Polarisation calibration
Introduction
The MeerKAT receivers have two orthogonal linear feeds. The correlator always produces all four polarisation products, though users who only need Stokes I images can choose to only download the parallel-hand (HH and VV) products from the archive. Although the polarisation characteristics of the receivers appear to be stable on a timescale of months (Plavin et al. 2020), it is recommended to include absolute polarisation calibrators in each observation, if possible.
There are somewhat different approaches to polarisation calibration, both in observational set-up and reduction methods, which depend on calibration source LST-coverage, reduction package used, and the user’s dynamic range and fidelity requirements. Moreover, much work is still being done on spectropolarimetric calibration across the full field of view. Below we attach two reports demonstrating calibration using Obit (Cotton, 2008) and CASA:
A MeerKAT Polarization Survey of Southern Calibration Sources (Taylor & Legodi 2024)
EVLA Memo 219: “Enabling MeerKAT Polarimetric Imaging in AIPS”
For polarimetry above 1380 MHz, or past the half-power beam width of the primary beam, please have a look at our page on the MeerKAT primary beam measurements.
For polarimetry below 1000 MHz (UHF-band), or past 0.23 degrees offset from the phase centre, please refer to the memo “Absolute linear polarization angle calibration using planetary bodies for MeerKAT and JVLA at cm wavelengths” (Hugo & Perley, 2024)
Also, please see Hugo & Perley (2024) (and also de Villiers, 2023) for S-band polarimetry, it is demonstrated that instrumental polarisation is most severe at the top of the S0 sub-band (1750 - 2625 MHz), yet the degree of contamination is lower than that in the L-band. In the S2 sub-band (2187 - 3062 MHz), variability is significant with parallactic angle, exceeding a few per cent near the edge of the beam and beyond. Although there is less variation with parallactic angle at the S4 sub-band (2625 - 3500 MHz), distinct “notches” appear beyond 3 GHz, and these increase in magnitude to several per cent beyond a 0.17-degree offset from the phase centre.
Leakage calibration
A strong unpolarised calibrator such as J1939-6342 can be used to calibrate the leakage terms. J0408-6545 could be used, but is weakly polarised at the 0.1% level in linear polarisation. Alternatively, a strong calibrator can be observed over a range (at least 60°) of parallactic angles. Leakage on all frequency bands (and sub-bands), except the S4 sub-band, is 2% or less at 0.25-degrees off-axis (Hugo & Perley 2024). The MeerKAT off-axis leakage performance across UHF, L, S0, S2 and S4 sub-bands is displayed in the figure below.
Absolute polarisation angle
Using celestial calibrators
MeerKAT uses 3C 286 (J1331+3030) as the preferred HV phase calibrator due to its multi-decade stability. However, due to its high northern declination, it is only visible to the telescope for ~5 hours above 20° elevation. The other commonly used calibrator is 3C 138 (J0521+1638). The MeerKAT L-band properties of these calibrators are summarised in Table 1 below. However, we have been finding anomalous results for 3C 138, and there are indications that the model for 3C 286 is not accurate in the UHF band. 3C 286 is seen to rapidly depolarise below 1 GHz, with an intrinsic rotation measure that gradually increases to about 0.12 rad/m2 (Hugo & Perley, 2024). MeerKAT UHF, L and S-band measurements are presented in great detail in the memo Hugo & Perley (2024) where a broken power law model is derived for 3C 286 using exclusively nighttime scans (that are at least 60 degrees in arc away from the Sun), which have ionospheric corrections applied. This model is:
Users are requested to contact th MeerKAT Science service desk. if they are concerned about their results – support tickets can be raised on the MeerKAT Science service desk.
Note that, despite uncertainties in calibrating the polarisation angle, it remains possible to obtain significant scientific results, e.g., Cotton et al. (2020). On average, the MeerKAT feed alignment across the array is consistent with the IAU polarisation convention. The antenna dipole orientation errors exhibit a standard deviation of no more than ~2° in S-band.
Table 1: Properties of suggested polarisation calibrators at the MeerKAT L-band (Taylor & Legodi 2024).
Calibrator | RM (rad / m2) | Fractional linear power (%) | Average linear angle (deg) | S1.28GHz Total intensity (Jy) |
|---|---|---|---|---|
3C 286 | -0.3 +/- 0.1 | 8.6 to 9.9 | 33 | 15.77 |
3C 138 | -2.4 +/- 0.1 | 5.6 to 8.4 | -14 to -10 | 8.99 |
While we have identified 10 new polarised sources with low (< 10 rad/m2) rotation measure, we have only recently started a monitoring programme to determine their long-term stability. Users interested in using one of these potential calibrators should contact the helpdesk when setting up their observation for scheduling.
Using the noise diode and antenna calibration tables
In the case where no absolute polarisation calibrator is available in the required LST range, the only option is to follow the polarisation calibration procedure outlined in the Obit report mentioned above. Note that this can only be done using either the SDP pipeline or Obit.
The reference antenna calibration tables needed for this method are attached below.
Parallactic angle of the polarisation calibrator
If a polarisation calibrator is included to calibrate the H-V phase of the system the observer should
consider an optimal LST time for the calibrator visit to ensure that power is available on the crosshand visibilities for their choice of parallactic angle (i.e. the parallactic angle rotated Stokes U component should be maximized). The Observation Planning Tool (OPT) calculates and plots source H-V power values (in Jy) as part of the OPT simulate functionality, along with a correlator mode-specific H-V limit (in Jy – yellow horizontal line) based on a 5-minute polarisation scan. Users can ensure that sufficient H-V power is obtained by confirming that the chosen calibrator (3C 138 or 3C 286) has a H-V power above the provided limit across the LST range it is observed for.
We recommend including a minimum of 10 minutes on a polarisation calibrator with sufficient H-V power for every 5 hours of observing. Where possible, these 10 minutes should be divided into two 5-minute scans (observed 2 to 3 hours apart) to minimise the risk of contamination by RFI and/or ionospheric effects. More than two scans can also be observed when sufficiently warranted (e.g. when using a calibrator with unknown polarisation) as these will provide better parallactic angle coverage of the polarisation calibrator and better mitigate transient contamination – an example observational strategy could involve three or four 5-minute scans spaced at least 1.5 hours apart during an epoch that lasts at least five hours.
It is generally not advised to use 3C 286 for both polarisation and bandpass calibration purposes. There is no full polarisation model for 3C 286 and instrumental polarisation effects cannot be accounted for. A strong unpolarised calibrator such as J1939-6342 is suggested to calibrate leakage terms, along with the bandpass. See the Calibration Strategies section for other related calibration parameters.
Cross-hand delays and V/H phase difference
The delay calibration script executed at the subarray build calculates the cross-hand polarisation phase offsets using the noise diodes. The polarisation characteristics of the receiver chain appear to remain stable to less than 10 ps in delay over timescales of hours, certainly within the timescale of a typical horizon-to-horizon track.
Note that when digitizers are rebooted or power cycled, a random delay of -4 to 4 samples may be introduced relative to the other polarisation on the antenna. This can lead to jumps of multiples of 90° in leakage phase solutions for the affected antenna from one epoch to another.
These delays can also be calibrated in the standard manner in CASA using the polarisation calibrator or by using the pipeline solutions derived from the delay calibration prior to the start of the observation. The H/V phase is not calibrated during delaycal - only the delay. Users can still expect significant elliptical polarisation fractions that must be calibrated for prior to imaging.
Note that some UHF and all S-band receivers have inverted HV phase. Visibility data not calibrated for HV phase will appear to have a rotation of the EVPA North through West as a result. HV phase must be corrected before the application of parallactic angle corrections.
Ionospheric Faraday rotation
Ionospheric Faraday rotation remains a significant challenge, particularly during periods of elevated solar activity (as observed in 2024), which leads to increased ionospheric disturbances. Recent findings by Hugo & Perley (2024) indicate that the ionosphere can introduce significant Faraday rotation at lower frequencies, particularly in the UHF and L bands. Ongoing efforts are focused on implementing total electron content (TEC) measurements derived from on-site dual-frequency GPS receivers. Individuals interested in contributing to this project or seeking updates are encouraged to contact the helpdesk.
Ionospheric rotation measure (RM) can be corrected a posteriori, and an approximate model for the polarisation calibrator can aid in resolving ambiguities in the residual X-Y phase. This model does not require high precision for this application, as the computation relies on arctan(V/U), with both XY and YX being primarily Stokes U – see e.g, Taylor & Legodi, 2024.
A model for the calibrator is not strictly required for polarisation angle calibration, as the polarisation angle in a linear feed basis is always defined relative to the chosen reference antenna. The MeerKAT receiver/dipole assemblies are nominally well aligned on the sky, with a maximum scatter of approximately two degrees from the nominal IAU convention for vertical and horizontal dipoles. As a validation step, imaging the calibrator in Stokes Q and U after initial polarisation calibration can serve as a reliability check.
To account for the temporal and spatial variability of the target field, it is recommended to use AIPS TECOR with JPL data or alternative options such as RMExtract or ALBUS to predict ionospheric corrections for the science target field. If a low RM is required for polarimetric measurements, observations should be scheduled during nighttime to minimise ionospheric variability. Daytime conditions exhibit strong diurnal fluctuations influenced by the solar zenith angle, with typical differentials ranging from 60 to 100 TECU.
A MeerKAT polarisation calibration recipe, based on CASA, can be found here https://github.com/africalim/Polcal-Primer .
Visibility product handedness
Perley, Greisen, and Hugo (2022) -- EVLA Memo 219 have established that the handedness of MeerKAT visibility products is incorrect, with the system defined as +X East and +Y North. This discrepancy relative to the IAU convention results in a sign reversal for Stokes Q, U, and V, depending on the cross-hand phase of the system and whether it reverses its response to right- and left-circularly polarised emission.
For a complete discussion, refer to Perley, Greisen, and Hugo (2022). To correct this issue, an anti-diagonal matrix should be applied to the raw visibilities, and the RECEPTOR feed angle should be reset to zero in Measurement Set v2 visibility products (as defined by Kemball & W. M. H., 2000, NRAO CASA Memo 229) before further processing.