Calibration

You are now ready to start the main calibration step. You should have a large number of Miriad datasets, each containing a single frequency band and source. The calibration process will determine bandpass functions (assuming you have not already averaged your data into a channel-0 dataset) and antenna gains as a function of time. If you have measured all four polarisation products, the process will also determine instrumental polarisation and the polarisation of the phase calibrator.

The calibration approach described here (and shown schematically in Figure 12.2 is quite general, and will apply, perhaps with slight modifications, in almost all situations at all wavelengths. However, for high frequency observations made with the old correlator, you may wish to follow the calibration approach described in Section 12.3.1.

You should keep in mind the following points when considering how to calibrate your observations:

• The two most commonly used flux calibrators at the ATCA are 1934-638 and the planet Uranus. For frequencies between 1 GHz and 10 GHz, 1934-638 is the preferred flux calibrator; its cm model is described in the memo ``A revised flux scale for the AT Compact Array'' (AT Memo 39.3/040). For frequencies above this, Uranus is the preferred flux calibrator, although until early 2010 the Miriad model did not correctly take into account how Uranus' brightness temperature changed with its orientiation to the Earth (a memo describing the new Uranus flux model is forthcoming). Other planets can be used as flux calibrators, but Uranus is the best choice in most situations since it is small enough to remain mostly unresolved on the short arrays that are used for most mm observations, and bright enough to provide an accurate flux in a short observation.

  Since May 2010, the Miriad model of 1934-638 covers frequencies all the way up to the top of the 7mm band (50 GHz), so it can be used a flux calibrator now for all bands other than 3mm. The flux model in the 12mm band is described in the memo by Bob Sault ``ATCA flux density scale at 12mm'' (2003). The flux model for frequencies above 25 GHz will be described in a forthcoming memo.

• It is possible to use other sources to flux calibrate your observations, but it is inadvisable to do so. If at all possible, make an observation of 1934-638 or Uranus.

  To flux calibrate your observation with another source, you must use the "bootstrapping" technique. In essence, this requires that you find an observation of the source you will be using as a flux calibrator within a few days of your observations. Most, if not all of the sources in the AT calibrator database will have fluxes that vary on timescales of days to weeks. If you can find such an observation, and that observation also observed one of the recognised flux calibrators, then you may be able to use the flux density determined from those observations to calibrate yours. However, the longer the time between your observations and the observation you are bootstrapping to, the less accurate this technique is likely to be.

• You should classify the sources in your observations into four categories: bandpass calibrator, flux calibrator, phase calibrator and program source.

  The bandpass calibrator should ideally be the brightest source you observed, or if you want to make a time-dependent bandpass solution, it should be the strongest source that you observed most frequently.

  The flux calibrator selection should be fairly obvious by now; if it isn't, reread the start of this section.

  The program source should also be obvious.

  The phase calibrator should be the source that was observed almost contemporaneously with the program source. There should be as least as many "cuts" of the phase calibrator as there is of the program source, unless you will be relying heavily on self-calibration later in the process. The phase calibrator must also be a point source, with as little confusion and defect as possible.

  The same source can be used for more than one of these roles. For example, 1934-638 can be used as a flux calibrator in all wavelengths between 20-cm and 7-mm, but is bright enough to be used as a bandpass calibrator as well at cm wavelengths.

Figure 12.2: Flow chart for calibration in Miriad for most situations.

1. We start by solving for the bandpass solution, using the bandpass calibrator,a ssuming that you have not averaged the data into a channel-0 dataset. To do this we use the task mfcal, which is described more completely in Section 11.4. After having solved for the bandpass function, mfcal writes a bandpass table in the visibility dataset - the data themselves are not modified. Although it is possible for mfcal to cope with datasets that contain multiple IF bands, and that frequency switch with time, we recommend the you do not use this feature; it is much easier to stick with datasets with a single frequency band.

   It is also possible for mfcal to determine a time-dependent bandpass solution, if you suspect that the instrumental response is changing significantly over the observation. For the CABB correlator's continuum IFs, the amount of bandpass variation observed is usually much less than the gain variations, making a time-dependent bandpass solution rather pointless for continuum observations where a moment map image will be created. However, for spectral line observations, using a time-dependent bandpass can halve the spectral rms noise. To make a time dependent bandpass solution, you will need to specify three numbers for the interval parameter in mfcal; for a bright source, interval=1,1,1 should work well, and give a bandpass solution every minute. Of course, the bandpass calibrator would need to be visited often during your observations for this to be effective!

   As well as determining a bandpass function, mfcal determines antenna gains. These gains are based upon the assumption that the source is unpolarised (which happens to be true for 1934-638) and that the instrumental polarisation is zero (which is not true). These assumptions do not affect the quality of the bandpass.

   If your data are to be combined (or compared) with pre-August 1994 ATCA data, you will probably also use the oldflux option (see Section 12.6).

   MFCAL
   vis=1934-638.5500	Specify bandpass calibrator.
   flux	Leave unset.
   line	Select good channels.
   refant=2	Specify the reference antenna.
   interval=1	Solution interval for gain solutions (minutes), or
   interval=1,1,1	Solution interval for gains, max interval, bandpass (minutes)
   options	Normally leave blank, but
   options=oldflux	set to oldflux to get the pre-August 1994 scale.

2. The next step copies the bandpass solution you just made to the flux and phase calibrators, and for this you should use the task gpcopy. If your bandpass calibrator is the same as your flux or phase calibrator, then you won't need to copy the solution in that case.

   Although gpcopy can be instructed to copy only the bandpass solution, there is no harm in copying the gains and leakage tables too, as they will be overwritten when you run gpcal later.

   GPCOPY
   vis=1934-638.5500	Specify bandpass calibrator.
   out=0220-349.5500	Specify phase calibrator.
   options	Normally leave blank, but
   options=nocal,nopol	You may optionally copy only the bandpass table.

3. We now proceed to determine the antenna gains and instrumental polarisation from the flux calibrator. Task gpcal is used for this (see Section 11.5 for more information). Task gpcal will generally use the bandpass determined by mfcal to partially correct the data. If you are using a planet as your flux calibrator, you must skip this step.

   When your flux calibrator is 1934-638, the only options that you will normally turn on is for the XY phases to be solved for as a function of time; options=xyvary. If your data are to be combined (or compared) with pre-August 1994 ATCA data, you will probably also use the oldflux option (see Section 12.6). Typical parameters for calibrating 1934-638 are thus

   GPCAL
   vis=1934-638.5500	Specify flux calibrator
   flux	Leave unset
   refant=2	Specify the reference antenna
   interval=0.1	Solution interval for gain solutions (minutes)
   options=xyvary	Solve for XY phase as a function of time, or
   options=xyvary,oldflux	add oldflux to get pre-August 1994 flux scale.

   Task gpcal will report the instrumental polarisation parameters (leakages) - two complex numbers per feed. Typically these are 1 to 2%, although they can be 4% under bad conditions. Typically these are quite constant with time, with similar values resulting from observations several months apart. However they are modestly frequency dependent.

   This task will scale the average flux of the entire band to the known flux of 1934-638 at the centre frequency of the band. This is not guaranteed to produce a correct flux scaling at this point. It is very important to remember that mfboot will be required later in the procedure to ensure that the flux scaling is accurate.

   Tasks appropriate to examine the effectiveness of the calibration are uvplt (to generate plots of the calibrated data - remember that many Miriad tasks apply any available calibration by default) and gpplt (to generate plots of the calibration tables - both antenna gains and bandpass functions). A particularly useful plot is the ``scatter diagram'' plot generated by uvplt with the following inputs

   UVPLT
   vis=1934-638.5500	Specify flux calibrator
   stokes=i,q,u,v	Plot all Stokes parameters.
   axis=real,imag	Plot real vs imaginary
   options=equal,nobase,nofqav	Equal X and Y axes. Plot all baselines, and don't average over
   	the bandwidth.
   device=/xs	Normal PGPLOT device - Xwindows for example

   This scatter diagram should show four concentrations of points - one for I at the flux density of the calibrator, and the others for Q, U and V probably near zero. If there are outliers, you probably need to do some more flagging. If you see arcs, the phase calibration is probably bad - you might try decreasing the solution interval.

4. Now we do the same for the phase calibrator using gpcal again. The primary difference is that we now wish to solve for the Stokes Q and U values for the source, which are not known a-priori. To do this we add the qusolve option. Additionally, if your observations have measured only the XX and YY correlations, you must add the nopol option, as there is not enough information to solve for antenna leakages.

   GPCAL
   vis=0220-349.5500	Specify phase calibrator.
   flux	Leave unset
   refant=2	Specify the reference antenna
   interval=0.1	Solution interval for gain solutions (minutes)
   options=xyvary,qusolve	Solve for Stokes Q and U, or
   options=xyvary,qusolve,nopol	Do not attempt to solve for leakages.

   In the unlikely event that your calibrator turns out to be more than about 5% polarised, you may wish to run gpcal again, but this time you should add options xyref and polref. This will solve for an XY phase offset on the reference antenna, as well as an instrumental polarisation characteristic that cannot be determined from a weakly polarised source.

   If gpcal fails with an error stating that the "Solution for requested parameters is degenerate", then it is likely that you do not have enough parallactic angle coverage to solve for Stokes Q and U. In that case, you will have to omit the qusolve option, and suffer the subsequent degradation of polarisation calibration.

   Good parallactic angle coverage enables you to disentangle the instrumental and secondary polarisations from each other. ``Good coverage'' generally means more than a few cuts. For sources near declination of -30 degrees, the parallactic angle remains constant through much of the observation, except near transit where it goes through a rapid change, whereas for sources near the poles, parallactic angle changes linearly with time. You can plot your parallactic angle coverage using the task varplt. More strictly, it plots the angle between the sky and the feed (i.e. parallactic angle plus 45 degrees for the ATCA).

   VARPLT
   vis=0823-500.4800	Specify secondary calibrator
   xaxis	Time is the default x axis
   yaxis=chi	Plot parallactic angle + 45 degrees
   device=/xs	PGPLOT device - xwindows in this case

5. At this point, both your flux and phase calibrators will have the same bandpass solution, but different flux scalings. The following table should make it clear what the calibration has achieved to this point.

   	Bandpass	Bandpass	Flux	Phase
   	Shape	Slope	Scaling	Solution
   Bandpass calibrator (not flux)	Correct	Incorrect	Incorrect	No
   Bandpass calibrator (is flux)	Correct	Correct	Incorrect	No
   Flux calibrator (not bandpass)	Correct	Incorrect	Incorrect	No
   Flux calibrator (planet)	Correct	Incorrect	Incorrect	No
   Phase calibrator (not flux)	Correct	Incorrect	Incorrect	Yes
   Phase calibrator (is flux)	Correct	Incorrect	Incorrect	Yes

   The goal is to get the phase calibrator calibrated such that it has the correct bandpass shape and slope, the correct flux scaling, and a useful phase solution. If you are lucky enough to have been observing 1934-638 as a phase calibrator, then you have almost finished your calibration, and you can skip to step 8.

   Before we go any further, we should understand what exactly we mean by each calibration.

   • Bandpass Shape: The bandpass shape is simply the instrumental response to the incoming spectrum. Given a flat spectrum (i.e. equal flux density at all frequencies), the ideal instrument would produce a flat bandpass shape. However, any real instrument will respond to different frequencies in an unequal way, and this gives rise to the bandpass shape which is solved for by mfcal.

   • Bandpass Slope: As we said above, a flat spectrum should produce a flat bandpass shape, but what happens when the input spectrum is not flat, as will be the case for most real sources? Unless mfcal knows how the flux density of the source varies with frequency, it will have no way to determine whether a change in flux is due to instrumental response or a flux density change of the source. If you have used a source other than 1934-638 for your bandpass calibration, you should assume that mfcal has not properly accounted for the source's flux behaviour when it has solved for the bandpass. In these cases, the bandpass slope will be incorrect.

   • Flux Scaling: If the flux scaling is correct, then the flux density at the centre of the band is correct. When gpcal (or mfcal) solves for the amplitude of a source for which it does not have flux density information, it assumes that the rms gain amplitudes are 1, and determines the calibrator flux density accordingly. While this will be a decent assumption if during array calibration you set the amplitude calibration with 1934-638, it is not guaranteed to be correct. The amount of flagging present through the band can also affect the flux scale after execution of gpcal.

   • Phase Solution: The phases (or more accurately, the complex gains) of the cross-correlations will change with time due to atmospheric conditions, system temperature variations, elevation of the antenna etc. To properly account for these effects, it is necessary to observe an unchanging point source throughout your observations. For this reason, calibration of a source that was observed once (or infrequently) during the alotted time will not result in an adequate phase solution, but by bookending each "cut" of the program source with a phase calibrator, you can solve for time-dependent antenna gains.

6. You should examine the calibration solutions for reasonableness.

   Four tasks are recommended for this - uvflux (how well does the phase calibrator data fit a point source model?), uvplt (plot the calibrated phase calibrator data), gpplt (plot the gain solutions) and gpnorm (compare phase calibrator solutions with those determined from the flux/bandpass calibrator or elsewhere).

   The first, and simplest, check of the calibration process is to use uvflux to check how well the calibrated data fits a point source. Task uvflux assumes the data represents a point source, and determines the source flux density and the rms scatter about this point. It also prints out the theoretical scatter based on thermal noise arguments. It will do this for any of the Stokes parameters. Typical inputs are

   UVFLUX
   vis=0220-349.5500	Specify phase calibrator
   stokes=i,q,u,v	Check all four Stokes parameters.
   options	Leave unset (apply calibration).

   The first numeric column given for each Stokes parameter is the theoretical scatter. Note if you are using the old correlator's 33 channel / 128 MHz system, and if no channel averaging has been performed, or the birdie option has not been used with atlod, then the theoretical scatter printed by uvflux is a factor of $\sqrt{2}$ higher than the true theoretical value. This is as, for this correlator configuration (and not for others), individual channels are not independent - they overlap by a factor of exactly 2 (in noise bandwidth). Task uvflux fails to take account of this. The second and third numeric columns are the mean visibility amplitude and phase respectively. The phase should be near 0 for I, but could be either 0 or 180 degrees for Q and U (assuming there is signal in these!). V should be noise. The fourth column gives the actual scatter. This should be close to the theoretical value. Do not be concerned if it is a factor of 2 or so bigger. If it is more than a factor of a few greater than the theoretical, you probably still have bad data or a bad gain solution.

   Using uvplt to plot the calibrated data is also recommended. As with the flux calibrator, a scatter diagram plot is quite useful and quick.

   UVPLT
   vis=0220-349.5500	Specify phase calibrator.
   stokes=i,q,u,v	Plot all Stokes parameters.
   axis=real,imag	Plot real vs imaginary
   options=equal,nobase	Equal X and Y axes. Plot all baselines
   	together.
   device=/xs	Normal PGPLOT device - Xwindows for example

   Outliers in the scatter diagram probably indicate bad data - you might want to go back and flag some more, and redo some calibration steps. Note, however, that the ultimate objective of the calibration process is to get good calibration solutions - you are not attempting to produce perfect flux or phase calibrator data. If you do not believe that outliers affect the calibration solutions unduly, ignore them.

   Another check is to plot the gain solutions and inspect them for consistency - use gpplt for this (see Section 11.7). Typical inputs for plotting the solved-for XY phases are given below. These XY phases are the difference between the actual XY phases and the XY phase correction applied by atlod. These should be constant (within the noise) and no more than a few degrees.

   GPPLT
   vis=0220-349.5500	Specify phase calibrator
   device=/xs	PGPLOT device - X windows in this case
   yaxis=phase	Plot the phase of the ratio
   options=xygains	of the X and Y gains

   In addition to plotting these solved-for XY phases, it is probably worthwhile plotting antenna and bandpass gains and phases. If you see glitches in the solutions, check the data again. This might be due to bad data or interference. You might do some more flagging, and redo some of the calibration again.

   A final check is to compare the instrumental polarisation solution (the leakage parameters). You can compare these with another independently derived set of these solutions. These solutions are moderately time independent (they are moderately consistent over months), although there is significant frequency variation. The independent set of solutions may have come from the flux calibrator (e.g. if you determined instrumental polarisation for the flux and phase calibrators independently - which was recommended if you had sufficient parallactic angle coverage and your flux calibrator was not a planet), or from a previous configuration, or possibly other phase or bandpass calibrators from the same observing run. The task to compare the different solutions is gpnorm. Apart from just taking some sort of difference between two sets of parameters, it adjusts certain parameters to minimise the difference. The parameters that it adjusts are the absolute feed orientation and ellipticity - two quantities that are not solved for in the preceding calibration process (unless you had a strongly polarised calibrator, and used options=polref in gpcal). Task gpnorm can also deduce an error in the absolute XY phase between the two observations (an error in the absolute XY phase leaves a signature in the instrumental polarisation parameters).

   Task gpnorm reports three numbers - an XY phase offset, the offset in absolute orientation and ellipticity, and a residual rms error. As the preceding calibration process should have corrected for the XY phase offset, this should be no more than a few degrees. The offset in absolute orientation and ellipticity should be no more than 2-3%. The rms residual error should be no more than 0.005. You would expect the agreement to degrade with time difference in the observations used to derive the parameters. Agreement should be very good for parameters derived from observations on the same day, whereas agreement should be less good for observations several months apart.

   Having solved for an offset in absolute XY phase, orientation and ellipticity, gpnorm can ``correct'' the calibration tables for these. This is generally not advisable.

   Typical inputs to gpnorm are

   GPNORM
   vis=0220-349.5500	The leakages to check.
   cal=1934-638.5500	The `good' set of leakages.
   options	Leave unset.

7. What this step will accomplish will depend on whether your flux calibrator is a planet or not.

   If your flux calibrator is not a planet, then this step will correct the phase calibrator's flux scale. To do this we use the task gpboot. This task takes two inputs: vis, which is a dataset with a flux scale that needs correcting, and cal, which is a dataset with the reference - or in this case, correct - flux scale.

   In principle, you should use observations of the phase and flux calibrators that were taken at the same time and elevation, because atmospheric opacity affects the amplitude gain calibration. For obvious reasons this is not always possible, although the further apart the observations are in time and elevation, the less accurate the flux calibration will be, especially at high frequencies. However, you can use the select keyword to select the data from the phase calibrator that will give you the best flux calibration. In stable weather conditions, it is probably best to select the time range of the phase calibration where its elevation corresponds most closely to the elevation during the flux calibrator's observation. When the weather changes significantly during the observation, it is probably best to use a time range of the phase calibrator which is close to the flux calibrator's observation. Tasks uvplt and varplt can plot source elevation as a function of time.

   GPBOOT
   vis=0220-349.5500	Specify phase calibrator.
   cal=1934-638.5500	Specify flux calibrator.

   The output of gpboot will be a number indicating how large a scaling adjustment was made, with 1.000 being no adjustment at all.

   If your flux calibrator is a planet, then this step will transfer the gain scaling from the phase calibrator to the flux calibrator, again using gpcal. This time though, the reference flux scale will be that of the phase calibrator. This step is necessary because the task that adjusts the flux scales using a planet requires that all the input datasets (which will be the flux and phase calibrators) have the same flux scale to begin with. It is more than likely that at this point both the flux calibrator and phase calibrator will have the same (or very similar) flux scalings anyway, since the operation of mfcal on the bandpass calibrator and gpcal on the phase calibrator should be similar enough to produce consistent scalings. Therefore, you should expect that the scaling factor applied by gpcal should be very close to 1, otherwise there may be a problem with your data.

   GPBOOT
   vis=uranus.43000	Specify flux calibrator.
   cal=0220-349.43000	Specify phase calibrator.

   The state of the calibration at this point is shown in the table below. Note that we are not attempting to further calibrate the bandpass calibrator. It is of course possible to calibrate the bandpass calibrator, in order to measure its flux (or something similar), but this is left as an exercise for the reader.

   	Bandpass	Bandpass	Flux	Phase
   	Shape	Slope	Scaling	Solution
   Flux calibrator (is bandpass)	Correct	Correct	Incorrect	No
   Flux calibrator (not bandpass)	Correct	Incorrect	Incorrect	No
   Flux calibrator (planet)	Correct	Incorrect	Incorrect	No
   Phase calibrator (flux is a planet)	Correct	Incorrect	Incorrect	Yes
   Phase calibrator (flux is not a planet)	Correct	Incorrect	Incorrect	Yes

8. At this point in the calibration, we need to correct both the bandpass slope of the phase calibrator, and the flux scaling. This step will accomplish both, using the task mfboot.

   For a known flux calibrator, be it a point source or a planet, mfboot constructs a model of what the flux should be on each baseline and for all frequencies across the band. It then determines by how much the gains must be scaled by to make the observed flux at the centre of the band match the model value. It then scales all the datasets it has been given by that factor.

   It also calculates the slope of the model between two points either side of the band centre, and then corrects the bandpass table to make the observed spectrum match that slope. Previous versions of mfboot did not perform this bandpass correction since spectral slopes were not as apparent across the narrow bands offered by the old correlator.

   The task operates a little differently to gpboot, which has separate inputs for the uncorrected dataset and the reference dataset. In contrast, mfboot has only one input type that takes a comma separated list of datasets, all of which are assumed to have the same bandpass and gain tables. The source to use as the flux calibrator is then selected using the standard select parameter.

   MFBOOT
   vis=1934-368.5500,0220-349.5500	Specify all the input datasets, or
   vis=uranus.43000,0220-349.43000	Specify all the input datasets.
   select=source(1934-638)	Specify the flux calibration source, or
   select=source(uranus)	Specify the flux calibration source
   options	Usually leave this unset, but
   options=noapply	Useful if you want to see what scaling will result,
   	without applying it

   This task will output the flux scaling and bandpass slope correction factors it applied to each of the datasets.

   The state of the calibration at this point is shown in the table below.

   	Bandpass	Bandpass	Flux	Phase
   	Shape	Slope	Scaling	Solution
   Flux calibrator	Correct	Correct	Correct	No
   Phase calibrator	Correct	Correct	Correct	Yes

9. All that remains is to transfer the calibration tables to the program source. Again we use gpcopy to do this. Typical inputs are

   GPCOPY
   vis=0220-349.5500	Specify phase calibrator
   out=vela.5500	Specify the program source dataset
   options	Leave unset
   mode	Leave unset