Mueller Matrix Research Articles

Spatial frequency domain Mueller matrix imaging.

Mueller matrix polarimetry (MMP) and spatial frequency domain imaging (SFDI) are wide-field optical imaging modalities that differentiate tissue primarily by structure alignment and photon transport coefficient, respectively. Because these effects can be related, combining MMP and SFDI may enhance tissue differentiation beyond the capability of each modality alone. An instrument was developed to combine MMP and SFDI with the goal of testing whether it enhances contrast of features in reflection mode. The instrument was constructed using liquid crystal elements for polarization control, a digital light processing projector for generating sinusoidal illumination patterns, and a digital camera for imaging. A theoretical analysis shows that the SFD Mueller matrix is complex-valued and does not follow the same behavior as a regular Mueller matrix. Images were acquired from an anisotropic tissue phantom, an optical fiber bundle, and cerebellum, thalamus, and cerebrum tissues. The measurement results suggest that singly scattered, few scattered, and diffusely scattered photon paths can be distinguished in some of the samples investigated. The combined imaging modality yields additional spatial frequency phase information, which highlights paths having only a few scattering events. The combination of MMP and SFDI offers contrast mechanisms inaccessible by each modality used alone.

Analysis of malaria infection byproducts with Mueller matrix transmission ellipsometry

In this work, hemozoin, a microcrystalline byproduct of the malaria parasites was studied by transmission Mueller matrix ellipsometry. Measurement data was collected for different magnetic field orientations and as a function of the density of the hemozoin suspension. Our ellipsometric study demonstrates the magnetic alignment of the hemozoin crystals via the corresponding large linear birefringence and dichroism signals. These results reveal optical anisotropies of this material, which could be utilized for future optimization of detection schemes or optical instruments for diagnostic use.

Light scattering by media consisting of Maxwell 3-foci concave particles in the geometrical optics approximation

We study light scattering by non-spherical Maxwell particles and media consisting of them using computer simulations. The particle shapes are defined by a generalization of the concept 3-foci ellipses introduced by J. C. Maxwell. We modify them for the 3-D case by replacing the distances between the foci and current points on the ellipsoid surface by their logarithms. This makes it possible to describe 3-D ellipsoids that have partially concave surfaces. We carry out simulations within the framework of geometrical optics based on reflection and refraction of 108 rays and calculate phase curves of the nonzero elements of the Mueller matrix. This enables us to clarify the origin of the characteristics of the phase curves, i.e., which scattering order is responsible for the curve features. It is shown that equality M12 = M21 and M34 = –M43 that are valid for isolated particles are broken by the interactions with neighboring particles. It is also shown that the opposition effect of such particulate surfaces is mainly formed by components having one or more internal reflections within particles.

Correlation of image textures of a polarization feature parameter and the microstructures of liver fibrosis tissues

Mueller matrix imaging is emerging for the quantitative characterization of pathological microstructures and is especially sensitive to fibrous structures. Liver fibrosis is a characteristic of many types of chronic liver diseases. The clinical diagnosis of liver fibrosis requires time-consuming multiple staining processes that specifically target on fibrous structures. The staining proficiency of technicians and the subjective visualization of pathologists may bring inconsistency to clinical diagnosis. Mueller matrix imaging can reduce the multiple staining processes and provide quantitative diagnostic indicators to characterize liver fibrosis tissues. In this study, a fiber-sensitive polarization feature parameter (PFP) was derived through the forward sequential feature selection (SFS) and linear discriminant analysis (LDA) to target on the identification of fibrous structures. Then, the Pearson correlation coefficients and the statistical T-tests between the fiber-sensitive PFP image textures and the liver fibrosis tissues were calculated. The results show the gray level run length matrix (GLRLM)-based run entropy that measures the heterogeneity of the PFP image was most correlated to the changes of liver fibrosis tissues at four stages with a Pearson correlation of 0.6919. The results also indicate the highest Pearson correlation of 0.9996 was achieved through the linear regression predictions of the combination of the PFP image textures. This study demonstrates the potential of deriving a fiber-sensitive PFP to reduce the multiple staining process and provide textures-based quantitative diagnostic indicators for the staging of liver fibrosis.

Quasi-achromatic rhomb compensator: Mueller matrix analysis versus azimuthal angle

A quasi-achromatic rhomb compensator has been developed to address shortcomings of the bi-plate compensator in rotating compensator spectroscopic ellipsometry (SE) and consequently to improve the accuracy of such measurements over broad spectral ranges. The compensator implemented here is based on a three-reflection in-line design comparable to that put forth by Krasilov in 1963, but altered for greater simplicity. Our design consists of 30°-60°-90° and 60°-60°-60° fused silica prisms in physical contact that generate total first and third internal reflections from their interfaces to the ambient. The 30°-60°-90° prism also generates the second internal reflection via an aluminum coating on the longer side opposite the hypotenuse. Prior to implementing the compensator as the rotating element of a SE instrument, its performance has been characterized versus azimuthal angle over the photon energy range from 1.2 eV to 5.4 eV. For this purpose, the compensator was aligned on a rotatable mount and its complete Mueller matrix was measured at selected azimuthal angles. We present an analysis of ψ for the aluminum coating, which generates a compensator dichroic angle ψC deviating from the ideal value of 45° by values ranging from 0.3° to 1.2° with increasing photon energy. This analysis also predicts a (fused silica)/Al interface contribution to the retardance of ∼ 176° to ∼ 160°. In addition, we present an analysis of the fused silica stress-induced deviations of the measured Mueller matrices from their ideal forms, the latter based on a dichroic compensator oriented at different azimuthal angles. The results of these analyses are expressions for the Mueller matrix elements which must be applied as functions of angle in order to completely characterize the polarization modifying properties of the device in rotating compensator instrument configurations.

Discriminating between Absorption and Scattering Effects in Complex Turbid Media by Coupling Polarized Light Spectroscopy with the Mueller Matrix Concept

The separation of the combined effects of absorption and scattering in complex media is a major issue for better characterization and prediction of media properties. In this study, an approach coupling polarized light spectroscopy and the Mueller matrix concept were evaluated to address this issue. A set of 50 turbid liquid optical phantoms with different levels of scattering and absorption properties were made and measured at various orientations of polarizers and analyzers to obtain the 16 elements of the complete Mueller matrix in the VIS-NIR region. Partial least square (PLS) was performed to build calibration models from diffuse reflectance spectra in order to evaluate the potential of polarization spectroscopy through the elements of the Mueller matrix to predict physical and chemical parameters and hence, to discriminate scattering and absorption effects, respectively. In particular, it was demonstrated that absorption and scattering effects can be distinguished in the Rayleigh regime with linear and circular polarization from the M22 and M44 elements of the Mueller matrix, correspondingly.

Mueller Matrix Microscopy for In Vivo Scar Tissue Diagnostics and Treatment Evaluation.

Scars usually do not show strong contrast under standard skin examination relying on dermoscopes. They usually develop after skin injury when the body repairs the damaged tissue. In general, scars cause multiple types of distress such as movement restrictions, pain, itchiness and the psychological impact of the associated cosmetic disfigurement with no universally successful treatment option available at the moment. Scar treatment has significant economic impact as well. Mueller matrix polarimetry with integrated autofocus and automatic data registration can potentially improve scar assessment by the dermatologist and help to make the evaluation of the treatment outcome objective. Polarimetry can provide new physical parameters for an objective treatment evaluation. We show that Mueller matrix polarimetry can enable strong contrast for in vivo scar imaging. Additionally, our results indicate that the polarization stain images obtained form there could be a useful tool for dermatology. Furthermore, we demonstrate that polarimetry can be used to monitor wound healing, which may help prevent scarring altogether.

Evaluation of Scattering by Spacecrafts Using Characteristic Mode Theory Considering Ionosphere Faraday Effect

This article is concerned with developing a viable procedure to evaluate the scattering property of a satellite object. First, to deal with the uncertainty of attitudes of the object with respect to the direction of incidence, the characteristic mode theory is exploited, which is independent of the incident waves. The total scattered field is obtained by summing up the individual characteristic scattered fields with modal weighting coefficients. Second, the ionosphere Faraday effect that may significantly change the polarization behaviors is considered when the frequency is at L-band or below for a ground-based identifying radar. The ionosphere is taken as a sparse and weakly magnetized plasma, and the approximate Wentzel–Kramers–Brillouin method is adopted to calculate the propagations of two intrinsic modes through the ionosphere. The Stokes vector is assumed to be the measured quantities, and the Mueller matrix is employed to fully describe the polarized scattering process.

Evaluation of optical features of fibronectin fibrils by backscattering polarization imaging

Polarization imaging provides an effective and convenient approach for examining the structural and optical features of scattering media. The present study utilizes a backscattering polarization imaging system to evaluate and compare the polarization features of three different fibronectin (FN) samples: (1) fibronectin-free in phosphate-buffered saline (PBS) solution, (2) fibronectin protein (PFN), and (3) fibrillated fibronectin (FFN). It is shown that the three samples can be qualitatively discriminated via a simple naked-eye observation of the Mueller matrix imaging results. Furthermore, a more quantitative evaluation of the polarization properties of the three samples can be obtained from an inspection of the Mueller Matrix Transformation (MMT) parameters and Frequency Distribution Histogram (FDH) statistics for the pixel intensities of the Mueller matrix elements. The results show that the PFN and PBS samples have isotropic properties, while the FFN sample has anisotropic properties. Overall, the results confirm that the proposed backscattering polarization imaging system provides a feasible means of differentiating between different fibronectin-containing biological samples. It thus has significant potential for various biomedical diagnosis applications, including early-stage cancer detection.

Revealing the Intrinsic Chiroptical Activity in Chiral Metal-Halide Semiconductors.

The combination of chirality and semiconducting properties has enabled chiral metal-halide semiconductors (MHS) to be promising candidates for spin- and polarization-resolved optoelectronic devices. Although several chiral MHS with rich chemical and structural diversity have been reported lately, the macroscopic origin of chiroptical activity remains elusive. Here, combining spectroscopic measurements and Mueller matrix analysis, we discover that the previously reported "apparent" anisotropy factor measured from circular dichroism (CD) in chiral MHS thin films is not an intrinsic chiroptical property, but rather, arising from an interference between the film's linear birefringence (LB) and linear dichroism (LD). We verify the presence of LB and LD effects in both one-dimensional and zero-dimensional chiral MHS thin films. We establish spectroscopic methods to decouple the genuine CD from other spurious contributions, which allows a quantitative comparison of the intrinsic chiroptical activity across different chiral MHS. The relationship between the structure and the genuine chiroptical activity is then uncovered, which is well described by the chirality-induced spin-orbit coupling in the chiral structures. Our study unveils the macroscopic origin of chiroptical activity of chiral MHS and provides design principles for obtaining high anisotropic factors for future chiral optoelectronic applications.

Extracting Pure Circular Dichroism from Hierarchically Structured CdS Magic Cluster Films.

Chiroptically active, hierarchically structured materials are difficult to accurately characterize due to linear anisotropic contributions (i.e., linear dichroism (LD) and linear birefringence (LB)) and parasitic ellipticities that produce artifactual circular dichroism (CD) signals, in addition to chiral analyte contributions ranging from molecular-scale clusters to micron-sized assemblies. Recently, we have shown that CdS magic-sized clusters (MSC) can self-assemble into ordered films that have a hierarchical structure spanning seven orders of length-scale. These films have a strong CD response, but the chiral origins are obfuscated by the hierarchical architecture and LDLB contributions. Here, we derive and demonstrate a method for extracting the "pure" CD signal (CD generated by structural dissymmetry) from hierarchical MSC films and identified the chiral origin. The theory behind the method is derived using Mueller matrix and Stokes vector conventions and verified experimentally before being applied to hierarchical MSC and nanoparticle films with varying macroscopic orderings. Each film's extracted "true CD" shares a bisignate profile aligned with the exciton peak, indicating the assemblies adopt a chiral arrangement and form an exciton coupled system. Interestingly, the linearly aligned MSC film possesses one of the highest g-factors (0.05) among semiconducting nanostructures reported. Additionally, we find that films with similar electronic transition dipole alignment can possess greatly different g-factors, indicating chirality change rather than anisotropy is the cause of the difference in the CD signal. The difference in g-factor is controllable via film evaporation geometry. This study provides a simple means to measure "true" CD and presents an example of experimentally understanding chiroptic interactions in hierarchical nanostructures.

Characterization of vine, Vitis vinifera, leaves by Mueller polarimetric microscopy

In this work, we present the study of vine leaves, Vitis vinifera, performed by imaging polarimetry in the visible (at the wavelength of 530 nm). The purpose is to demonstrate, on a case study example, the high potential of imaging polarimetry and of polarimetric microscopy, in particular, for the characterization of vegetal tissues. The analysis of the Mueller matrix image of the sample provided by the polarimetric microscope by means of a matrix decomposition protocol yields a series of observables that are directly related to the fundamental physical properties that characterize the sample. Birefringence and dichroism are related to the structural properties of the medium and can be advantageously used as non-chemical, non-contact, non-destructive and non-toxic markers to highlight the presence of specific structures in the probed sample. Polarimetric images may also be used to enhance the contrast of the measured images. Specifically, we use the polarimetric properties and the depolarization indices to unveil the presence of structures such as raphides, some of them invisible under non-polarized light, and to investigate their properties.

Holistic and efficient calibration method for Mueller matrix imaging polarimeter with a high numerical aperture.

High-numerical aperture (N A>0.6) Mueller matrix imaging polarimeter (MMIP) (high-NA MMIP) is urgently needed for higher resolution. Usually, the working distance of high-NA MMIP is too short to perform in situ calibration by a usual reference sample, such as polarizer and retarder plates. The polarization effects of the substrate that attach the sample are never calibrated. So, the resolution and accuracy of the MMIP is hard to further promote. In this paper, a holistic and efficient calibration method is innovated for high-NA MMIP. Two film polarizers and a film retarder as well as a blank substrate are first adopted as the reference samples in calibration. Different from the conventional eigenvalue calibration method (ECM), the holistic calibration theory and process are established. All polarimetric errors arising from the devices, subsystems, and the substrate can be calibrated in one process. The normalized measurement error is less than 0.0024 for NA 0.95 MMIP, which is an order of magnitude lower than those of NA 0.1 and 0.2 MMIPs in publications. The excellent performance of calibrated high-NA MMIP is demonstrated by tissue polarimetry with higher resolution, accuracy, and more appropriate dynamic range.

Multistatic fiber-based system for measuring the Mueller matrix bidirectional reflectance distribution function.

Bidirectionality effects can be a significant confounding factor when measuring hyperspectral reflectance data. The bidirectional reflectance distribution function (BRDF) can effectively characterize the reflectivity of surfaces to correct remote sensing measurements. However, measuring BRDFs can be time-consuming, especially when collecting Mueller matrix BRDF (mmBRDF) measurements of a surface via conventional goniometric techniques. In this paper, we present a system for collecting mmBRDF measurements using static optical fiber detectors that sample the hemisphere surrounding an object. The entrance to each fiber contains a polarization state analyzer configuration, allowing for the simultaneous acquisition of the Stokes vector intensity components at many altitudinal and azimuthal viewing positions. We describe the setup, calibration, and data processing used for this system and present its performance as applied to mmBRDF measurements of a ground glass diffuser.

Particulate Mueller matrix polarimetry

Probing the suspended particles in natural water is significant for environmental monitoring and ecological research, such as early warning of water blooms and assessment of water quality. In this article, a conceptual Mueller matrix measurement method for individual suspended particles is proposed by simultaneously measuring the polarization states of the illuminating and scattered light. This so-called particulate Mueller matrix polarimetry (PMP) based on polarized light scattering at 120° is successfully achieved for the first time, and its performance and signal processing are revealed in detail. The physical properties and polarization features of suspended particles can be effectively obtained. Experiments with standard particles, different microplastics, and marine microalgae show that these particles can be effectively classified using PMP powered by the convolutional neural network. This presented laboratory system can serve as the proof-of-concept setup of new instrumentation for applications onboard or underwater.

Combined Jones and Mueller matrix method for the evaluation the optical rotation and circular dichroism in chiral medium

Optical activity and circular dichroism are the intrinsic properties of chiral medium. The control of these proprieties of a medium has drawn considerable attention due to the recent developments due to recent developments in the field of materials and the deeper understanding of light-matter interaction in chiral structures media. With the extensive use of optical polarimetric technic, the relationships between the parameters related to optical activity (optical rotation and circular dichroism) and the Mueller matrix elements have been derived. In this work, we begin with a presentation of a theoretical model for the determination of the Jones and the Mueller matrices, whose objective is to identify pairs of this Mueller matrix elements suitable for the measurement of the optical rotation (OR) and circular dichroism (CD) for incident waves normally to a chiral medium. Then, an experimental configuration to determine the Mueller matrix is described. These investigations have potential applications in medicine, biochemistry, defense and for the homeland security. Some of the merits of the method, such as, a simple optical set-up, high accuracy, low cost and easier operation.

Polarization clustering of biological structures with Mueller matrix parameters.

Mueller matrix imaging polarimetry (MMIP) is a promising technique for the characterization of biological tissues, including the classification of microstructures in pathological diagnosis. To expand the parameter space of Mueller matrix parameters, we propose new vector parameters (VPs) according to the Mueller matrix polar decomposition method. We measure invasive bladder cancer (IBC) with extensive necrosis and high-grade ductal carcinoma in situ (DCIS) with MMIP, and the regions of cancer cells and fibrotic stroma are classified with the VPs. Then the proposed and existing VPs are mapped on the Poincaré sphere with 3D visualization, and an indicator of spatial feature is defined based on the minimum enclosing sphere to evaluate the classification capability of the VPs. For both IBC and DCIS, the results show that the proposed VPs exhibit evident contrast between the regions of cancer cells and fibrotic stroma. This study broadens the fundamental Mueller matrix parameters and helps to improve the characterization ability of the MMIP technique.

Efficient Rigorous Coupled-Wave Analysis Simulation of Mueller Matrix Ellipsometry of Three-Dimensional Multilayer Nanostructures.

Mueller matrix ellipsometry (MME) is a powerful metrology tool for nanomanufacturing. The application of MME necessitates electromagnetic computations for inverse problems of metrology determination in both the conventional optimization process and the recent neutral network approach. In this study, we present an efficient, rigorous coupled-wave analysis (RCWA) simulation of multilayer nanostructures to quantify reflected waves, enabling the fast simulation of the corresponding Mueller matrix. Wave propagations in the component layers are characterized by local scattering matrices (s-matrices), which are efficiently computed and integrated into the global s-matrix of the structures to describe the optical responses. The performance of our work is demonstrated through three-dimensional (3D) multilayer nanohole structures in the practical case of industrial Muller matrix measurements of optical diffusers. Another case of plasmonic biosensing is also used to validate our work in simulating full optical responses. The results show significant numerical improvements for the examples, demonstrating the gain in using the RCWA method to address the metrological studies of multilayer nanodevices.

Backscattering Mueller Matrix polarimetry on whole brain specimens shows promise for minimally invasive mapping of microstructural orientation features

Understanding microscale physiology and microstructural cellular features of the brain is key to understanding mechanisms of neurodegenerative diseases and injury, as well as prominent changes undergone in development and aging. Non-invasive imaging modalities sensitive to the microscale, especially diffusion magnetic resonance imaging (dMRI), are promising for mapping of cellular microstructure of brain tissues; however, there is a need for robust validation techniques to verify and improve the biological accuracy of information derived. Recent advances in dMRI have moved toward probing of the more complex grey matter architecture, challenging current validation techniques, which are largely based on ex vivo staining and microscopy focusing on white matter. Polarized light imaging (PLI) has been shown to be successful for high resolution, direct, microstructural imaging and has been applied to dMRI validation with clear advantages over staining and microscopy techniques. Conventionally, PLI is applied to thin, sectioned samples in transmission mode, but PLI has also been extended to operate in reflectance mode to bridge the gap toward in vivo measurements of the brain. In this report we investigate the use of backscattering Mueller Matrix polarimetry to characterize the microstructural content of intact ferret brain specimens. The results show that backscattering polarimetry can probe white matter fiber coherence and fiber orientation, and show promise for probing grey matter microstructure. Ultimately, this motivates further study to fully understand how best to implement backscattering polarimetry for in vivo microstructural imaging of the brain.

Underwater wireless optical communication employing polarization multiplexing modulation and photon counting detection.

Wireless optical communication is a crucial direction for improving the data transmission rate in underwater environments. In order to improve the communication performance over the water channel, this paper studies underwater wireless optical communication (UWOC) employing polarization multiplexing modulation and photon counting detection. The improvements in bit error rates and communication capacities are analyzed theoretically by constructing the communication model of polarization multiplexing modulation UWOC based on photon counting. Under specific conditions, the polarization maintenance characteristics of photons over water channels are demonstrated by measuring the Mueller matrix, the fidelity of quantum states, depolarization ratio, and calculating the ratios of ballistic photons. Based on these results, by designing and developing the experimental system of UWOC with the polarization multiplexing modulation and photon counting detection, the data transmission rates of 14.58Mbps and 7.29Mbps are realized over a water channel of 92 m by using polarization on-off keying multiplexing modulation and polarization 2-pulse-position multiplexing modulation, respectively.