Mueller Matrix Parameters Research Articles

Mechanical stability of polarization signatures in biological tissue characterization.

Mueller matrix imaging polarimetry (MMIP) is a promising technique for investigating structural abnormalities in pathological diagnosis. The characterization stability of polarization signatures, described by Mueller matrix parameters (MMPs), correlates with the mechanical state of the biological medium. In this study, we developed an MMIP system capable of applying quantitative forces to samples and measuring the resulting polarization signatures. Mechanical stretching experiments were conducted on a mimicking phantom and a tissue sample at different force scales. We analyzed the textural features and data distribution of MMP images and evaluated the force effect on the characterization of MMPs using the structural similarity index. The results demonstrate that changes in the mechanical microenvironment (CMM) can cause textural fluctuations in MMP images, interfering with the stability of polarization signatures. Specifically, parameters of anisotropic orientation, retardance, and optical rotation are the most sensitive to CMM, inducing a dramatic change in the overall image texture, while other parameters (e.g., polarization, diattenuation, and depolarization) exhibit locality in their response to CMM. For some MMPs, CMM can enhance regional textural contrasts. This study elucidates the mechanical stability of polarization signatures in biological tissue characterization and provides a valuable reference for further research toward minimizing CMM influence.

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.

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.

A quantitative technique to analyze and evaluate microstructures of skin hair follicles based on mueller matrix polarimetry

In this study, we propose a quantitative technique to analyze and evaluate microstructures of skin hair follicles based on Mueller Matrix transmission microscopy. We measure the Mueller matrix polar decomposition (MMPD) parameter images to reveal the characteristic linear birefringence distribution induced by hair follicles in mouse skin tissue samples. The results indicate that the Mueller matrix-derived parameters can be used to reveal the location and structural integrity of hair follicles. For accurate hair follicle location identification and quantitative structural evaluations, we use the image segmentation method, sliding window algorithm, and image texture analysis methods together to process the Mueller matrix-derived images. It is demonstrated that the hair follicle regions can be more accurately recognized, and their locations can be precisely identified based on the Mueller matrix-derived texture parameters. Moreover, comparisons between manual size measurement and polarimetric calculation results confirm that the Mueller matrix parameters have good performance for follicle size estimation. The results shown in this study suggest that the technique based on Mueller matrix microscopy can realize automatically hair follicle identification, detection, and quantitative evaluation. It has great potential in skin structure-related studies and clinical dermatological applications.

Front Cover

Affected by the scattering microenvironment within biological tissues, the emitted polarized light forms a specific two‐dimensional distribution pattern on the imaging focal plane. In the polarization domain, the pursuit of high imaging magnification does not necessarily lead to preponderant image contrast, and may even produce deteriorating results. This study investigates the spatial scale stability of Mueller matrix parameters (MMPs) and analyzes the nonlinear effect of imaging magnification on the MMPs image contrast.Further details can be found in the article by Yongtai Chen, Jinkui Chu, William C. Tang, Ran Zhang, Mingyu Zhao, and Benda Xin (e202100269) image

Angular-Based Mueller Matrix Polarimetry Parameters for Subwavelength Pore Size Differentiation

Mueller matrix polarimetry is exploited to find a potential polarization feature sensitive to subwavelength pore size variation in porous alumina samples. After careful analysis using standard machine learning methods, it is observed that existing Mueller matrix decomposition methods and parameters are insufficient to distinguish areas with different pore sizes. Thus, a new angular-based Mueller matrix polarimetry parameter capable of linearly separating areas with varying pore sizes is proposed. Such an angular-based parameter is novel because it is based on angular parameters, it utilizes multi-angle measurements, and it extracts physical information independent of existing decomposition methods or parameters. Hopefully this work should inspire future research on the angular parameters in Mueller matrix polarimetry and their relationships to microstructure information.

Distinguishing tissue structures via polarization staining images based on different combinations of Mueller matrix polar decomposition parameters

Mueller matrix polarimetry is gaining wide attention in the field of biophotonics due to its great potential in detecting the microstructures and optical properties of tissue samples label-freely. Individual Mueller matrix derived parameters were often used to characterize certain kind of tissue structure. However, it is found that the individual Mueller matrix parameters only contain partial structural information. Thus, it is difficult to accurately and comprehensively indentify different structures using a single polarization parameter image. Here we introduce an image fusion method based on color spaces to combine different Mueller matrix derived parameters to provide multi-dimensional structural information pixel by pixel in a single polarization staining image. The results of rat back skin tissue specimens indicate that different fibrous structures can be easily distinguished using the polarization staining image. Then, in order to quantitatively analyze the texture characteristics of the polarization staining images for different structures, the Tamura image processing and the gray level co-occurrence matrix (GLCM) methods are adopted to provide various evaluation indices after the images segmentations. The experimental results confirm that the information provided by the polarization staining images based on different Mueller matrix derived parameters can be used for accurate tissue structures discrimination. Combining with machine recognition systems and fast developing artificial intelligence techniques, the strategy proposed in this study can be very helpful for precise abnormal tissues detection and pathological diagnoses.

Study of the spatial scale stability of Mueller matrix parameters for textural characterization of biological tissues.

Mueller matrix imaging polarimetry (MMIP) is a promising technique for the textural characterization of biological tissue structures. To reveal the influence of imaging magnification on the robustness of Mueller matrix parameters (MMPs), the spatial scale stability of MMPs was studied. We established a new MMIP detector and derived the mathematical model of the spatial scale stability of MMPs. The biological tissues with well-defined structural components were imaged under different magnifications. Then, we compared and analyzed the textural features of the MMPs in the resulting images. The experimental results match the predictions of the mathematical model in these aspects: (a) magnification exhibits a strong nonlinear effect on the textural contrasts of MMPs images; (b) higher magnification does not necessarily lead to superior contrast for textural characterization; and (c) for different biological tissues, MMPs contrasts can be optimized differently, with some showing superior results. This study provides a reference for the experimental design and operation of the MMIP technique and is helpful for improving the characterization ability of MMPs.

Mueller Matrix-Based Approach for the Ex Vivo Detection of Riboflavin-Treated Transparent Biotissue

Corneal collagen cross-linking is an established procedure for the treatment of certain eye diseases which is applied to enhance the mechanical stability of such biotissue without deteriorating its functionality. However, being transparent, the optical analysis of the outcome of such treatments is cumbersome and relies on relatively expensive experimental equipment. We aim to apply the Mueller matrix polarimetry for the detection of photo-induced collagen cross-linking in transparent biotissue after treatment with riboflavin and UV irradiation. A simple Mueller matrix polarimetry setup could provide a fast and non-invasive analysis of transparent media to sensitively detect small photo-induced cross-linking effects in biotissue. We demonstrated the current capabilities of the approach on non-planar porcine cornea samples ex vivo. We reported the distinction between untreated and riboflavin-treated samples. The differences observed were correlated with the variation of certain Mueller matrix elements and parameters derived from the decomposition. The measurement data show variation in the cross-linked and non-cross-linked samples, although the effect of the UV treatment on the riboflavin-treated samples was not at the same level of significance yet and needs further investigation. The Mueller matrix measurement represents a promising approach for the detection of the effects of corneal collagen cross-linking. Further studies with a larger sample number are required to validate this approach. In the future, this could enable the reliable and non-invasive detection of photo-induced effects in biotissue and open the possibility for in vivo application, e.g., in eye disease treatment or the detection of scar collagen development.

Analysis of experimental errors in Mueller matrix channeled polarimeters.

This work analyzes the effect of experimental errors and measurement noise on Mueller matrix channeled spectropolarimeters. The main advantage of this type of polarimeter is the independence on temporal resolution, as it can be used as a snapshot polarimeter. The simulation of the polarimeters with experimental errors and two published extraction methods of the sample Mueller matrix are also presented. The Mueller matrix channeled spectropolarimeter (MMCS) setup consists of a mirrored Stokes channeled spectropolarimeter (SCS) as the polarization states generator (PSG) and a SCS as the polarization states analyzer (PSA). The SCS setup comprises two thick birefringent retarders followed by a horizontal linear polarizer. The effects of the thickness ratio of the retarders, the global retardance factor, retardance errors, axes alignment errors, and additive Gaussian noise are further studied to optimize the MMCS setups. In this work, we do not include a calibration procedure to improve the measured Mueller matrix parameters, but we study the sensitivity of the polarimeter to different configurations and error sources.

Probing variations of fibrous structures during the development of breast ductal carcinoma tissues via Mueller matrix imaging.

Recently, we developed a label-free method to probe the microstructural information and optical properties of unstained thin tissue slices based on microscopic Mueller matrix imaging technique. In this paper, we take the microscopic Mueller matrix images of human breast ductal carcinoma tissue samples at different pathological stages, and then calculate and analyze their retardance-related Mueller matrix-derived parameters. To reveal the microstructural features more quantitatively and precisely, we propose a new method based on first-order statistical properties of image to transform the 2D images of Mueller matrix parameters into several statistical feature vectors. We evaluate each statistical feature vector by corresponding classification characteristic value extracted from the statistical features of Mueller matrix parameters images of healthy breast duct tissue samples. The experimental results indicate that these statistical feature vectors of Mueller matrix derived parameters may become powerful tools to quantitatively characterize breast ductal carcinoma tissue samples at different pathological stages. It has the potential to facilitate automating the staging process of breast ductal carcinoma tissue, resulting in the improvement of diagnostic efficiency.

Mueller matrix-based calculating model for extracting polarization parameters in the analysis system for sea surface oil-spill

As a new analytical method to identify oil spill on the sea, the main effect of polarization measurement based on Mueller matrix is extracting surface feature of oil film, so that the polarization information of the target can be enriched. In this paper, the Mueller matrix and the Jones matrix have been used to establish a physical model, combined with the Fresnel formula, to obtain the Mueller matrix parameters and calculate the optical constant of oil film. To detect oil film faster and more accurately, the relationship between refractive index, incident angle and the degree of polarization (DoP) was established by the intermediate quantity (amplitude ratio P). The characteristics of DoP curve were discussed to distinguish between water and oil film. The experimental results indicate that the research method has great value in the identification and evaluation of marine oil spills, and the data is accurate and reliable.

Optimal Measurement Matrix of Partial Polarimeter for Measuring Ellipsometric Parameters With Eight Intensity Measurements

We demonstrate that the ellipsometric parameters of the isotropic samples can be measured by a partial polarimeter with only eight intensity measurements. Under the Gaussian and Poisson noises, we propose the optimal measurement matrices for the polarization state generator and the polarization state analyzer that minimize the total estimation variance of eight nonzero Mueller elements related to the ellipsometric parameters. In addition, since considering only four of the eight elements, the estimation variance can be further reduced, and we also introduce two proper criteria to find the optimal measurement matrices that robustly minimize the total estimation variance for these four Mueller elements. Compared with the existing measurement matrices based on 16 intensity measurements, our proposed matrices can effectively decrease the total estimation variance and, thus, improve the measurement precision of the Mueller matrix and ellipsometric parameters with only eight measurements. Furthermore, the proposed optimal measurement matrices do not depend on the Mueller elements of samples and thus not on the ellipsometric measurements.

Coherency and differential Mueller matrices for polarizing media

The elements of the coherency matrix give the strength of the components of a Mueller matrix in the coherency basis. The Z-matrix (called the polarization-coupling matrix or state-generating matrix) represents a partial sum of the coherency expansion. For transmission through a deterministic medium, the coherency elements can be used directly as generators to calculate the development of polarization upon propagation. The commutation properties of the coherency elements are investigated. New matrices that we call the W-matrix and the X-matrix, both different representations of the Z-matrix in a Jones basis, are introduced. The W-matrix controls the transformation of the Jones vector and also the covariance matrix. The product of the X-matrix with its complex conjugate gives the matrix representation of the Mueller matrix in the Jones basis. The development of Mueller matrix and coherency matrix elements upon propagation through some examples of a uniform medium is investigated. It is shown that the coherency matrix is more easily interpreted than the Mueller matrix. Analytic expressions are presented to calculate the elementary polarization properties from coherency matrix elements or Mueller matrix parameters.

Mueller polarimetric imaging for characterizing the collagen microstructures of breast cancer tissues in different genotypes

Abstract Mueller polarimetric imaging has been proven a valid method for detecting tissue in biomedical field. In the present study, we applied the Mueller matrix microscopy to characterize the microstructures of breast cancer tissues in different genotypes. The experimental results demonstrated that Mueller matrix parameters were effective in distinguishing the genotypes of breast cancer, especially for triple-negative type. Then, we conducted quantitative analysis of Mueller matrix and immunohistochemistry (IHC) experiments. On that basis, we verified the relationship between collagen structures and polarization properties as well as the remodeling of collagen structures in breast cancer, which could provide new evidence for using high invasiveness and metastatic dissemination as triple-negative breast cancer. In comparison with traditional methods, Mueller polarimetry is independent of complex tumor marks. Besides, it is quick, sensitive and non-stained. Thus, it has a potential in the application for clinical diagnosis and is expected as a new method for researching the pathological process of breast cancer.

Comparative study of the imaging contrasts of Mueller matrix derived parameters between transmission and backscattering polarimetry.

Mueller matrix polarimetry is a potentially powerful tool for biomedical diagnosis. Recently, the transmission Mueller matrix microscope and backscattering Mueller matrix endoscope were developed and applied to various pathological samples. However, a comparative study of imaging contrasts of Mueller matrix derived parameters between transmission and backscattering measurements is still needed to help decide which information obtained from transmission Mueller matrix microscope can be directly applied to in vivo Mueller matrix imaging. Here, to compare the imaging contrasts of Mueller matrix derived parameters between transmission and backscattering polarimetry, we measure porcine liver tissue samples and human breast carcinoma tissue specimens. The experiments and corresponding Monte Carlo stimulation results demonstrate that the backscattering and transmission retardance-related Mueller matrix parameters have very similar contrasts to characterize the anisotropic and isotropic structures of pathological tissues, meaning that the conclusions made from Mueller matrix microscopic imaging based on retardance can also be helpful to guide the in situ backscattering Mueller matrix polarimetric diagnosis. However, the values and contrasts of depolarization-related Mueller matrix parameters have some differences between transmission and backscattering polarimetry.

A quantitative and non-contact technique to characterise microstructural variations of skin tissues during photo-damaging process based on Mueller matrix polarimetry

Skin tissue consists of collagen and elastic fibres, which are highly susceptible to damage when exposed to ultraviolet radiation (UVR), leading to skin aging and cancer. However, a lack of non-invasive detection methods makes determining the degree of UVR damage to skin in real time difficult. As one of the fundamental features of light, polarization can be used to develop imaging techniques capable of providing structural information about tissues. In particular, Mueller matrix polarimetry is suitable for detecting changes in collagen and elastic fibres. Here, we demonstrate a novel, quantitative, non-contact and in situ technique based on Mueller matrix polarimetry for monitoring the microstructural changes of skin tissues during UVR-induced photo-damaging. We measured the Mueller matrices of nude mouse skin samples, then analysed the transformed parameters to characterise microstructural changes during the skin photo-damaging and self-repairing processes. Comparisons between samples with and without the application of a sunscreen showed that the Mueller matrix-derived parameters are potential indicators for fibrous microstructure in skin tissues. Histological examination and Monte Carlo simulations confirmed the relationship between the Mueller matrix parameters and changes to fibrous structures. This technique paves the way for non-contact evaluation of skin structure in cosmetics and dermatological health.

Parameterization of the deterministic Mueller matrix: application to a uniform medium.

The extraction of the elementary polarization properties of a uniform medium from a deterministic Mueller matrix has been considered by several researchers. The relationship between a parameterization of the deterministic Mueller matrix that we described recently and the elementary polarization properties for a uniform medium is investigated. The elementary polarization properties can be calculated exactly from the Mueller matrix parameters. Simplified forms for the Mueller matrix parameters in terms of the elementary polarization properties are presented. The effect on the Mueller matrix of varying the ratio of the total diattenuation to the total retardance is investigated. Approximate forms for the elementary polarization properties in terms of the Mueller matrix parameters, valid for weak optical media, are given.

Characterizing the Effects of Washing by Different Detergents on the Wavelength-Scale Microstructures of Silk Samples Using Mueller Matrix Polarimetry.

Silk fibers suffer from microstructural changes due to various external environmental conditions including daily washings. In this paper, we take the backscattering Mueller matrix images of silk samples for non-destructive and real-time quantitative characterization of the wavelength-scale microstructure and examination of the effects of washing by different detergents. The 2D images of the 16 Mueller matrix elements are reduced to the frequency distribution histograms (FDHs) whose central moments reveal the dominant structural features of the silk fibers. A group of new parameters are also proposed to characterize the wavelength-scale microstructural changes of the silk samples during the washing processes. Monte Carlo (MC) simulations are carried out to better understand how the Mueller matrix parameters are related to the wavelength-scale microstructure of silk fibers. The good agreement between experiments and simulations indicates that the Mueller matrix polarimetry and FDH based parameters can be used to quantitatively detect the wavelength-scale microstructural features of silk fibers. Mueller matrix polarimetry may be used as a powerful tool for non-destructive and in situ characterization of the wavelength-scale microstructures of silk based materials.

Mueller matrix microscope: a quantitative tool to facilitate detections and fibrosis scorings of liver cirrhosis and cancer tissues.

Today the increasing cancer incidence rate is becoming one of the biggest threats to human health.Among all types of cancers, liver cancer ranks in the top five in both frequency and mortality rate all over the world. During the development of liver cancer, fibrosis often evolves as part of a healing process in response to liver damage, resulting in cirrhosis of liver tissues. In a previous study, we applied the Mueller matrix microscope to pathological liver tissue samples and found that both the Mueller matrix polar decomposition (MMPD) and Mueller matrix transformation (MMT) parameters are closely related to the fibrous microstructures. In this paper,we take this one step further to quantitatively facilitate the fibrosis detections and scorings of pathological liver tissue samples in different stages from cirrhosis to cancer using the Mueller matrix microscope. The experimental results of MMPD and MMT parameters for the fibrotic liver tissue samples in different stages are measured and analyzed. We also conduct Monte Carlo simulations based on the sphere birefringence model to examine in detail the influence of structural changes in different fibrosis stages on the imaging parameters. Both the experimental and simulated results indicate that the polarized light microscope and transformed Mueller matrix parameter scan provide additional quantitative information helpful for fibrosis detections and scorings of liver cirrhosis and cancers. Therefore, the polarized light microscope and transformed Mueller matrix parameters have a good application prospect in liver cancer diagnosis.