Calibration Strategies

The science goals of a given project will guide how the schedules are designed. Different types of observing modes (polarimetry, spectral line, pulsar, etc.) require different approaches to calibration. This chapter will cover the calibration strategies for several observing modes, which will dictate the setup of those observations. These strategies are for VLBA-only observations. High Sensitivity Array (HSA) and Global VLBI observations will be discussed in the next chapter.

Basic Continuum of Bright Sources

The most basic VLBA project would be continuum observations of very bright (> a few Jy) sources at observing frequencies below about 12 GHz. For this case, all of the targets are assumed to have high enough flux density to self calibrate and atmospheric opacity is generally not an issue. Therefore, there is no need to do any phase referencing. The only calibration scans necessary are for fringe-finding and bandpass calibration.

Fringe Finder

Fringe finder sources need to be bright (>1 Jy) and preferably compact in order to calibrate the phases and delays for every baseline in an observation. In general, a 2-minute scan should be made on the fringe finder at every observing band for every 3 to 4 hours of observing. Because the fringe finder scans are so important to proper correlation, it is recommended that they be scheduled near the middle and/or end of the observation. This reduces the chances of any early hiccups in the observation impacting these scans and also helps to ensure that fringe finder will be visible at all stations. Many observers schedule two or three scans on a fringe finder over the course of an observation to ensure good correlation and provide a good source for initial instrumental phase and delay calibration. The NRAO maintains a list of recommended fringe finders, but users are free to choose whichever source they believe will work.

Note that a judicious selection of a fringe finder source could also be used as a bandpass calibration source (discussed more below).

For observations lasting longer than about 4 hours, at least two fringe finder scans should be scheduled. If the first fringe finder is also the bandpass calibrator, the second fringe finder scan should be on the same source as the first fringe finder scan. If the observers have opted to use a separate source for bandpass calibration, the second fringe finder scan can be on a different source than the first fringe finder scan.

Bandpass Calibration

In order to properly characterize the bandpass response for each subband, at least one 2-minute scan should be scheduled on a bright source at every observing band for every 3 to 4 hours of observing. As mentioned above, the bandpass calibration source can be the same as the fringe finder. In fact, it is often a good strategy to use the same source for both because this will reduce overhead in the schedule and leave more time for scans on the science target(s).

As with fringe finder scans, long schedules should include multiple bandpass calibration scans. However, the same bandpass calibrator should be used for every bandpass calibration scan in order to track any changes in the telescope response over the course of the observation.

Basic Continuum at Frequencies Above 12 GHz

Basic continuum observations at frequencies of about 12 GHz and higher require some extra planning in order to track the system temperature as a function of elevation. Observers should ensure that at least one relatively bright source is observed frequently over the entire range of elevation. This is then used to determine the tropospheric opacity corrections during calibration.

Phase Referencing

A slightly more complicated observation involves a science target that is not expected to be bright enough for self calibration. In this case, the phase solutions from a nearby bright source must be transferred to the science target. Therefore, observations of the science target are interspersed with observations of the phase calibration target, which is known as the “phase reference calibrator”. Observers who are creating schedules for phase referencing projects are encouraged to consult Wrobel et al. (2000) and Reid & Honma (2014) for more information on the strategies involved.

The phase reference calibrator should be as close to the science target as possible. This ensures that the phase solutions derived for the phase reference source can be applied to the science target, reduces the uncertainty in the position of the science target, and reduces slew time (which reduces total observation time). The exact observing strategy depends on the observing frequency:

• For observations below 1 GHz, observers should find a phase reference calibrator that is within the primary beam when observing the science target. Observers will not need to schedule scans on calibrator, but they likely will need to request two correlation passes: 1 on the science target and one on the calibrator.
  
• For observations between 1 and 2 GHz, it is highly recommended to use a phase reference calibrator that is within the primary beam when observing the science target. If an in-beam calibrator is not available, observers should choose the nearest appropriate calibrator.  The maximum recommended angular distance between the science target and the calibrator is 4 degrees. 
• For frequencies between 2 and 5 GHz, observers should choose a phase reference calibrator within about 4 degrees of the science target to reduce the effects of the ionosphere on the calibration.
• For frequencies above 5 GHz, observers should choose a phase reference calibrator within about 5.7 degrees (0.1 radians) of the science target to ensure that any atmospheric effects can be successfully calibrated out of the data.

The phase reference calibrator should be bright enough to successfully fringe fit, which requires a signal-to-noise ratio (SNR) of at least 7 at the observing frequency. Ideally, the calibrator should have a SNR greater than 7 for all baselines. However, as long as the SNR is at least 7 for all baselines from a reference antenna (usually a station near the center of the array such as FD, PT, or LA), solutions will be found for the longer baselines. The VLBA OSS has a table of the VLBA baseline sensitivities to help determine the SNR at any observing frequency. However, the table assumes that observations are made using the maximum possible data rate and that all data channels will be combined for the calibration. Observers who want to calibrate each data channel independently should use the EVN Sensitivity Calculator to determine the baseline sensitivity in each data channel.

The phase reference calibrator should have a well-known position. It is therefore recommended to choose a calibrator from one of the astrometric catalogs such as the IAU standard International Coordinate Reference Frame 3 (ICRF3) maintained by the International VLBI Service (IVS), or the Radio Fundamental Catalog (RFC) maintained by NASA’s L. Petrov. The new VLBA Calibrator Search Tool and the NASA VLBI Calibrator Search tools can help observers find good phase reference calibrators for their science target(s). The positional uncertainty of the phase reference calibrator should be <10 mas in both RA and DEC, but <1 mas is preferred.

Phase referencing is recommended for all astrometric projects because the self calibration process does not preserve the absolute location data of the target source.

For more information on phase referencing strategies, see Wrobel et al. (2000).

Observers are encouraged to contact the VLBA staff via the NRAO helpdesk if they have any questions about choosing a phase reference calibrator.

Phase Referencing Schedules

Building a schedule for a phase referenced observation of a single science target is fairly simple. Every scan on the science target should be bracketed by scans on the phase reference calibrator. Each set of scans (phase cal, science target, phase cal) should be timed such that the mid points of each phase reference calibrator scan are separated by no more than the coherence time at the observing frequency. Observers can estimate the tropospheric coherence time at a given observing frequency using t ~ 2300/(observing frequency in GHz) seconds (see Reid & Honma 2014). Note that this estimate only works for frequencies above 5 GHz; lower frequencies are impacted more by the ionosphere and observers should assume coherence times of ~120 seconds for 300 to 700 MHz, and ~300 seconds for 1 to 5 GHz. For more details on the tropospheric coherence times, see Moran & Dhawan (1995).

As an example, the estimated coherence time at 8.4 GHz (4 cm) is about 274 seconds and the recommended fringe-fit interval is 120 seconds (see Wrobel et al. 2000). The “typical” VLBA 8.4 GHz phase referenced observation would have phase reference calibrator scans of 120 seconds and science target scans of 150 seconds (120/2 + 150 + 120/2 = 270). This assumes a fairly dim phase reference calibrator (requiring 120 second scans to get good SNR) which is very close to the science target (such that the slew time is very low). If the phase reference calibrator is bright enough, the calibration scans can be shortened to as little as 30 seconds on-source, and the science target scans can be lengthened accordingly. If the phase reference calibrator is far away from the science target, the scan times will need to be adjusted to allow for longer slews.

Note that the coherence time estimate assumes reasonably good weather at each station.  Observations at frequencies of 12 GHz and higher should assume a shorter coherence time than the estimate provides to account for possible adverse weather conditions. For example, while the estimated coherence time at 22 GHz is about 105 seconds, it is recommended to assume a coherence time of between 60 and 90 seconds.

Additionally, note that observations at low elevations will have shorter coherence times, so observers should adjust their schedules accordingly. See Ulvestad (1999) for more details on this effect.

Check Sources

It is often a good idea to include a handful of scans on one or two additional bright sources, which are referred to as “phase-check sources” or just “check sources”.  The check sources should be calibrated in the same way as the science target (i.e., do not fringe fit on the check sources, but apply the fringe fit solutions from the phase reference calibrator).

The check sources should be bright enough to allow for self calibration. A source with flux density of 50 mJy/beam will likely work, but >100 mJy/beam is preferred (the brighter, the better). This allows the observer to check that the solutions derived from the phase reference calibrator properly calibrate the phases for the check source. The check sources should be about as far from the phase reference calibrator as the science target, but still within ~5.7 degrees of the phase reference source (closer for low frequencies or low elevations). A check source with a well-known position (uncertainties <1 mas) will also allow the observer to check the astrometric precision of the calibration. Check sources do not necessarily need to be point sources, so a source with flux density that falls off on the longer baselines is acceptable.

Polarimetry

Polarimetric calibration requires three additional steps beyond continuum calibration:

1. Determining the leakage terms (i.e., the polarization impurity between the R and L polarizations), a.k.a. the “D-term” calibration.

2. Calibrating the absolute electric vector polarization angle (EVPA) by determining the phase difference between the right circular polarization (RCP) and left circular polarization (LCP).

3. Calibrating the RCP-LCP delays.

For the VLBA, polarimetric observations must include scans on calibrator sources for each of these steps. There is a list of calibrator monitoring for VLBA observations starting with the 21A semester.

Note that ionospheric Faraday rotation may be an issue for observations at 20cm and longer wavelengths.

Leakage/D-term Calibration

The strategy for determining the leakage terms depends on the total length of the observation. For short (<4 hours) observations, at least one scan on a strong unpolarized (>1 Jy, less than 1% polarized) calibrator source will be required. For longer observations, at least 5 scans on one strong calibrator (>1 Jy) over a wide range (at least 100 degrees) of parallactic angle should be scheduled throughout the observation. It is even better if the strong calibrator has a known and constant EVPA. Some D-term calibrators may also work as fringe finders and/or bandpass calibrators. Each scan on the D-term calibrator should last at least 2 minutes, but 5 to 10 minutes is better.

Some recommended VLBA D-term calibrators are:
Bright, unpolarized: OQ208 (J1407+2827) Note – steep spectrum, only recommended for observations below ~9 GHz.
Bright, low polarization fraction: 3C84 (J0319+4130)
Bright, polarized: NRAO150 (J0359+5057), DA193 (J0555+3948), 3C286 (J1331+3030), BL Lac (J2202+4216), 3C454.3 (J2253+1508)

EVPA Calibration

To accurately determine the EVPA of a target, the observation must include several scans on 1, 2, or 3 sources with known EVPA. Each EVPA calibrator should be observed at least twice, and preferably 4 times, over as wide a range of parallactic angle as possible. Each scan should be at least 3 minutes long. The VLBA OSS Polarimetry section lists some recommended EVPA calibrators for observing frequencies between 1 and 5 GHz. A collection of EVPA calibrators useful for observing frequencies of 5 GHz and above can be found at the VLA/VLBA Polarization Calibration page.

Observers planing to use polarimetric calibration should request VLA observations of their EVPA calibrators within +/- 2 weeks of the VLBA observation. The closer in time the VLA observations are made, the better. The request for one or more VLA observations for EVLA calibration should include the sources and frequencies needed, along with any information about the desired timing of the VLA observations. The request should be included in the SCHED .key file, and can also be emailed to vlbiobs@nrao.edu. Note that some calibrators are monitored regularly by the VLA and may not need to be specially requested. To see which calibrators are being observed, search the NRAO Data Archive for projects TPOL0003 and TCAL0009.The measured EVPAs in the VLA observations must then be transferred to the VLBA data using the AIPS task CLCOR or RLCOR, as described in the AIPS Cookbook.

RCP-LCP Delay Calibration

To determine the RCP-LCP delays, observers should schedule a single 2-minute scan on a very strong (~10 Jy) source. This source can often also serve as the fringe finder and bandpass calibrator.

Spectral Line Observations

Spectral line projects should include scans on fringe finders and bandpass calibrators. The same source may be used for both purposes. The bandpass calibrator should be bright enough, or observed long enough, so that the bandpass calibration does not significantly contribute to the noise in the image. For a given channel width,

\[ ( S_{cal} \cdot \sqrt{t_{cal}} ) / ( S_{obj} \cdot \sqrt{t_{obj} } ) \gt 2  \]

where \(S_{cal}\) is the flux density of the bandpass calibrator, \(t_{cal}\) is the total time on the bandpass calibrator, \(S_{obj}\) is the flux density of the science target, and \(t_{obj}\) is the total time on the science target. 

The exact ratio between the two values will be determined by the science goals, but it should be no smaller than 2. Note that for extremely narrow channels or very weak bandpass calibrators, those typical flux requirements can lead to extremely long integration times.

If the science target has strong continuum emission (e.g., absorption line studies) or a strong emission line (e.g., a maser line), phase referencing may not be necessary. For such cases, self-calibrating the continuum source or the strong emission line would be sufficient to calibrate the delay and fringe-rate. In all other cases, including when preserving the absolute position of the target (i.e., astrometry) is necessary, phase referencing as described previously should be utilized.

Observations on the spectral line target should have the pulse cal generators disabled: in SCHED .key file, set pcal=’off’. If the pulse cal is not set to ‘off’, the pulse tones will corrupt the spectral line data. It is highly recommended that the pulse cal generators be turned off for all scans in the observation, including scans on calibration sources (bandpass calibrator, phase reference calibrator, etc.), otherwise the pulse cal tones on those sources may contaminate the spectral calibration of the science target(s).

Spectral line projects often require the bandpass to be very well-calibrated. It is therefore highly recommended to include scans on the bandpass calibrator once every two hours. This ensures the availability of bandpass calibration information even if one or more antennas fail throughout the observation.

Pulsar Observations

The strategy for pulsar observations is essentially identical to a phase referenced observation. The schedules will require scans on a fringe finder, a bandpass calibrator, and a phase reference calibrator. However, absolute amplitude calibration is lost during correlation for observations using the pulsar gating and pulsar binning modes.

Observers conducting pulsar observations will need to submit two additional files for correlator configuration. First, a pulsar ephemeris file (.polyco) to predict the phase of the pulsar. Second, a bin configuration (.binconfig) file containing details for the correlation of the observation. These two files should be submitted no later than 1 week after the pulsar observation took place, but can be submitted along with the normal scheduling files. Note that a separate pair of ephemeris and bin configuration files must be submit for each pulsar in a multi-pulsar observation.

Details of the DiFX pulsar modes can be found in Brisken & Deller (2010).