Physically Realizable Space for the Purity-Depolarization Plane for Polarized Light Scattering Media

Discrepancy of coordinate system selection in backscattering Mueller matrix polarimetry: exploring photon coordinate system transformation invariants

In biomedical studies, Mueller matrix polarimetry is gaining increasing attention because it can comprehensively characterize polarization-related vectorial properties of the sample, which are crucial for microstructural identification and evaluation. For backscattering Mueller matrix polarimetry, there are two photon coordinate selection conventions, which can affect the following Mueller matrix parameters calculation and information acquisition quantitatively. In this study, we systematically analyze the influence of photon coordinate system selection on the backscattering Mueller matrix polarimetry. We compare the Mueller matrix elements in the right-handed-nonunitary and non-right-handed-unitary coordinate systems, and specifically deduce the changes of Mueller matrix polar decomposition, Mueller matrix Cloude decomposition and Mueller matrix transformation parameters widely used in backscattering Mueller matrix imaging as the photon coordinate system varied. Based on the theoretical analysis and phantom experiments, we provide a group of photon coordinate system transformation invariants for backscattering Mueller matrix polarimetry. The findings presented in this study give a crucial criterion of parameters selection for backscattering Mueller matrix imaging under different photon coordinate systems.

Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

Depolarization has been found to be a useful contrast mechanism in biological and medical imaging. The Mueller matrix can be used to describe polarization effects of a depolarizing material. An historical review of relevant polarization algebra, measures of depolarization, and purity spaces is presented, and the connections with the eigenvalues of the coherency matrix are discussed. The advantages of a barycentric eigenvalue space are outlined. A new parameter, the diattenuation-corrected purity, is introduced. We propose the use of a combination of the eigenvalues of coherency matrices associated with both a Mueller matrix and its canonical Mueller matrix to specify the depolarization condition. The relationships between the optical and polarimetric radar formalisms are reviewed. We show that use of a beam splitter in a reflectance polarization imaging system gives a Mueller matrix similar to the Sinclair–Mueller matrix for exact backscattering. The effect of the reflectance is canceled by the action of the beam splitter, so that the remaining features represent polarization effects in addition to the reflection process. For exact backscattering, the Mueller matrix is at most Rank 3, so only three independent complex-valued measurements are obtained, and there is insufficient information to extract polarization properties in the general case. However, if some prior information is known, a reconstruction of the sample properties is possible. Some experimental Mueller matrices are considered as examples.

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.

Polarisation optics for biomedical and clinical applications: a review

Many polarisation techniques have been harnessed for decades in biological and clinical research, each based upon measurement of the vectorial properties of light or the vectorial transformations imposed on light by objects. Various advanced vector measurement/sensing techniques, physical interpretation methods, and approaches to analyse biomedically relevant information have been developed and harnessed. In this review, we focus mainly on summarising methodologies and applications related to tissue polarimetry, with an emphasis on the adoption of the Stokes-Mueller formalism. Several recent breakthroughs, development trends, and potential multimodal uses in conjunction with other techniques are also presented. The primary goal of the review is to give the reader a general overview in the use of vectorial information that can be obtained by polarisation optics for applications in biomedical and clinical research.

Polarimetric data-based model for tissue recognition

We highlight the potential of a predictive optical model method for tissue recognition, based on the statistical analysis of different polarimetric indicators that retrieve complete polarimetric information (selective absorption, retardance and depolarization) of samples. The study is conducted on the experimental Mueller matrices of four biological tissues (bone, tendon, muscle and myotendinous junction) measured from a collection of 157 ex-vivo chicken samples. Moreover, we perform several non-parametric data distribution analyses to build a logistic regression-based algorithm capable to recognize, in a single and dynamic measurement, whether a sample corresponds (or not) to one of the four different tissue categories.

Polarimetric imaging microscopy for advanced inspection of vegetal tissues

Optical microscopy techniques for plant inspection benefit from the fact that at least one of the multiple properties of light (intensity, phase, wavelength, polarization) may be modified by vegetal tissues. Paradoxically, polarimetric microscopy although being a mature technique in biophotonics, is not so commonly used in botany. Importantly, only specific polarimetric observables, as birefringence or dichroism, have some presence in botany studies, and other relevant metrics, as those based on depolarization, are underused. We present a versatile method, based on a representative selection of polarimetric observables, to obtain and to analyse images of plants which bring significant information about their structure and/or the spatial organization of their constituents (cells, organelles, among other structures). We provide a thorough analysis of polarimetric microscopy images of sections of plant leaves which are compared with those obtained by other commonly used microscopy techniques in plant biology. Our results show the interest of polarimetric microscopy for plant inspection, as it is non-destructive technique, highly competitive in economical and time consumption, and providing advantages compared to standard non-polarizing techniques.

Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices

The information contained in an n-dimensional (nD) density matrix ρ is parametrized and interpreted in terms of its asymmetry properties through the introduction of a family of components of purity that are invariant with respect to arbitrary rotations of the nD Cartesian reference frame and that are composed of two categories of meaningful parameters of different physical nature: the indices of population asymmetry and the intrinsic coherences. It is found that the components of purity coincide, up to respective simple coefficients, with the intrinsic Stokes parameters, which are also introduced in this work, and that determine two complementary sources of purity, namely the population asymmetry and the correlation asymmetry, whose weighted square average equals the overall degree of purity of ρ. A discriminating decomposition of ρ as a convex sum of three density matrices, viz. the pure, the fully random (maximally mixed) and the discriminating component, is introduced, which allows for the definition of the degree of nonregularity of ρ as the distance from ρ to a density matrix of a system composed of a pure component and a set of 2D, 3D,… and nD maximally mixed components. The chiral properties of a state ρ are analyzed and characterized from its intimate link to the degree of correlation asymmetry. The results presented constitute a generalization to nD systems of those established and exploited for polarization density matrices in a series of previous works.

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.

Purity-depolarization relations and the components of purity of a Mueller matrix

A comprehensive physically realizable space, namely, the overall purity index-components of purity (PI_4D-CP) space is proposed for the characterization of the depolarization caused by random (or deterministic) media. The overall purity index (PI_4D)is obtained via indices of polarimetric purity which are incurred by the eigenvalues of the covariance matrix, whereas the components of purity (CP) are the functions of the elements of a Mueller matrix. On the one hand, the proposed space is useful in studying the depolarization caused by material media and on the other hand, it provides information on the diattenuation-polarizance properties of a Mueller matrix. Thus, it gives a remarkable physical insight of the depolarization problem.

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.

An Angle of Polarization (AoP) Visualization Method for DoFP Polarization Image Sensors Based on Three Dimensional HSI Color Space

A demand for division of focal plane (DoFP) polarization image sensors grows rapidly as nanofabrication technologies become mature. The DoFP sensor can output real time data of polarization information. In this paper, a novel visualization method for angle of polarization (AoP) is proposed for DoFP polarization image sensors. The data characteristics of AoP are analyzed, and strategies for a visualization method are proposed which conforms to the characteristics of AoP data. According to these strategies, we propose a visualization method for AoP data based on three dimensional HSI color space. This method uses intensity and saturation to characterize the magnitude of the angle between the polarization direction and the horizontal direction wherein the hue indicates the deflection direction. It is shown by the numerical simulation that the noise in the AoP image can be suppressed by our visualization method. In addition, the real-world experiment results are consistent with the numerical simulation and verify that the AoP image obtained by our method can suppress the influence of characterization noise, and the image is simple and intuitive, which is advantageous to human vision. The proposed method can be directly used for the commercialized DoFP polarization image sensor to display real-time AoP data.

Depolarizing metrics for plant samples imaging

Optical methods, as fluorescence microscopy or hyperspectral imaging, are commonly used for plants visualization and characterization. Another powerful collection of optical techniques is the so-called polarimetry, widely used to enhance image contrast in multiple applications. In the botanical applications framework, in spite of some works have already highlighted the depolarizing print that plant structures left on input polarized beams, the potential of polarimetric methods has not been properly exploited. In fact, among the few works dealing with polarization and plants, most of them study light scattered by plants using the Degree of Polarization (DoP) indicator. Other more powerful depolarization metrics are nowadays neglected. In this context, we highlight the potential of different depolarization metrics obtained using the Mueller matrix (MM) measurement: the Depolarization Index and the Indices of Polarimetric Purity. We perform a qualitative and quantitative comparison between DoP- and MM-based images by studying a particular plant, the Hedera maroccana. We show how Mueller-based metrics are generally more suitable in terms of contrast than DoP-based measurements. The potential of polarimetric measurements in the study of plants is highlighted in this work, suggesting they can be applied to the characterization of plants, plant taxonomy, water stress in plants, and other botanical studies.