_Data_Combination VLA Data Combination Guide].
 
===X-band, 4GHz bandwidth, 4mm pwv, 1h integration time, A-configuration===
 
Finally, we will go for a '''X-band (10GHz)''', A-configuration simulation. Since X-band has a maximum bandwidth of 4GHz, we will reduce it to this value. We will also lower the flux of the model to 0.01mJy given that a the flux of the model will likely be lower, too.


<source lang="python">
<source lang="python">
graphics = "both"
# In CASA
verbose = True
simobserve(project='psimvla7',  skymodel='ppdisk672_GHz_50pc.fits', inbright='1e-5Jy/pixel',  incenter='10GHz', inwidth='4GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)
overwrite = True
</source>
</source>


Run simanalyze.
When expressed in wavelengths, the uv-coverage and synthesized beam are somewhere in between that of Q-band A-configuration and C-configuration as expected (Fig. 19).
 
{|
|[[Image:VLAsim-psim8-obs.png|600px|thumb|left|'''Fig. 19:''' Output of {{simobserve}} for X-band observations. ]]
|}


<source lang="python">
<source lang="python">
simanalyze()
# In CASA
simanalyze(project='psimvla7', image=True, vis='psimvla7.vla.a.noisy.ms',  imsize=[192, 192], interactive=False, niter=1000, threshold='3e-5Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
</source>
</source>


==Simulation Output==


{| cellspacing=2
The larger primary beam of the X-band data is shown in Fig. 20, where the model image is barely visible in the center. The simulated images are shown in Fig. 21. The ring shape is still visible in the results although quite blurred. We note that the noise is considerably lower as expected from the lower band noise properties of the receiver and atmosphere. We adjusted the clean threshold accordingly. Again, {{simanalyze}} was overriding the image size as the psf would not have been adequately covered for the lower frequency.  
|Input:<br> [[File:psim2-4.0.alma.out20.skymodel.png|300px]]
 
|simobserve:<br> [[File:psim2-4.0.alma.out20.observe.png|300px]]
{|
|-
|[[Image:VLAsim-psim8-sky.png|600px|thumb|left|'''Fig. 20:''' X-band sky coverage]]
|simanalyze image:<br> [[File:psim2-4.0.alma.out20.image.png|300px]]
|[[Image:VLAsim-psim8-ana.png|600px|thumb|left|'''Fig. 21:''' X-band simulation results.]]
|simanalyze output:<br> [[File:psim2-4.0.alma.out20.analysis.png|300px]]
|}
|}
<!--
===test===
importfits(fitsimage="ppdisk672_GHz_50pc.fits", imagename="ppdisk_Q_50pc.im")
for x in range (0, 64):
    os.system("cp -r ppdisk_Q_50pc.im ppdisk_Q_50pc_"+str(x)+".im")
    y=40+x*0.128
    imhead(imagename="ppdisk_Q_50pc_"+str(x)+".im", mode="put", hdkey="crval4", hdvalue=str(y)+"GHz")
    imhead(imagename="ppdisk_Q_50pc_"+str(x)+".im", mode="put", hdkey="cdelt4", hdvalue="128MHz")
comb=ia.imageconcat(outfile="ppdisk-combined.im", infiles="ppdisk_Q_50pc_*.im",  axis=3, relax=True, tempclose=False, reorder=True, overwrite=True)
comb.close()
<source lang="python">
# In CASA
simobserve(project='psimvlatest',  skymodel='ppdisk-combined.im', inbright='3e-5Jy/pixel',  setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)
</source>
plotms(vis='psimvlatest/psimvlatest.vla.a.noisy.ms', xaxis='Uwave', yaxis='Vwave',coloraxis='channel')
tclean(vis='psimvlatest/psimvlatest.vla.a.noisy.ms', imagename='8GHzmfs', imsize=[192, 192], cell='3.11e-3arcsec', specmode='mfs', gridder='standard', deconvolver='hogbom', niter=1000, threshold='2e-4Jy', weighting='briggs', robust=0.5)
viewer('8GHzmfs.image')
<source lang="python">
# In CASA
simanalyze(project='psimvlatest', image=True, vis='psimvlatest.vla.a.noisy.ms',  imsize=[192, 192], interactive=False, niter=1000, threshold='2e-4Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)
</source>
-->

Latest revision as of 20:38, 30 October 2018

The following tutorial shows how to adopt typical parameters for simulating Karl G. Jansky VLA data. We will use the same image as the ALMA tutorial "Protoplanetary Disk Simulation". Follow this link to obtain the protoplanetary disk model image. Model images are in units of Jy/pixel. Other simulation options, e.g. using component lists, or how to use the toolkit are explained in the Simulations in CASA section of the CASAguides.

In Fig. 1 we show the model that we will use for this simulation tutorial.

Fig. 1: Model image of a protoplanetary disk with units of Jy/pixel that we use for this simulation guide.

The ALMA version of the tutorial shows a way on how to derive the center of the image. We will use their results and specify direction='J2000 18h00m00.031s -22d59m59.6s' for all of our simulations. The image center can also be determined with the CASA viewer. Given that the VLA primary beams at the VLA frequencies are much larger than the image, the precise pointing direction center is less important.

We will use the simobserve and simanalyze tasks similar to the ALMA tutorials (in particular the plotted image sequence). As the model is specified for 672GHz so we will adapt it to work at VLA frequencies.

Note that simobserve has a few limitations. E.g. it cannot simulate different spectral windows. If this is desired, one needs to set up the simulation for each spw separately, and then use concat to merge all MeasurementSets. simobserve also has no option to add pointing errors to the simulated data. All VLA configurations and the VLA receiver temperatures are, however, accessible in simobserve.


Q-band, 128MHz bandwidth, noiseless image, 1h integration time, A-configuration, no deconvolution

Let's start with a simulation at Q-band at 44GHz, with a bandwidth of 128MHz. We will use the VLA A-configuration as it provides the resolution that is needed for the disk to be well resolved. To start with we do not apply any noise to the data: 

# In CASA
simobserve(project='psimvla1', skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel', incenter='44GHz', inwidth='128MHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='', graphics='both', overwrite=True)

project: The name of our project is psimalma1

skymodel: The input model image in Jy/pixel units. We adjust the peak to a lower [math]\displaystyle{ 3\times10^{-5} }[/math]Jy/pixel value with the inbright parameter, as expected at a lower frequency. We also overwrite the fits header to assume that the model is valid for 44GHz with incenter and the bandwidth to 128MHz with inwidth

setpointings: will allow simobserve to derive the pointing positions by its own algorithm. Given that the primary beam at Q-band is about 1arcminutes (see the VLA [observational status summary], and the size of the model is less than an arcsecond, a single pointing will be more than enough.

integration: To avoid time smearing, we follow the guidance for data rates in the OSS and assume 2s per visibility integration.

direction: the center of the map. For a single pointing this is equivalent to the pointing center.

obsmode: int is used for interferometric data such as VLA observations.

antennalist: the VLA configuration antenna position file. The files are available in CASA via 'vla.x.cfg' where 'x' is the name of the array configuration. Here 'vla.a.cfg' is the VLA A configuration (the python command os.getenv("CASAPATH").split()[0]+"/data/alma/simmos/" shows the directory that contains all configurations that are packaged in CASA)

hourangle: is used to simulate observations at a specific hour angle. We use 'transit' for culmination.

totaltime: This is the time on source.

thermalnoise: We leave this parameter empty for this noise-less simulation.

graphics: 'both' will show graphics on the screen and save them as png files in the project directory.

overwrite: True will overwrite previous results: be careful when running multiple setups as the files may have different names and only the files with the same names will be overwritten.

The output of the simulation is shown in Figs. 2 and 3. The first image is the sky coverage which shows clearly that the primary beam exceeds the size of the model image by far. The other ouputs are explained in the caption of Fig. 3.

Fig. 2: Sky Coverage.
Fig. 3: Output of simobserve. Upper left: Elevation vs time of the modeled source (blue). The vertical green line marks the transit time and the red bar is the time span of the simulated observations. Upper right: The VLA antenna positions in units of meters to the central VLA reference point. Lower left: The uv-coverage of the simulations (note that they do not account for the bandwidth). Lower right: the psf of the observation with fitted Gaussian major and minor beam sizes.


The task simanalyze can now process the newly created MeasurementSet and image the data: 

# In CASA
simanalyze(project='psimvla1', image=True, vis='psimvla1.vla.a.ms',  imsize=[192, 192], interactive=False, niter=0, weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)

project: The project name, same as in our call for simobserve.

image: True will image the visibilities with the following sub-parameters.

vis: The input MeasurementSet. Note that simobserve's notation is to use the project name appended by the antenna configuration file name.

imsize: the number of pixels for the image dimensions. We use 192 for each axis. By default simobserve will use the pixel size of the model image as the cell size for each pixel (3.11 milli-arcseconds in our case).

interactive: If set to True, the cleaning will be interactive to allow the step by step setting of clean boxes and clean depths (see the [VLA imaging topical guide]). We will turn this feature off.

niter: number of clean iterations. We start with a dirty map and set niter=0.

weighting: (cf. Image weighting schemes. We will use briggs which defaults to a robust = 0.5.

pbcor: If set to True the image will be primary beam corrected. In our case of a very large primary beam (see Fig. 1), primary beam correction will introduce very small corrections, so we turn it off.

stokes: The Stokes polarization to be produced, we want Stokes I.

analyze: When set to True simobserve will perform basic analysis of the produced images and produce hard copies of the following displays.

showuv: We set this to False as we already show the uv-coverage in the {simobserve}} output (Fig. 3).

showpsf: Although we already have a plot of that in Fig. 3, we show it here again to have the comparison to the other plots.

showconvolved: produces a plot of the model convolved with the synthesized clean beam.

showclean: shows the deconvolved image (in our case we do not perform deconvolution, but show the plot anyways to be consistent with subsequent runs).

showresidual: a plot of the residual image after deconvolution.

showdifference: displays the difference between output cleaned image and input model sky image convolved with output clean beam, i.e. it shows remaining clean artefacts.

showfidelity: a fidelity image, as defined by [math]\displaystyle{ \frac{I}{|I-T|} }[/math] where [math]\displaystyle{ I }[/math] is the observed image and [math]\displaystyle{ T }[/math] the sky model, see the simanalyze CASAdoc help.

The resulting plots of our first simulation are shown in Fig. 4. Since this is a dirty image only (niter=0), the image and residual are the same dirty image. SInce we also did not turn on any thermal noise, the image corruptions are all due to the incomplete uv-coverage of our observations.

Fig. 4: Simulated Images for noise-less Q-band observations. Upper left: the psf of the observations with the clean beam parameters. Upper center: the Sky model. Upper right: The sky model convolved with the clean beam. Bottom left: the simulated image. Bottom center: the residual image from deconvolution. Bottom right: the fidelity image (note that a bug in CASAS shows two color wedges for this plot; the inner one is the correct one to use).

Q-band, 128MHz bandwidth, noiseless image, 1h integration time, A-configuration, cleaned

As a second step we will deconvolve this data set. This could be done with inside the same project, but for a cleaner separation of our use cases, we will create a new MS with simobserve with a modified call of simanalyze: 

# In CASA
simobserve(project='psimvla2', skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel', incenter='44GHz', inwidth='128MHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='', graphics='both', overwrite=True)

simanalyze(project='psimvla2', image=True, vis='psimvla2.vla.a.ms',  imsize=[192, 192], interactive=False, niter=1000, threshold='1e-4Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)

The only difference to the earlier call of simobserve is our setting of niter=1000, threshold='1e-4Jy' which corresponds to a maximum number of 1000 clean iterations and a clean threshold of 0.1mJy. The threshold was chosen based on the previous image to be a few times above the rms of the image. The residual image is now flatter as expected and the bulk of the sidelobes disappear.

Fig. 5: Same as Figure 4, this time, however, with a cleaned image.

Q-band, 128MHz bandwidth, 4mm pwv, 1h integration time, A-configuration

We now add a precipitable water vapor of 4mm and a ground temperature for spillover of 270K. This can be achieved by the user_pwr and t_ground parameters. simobserve only adds thermal noise due to the sky brightness, but not phase noise due to pwv variations across the array. The sm.settrop tool can be used for the more sophisticated troposhperic models. A description is given in Corrupting Simulated Data. 

# In CASA
simobserve(project='psimvla3', skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel', incenter='44GHz', inwidth='128MHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)

The simobserve output will be identical to Fig. 2 and 3 since we do not change any of the displayed parameters. Now let's analyze the MS: 

# In CASA
simanalyze(project='psimvla3', image=True, vis='psimvla3.vla.a.noisy.ms', imsize=[192, 192], interactive=False, niter=1000, threshold='4e-4Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)

Note that we adjusted the cleaning threshold to account for the higher noise. The results are displayed in Fig. 6. The noise is dominating the image now, which is expected.

Fig. 6: Output of simanalyze after injecting noise.


Comparison with the VLA Exposure Calculator

We can compare the simulation to the predicted VLA sensitivity via the VLA Exposure Calculator Tool (ECT) (Description). Using winter observing conditions (for good pwv), a medium elevation (cf. Fig. 3), 128MHz bandwidth at a frequency of 44GHz, the ECT predicts a beam size of 0.067" and which is very close to our simulations (cf. Fig. 3 and 6). The ECT output is shown in Fig. 7.

Fig. 7: Exposure Calculation for 4mm pwr, 128MHz bandwidth

The rms provided in Fig. 6 is over the entire image and includes the source. It is therefore not representative to the thermal noise. To obtain a better noise figure, we produce an image with the same parameters as simanalyze, but with a larger image size directly via tclean. Since the briggs parameter in simanalyze defaults to robust=0.5, we will use the same value here: 

# In CASA
tclean(vis='psimvla3/psimvla3.vla.a.noisy.ms', imagename='psim3-bigimage', imsize=[640, 640], cell='3.11e-3arcsec',  specmode='mfs',  gridder= 'standard', deconvolver='hogbom', weighting='briggs', robust=0.5, niter=1000, threshold='4e-4Jy')

opening the image in the viewer 

# In CASA
viewer('psim3-bigimage.image')

and measuring the noise statistics away from the source (Fig. 8), gives a value of about 7e-5Jy/beam which is a very good agreement with the predicted noise figure of 6.9e-5 Jy/beam.

Fig. 8: Larger image of the simulation given in Fig. 6, measuring the rms noise in the purple rectangle regions away from the emission. A few low-level sidelobes are still present, however.

Q-band, 8GHz bandwidth, 4mm pwv, 1h integration time, A-configuration

To compensate for noise, we will extend our bandwidth from 128MHz to 8GHz. At this time, simobserve has no chanelization so the simulation will not have the better uv-coverage that is obtained in multi-frequency imaging. Consecutive simulations with different spectral windows, and combined MSs, however, can achieve that and we will show how to obtain a multi-channel MS shortly. For large bandwidths, one needs to be careful to not introduce [bandwidth smearing]. Our source is at the center of the image and bandwidth smearing will be minimal. 

# In CASA
simobserve(project='psimvla4',   skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel', incenter='44GHz', inwidth='8GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)

The simobserve output again is identical with Fig. 3. 

# In CASA
simanalyze(project='psimvla4', image=True, vis='psimvla4.vla.a.noisy.ms',  imsize=[192, 192], interactive=False, niter=10000, threshold='5e-5Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)

The image (Fig. 9) is clearly better defined, as expected from a broader bandwidth. We also decreased the cleaning threshold to 0.05mJy and added a few more iterations to allow to reach this threshold.

Fig. 9: Imaging with 8GHz bandwidth.


Multi-Term-Multi-Frequency Synthesis Imaging

In reality, the 8GHz bandwidth is not confined to a single channel but to many channels. This results in a spread out uv-coverage as it depends on the projected baselines expressed in number of wavelengths. Combining the channels in a multi-frequency synthesis (mfs), therefore does not only increase the sensitivity, but also the image fidelity. This leads to a better defined psf. Channelization and mfs imaging are also reducing bandwidth smearing effects.

As mentioned above, simobserve, naturally, does not channelize the visibilities when the input image is not chanelized.

In the following, we will channelize the MS and, to show the procedure, we will also apply a spectral index of [math]\displaystyle{ S\propto\nu^{-1.5} }[/math] at the same time.

To start with, we need to produce a multi-channel model image. The following script converts our current model image from fits to the CASA image format with importfits. We then create 64 planes, apply the spectral index, and fix the headers accordingly to bring them into consecutive frequency order. Each channel is specified to a width of 128MHz (real VLA data would have typical channel widths of 2MHz). Finally, our individual planes are combined into a cube with the ia.imageconcat tool method. 

# In CASA
importfits(fitsimage="ppdisk672_GHz_50pc.fits", imagename="ppdisk_Q_50pc.im")
stats=imstat(imagename='ppdisk_Q_50pc.im')
maximum=stats['max'][0]
ratio=3e-5/maximum
for x in range (0, 64):
     y=40+x*0.128
     immath(imagename="ppdisk_Q_50pc.im", mode='evalexpr', expr="IM0*"+str(ratio)+"*(("+str(y)+"/40)^-1.5)", outfile="ppdisk_Q_50pc_spx_"+str(x)+".im")
     imhead(imagename="ppdisk_Q_50pc_spx_"+str(x)+".im", mode="put", hdkey="crval4", hdvalue=str(y)+"GHz")
     imhead(imagename="ppdisk_Q_50pc_spx_"+str(x)+".im", mode="put", hdkey="cdelt4", hdvalue="128MHz")

comb=ia.imageconcat(outfile="ppdisk-combined_spx.im", infiles="ppdisk_Q_50pc_spx*.im",  axis=3, relax=True, tempclose=False, reorder=True, overwrite=True)
comb.close()

Using this model cube in simobserve will produce the channelized visibilities: 

# In CASA
simobserve(project='psimvla4mfs',   skymodel='ppdisk-combined_spx.im',  setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='none', overwrite=True)

The graphical output of simobserve and simanalyze would treat such data as a data cube rather than a multi-channel continuum data set. So we will produce our own graphics and imaging.

Let's first have a look at the new uvcoverage, each channel is displayed in a different color in Fig. 10 (note that the graphical output of simobserve 

# In CASA
plotms(vis='psimvla4mfs/psimvla4mfs.vla.a.noisy.ms', xaxis='Uwave', yaxis='Vwave',coloraxis='channel')
Fig. 10: uv-coverage of chanelized visibilities.

simanalyze would assume that these data are to be imaged as a cube. Our aim, however, is to create a continuum image with the mfs technique, and, to recover the spectral index, we will use the Multi-term Taylor expansion in frequency (mtmfs, see CASAdocs Deconvolution Algorithms). We will use nterms=2 to derive the spectral index. The spectral index map, however, is fairly sensitive to the scales in the image. A regular Hogbom clean based on point sources, typically creates maps with too steep spectral indices when applied to extended emission. To avoid this effect, we therefore use the multi-scale algorithm with a range of scales: 

# In CASA
tclean(vis='psimvla4mfs/psimvla4mfs.vla.a.noisy.ms', imagename='psimvla4mfs/8GHzmfs', imsize=[192, 192], cell='3.11e-3arcsec', specmode='mfs', gridder='standard', deconvolver='mtmfs', nterms=2, scales=[0,2,4,8,13,20,40],  niter=1000, threshold='2e-4Jy', weighting='briggs', robust=0.5)

As before, we are not attempting primary beam corrections as the image is very small compared to the primary beam (cf. Fig. 2).


The images can be displayed with the viewer, note that the image itself is now called psimvla4mfs/8GHzmfs.image.tt0 (Fig. 11) and the spectral index map: psimvla4mfs/8GHzmfs.alpha (Fig. 12). In Fig. 12 we also show the contours of the image on the spectral index map, to check for the signal-to-noise at each position.

Fig. 11: The image of Fig. 9 but using multi-frequency-synthesis (mfs) imaging.
Fig. 12: The spectral index map with image contours overlaid.

As seen in Fig. 11, this method should produce a somewhat better fidelity than the non-mfs image shown in Fig. 9, although a direct comparison is difficult given the spectral index that we introduced. The spectral index map itself (Fig. 12), unfortunately, is dominated by noise, even at the brightest regions, due to the pwv that we assumed. This results in a relatively unreliable spectral index map overall, although the values scatter around the spectral index of -1.5 that we inserted earlier.

Q-band, 8GHz bandwidth, 4mm pwv, 4h integration time, A-configuration

Let's improve the depth of the observations even further by going to 4h on-source integration, via totaltime='14400s' . 

# In CASA
simobserve(project='psimvla5',   skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel',  incenter='44GHz', inwidth='8GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='14400s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)

Fig. 13 shows a better uv-coverage (lower left image) and the 4h observation is also marked by a wider red bar in the top left image. This also improved the shape of the psf.

Fig. 13: Output of simobserve with 8GHz bandwidth of 4h of on-source observing time.
# In CASA
simanalyze(project='psimvla5', image=True, vis='psimvla5.vla.a.noisy.ms',  imsize=[192, 192], interactive=False, niter=1000, threshold='2e-5Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)

Given the expected deeper image we reduced the cleaning threshold to 0.02mJy, and the result is shown in Fig. 14. The image now is an almost perfect representation of the true sky model convolved with the clean beam.

Fig. 14: Images after increasing the integration time to 4h.


Comparison with the VLA Exposure Calculator

We compare again the simulation to the predicted VLA sensitivity via the VLA Exposure Calculator Tool (ETC) (Description). Using 8GHz bandwidth 4h on-source, and a low elevation due to the longer observations, the ECT predicts a rms of 7.1[math]\displaystyle{ \mu Jy }[/math] (Fig. 15):

Fig. 15: Exposure time calculation for 4mm pwr, 8GHz bandwidth

Note that the VLA exposure calculator switched to 3bit observing to accommodate the large bandwidth. The simulator, however, assumes 8bit samplers, which provide about 15% better sensitivity than VLA 3bit correlations (For a discussion, see the VLA Samplers page).

Similar to the case of 128MHz bandwidth 1h case, we produce a larger image to be able to measure the image rms in a signal-free region: 

# In CASA
tclean(vis='psimvla5/psimvla5.vla.a.noisy.ms', imagename='psim5-bigimage', imsize=[640, 640], cell='3.11e-3arcsec',  specmode='mfs',  gridder= 'standard', deconvolver='hogbom', weighting='briggs', robust=0.5, niter=10000, threshold='5e-5Jy')

opening the image in the viewer 

# In CASA
viewer('psim5-bigimage.image')

and measuring the noise statistics away from the source (Fig. 16), gives a value of about 7mJy/beam which is in reasonable agreement with the exposure calculator prediction.

Fig. 16: Larger Image of the 8GHz simulation in Fig. 14, measuring the rms noise in the purple rectangle regions away from the emission.



Q-band, 8GHz bandwidth, 4mm pwv, 1h integration time, C-configuration

Our last Q-band simulation will use a precipitable water vapor of 4mm again, but to we will now simulate the observations with the VLA C-configuration (specified with the antennalist parameter). 

# In CASA
simobserve(project='psimvla6',   skymodel='ppdisk672_GHz_50pc.fits', inbright='3e-5Jy/pixel',  incenter='44GHz', inwidth='8GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.c.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)

As expected, the uv-coverage decreases by a factor of about 10 and and the synthesize beam increases by the same factor, as seen in Fig. 17.

Fig. 17: Output of simobserve using the C-configuration.
# In CASA
simanalyze(project='psimvla6', image=True, vis='psimvla6.vla.c.noisy.ms',  imsize=[1728, 1728], interactive=False, niter=1000, threshold='1e-4Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)

Note that the output filenames will now change and reflect C-configuration in their names. The resulting images are displayed in Fig. 18, where the images now look like a point source with the degraded resolution. The surface brightness sensitivity of the observations, however, increase and we can clean to a lower threshold of 0.1mJy. simobserve automatically detected that the beam is massively oversampled and that a larger image size will provide a better field of view.

Fig. 18: C-configuration results.

To combine data of two different array configurations, we refer to the VLA Data Combination Guide.

X-band, 4GHz bandwidth, 4mm pwv, 1h integration time, A-configuration

Finally, we will go for a X-band (10GHz), A-configuration simulation. Since X-band has a maximum bandwidth of 4GHz, we will reduce it to this value. We will also lower the flux of the model to 0.01mJy given that a the flux of the model will likely be lower, too. 

# In CASA
simobserve(project='psimvla7',   skymodel='ppdisk672_GHz_50pc.fits', inbright='1e-5Jy/pixel',  incenter='10GHz', inwidth='4GHz' , setpointings=True, integration='2s',  direction='J2000 18h00m00.031s -22d59m59.6s',  mapsize= '0.78arcsec', obsmode='int', antennalist='vla.a.cfg', hourangle='transit', totaltime='3600s',  thermalnoise='tsys-atm', user_pwv=4, t_ground=270.0, graphics='both', overwrite=True)

When expressed in wavelengths, the uv-coverage and synthesized beam are somewhere in between that of Q-band A-configuration and C-configuration as expected (Fig. 19).

Fig. 19: Output of simobserve for X-band observations.
# In CASA
simanalyze(project='psimvla7', image=True, vis='psimvla7.vla.a.noisy.ms',  imsize=[192, 192], interactive=False, niter=1000, threshold='3e-5Jy', weighting='briggs',  pbcor=False, stokes='I', analyze=True, showuv=False, showpsf=True, showmodel=True, showconvolved=True, showclean=True, showresidual=True, showdifference=True, showfidelity=True, graphics='both', overwrite=True)


The larger primary beam of the X-band data is shown in Fig. 20, where the model image is barely visible in the center. The simulated images are shown in Fig. 21. The ring shape is still visible in the results although quite blurred. We note that the noise is considerably lower as expected from the lower band noise properties of the receiver and atmosphere. We adjusted the clean threshold accordingly. Again, simanalyze was overriding the image size as the psf would not have been adequately covered for the lower frequency.

Fig. 20: X-band sky coverage
Fig. 21: X-band simulation results.


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