Scattering of light by cosmic dust: Parameterized Mueller matrix

Department of Physics, University of Helsinki, Gustaf Hällströmin katu 2, PO Box 64, 00014 Helsinki, Finland

^★ Corresponding author: Karri.Muinonen@helsinki.fi

Received: 16 May 2025
Accepted: 15 October 2025

Abstract

Context. The scattering matrix averaged for a particle ensemble is a 4 × 4 Mueller matrix that describes, as a function of the scattering angle, θ, the relation between polarized light incident on and scattered by the ensemble. An empirical system is provided for the angular dependencies of the matrix elements for the commonly occurring case of arbitrarily shaped particles and their mirror particles that are both oriented randomly. The resulting Mueller matrix, F, is of a block-diagonal form and is given by six nonzero functions F₁₁, F₁₂ = F₂₁, F₂₂, F₃₃, F₃₄ = -F₄₃, and F₄₄.

Aims. It is our goal to show that the complex angular dependencies of the Mueller matrix can be parameterized with the help of analytical basis functions. The empirical system strives to remove obstacles arising from, for example, measured or computed scattering matrices violating the strict symmetry relations among the elements. The system further allows for efficient application of the scattering matrices.

Methods. The empirical system is based on insights from the physics of light scattering. The angular dependencies are taken to be functions of q = sin 1/2θ, a functional form frequently present in scattering problems. With the proposed modeling, common matrices can be represented by using a minimum of 28 free parameters in total; that is, less than five parameters as per the matrix element. Markov chain Monte Carlo schemes are provided for the estimation of the parameters and their uncertainties.

Results. Examples of experimentally measured and theoretical scattering matrices are analyzed with the help of the empirical system. The Mueller matrix elements are typically matched, in a relative sense, with a root-mean-square value on the order of 1%. The example Mueller matrices provide a range of angular patterns, acting as a credible test bench for the system.

Conclusions. The system with related numerical methods is successful in capturing the angular dependencies of the scattering matrix elements. The system allows for applications in both forward and inverse scattering problems concerning cosmic dust particles, with prospects for applications in scattering problems at large.