Spectral decomposition of the Mueller matrix: A geometrical model

TL;DR

This paper introduces a spectral decomposition method for Mueller matrices, representing them as a sum of deterministic matrices, and provides a geometric interpretation of the eigenvalues based on matrix invariants.

Contribution

It presents a novel spectral decomposition approach for Mueller matrices and offers a geometric model for understanding their eigenvalues.

Findings

Decomposition of Mueller matrices into up to four Mueller-Jones matrices.

Eigenvalues are represented geometrically using matrix invariants.

Provides a new geometric interpretation of the spectral components.

Abstract

An arbitrary Mueller matrix can be decomposed into a sum of up to four deterministic Mueller-Jones matrices, with strengths given by the eigenvalues of an associated Hermitian matrix. A geometrical representation of the eigenvalues in terms of the matrix invariants is presented.