## 2.2. Calibration

### 2.2.1. What type of calibration do I need to do?

During a normal observing run you will have to do calibration before you can start your observations, and then you will need to schedule time on one or more calibration sources.

At the beginning of your observing run you may find that while observing a strong point source, the phases will not be constant as a function of frequency across the band; this indicates that the array requires delay calibration. To successfully perform delay calibration will require a point source of at least moderate brightness ($\mathrm{S} \gtrsim 1\mathrm{\,Jy}$). This is so the correlator can accurately determine the phase slope with frequency; the accuracy improves with the signal-to-noise ratio.

The response of each antenna to the incoming radiation must also be determined, and this is comprised of bandpass and flux density calibration. This calibration can be done with only one source if the flux density of that source is known, it is a point source, and it is sufficiently bright. Otherwise a bright point source can be observed as the bandpass calibrator (the source used for the delay calibration can usually be used for this purpose), and a fainter source with a known flux density, or a planet can be used for flux density calibration.

Over the duration of the experiment, several factors that affect the antenna response will change. These include atmospheric phase, opacity, elevation-dependent dish surface distortions and focus changes, aperture illumination and spillover. To monitor these changes you will need to observe a point source nearby to your science target. This point source will need to be reasonably bright, but averaging over a short period of time can be used if the nearest source isn't very bright.

If you need to measure the polarisation of your science target, you will want to determine the leakage parameters; the fraction of linearly-polarised photons that are detected by the receptor that should not.

If you are observing at high frequency, where the primary beam of the antenna is small, it is important that the maximum response of the beam is directed toward the source you're observing. To ensure this is the case, you should do periodic pointing-correction scans on a nearby point source of reasonable brightness.

Finally, if you're observing in the 3mm band, you will need to use the receiver's absorber paddle to keep track of how the system temperature varies over time. This is done periodically on-line using “paddle” scans.

A summary of what type of calibration you will require for each observing band is given in Table 2.3.

Table 2.3. Calibration required by observing band.

Calibration16cm4cm15mm7mm3mm
Delay calibrationRequired
Bandpass calibrationRequired
Flux density calibrationRequired on 1934-638Required, on Uranus
Gain calibrationRequired
Polarisation calibrationRequired
Pointing calibrationNot requiredRequired

For more detail on each of these types of calibration, read the sections below. It is important to note that you must repeat all the calibration for every frequency configuration that you observe, as it is not generally possible to interpolate or extrapolate the calibration parameters determined from one frequency configuration to another.

### 2.2.2. What sources can be used for delay calibration?

The calibrator you use to calibrate the delays is largely dependent on the band you are observing in, and the LST when you are setting up.

For the centimetre bands (16cm and 4cm), delay calibration is best done with one of two sources. When the LST is between 11:00 and 04:18, you should use PKS 1934-638 to calibrate the delays, because it is strong and you'll need to observe it anyway for flux density calibration purposes. At all other times you should use 0823-500.

For the higher frequency bands, you will need to use one of the many available bright sources in the ATCA calibrator database, such as:

• 0003-066

• 0420-014

• 0537-441

• 0727-115

• 1034-293

• 1253-055

• 1424-418

• 1613-586

• 1921-293

• 2155-152

You should choose whichever is highest, or nearest to your targets. There are many more sources that are bright in the millimetre bands, and you can search for the brightest calibrators using the ATCA calibrator database search interface.

### 2.2.3. How do I calibrate the bandpass response of the antennas?

The bandpass calibration is best done with a very bright source, since you're trying to precisely determine how each frequency channel responds to a known amount of flux density.

To do this ideally, the response should be dominated by the signal rather than the thermal noise in each channel. Since this is also a very useful property for a delay calibrator to have, the same calibrators that can be used for delay calibration (Section 2.2.2) are ideal for bandpass calibration as well. If the bandpass calibrators is used as the delay calibrator, then the bandpass calibration observation can be made immediately following the completion of the setup without further slewing overhead. If the observations are at 3mm, a paddle measurement should be made immediately before the bandpass observation.

As the receiver response does not change greatly as a function of time, for a continuum observation it is usually sufficient to make an observation of a bandpass calibrator at the very start of the allocated time. The amount of time spent integrating on the bandpass calibrator depends on its flux, but generally 5-10 minutes is sufficient at all frequencies.

For spectral line observations though, it has been noted that the CABB bandpass is not perfectly stable over the course of a normal 12 hour observation, and for this reason it is advisable to observe a bandpass calibrator more than once per observation. Visiting it three times (once at the start, once at the end, and once sometime near the middle) during a 12 hour observation should be sufficient to obtain a reliable bandpass solution. Alternatively, provided the gain calibrator is reasonably bright, the periodic visits to it may provide accurate enough information to determine how the bandpass solution changes over time.

The integration time spent on the bandpass calibrator will have an effect on the accuracy of the flux that is measured after reduction. It is necessary to obtain each correlator channel's flux to the same accuracy as required for the flux calibrator, ie. obtain a signal-to-noise ratio of 100 per channel if the required flux accuracy is 1%. Since any point source can be a bandpass calibrator, the sensitivity calculator should be used to find out the RMS noise per channel for your observations, and then a calibrator found from the calibrator database that provides enough flux to meet the signal-to-noise ratio requirements. For example, a typical CABB observation has 2048 channels, and at 50 GHz, the RMS noise per channel is about 35 mJy for a 5 minute observation. For a signal-to-noise ratio of 100, a calibrator with flux greater than 3.5 Jy is required, and a search through the calibrator database identifies 19 such sources. Of course, if a primary flux calibrator is strong enough to be a bandpass calibrator as well, then observing time can be conserved by not having a separate bandpass calibrator.

### 2.2.4. How do I calibrate the flux density of my observations?

Flux density calibration is required to translate the arbitrary gain scaling that is produced by an observation to an absolute flux density scale. The most effective way of doing this is by observing a calibrator that has a known flux density (on the absolute flux density scale) and comparing it to the sources that you are observing that have unknown flux densities.

For the ATCA, there are currently only four flux density calibrators, and of those only two are regularly used.

For frequencies between 1 GHz and 25 GHz, the preferred flux density calibrator is PKS 1934-638. It has a known, stable flux, and conveniently has no linear or circular polarisation, at least at low frequencies. The flux density model for 1934-638 that is installed in Miriad are based on the models described in the memo

and the paper

• Absolute calibration of the radio astronomy flux density scale at 22 to 43 GHz using Planck (Partridge et. al, 2016)

The model is separated into two frequency ranges. Below 11 GHz, the Reynolds model is used, which is:

Equation 2.1. Flux density model for 1934-638 from Reynolds 1994

where $\mathrm{S}$ is the flux density in Jy and $\nu$ is the frequency in MHz. For frequencies above 11 GHzMiriad uses the model from the Planck study:

Equation 2.2. Flux density model for 1934-638 for frequencies above 11 GHz

The high-frequency model has been shown by Partridge et al. (2016) to match quite well with the VLA, but unfortunately the low-frequency model does not.

For frequencies higher than 50 GHz you can use 1934-638 as the flux density calibrator, but the planet Uranus is brighter. Its flux density is known to vary with time, but it does so in a way that is understood and can be modelled. The planets Mars and Neptune can also be used, but Uranus is preferred because its angular size is smaller than Mars (making it easier to observe with typical Compact Array baselines), and it is brighter than Neptune (which would require a longer scan to provide the same signal-to-noise level).

To be as effective as possible, the flux density calibrator should be observed when it is at the same elevation as the target source, and at as high an elevation as possible. Doing this means that any gain-elevation dependence is reduced, and the effect of airmass is also reduced. At low frequencies (below 7 GHz), these requirements are not as important as they are for higher frequencies, where the atmospheric effects become a large factor. Indeed, many (if not most) centimetre observers simply make a scan on 1934-638 at the beginning of their observations, and this is usually good enough to get a flux density uncertainty of only a few percent.

Because 1934-638 is a point source (at least at the resolution of the Compact Array), it can be observed the same way as any other calibrator. That is, a scan on 1934-638 should be included in the schedule, and should be preceded by a pointing scan when it is observed with the 15mm or 7mm receivers.

Observing the planets is a little more complicated. Because they are not point sources on even the most compact of ATCA baselines, they cannot be used as a pointing reference. A nearby source must therefore be used to determine the pointing offsets before observing the planet. Also, because the planets will substantially fill the primary beam of the ATCA antenna, the apparent system temperature of the antenna will be increased while a planet is being observed. Because of this, if a paddle scan is made while observing a planet, the system temperature will not be correctly determined, and the flux scaling will be in error. When observing with the 3mm system therefore, the paddle scan should be made while observing the same nearby pointing reference calibrator.

To make a good observation of Uranus, follow the procedure:

• Determine a suitable nearby calibrator that can be used for pointing/paddle measurements. First, checking the ephemeris of Uranus with the planet task in Miriad. After the position of Uranus on the date of the observation has been determined, use the calibrator database or the “Search Cal” button in the Web Scheduler to find the closest suitable calibrator.

• If observing at 3mm, make a paddle measurement while tracking the calibrator.

• Determine the pointing offsets using the calibrator.

• Observe the calibrator for 2 minutes.

• Observe Uranus for a sufficient amount of time (10-15 minutes is usually more than enough).

• Observe the calibrator again for 2 minutes.

The procedure is similar for the other planets. Note that because the phases of the nearby calibrator are not used by the Miriad flux calibration task mfboot, it is not absolutely necessary to bracket the planet with a calibrator observation. It can however be useful to have that data to diagnose potential problems, should they arise.

The integration time spent on the flux density calibrator is largely governed by the precision required for the observations to be successful, and the strength of the primary flux density calibrator at the observing frequency. If a flux density precision of 1% is required, then the aim should be to make an observation with a signal-to-noise ratio of 100. For a observation with 2 GHz bandwidth, this is relatively easy, as even a 5 minute observation of 1934-638 at 50 GHz gives a signal-to-noise ratio in excess of 1000.

The sensitivity calculator should be used to estimate the observing time required to achieve the desired flux density precision. However, it is never a bad idea to pad the required time out a little to ensure that enough good data will remain after flagging.

### 2.2.5. How do I best calibrate the time-varying gains?

The gain parameters that vary significantly over time include:

• atmospheric phase

• atmospheric opacity

• forward gain due to structural deformation

• aperture illumination

As these factors vary, the path lengths between the antennas will vary (which varies the phase), and the system temperatures may change, thus changing the sensitivity. To accurately correct for these changes, they must be regularly monitored.

The best way to monitor these changing parameters is to observe a simple source (a point source in an otherwise empty field is the ideal case) every time the observing configuration (elevation, weather, etc.) changes significantly. The definition of “significant” change depends on the observing frequency and the observing conditions (such as array configuration, atmospheric seeing, temperature, precipitation etc.). More precisely, by observing a source that looks the same irrespective of time or (u,v) coordinates, changes in gain can be determined directly. Therefore, gain calibrators should be unresolved, with a stable flux over the observation timescale.

The ATCA provides a calculator to advise observers on how often to visit their phase calibrator. For this calculator:

• Input the central observing frequency and the maximum baseline of interest (ie. don't include the 6km antenna if its data will be discarded).

• For the seeing monitor RMS phase, give a nominal value of 300 microns if the observations will be performed in winter, and 700 microns if they will be in daytime during summer; for other times, choose a value between those two extremes. You can adjust using the actual values on the day if you want, but these values will generally prevent you from not calibrating frequently enough.

• For the phase screen speed, choose 5 m/s.

• For the Kolmogorov exponent, leave the default 0.83 unless the 6km antenna will be required, in which case enter 0.33 instead.

For example, for an observation at 19 GHz, with a seeing RMS of 300 microns, in a 750m array, the calculator determines that if the gain calibrator was visited every 2 minutes, the observations would have an RMS phase of 15°, be decorrelated by 3%, and have a maximum dynamic range of just 282. However it also determines that this is as bad as it gets, so that a 10 minute visit interval would give the same results. Since 2 minutes is a very frequent visit schedule, it would seem that self-calibration would be preferable for high dynamic range observations.

Dropping the seeing RMS to 100 microns (which would be a good winter day) improves matters significantly, allowing a dynamic range of 874 with no decorrelation and a 5° RMS phase for any visit interval greater than 2 minutes.

It is important however not to extend the interval too far, as then the atmosphere being sampled by the gain calibrator will be different to that the source has sampled during that time. For cm observations, one might need only visit the gain calibrator once or twice per hour in good conditions, while for mm observations, it is unwise to visit the calibrator less frequently than once every 15 minutes.

The ATCA has a large list of gain calibrators, spread over the viewable sky. This list can be queried using a web interface. This interface queries the database in one of three ways:

• Quick-find calibrator: finds a calibrator with a specified name. The quick-find box will show all sources that match the string you enter into it. For example, there are five sources in the database which match with “0537”: 0537-441, 0537-158, 0537-286, J0537-3357 and 0537+531. When this list of sources is displayed, you can click on the one you want to get a small list of that calibrator's most recent flux densities and its position.

• Cone search: finds calibrators within a specified angular distance from a given sky position. Can optionally be restricted to sources brighter than a given flux in a specified wavelength band. You can also enter a resolvable name into the position box instead of an RA and Dec.

• Patch search: finds all calibrators within a specified RA and Dec range. Can optionally be restricted to sources brighter than a given flux in a specified wavelength band.

Selection of an appropriate gain calibrator can also be done while you are preparing the schedule in the CABB web scheduler (see Section 2.3.12 for an example of how this works). Ideally, choose the nearest possible point source calibrator to your target. Sometimes that calibrator may not be very bright though, and you may wish to choose a brighter calibrator that is further away in order to lessen your overhead: a brighter calibrator can give a good measurement of the gain in a shorter time than a dimmer calibrator. For continuum observations this is largely irrelevant since the large CABB bandwidths allow for a very accurate measure of gain in just a few cycles. For spectral line observations though, the brighter the source the better.

### 2.2.6. What do I need to do for polarisation calibration?

The ATCA uses dual linear orthogonal feeds to measure the incident radiation. Ideally, these two feeds would be independent: in reality this is not the case, and a fraction of the radiation measured by one feed is also receiver by the other; this effect is called “leakage”. Polarisation calibration is primarily concerned with measuring the leakage fraction and the possibly non-zero signal phase (the so-called XY-phase) between the two feeds.

A paper by Sault and Cornwell (1999, in “Synthesis Imaging in Radio Astronomy II”, ASP Conf. 180, p657) showed that for an observation where a calibrator with apriori unknown polarisation properties can be observed with at least three different parallactic angles (what they call the “parallactic angle rotation trick”), polarisation calibration is required to determine the absolute alignment of linear polarisation angle and the term which causes leakage between Stokes I and V.

The absolute alignment of linear polarisations is achieved by injecting a linearly polarised signal at 45° to the linear orthogonal feeds several times per second: this is known as the “noise diode”. This signal is measured by the correlator on each antenna, and the XY-phase is used later in data reduction to determine the absolute linear polarisation angle. All the receivers except for the 3mm system have a noise diode on each antenna. For 3mm observations, CA02 has got the Mopra spare receiver installed, which has a noise diode, while all other antennas do not. Should Mopra require the spare at any point however, this capability may be removed from the ATCA; in this case you would need to use a different observational strategy to recover the absolute alignment information.

This means that to complete the linear polaristion calibration, any of the point source calibrators in the ATCA calibrator database can be observed at least a few times over the course of an Earth-rotation synthesis observation. Since this is likely being done for normal gain calibration, most observations will contain enough information to calibrate the linear polarisation.

If you can't play the parallactic angle rotation trick (if for instance you are observing for only a short time), then you will need to know the polarisation parameters for the calibrators you are observing. At low frequencies (in the 16cm band), it is known that PKS B1934-638 has zero linear polarisation. For short observations then, you can use the flux density calibration observations to calibrate linear polarisation as well.

Dave Rayner's “Circular Polarization User's Guide” is a useful guide on how to accurately measure circular polarisation with the ATCA.

### 2.2.7. When is pointing calibration required?

The global pointing model for the ATCA antennas is usually good to a few arcseconds under ideal conditions, and the tracking accuracy is better than an arcsecond. But changes in temperature can make the pointing model incorrect by a few 10s of arcseconds, and this would mean that for the millimetre bands the pointing may be incorrect by a significant fraction of the primary beam size (see Table 1.1). This would adversely affect the sensitivity of the observations of your targets.

While observing, you can correct the pointing model to ensure that the peak response of the primary beam is pointing directly at your target. A pointing correction scan is made by observing a reasonably bright point source directly and at the half-power point of the primary beam in each of the azimuth and elevation axes, and comparing the amplitude seen at each of these points.

With 2 GHz of bandwidth, almost any point source in the ATCA calibrator database can be used to determine the pointing corrections, however the pointing corrections only really improve the global pointing model within 20° of the azimuth/elevation at which the corrections were determined. The natural choice of calibrator for this purpose is therefore the same as for the gain calibration, and in general you should use your gain calibrator for pointing calibration.

Because the pointing corrections are only valid with 20°, a pointing correction scan will be required approximately every hour while you're observing if you're tracking the same source as it crosses the sky, or more frequently if you're observing multiple sources across the sky.

### 2.2.8. When is paddle calibration required?

The “paddle” is a mechanical arm that holds an absorbing material large enough to cover the 3mm feed horn. By observing the paddle, the temperature of which is assumed to be the ambient temperature in the antenna vertex room (which is monitored), and comparing it to the assumed temperature of the mostly empty sky, you get a system temperature that includes the effect of the atmosphere. This is sometimes referred to as the “above-the-atmosphere” system temperature, because in this case the system includes the atmosphere.

Because changes to the system temperature affect the response of the system to an otherwise equivalent amount of radiation, it is important to keep track of these changes as your observations progress. With the other receivers, the injected noise signal (the temperature of which is assumed to stay constant) is monitored constantly, and no overhead is incurred for sytem temperature monitoring. For observations with the 3mm receiver however, you will need to observe the paddle reasonably frequently and incur a couple of minutes overhead each time you do.

How often the paddle is used depends on the conditions. Since in principle you are using the paddle scans to interpolate the actual system temperature at any particular point in time during your observations, you will need to observe the paddle frequently enough to catch any departures from a linear change to the system temperature. If you are observing in good and stable weather, you can go 20 minutes between paddle scans. If the atmosphere is very turbulent though you may have to use the paddle more often.

It is important to remember that the system temperature calculation depends on the assumption that it will be looking at mostly empty sky after it looks at the paddle. For most point source calibrators this assumption will be valid, but if you are pointing at a planet, the system response will include its temperature, and this will affect the system temperature calculations.