The polarization quaternion and its applications: a joint representation of the Q/U Stokes parameters and E/B mode polarizations

TL;DR

This paper introduces a polarization quaternion that unifies Q/U Stokes parameters and E/B mode polarizations, simplifying transformations and enabling new analysis methods for polarization data.

Contribution

It proposes a novel quaternion representation for polarization parameters, simplifying mathematical transforms and providing a new tool for polarization pattern analysis.

Findings

Quaternion representation simplifies polarization transforms to a single multiplication.

Preliminary application detects peculiar polarization patterns.

Unified framework enhances analysis of polarization data.

Abstract

In this work, we point out that the Q/U Stokes parameters and E/B mode polarizations are the four components of a unique quaternion, which describes at the same time the directions and the parity states of spherical linear polarizations. We then point out that, with this polarization quaternion, the mathematical form of all Q/U and E/B transforms are greatly simplified, to an extent that requires only one quaternion multiplication for each transform. A preliminary application of the polarization quaternion is shown as an example to detect peculiar pixel domain patterns within the E- and B-families, which are the former and latter halves of the polarization quaternion.