Stokes-Mueller Polarimetry Research Articles

Studies of anisotropic polarization in graphene oxide doped in PVA

We have observed and measured the optical anisotropy of graphene oxide (GO) in polyvinyl alcohol (PVA) using Stokes-Mueller Polarimetry (SMP). We found that it depends on the films with varying weight percent of GO in PVA. Analysis of polarized light transmitted through the ordered microstructure of GO in PVA reveals the anisotropic behavior due to its preferential alignment. The complex refractive index analysis of GO-PVA films complements the results of SMP.

Unified Stokes-Mueller polarimetry for multi-photon processes at varying wavelengths.

Existing polarimetry, mainly focusing on harmonic generations, overlooks the differences in retardance (DRs) caused by illuminations with different wavelengths in nonlinear processes, consequently falling short in accuracy beyond frequency doubling. In this Letter, with DRs considered, we propose a universal nonlinear Stokes-Mueller (NSM) polarimetry design involving illuminations with different wavelengths. Then, we optimize the NSM measurement model, applied to sum-frequency generation (SFG) and difference frequency generation. To demonstrate the necessity of consideration of DRs, the processes of polarization measurement for SFG are simulated, where the condition number decreases by 51.2%, and the root mean square error of the nonlinear Mueller matrix decreases by 20.48%.

Characterization and classification of ductal carcinoma tissue using four channel based stokes-mueller polarimetry and machine learning

Interaction of polarized light with healthy and abnormal regions of tissue reveals structural information associated with its pathological condition. Even a slight variation in structural alignment can induce a change in polarization property, which can play a crucial role in the early detection of abnormal tissue morphology. We propose a transmission-based Stokes-Mueller microscope for quantitative analysis of the microstructural properties of the tissue specimen. The Stokes-Mueller based polarization microscopy provides significant structural information of tissue through various polarization parameters such as degree of polarization (DOP), degree of linear polarization (DOLP), and degree of circular polarization (DOCP), anisotropy (r) and Mueller decomposition parameters such as diattenuation, retardance and depolarization. Further, by applying a suitable image processing technique such as Machine learning (ML) output images were analysed effectively. The support vector machine image classification model achieved 95.78% validation accuracy and 94.81% testing accuracy with polarization parameter dataset. The study's findings demonstrate the potential of Stokes-Mueller polarimetry in tissue characterization and diagnosis, providing a valuable tool for biomedical applications.

Stokes–Mueller polarization-based analysis of model SARS-CoV-2 virions

Understanding the virology of the coronavirus at the structural level has gained utmost importance to overcome the constant and long-term health complications induced by them. In this work, the light scattering properties of SARS-CoV-2 of size 140 nm were simulated by using discrete dipole approximation (DDA) for two incident wavelengths 200 nm and 350 nm, respectively. Three different 3-dimensional (3D) models of SARS-CoV-2 corresponding to 15, 20, and 40 numbers of spike proteins on the viral capsid surface were constructed as target geometries for the DDA calculations. These models were assessed by employing Stokes–Mueller polarimetry to obtain individual polarization properties such as degree of polarization (DOP), degree of linear polarization (DOLP), and degree of circular polarization (DOCP). Irrespective of its spike numbers, all the coronavirus models were found to display higher DOP and DOCP values and negligibly small DOLP values for circularly polarized incident light, indicating the presence of chiral structures. On the other hand, the lack of understanding about the dependence of the Mueller matrix on its microstructural properties was overcome by transforming 16 Mueller elements into sub-matrices with specific structural and physical properties using Lu–Chipman-based Mueller matrix polar decomposition method. The obtained properties such as retardance, diattenuation, and depolarization were used for investigating the composition and microstructural information. The approach presented in this work has the potential to understand the virology of the coronavirus at the structural level and, therefore, will be beneficial in developing effective detection strategies by exploiting their characteristic electromagnetic scattering signatures.

Study of a bi-axial (KTP) crystal using double Stokes–Mueller polarimetry

In this paper, we report the significance of the double Stokes–Mueller polarimetry (DSMP) technique, to characterize a large size ([Formula: see text][Formula: see text]mm) Potassium titanyl phosphate (KTP) crystal. The crystal undergoes second harmonic generation with type II phase matching. The study of standard KTP crystal using the DSMP technique helps to validate the efficiency of this technique. We were able to extract the crystal’s double Mueller matrix, relative contribution of the susceptibility tensor components, the phase difference between the susceptibility tensor components, etc. We could determine the crystal axes orientation using this optical technique, which was not possible through a single crystal X-Ray diffraction technique for such a large size crystal for which both optic axes and crystallographic axes are the same. Axes direction determined from polarization microscope measurements and Laue diffraction measurements on KTP crystal is compared with those obtained from DSMP measurements.

Optimal nonlinear Stokes-Mueller polarimetry for multi-photon processes.

In this Letter, we present an optimization model for nonlinear Stokes-Mueller polarimetry (SMP) to improve the precision in estimating the nonlinear Mueller matrix (MM) for two- and three-photon processes. Although nonlinear polarimeters can measure the polarization properties of multi-photon processes or materials, existing methods are suboptimal, leading to low measurement precision. Based on the model and its solution, we have designed a new measurement strategy to substantially reduce the estimation variance of nonlinear MM coefficients by approximately 58.2% for second-harmonic generation polarimetry and 78.7% for third-harmonic generation polarimetry. The model and measurement method can be directly applied to multi-photon processes to improve the precision of SMP.

Characterization of healthy and cancerous human skin tissue utilizing Stokes–Mueller​ polarimetry technique

Characterizing polarization of skin pathologies is still an interested issue for the dermatology community. In a previous study, the present group proposed a Stokes–Muellermatrix polarimetry for differentiating between squamous cell carcinoma tissue and normal healthy tissue in mice. The present study extends our method to the detection of squamous cell carcinoma, basal cell carcinoma and melanoma skin cancer in humans. Using the proposed method, the orientation angle of linear birefringence (α), phase retardance (β), optical rotation angle of circular birefringence (γ), orientation angle of linear dichroism (θd), linear dichroism (D), circular dichroism (R), degrees of linear depolarization (e1 and e2), degree of circular depolarization (e3), and depolarization index (Δ) are extracted for 72 slices of 12 squamous cell carcinoma samples, 72 slices of 12 basal cell carcinoma samples, 18 slices of 3 melanoma skin cancer samples, and 36 slices of 6 healthy samples. The experimental results show that the cancerous tissue exhibits lower phase retardance (β) and linear dichroism (D) than healthy skin tissue. Overall, the proposed method provides a useful insight into the characterization optical properties of human skin cancer by Stokes–Mueller matrix polarimetry.

Dual- and single-shot susceptibility ratio measurements with circular polarizations in second-harmonic generation microscopy.

Polarization-resolved second-harmonic generation (P-SHG) microscopy is a technique capable of characterizing nonlinear optical properties of noncentrosymmetric biomaterials by extracting the nonlinear susceptibility tensor components ratio , with z-axis parallel and x-axis perpendicular to the C6 symmetry axis of molecular fiber, such as a myofibril or a collagen fiber. In this paper, we present two P-SHG techniques based on incoming and outgoing circular polarization states for a fast extraction of : A dual-shot configuration where the SHG circular anisotropy generated using incident right- and left-handed circularly-polarized light is measured; and a single-shot configuration for which the SHG circular anisotropy is measured using only one incident circular polarization state. These techniques are used to extract the of myosin fibrils in the body wall muscles of Drosophila melanogaster larva. The results are in good agreement with values obtained from the double Stokes-Mueller polarimetry. The dual- and single-shot circular anisotropy measurements can be used for fast imaging that is independent of the in-plane orientation of the sample. They can be used for imaging of contracting muscles, or for high throughput imaging of large sample areas.

Complex Susceptibilities and Chiroptical Effects of Collagen Measured with Polarimetric Second-Harmonic Generation Microscopy

Nonlinear optical properties of collagen type-I are investigated in thin tissue sections of pig tendon as a research model using a complete polarimetric second-harmonic generation (P-SHG) microscopy technique called double Stokes-Mueller polarimetry (DSMP). Three complex-valued molecular susceptibility tensor component ratios are extracted. A significant retardance is observed between the chiral susceptibility component and the achiral components, while the achiral components appear to be in phase with each other. The DSMP formalism and microscopy measurements are further used to explain and experimentally validate the conditions required for SHG circular dichroism (SHG-CD) of collagen to occur. The SHG-CD can be observed with the microscope when: (i) the chiral second-order susceptibility tensor component has a non-zero value, (ii) a phase retardance is present between the chiral and achiral components of the second-order susceptibility tensor and (iii) the collagen fibres are tilted out of the image plane. Both positive and negative areas of SHG-CD are observed in microscopy images, which relates to the anti-parallel arrangement of collagen fibres in different fascicles of the tendon. The theoretical formalism and experimental validation of DSMP imaging technique opens new opportunities for ultrastructural characterisation of chiral molecules, in particular collagen, and provides basis for the interpretation of SHG-CD signals. The nonlinear imaging of chiroptical parameters offers new possibilities to further improve the diagnostic sensitivity and/or specificity of nonlinear label-free histopathology.

Polarization-resolved Stokes-Mueller imaging: a review of technology and applications.

Polarization microscopy, a powerful optical tool to study anisotropic properties of biomolecules, provides better microstructural information of a sample as compared with conventional optical microscopic techniques. The measurement and analysis of polarization states of light can be performed using both Jones matrix as well as Stokes algebra. Further, the details of optical properties of specimen are characterized by Mueller matrix. However, the application of Jones calculus is limited to perfectly polarized light, but Stokes-Mueller polarimetry is emerging as a promising tool for tissue imaging due to its application irrespective of polarization state of the light. In this review article, we explain the development of Stokes-Mueller formalism in context of linear optics. Furthermore, application of Mueller matrix decomposition (MMD) method to derive sample properties is demonstrated in several bio-medical studies.

Three-dimensional nonlinear Stokes–Mueller polarimetry

The formalism is developed for a tree-dimensional ($3D$) nonlinear Stokes-Mueller polarimetry. The expressions are derived for the generalized $3D$ linear and nonlinear Stokes vectors, and the corresponding nonlinear Mueller matrix. The coherency-like Hermitian square matrix $X$ of susceptibilities is introduced, which is derived from the nonlinear Mueller matrix. The $X$-matrix is characterized by the index of depolarization. Several decompositions of the $X$-matrix are introduced. The $3D$ nonlinear Stokes-Mueller polarimetry formalism can be applied for three and higher wave mixing processes. The $3D$ polarimetric measurements can be used for structural investigations of materials, including heterogeneous biological structures. The $3D$ polarimetry is applicable for nonlinear microscopy with high numerical aperture objectives.

Monte Carlo simulation of polarization-sensitive second-harmonic generation and propagation in biological tissue.

Polarization-sensitive second harmonic generation (p-SHG) is a nonlinear optical microscopy technique that has shown great promise in biomedicine, such as in detecting changes in the collagen ultrastructure of the tumor microenvironment. However, the complex nature of light-tissue interactions and the heterogeneity of biological samples pose challenges in creating an analytical and experimental quantification platform for tissue characterization via p-SHG. We present a Monte Carlo (MC) p-SHG simulation model based on double Stokes-Mueller polarimetry for the investigation of nonlinear light-tissue interaction. The MC model predictions are compared with experimental measurements of second-order nonlinear susceptibility component ratio and degree of polarization (DOP) in rat-tail collagen. The observed trends in the behavior of these parameters as a function of tissue thickness, as well as the overall extent of agreement between MC and experimental results, are discussed. High sensitivities of the susceptibility ratio and DOP are observed for the varying tissue thickness on the incoming fundamental light propagation pathway.

Optical characterization of porcine articular cartilage using a polarimetry technique with differential Mueller matrix formulism.

A method is proposed for characterizing the optical properties of articular cartilage sliced from a pig's thighbone using a Stokes-Mueller polarimetry technique. The principal axis angle, phase retardance, optical rotation angle, circular diattenuation, diattenuation axis angle, linear diattenuation, and depolarization index properties of the cartilage sample are all decoupled in the proposed analytical model. Consequently, the accuracy and robustness of the extracted results are improved. The glucose concentration, collagen distribution, and scattering properties of samples from various depths of the articular cartilage are systematically explored via an inspection of the related parameters. The results show that the glucose concentration and scattering effect are both enhanced in the superficial region of the cartilage. By contrast, the collagen density increases with an increasing sample depth.

Full-Field Stokes-Mueller Matrix Imaging Polarimetry System Based on Electro-Optical Modulators

A new full-field Stokes–Mueller polarimetry system with no moving parts is proposed for imaging the Mueller matrix of optical samples. The polarization state generator (PSG) of the proposed system contains two electro-optical (EO) modulators to generate six polarization states of the input light, while the polarization state analyzer (PSA) contains two further EO modulators to produce an additional eight polarization states of the light emerging from the sample. A total of 48 polarization states of the output light are thus captured at the detector (a charge couple device (CCD) camera). The feasibility of the proposed system is demonstrated by imaging the Mueller matrixes of blank air and a quarter-wave plate with the fast axis set to the horizontal direction, respectively. It is shown that the proposed system is capable of measuring the Mueller matrix of the two samples with a resolution of 10−2 . In general, the results show that the system provides a convenient and reliable means of imaging the Mueller matrix of optical samples.

Characterization of heterogeneous media using nonlinear Stokes–Mueller polarimetry

The nonlinear optical properties of heterogeneous media are described by an algebraic decomposition of the correlation matrix X(n) of the nth-order nonlinear susceptibility tensor values, obtained from the generalized nonlinear Stokes–Mueller polarimetry measurements. The correlation matrix X(n) forms a square Hermitian semidefinite positive matrix, which can be further decomposed into separate components using projection matrices and calculating eigenvalues and the corresponding eigenvectors for pure states of the heterogeneous media. Up to eight pure states can be deduced for the sum-frequency generation process and up to sixteen states can be presented for a four-wave mixing process. The obtained eigenvalues are used to define the entropy characterizing a heterogeneous media. Filtering and maximum-likelihood estimation approaches are presented to determine the physically realizable values of the nonlinear susceptibility from the X(n) matrix that is obtained by the Stokes–Mueller polarimetry experiments. The Cholesky decomposition is employed for the maximum-likelihood estimation of the correlation matrix X(n). The structural characterization can be used, for example, in nonlinear microscopy for determining the ultrastructure organization of heterogeneous biological samples.