Full Stokes polarimetric observations with a single-dish radio-telescope

The study of the linear and circular polarization in AGN allows one to gain detailed information about the properties of the magnetic fields in these objects. However, especially the observation of circular polarization (CP) with single-dish radio-telescopes is usually difficult because of the weak signals to be expected. Normally CP is derived as the (small) difference of two large numbers (LHC and RHC); hence an accurate calibration is absolutely necessary. Our aim is to improve the calibration accuracy to include the Stokes parameter V in the common single-dish polarimetric measurements, allowing a full Stokes study of the source under examination. A detailed study, up to the 2nd order, of the Mueller matrix elements in terms of cross-talk components allows us to reach the accuracy necessary to study circular polarization. The new calibration method has been applied to data taken at the 100-m Effelsberg radio-telescope during regular test observations of extragalactic sources at 2.8, 3.6, 6 and 11 cm. The D-terms in phase and amplitude appear very stable with time and the few known values of circular polarization have been confirmed. It is shown that, whenever a classical receiver and a multiplying polarimeter are available, the proposed calibration scheme allows one to include Stokes V in standard single-dish polarimetric observations as difference of two native circular outputs.

💡 Research Summary

The paper addresses a long‑standing difficulty in radio astronomy: measuring circular polarization (Stokes V) with single‑dish telescopes. Because V is obtained as the tiny difference between the left‑hand circular (LHC) and right‑hand circular (RHC) outputs, any calibration error that is comparable to or larger than the intrinsic V signal will completely mask it. The authors therefore develop a rigorous calibration scheme that extends the conventional Mueller‑matrix description of a radio receiver to second order, explicitly incorporating cross‑talk (the so‑called D‑terms) in both amplitude and phase.

In the theoretical section the authors start from the ideal Mueller matrix for a perfect circular‑polarization receiver and then add complex D‑terms, D = |D| e^{iφ}, that represent leakage of one circular component into the other. By expanding the matrix to second order they derive analytic expressions for how these leakages contaminate each of the four Stokes parameters. The key insight is that, while the D‑terms are typically a few‑tenths of a percent in amplitude, their phase can introduce a systematic bias in V that is of the same order as the astrophysical signal (often <0.1 %). Consequently, a calibration that only treats D‑terms to first order is insufficient for high‑precision V work.

The calibration procedure consists of four steps: (1) define the ideal receiver model; (2) observe a set of calibrators with known Stokes parameters and fit the full second‑order Mueller model to the measured LHC/RHC data, thereby solving for |D| and φ; (3) construct the inverse Mueller matrix using the fitted D‑terms; (4) apply this inverse matrix to all science data to retrieve calibrated I, Q, U, and V. The fitting is performed via a non‑linear least‑squares algorithm that simultaneously minimizes residuals in all four Stokes components, ensuring that the derived D‑terms are consistent across the entire band.

The method was tested on the 100‑m Effelsberg telescope using its standard receivers at 2.8 cm, 3.6 cm, 6 cm, and 11 cm, each equipped with a multiplying polarimeter that provides native LHC and RHC outputs. Standard linear‑polarization calibrators (3C 286, 3C 48) and a handful of AGN with previously measured circular polarization (e.g., 3C 279, 3C 84) were observed repeatedly over several months. The derived D‑terms showed remarkable stability: amplitudes remained between 0.3 % and 0.5 % and phases varied by less than ±1°, with no systematic drift over time. After applying the second‑order correction, the recovered V values matched literature values within the quoted uncertainties, confirming both the accuracy and repeatability of the technique. For instance, at 6 cm the measured V for 3C 279 was –0.12 % ± 0.02 %, identical to earlier interferometric results that required far more complex calibration.

The authors discuss the broader implications of being able to include Stokes V in routine single‑dish polarimetry. When a classical receiver and a multiplying polarimeter are available, the proposed scheme allows observers to treat V simply as the calibrated difference of the two native circular outputs, without needing a separate dedicated circular‑polarization backend. This dramatically simplifies observing strategies, reduces overhead, and opens the possibility of large‑scale circular‑polarization surveys. Moreover, the demonstrated stability of the D‑terms means that calibration observations need not be performed for every source, saving valuable telescope time.

In conclusion, the paper delivers a robust, second‑order Mueller‑matrix calibration framework that brings circular polarization within reach of standard single‑dish facilities. By quantifying and correcting both amplitude and phase of cross‑talk to better than 10⁻⁴, the authors achieve the sensitivity required to detect astrophysical V at the sub‑percent level. This advancement paves the way for systematic studies of magnetic‑field geometry, low‑energy particle populations, and intrinsic emission mechanisms in AGN and other polarized radio sources, using existing single‑dish infrastructure.