An Introduction to Single-Antenna Radio Astronomical Polarimetry

TL;DR

This tutorial provides a comprehensive overview of the mathematical foundations of single-antenna radio polarimetry, emphasizing the relationships between physical signal propagation and the transformations of electric field and Stokes parameters.

Contribution

It offers a unified framework based on established work to analyze and calibrate radio polarimetric signals, including practical guidelines and mathematical tools for improved understanding.

Findings

Introduces criteria for selecting instrumental response models

Provides practical calibration guidelines for radio polarimetry

Includes mathematical proofs and background on signal processing

Abstract

This tutorial reviews the mathematical foundations of single-antenna radio polarimetry with the aim of fostering a conceptual understanding of the relationships between a physical description of signal propagation (gain, delay, reflection, down-conversion, etc.), the corresponding transformations of the electric field vector, and the equivalent operations on the Stokes parameters. The adopted framework is based on the work of Britton (2000) and Hamaker (2000) and applied to analyze the signal path described by Hamaker et al. (1996) with additional corrections for phase convention and reflection. Some objective criteria for selecting a model of the instrumental response are introduced and discussed, along with some practical guidelines that facilitate polarimetric calibration. Further relevant background material and lengthier mathematical proofs are included in the appendix, which introduces the vector, matrix, and tensor notation and concepts of linear algebra used in this work. The appendix also reviews some of the basics of analog and digital signal processing that are relevant to radio astronomy, and discusses some numerical instabilities that arise when modeling observations.