The Cone of Mueller Matrices

TL;DR

This paper introduces the Mueller cone, a geometric structure for Mueller matrices in polarized light analysis, and provides computational tools for calibration and approximation of Mueller matrices based on this cone.

Contribution

It defines the Mueller cone, explores its properties, and develops computational algorithms for Mueller matrix calibration and approximation.

Findings

Mueller matrices form a cone in 4x4 matrix space.

Properties of the Mueller cone are derived and related to Stokes vectors.

Provides algorithms for Mueller matrix calibration and approximation.

Abstract

In the study of polarized light, there are two basic notions: the Stokes vectors and the matrices which preserve them, called Mueller matrices. The set of Stokes vectors forms a cone: the Future Light Cone. In this work we will see that the Mueller matrices also form a cone in the vector space of real matrices of size 4X4, called the Mueller Cone. We obtain some properties of the Mueller cone, which in turn will be translated into properties of the Stokes vectors. As an application we will give a computational program to calibrate polarimeters by means of the eigenvectors of Mueller matrices (ECM). We include computational programs to 1. Deduce if a matrix is a Mueller matrix, 2. Give an approximation of a matrix by a Mueller matrix, 3. An approximation of a Mueller matrix by Mueller invertibles, 4. An approximation of a Mueller matrix by a Stokes-cone-primitive Mueller matrix, see (4.7) and 5. An Eigenvalue Calibration Method. All these programs and implementations can be found in https://github.com/IvanLopezR22/cone-of-mueller-matrices/tree/master