Q(M) and the depolarization index scalar metrics

Unraveling the physical information of depolarizers

The link between depolarization measures and physical nature and structure of material media inducing depolarization is nowadays an open question. This article shows how the joint use of two complementary sets of depolarizing metrics, namely the Indices of polarimetric purity and the Components of purity, are sufficient to completely describe the integral depolarizing properties of a sample. Based on a collection of illustrative and representative polarimetric configurations, a clear and meaningful physical interpretation of such metrics is provided, thus extending the current tools and comprehension for the study and analysis of the depolarizing properties of material media. This study could be of interest to those users dealing with depolarization or depolarizing samples.

Nonuniform depolarization properties of typical nanostructures and potential applications

Nonuniform depolarization properties of ${\text{SiO}_2}$SiO₂ thin film, two-dimensional (2D) Si grating, and three-dimensional Si cylinder grating, were systematically investigated by Lu-Chipman decomposition. We find that introducing surface profiles with dimensions comparable to the detecting wavelengths can lead to obvious nonuniform depolarization, and control of the sample azimuth can manipulate the uniformity of the depolarizer components. The results indicate that the 2D nanostructure shows obvious nonuniform depolarization at 0° and 90° azimuths, while almost uniform depolarization at 45° azimuth. These discovered phenomena may give rise to some potential applications, such as the detection of the existence of nanostructures without a priori information about the sample, and the design of a uniform or nonuniform depolarizer.

Eigenvalue-based depolarization metric spaces for Mueller matrices

We present a unified formal description and a detailed study of the depolarization spaces defined by various depolarization metrics based on the eigenvalues of the covariance matrix associated with a given Mueller matrix. By introducing natural generalizations of the common and Lorentz depolarization metrics, we likewise advance novel spaces appropriate for the description of extrinsic and intrinsic depolarization. We show the intimate relation existing between the depolarization spaces and the depolarization diagrams and solve the problem of the experimentally observed forbidden depolarization region. The theoretical developments are illustrated on numerical, analytical, and experimental examples of depolarizing Mueller matrices.

Physically meaningful depolarization metric based on the differential Mueller matrix

We present a novel depolarization metric for Mueller matrices based on the differential Mueller formalism. The proposed metric relies on the statistical interpretation of the differential Mueller matrix. We show that the differential depolarization index successfully quantifies depolarization even when applied to specific types of Mueller matrices for which some widely used depolarization metrics yield erroneous results. Moreover, the fact that the presented metric is directly linked to the variances and covariances of the elementary anisotropic properties of the sample makes it a valuable tool to quantify depolarization on a physically meaningful basis.

Components of purity of a Mueller matrix

The degree of polarimetric purity of a Mueller matrix, also called "depolarization index" [Opt. Acta 33, 185 (1986)] is expressed as a quadratic average of two contributions of different nature. The contribution due to the polarizance and diattenuation properties is given by a unique parameter called "degree of polarizance," and the complementary contribution due to nonpolarizing properties is given by a parameter called "degree of spherical purity." These two intrinsic quantities are useful in order to analyze the sources of the polarimetric purity of a material sample whose Mueller matrix has been measured and provide criteria for the classification of Mueller matrices.

Design and optimization of partial Mueller matrix polarimeters

Mueller matrix polarimeters (MMPs) are designed to probe the polarization properties of optical scattering processes. When using a MMP for a detection, discrimination, classification, or identification task, a user considers certain elements of the Mueller matrix. The usual way of performing this task is to measure the full Mueller matrix and discard the unused elements. For polarimeter designs with speed, miniaturization, or other constraints, it may be desirable to have a system with reduced dimensionality that measures only elements of the Mueller matrix that are important in a particular application as efficiently as possible. In this paper, we develop a framework that allows partial MMPs to be analyzed. Quantitative metrics are developed by considering geometrical relationships between the space spanned by a particular MMP and the space occupied by the scene components. The method is generalized to allow the effects of noise to be considered. The results are general and can also be used to optimize complete and overspecified MMPs for performing specific tasks, as well.