Structured decomposition design of partial Mueller matrix polarimeters

Abstract

Partial Mueller matrix polarimeters (pMMPs) are active sensing instruments that probe a scattering process with a set of polarization states and analyze the scattered light with a second set of polarization states. Unlike conventional Mueller matrix polarimeters, pMMPs do not attempt to reconstruct the entire Mueller matrix. With proper choice of generator and analyzer states, a subset of the Mueller matrix space can be reconstructed with fewer measurements than that of the full Mueller matrix polarimeter. In this paper we consider the structure of the Mueller matrix and our ability to probe it using a reduced number of measurements. We develop analysis tools that allow us to relate the particular choice of generator and analyzer polarization states to the portion of Mueller matrix space that the instrument measures, as well as develop an optimization method that is based on balancing the signal-to-noise ratio of the resulting instrument with the ability of that instrument to accurately measure a particular set of desired polarization components with as few measurements as possible. In the process, we identify 10 classes of pMMP systems, for which the space coverage is immediately known. We demonstrate the theory with a numerical example that designs partial polarimeters for the task of monitoring the damage state of a material as presented earlier by Hoover and Tyo [Appl. Opt.46, 8364 (2007)10.1364/AO.46.008364APOPAI1559-128X]. We show that we can reduce the polarimeter to making eight measurements while still covering the Mueller matrix subspace spanned by the objects.

Complete Mueller matrix from a partial polarimetry experiment: the nine-element case

“…Before ending the theoretical part and proceeding to its experimental validation, it should be noted that the ultimate objective of partial Mueller polarimetry is not always the recovery of the complete Mueller matrix. There exist alternative approaches, belonging to the so-called adaptive polarimetry [23] whereby only a selection of measurable linear combinations of Mueller matrix elements (termed "channels") [24], instead of the reconstructed complete Mueller matrix, is applied to the problems of remote sensing or invariant discrimination [25].…”

Evaluating the Utility of Mueller Matrix Imaging for Diffuse Material Classification

“…The training set is used to compute a solution for the PSG/PSA states which maximize Eq. (7). The training set is also used to estimate the mean and covariance terms on the RHS of Eq.…”

“…However, researchers recognize that not all 16 Mueller matrix elements are necessary for many applications. Use of terms like ''adaptive polarimetry'' [5] and ''partial polarimetry'' [6,7] appear in the literature and have been adopted in limited applications. A method to access the information content of polarimetric measurements and inform the design of partial polarimetric systems for broad applications is still needed.…”

Bandwidth and information in the design and analysis of polarimeters

“…Alenin extended this to develop a full theory of partial polarimeters. 25 Alenin showed that a matrix B that he termed the "reconstructables" matrix could be computed by considering the diagonal elements of W + W. This matrix provides the elements that can be reconstructed from any particular combination of PSG/PSA state pairs, and provides a mechanism that can be used to design optimal partial polarimeters. Alenin presented several canonical categories of partial polarimeters, and demonstrated that at least seven -but more realistically eight -measurements are necessary to perform the discrimination task described in Fig.…”