Merit functions and measurement schemes for single parameter depolarization models

TL;DR

This paper introduces a simplified one-dimensional parameter for depolarization in Mueller matrices, enabling efficient measurement schemes using only two polarimetric measurements, and demonstrates its applicability across various materials.

Contribution

It relates the depolarization parameter to the relative weight between a Fresnel matrix and an ideal depolarizer, simplifying the measurement process.

Findings

The depolarization parameter can be derived from two measurements.

Triple degeneracy in weights is observed across different plastics and textures.

The method applies across multiple geometries and wavebands.

Abstract

Mueller polarized bi-directional scattering distribution functions (pBSDFs) are 4x4 matrix-valued functions which depend on acquisition geometry. The most popular pBSDF is a weighted sum between a Fresnel matrix and an ideal depolarizer. This work's main contribution is relating the relative weight between an ideal depolarizer and Fresnel matrix to a single depolarization parameter. Rather than a 16-dimensional matrix norm, this parameter can form a one-dimensional merit function. Then, instead of a full Mueller matrix measurement, a scheme for pBSDF fitting to only two polarimetric measurements is introduced. Depolarization can be mathematically expressed as the incoherent addition of coherent states. This work shows that, for a Mueller matrix to be in the span of a Fresnel matrix and an ideal depolarizer, the weights in the incoherent addition are triply degenerate. This triple degeneracy is observed in five different colored opaque plastics treated with nine different surface textures and measured at varying acquisition geometries and wavebands.