Mueller Matrix Formalism Research Articles

Demonstration of the Optical Isotropy of TiO2 Thin Films Prepared by the Sol-Gel Method.

Titanium dioxide (TiO2) thin films prepared by the sol-gel technique have been shown to be optically isotropic and, unlike the films obtained by competitive methods, do not exhibit measurable birefringence. A series of submicrometer-thin titanium dioxide films were prepared using the sol-gel technique and then thermally annealed at different temperatures. The samples were analyzed by spectroscopic ellipsometry using the Mueller matrix formalism, X-ray diffractometry and scanning electron microscopy. The conversion of amorphous titanium dioxide to polycrystalline anatase occurred at 400 °C or higher. Crystallites of a few percent of the film thickness were observed. Nevertheless, the crystallization process did not trigger the appearance of birefringence. These observations demonstrate that high-quality planar optical waveguides can be successfully fabricated on flexible substrates, in particular those composed of efficient polymers that can withstand the aforementioned temperatures.

Investigating Isogyres in Ferrofluids and Horocycles from Parlaseric Circle in a Ferrocell

This study explored the complex relationship between magnetic fields and light polarization in thin films of ferrofluid. Utilizing techniques such as polarized light imaging, multipolar expansion, and Mueller matrix formalism, this work investigated the formation of isogyres, which are distinct patterns observed when polarized light passes through the ferrofluid under various magnetic field configurations. The analysis revealed that the alignment of nanoparticles in response to the magnetic field resulted in the formation of a diffraction grating, influencing light polarization. Through the application of Stokes vectors and Mueller matrices, we gained insights into the complex interplay between magnetic fields and optical properties. The experiment presents the evolution of isogyres from straight lines to parabolas under the influence of a hexapolar magnetic field. The Mueller matrix effectively represented the magnetic field's impact on polarized light, highlighting dark regions corresponding to isogyres. We also report the formation of some patterns related to atmospheric optics and their analogy with the formation of patterns of the parlaseric circle and the luminous horocycle.

Using a dynamic Mueller matrix in modeling of retinal birefringence scanning systems

Polarization modeling by means of the Mueller matrix formalism is widely used for representation and optimization of the performance of complex polarization-sensitive systems. Yet, this turns out to be a challenge, as soon as such systems become dynamic, as is the case with scanning systems using polarized light. This work explores the possible use of dynamic Mueller matrices, in order to enable modeling of the optical system at any given moment, regardless of the position or orientation of any moving part. To achieve this, first the dynamic optical part (or a whole optical module) is measured using ellipsometry, to obtain several Mueller matrices characterizing the part at different moments in time. Then, all transitional matrices are calculated by means of interpolating their elements. This method is particularly useful when modeling scanning systems employing a scanning mirror. The author demonstrates its performance on a retinal birefringence scanning system. It was shown that the system itself is changing polarization quite significantly. It was determined how the six degenerate states can be changed by the dynamic system alone, and which Stokes vector elements are most prone to matrix element fluctuations. It is also suggested that a dynamic Mueller matrix can facilitate precise polarization modeling, and accelerate system optimization.

Instant polarized light microscopy pi (IPOLπ) for quantitative imaging of collagen architecture and dynamics in ocular tissues

Collagen architecture determines the biomechanical environment in the eye, and thus characterizing collagen fiber organization and biomechanics is essential to fully understand eye physiology and pathology. We recently introduced instant polarized light microscopy (IPOL) that encodes optically information about fiber orientation and retardance through a color snapshot. Although IPOL allows imaging collagen at the full acquisition speed of the camera, with excellent spatial and angular resolutions, a limitation is that the orientation-encoding color is cyclic every 90° (π/2 radians). In consequence, two orthogonal fibers have the same color and therefore the same orientation when quantified by color-angle mapping. In this study, we demonstrate IPOLπ, a new variation of IPOL, in which the orientation-encoding color is cyclic every 180° (π radians). Herein we present the fundamentals of IPOLπ, including a framework based on a Mueller-matrix formalism to characterize how fiber orientation and retardance determine the color. The improved quantitative capability of IPOLπ enables further study of essential biomechanical properties of collagen in ocular tissues, such as fiber anisotropy and crimp. We present a series of experimental calibrations and quantitative procedures to visualize and quantify ocular collagen orientation and microstructure in the optic nerve head, a region in the back of the eye. There are four important strengths of IPOLπ compared to IPOL. First, IPOLπ can distinguish the orientations of orthogonal collagen fibers via colors, whereas IPOL cannot. Second, IPOLπ requires a lower exposure time than IPOL, thus allowing faster imaging speed. Third, IPOLπ allows visualizing non-birefringent tissues and backgrounds from tissue absorption, whereas both appear dark in IPOL images. Fourth, IPOLπ is cheaper and less sensitive to imperfectly collimated light than IPOL. Altogether, the high spatial, angular, and temporal resolutions of IPOLπ enable a deeper insight into ocular biomechanics and eye physiology and pathology.

Noninvasive polarization-based technique for hematocrit monitoring

Subject of study. Polarization images corresponding to the 2D distributions of polarization state parameters for light scattered by biological specimens with different hematocrit levels were obtained by shining laser light in a given polarization state of blood-containing tissue through the nail bed of the left fifth finger. Aim of work. The aim of this work is to determine whether active video polarimetry is suitable for noninvasive real-time monitoring of blood hematocrit and to develop data-based criteria to identify hematocrit levels corresponding to various body states of human test subjects. Method. Physical models of changes in the parameters of polarized radiation during interaction with a biological specimen are used. A prototype optical design was developed for a Stokes video polarimeter capable of recording the irradiance distribution within a single analysis field on the sensitive area of a photodetector array. The digital images were processed using the Stokes–Mueller matrix formalism. A comparative statistical analysis of the 3D distributions for various parameters describing the polarization state (degree of polarization and the azimuth and ellipticity of the polarization ellipse) was performed to determine whether it is possible to detect differences in the hematocrit levels of human blood. Main results. A new approach to noninvasive hematocrit monitoring based on optical polarization is proposed. We obtained 3D distributions and histograms of light polarization state parameters for two human test subjects known to have different hematocrits. Statistical analysis revealed that significant differences in the second–fourth order statistical moments of the light polarization parameters are the most relevant diagnostic indicators for comparative analysis of biological tissues having different blood hematocrit levels. Practical significance. With further development, the proposed method can be applied to both medical diagnosis and emergency treatment. Timely detection of significant deviations from the normal hematocrit based on automated calculation and analysis of the data parameters identified will enable continuous hematocrit monitoring during surgical operations and effective real-time adjustment of blood viscosity.

Crosspolarization with imperfect infrared polarizers

The analysis of vibrational bands is a core application of infrared (IR) spectroscopy. Polarization-dependent measurements enable the study of anisotropic materials. However, imperfect IR polarizers exhibit polarizer leakage, which causes pronounced bandshape and baseline distortions for samples with weak optical anisotropy. Based on the 4 × 4 Mueller-matrix formalism, we propose a polarimetric measurement scheme for handling imperfect polarizers and source prepolarization that delivers correct co- and crosspolarized transmission and reflection IR spectra. The scheme is applied to a weakly anisotropic polypropylene sheet, resolving crosspolarized signatures as small as 5⋅10−5. We determine the polymer’s direction-dependent complex refractive index in the vibrational fingerprint range.

Exploring the Polarization of Light in Ferrofluids with Mueller Matrices

We studied the polarization of light in a thin film of ferrofluid subjected to a magnetic field using the Mueller matrix formalism. By observing the results of some experiments, we relate the observed light patterns with Stokes vectors that can be operated by Mueller matrices, which represent the magnetic field applied to the sample. We observed that the changes in the dichroism of this system can be monitored along the sample, allowing for the visualization of magneto-optical effects mainly for linear polarized light, and the effects of circular polarized light are related to birefringence.

Shear-Coated Linear Birefringent and Chiral Cellulose Nanocrystal Films Prepared from Non-Sonicated Suspensions with Different Storage Time.

Nanocelluloses are very attractive materials for creating structured films with unique optical properties using different preparation techniques. Evaporation-induced self-assembly of cellulose nanocrystals (CNC) aqueous suspensions produces iridescent films with selective circular Bragg reflection. Blade coating of sonicated CNC suspensions leads to birefringent CNC films. In this work, fabrication of both birefringent and chiral films from non-sonicated CNC suspensions using a shear-coating method is studied. Polarization optical microscopy and steady-state viscosity profiles show that non-sonicated CNC suspensions (concentration of 6.5 wt%) evolve with storage time from a gel-like shear-thinning fluid to a mixture of isotropic and chiral nematic liquid crystalline phases. Shear-coated films prepared from non-sonicated fresh CNC suspensions are birefringent, whereas films prepared from suspensions stored several weeks show reflection of left-handed polarized light. Quantification of linear and circular birefringence as well circular dichroism in the films is achieved by using a Mueller matrix formalism.

Sensitivity enhanced roll-angle sensor by means of a quarter-waveplate

Abstract Attitude metrology (roll, pitch, and yaw) plays an important role in many different fields. Roll angle is considered the most difficult measurement quantity in angular displacements compared to pitch and yaw angles because the rotation axis of the roll angle is parallel to the probe beam. In this work, a sensitivity enhanced roll-angle sensor is presented. The principle is based on the polarization change of a sensing unit (quarter-waveplate). The polarization model is analyzed by Mueller matrix formalism. The Stokes parameters are detected by a Stokes polarimeter. The novel coaxial design improves the sensitivity and reduce the complexity of optical system alignment by means of a fixed quarter-waveplate. The proposed sensor provides a simple setup to measure roll angles with a high sensitivity of 0.006∘ and a long unambiguous measurement range of 180∘.

Combination of surface plasmon resonance and differential Mueller matrix formalism for noninvasive glucose sensing

A novel technique is proposed for circular birefringence (CB) sensing using a surface plasmon resonance (SPR) prism coupler and differential Mueller matrix polarimetry. In the proposed system, the SPR prism coupler is placed in front of the sample in order to generate a weak-scattering medium model and enhance the sensitivity of the measurement process. The CB properties of the sample are then extracted using a dynamic Stokes-Mueller matrix polarimetry measurement system in the reflectance mode. The practical feasibility of the system is demonstrated by measuring the CB properties of aqueous glucose solutions and glucose phantom solutions containing 2% lipofundin. The oral glucose tolerance tests pilot study was performed on four healthy human volunteers aged between 20 and 25 years old. The experimental results show that the proposed method has a resolution of just 10 mg/dL. In general, the results confirm that the proposed polarimetry-SPR system provides a fastand reliable approach for CB detection and has significant potential for noninvasive glucose monitoring device (NIGMD) applications.

Zebrafish structural development in Mueller-matrix scanning microscopy

Zebrafish are powerful animal models for understanding biological processes and the molecular mechanisms involved in different human diseases. Advanced optical techniques based on fluorescence microscopy have become the main imaging method to characterize the development of these organisms at the microscopic level. However, the need for fluorescence probes and the consequent high light doses required to excite fluorophores can affect the biological process under observation including modification of metabolic function or phototoxicity. Here, without using any labels, we propose an implementation of a Mueller-matrix polarimeter into a commercial optical scanning microscope to characterize the polarimetric transformation of zebrafish preserved at different embryonic developmental stages. By combining the full polarimetric measurements with statistical analysis of the Lu and Chipman mathematical decomposition, we demonstrate that it is possible to quantify the structural changes of the biological organization of fixed zebrafish embryos and larvae at the cellular scale. This convenient implementation, with low light intensity requirement and cheap price, coupled with the quantitative nature of Mueller-matrix formalism, can pave the way for a better understanding of developmental biology, in which label-free techniques become a standard tool to study organisms.

A simple method for in situ measurement of vacuum window birefringence.

We present a simple method to measure the degrees of circular polarization (DoCP) of laser light inside a vacuum chamber and the birefringence of a vacuum window by detecting the fluorescence emitted by Doppler cooled ions in an ion trap. Imperfect laser polarization will cause ions to be pumped to the dark state which will decrease the fluorescence rates of the ions. With a simulation based on the rate equations of the relevant energy levels of 25Mg+ ions, we find that the fluorescence rate is sensitive to the DoCP of the laser. Based on the simulation result, we present a new method to optimize the DoCP of the laser inside the vacuum chamber by adjusting fast axis azimuthal angles of a half-wave plate and a quarter-wave plate outside the vacuum chamber. The laser light is optimized to be circularly polarized with an uncertainty of the DoCP of 7.8 × 10-5. With the obtained polarization information on both sides of the vacuum window and treating the vacuum window as an unknown wave plate, the phase delay and the fast axis azimuthal angle of the vacuum window can be determined in the form of Mueller matrix. The phase delay is determined to be 197.60(39)°, and the fast axis azimuthal angle is determined to be 104.00(5)°.

A method of calculating compensators in polarization-sensitive optical systems

A simple method to measure and compensate polarization-sensitive optical components (retarders) is proposed, based on Stokes vector polarimetry. First, the Mueller matrix of an unknown polarization-sensitive element with arbitrary retardance and fast-axis orientation is obtained by means of a conventional measurement and calculation polarimetric procedure. Then a novel numerical technique is proposed, allowing to express the measured retarder’s Mueller matrix in terms of retardance δ and fast axis orientation θ. Further, a method for calculating polarization compensators is proposed, to balance phase differences introduced by one or more retarders. Compensation is achieved by a single compensating retarder whose parameters are derived from the original retarder’s Mueller matrix, or its equivalent (δ,θ) pair. The technique works for all possible fast-axis orientations of the original retarder. The method was validated using an electrically controllable liquid crystal retarder as a compensator. The approach described here is constrained to optical elements that behave as nearly pure retarders, i.e. their diattenuation and depolarization are negligible. Possible applications are in the design of polarization-sensitive systems (biomedical, environmental, chemical, optical communications, etc.) where recovery and/or precise control of the polarization state of light is needed, in polarization tracing models based on the Mueller matrix formalism, and others.

Digital histology with Mueller microscopy: how to mitigate an impact of tissue cut thickness fluctuations.

.Mueller microscopy studies of fixed unstained histological cuts of human skin models were combined with an analysis of experimental data within the framework of differential Mueller matrix (MM) formalism. A custom-built Mueller polarimetric microscope was used in transmission configuration for the optical measurements of skin tissue model adjacent cuts of various nominal thicknesses (5 to ). The maps of both depolarization and polarization parameters were calculated from the corresponding microscopic MM images by applying a logarithmic Mueller matrix decomposition (LMMD) pixelwise. The parameters derived from LMMD of measured tissue cuts and the intensity of transmitted light were used for an automated segmentation of microscopy images to delineate dermal and epidermal layers. The quadratic dependence of depolarization parameters and linear dependence of polarization parameters on thickness, as predicted by the theory, was confirmed in our measurements. These findings pave the way toward digital histology with polarized light by presenting the combination of optimal optical markers, which allows mitigating the impact of tissue cut thickness fluctuations and increases the contrast of polarimetric images for tissue diagnostics.

Transmittance enhancement of nematic liquid crystal dichroic dye doped mixtures by addition of chiral dopants: a polarimetric analysis

We propose an attempt of explanation for the improvement of the transmittance dynamic of nematic liquid crystals, combined with neutral dichroic dyes, by the addition of chiral dopants. It is based on a fine polarimetric analysis of the liquid crystal medium, using the Mueller matrix formalism. This enables us to determine the polarization mode propagation and the residual scattering in the bulk. To calibrate our measurements we analyse two asymptotic cases, that have been extensively studied: the pure nematic case (no chiral dopants) and the cholesteric one (with high concentration of chiral dopants) in a Bragg regime. The mixture of interest in our case exhibits intermediate dopant concentrations. We present some experimental results explaining the impact of the addition of these chiral dopants on both dichroic efficiency, and scattering. Finally, we discuss how the complete polarimetric analysis can be used efficiently to describe the medium complexity.

Investigation of the optical properties of the liquid crystal-based devices via Mueller matrix formalism

A model approach for the Mueller matrix (MM) of the twisted nematic liquid crystal spatial light modulator (TNLC-SLM) was proposed. In the first part of the study, the MM of the TNLC cell in the absence of applied voltage was investigated both theoretically and experimentally. In the second part, the model approach was improved by considering the reorientation of both tilt and azimuth angles of the liquid crystal (LC) molecules in the presence of applied voltage. Comparison of the theoretical MM elements with the experimental ones from the literature showed that, instead of decaying exponentially, the azimuth angle rotates with respect to the cell walls in a critical voltage range before the molecules are completely untwisted. It also pointed out that the effect of the tilt and the azimuth angles of the molecules on the optical properties of the light travelling in the LC cell could change depending on the polarization state of the input light and the voltage applied to the cell.

Label-free discrimination of lung cancer cells through mueller matrix decomposition of diffuse reflectance imaging

Abstract In this article, we explore the potential of an original label-free Near-Infrared (NIR) imaging technique, based on Mueller Matrix decomposition reflectance, for efficient detection and classification of histopathological samples of lung cancer cells. Experimental results were acquired, processed, and analyzed by means of an accurate, fully-automated, auto-calibrated liquid-crystal NIR polarimetric imaging system, developed for real-time Mueller matrix analysis and optical characterization of target media. The polarimetric Figure-of-Merits (FOMs), estimated using Mueller matrix decomposition, as well as the statistics associated with the sixteen Mueller matrix elements of each lung cell sample indicate that enhanced discrimination among the samples can be achieved. Similarly, polarimetric Exploratory Data Analysis (pEDA), based on histograms obtained from diffuse reflectance polarimetric signals, has been used to determine if aberrations and/or changes in the spread of the histogram between different stages of lung cancer can be proved effective biomarkers for its progression and also discrimination among different lung pathologies. The outcome of this study indicates that Mueller matrix formalism may be proved extremely useful in discriminating among healthy and malignant lung cells as well as differentiating among the different types of malignancies with high accuracy. As a result, it may contribute positively to the enhancement and implementation of the operational principles of the Whole Slide Imaging (WSI) field.

Analysis of optically anisotropic properties of biological tissues under stretching based on differential Mueller matrix formalism.

The optical properties of biological tissues under stretching are investigated using a full-field ellipsometry technique based on a differential Mueller matrix formalism. Traditional photoelastic-based formalism for extracting the linear birefringence (LB) properties of stretched anisotropic optical samples ignores the effects of the other optical properties of the sample. By contrast, in the formalism proposed in this study, the LB, linear dichroism (LD), circular birefringence (CB), circular dichroism (CD), and depolarization (Dep) properties are fully decoupled. Simulations are performed to evaluate the performance of the two formalisms in extracting the LB properties of optically anisotropic samples with different degrees of Dep, CB, LD, and CD. The practical feasibility of the proposed all-parameter decoupled formalism is then demonstrated using chicken breast muscle tissue. In general, the results show that both formalisms provide a reliable LB measurement performance for healthy chicken breast tissue under stretching. However, while the LB-only formalism has good robustness toward scattering, its measurement performance is seriously degraded for samples with high CB. Thus, of the two formalisms, the proposed all-parameter decoupled formalism provides a more effective approach for examining the anisotropic properties of biological tissues under stretching.

Polarization-Tailored Fano Interference in Plasmonic Crystals: A Mueller Matrix Model of Anisotropic Fano Resonance

Fano resonance is observed in a wide range of micro- and nano-optical systems and has been a subject of intensive investigations due to its numerous potential applications. Methods that can control or modulate Fano resonance by tuning some experimentally accessible parameters are highly desirable for realistic applications. Here we present a simple yet elegant approach using the Mueller matrix formalism for controlling the Fano interference effect and engineering the resulting asymmetric spectral line shape in an anisotropic optical system. The approach is founded on a generalized model of anisotropic Fano resonance, which relates the spectral asymmetry to physically meaningful and experimentally accessible parameters of interference, namely, the Fano phase shift and the relative amplitudes of the interfering modes. The differences in these parameters between orthogonal linear polarizations in an anisotropic system are exploited to desirably tune the Fano spectral asymmetry using pre- and postselection of optimized polarization states. The concept is demonstrated on waveguided plasmonic crystals using Mueller matrix-based polarization analysis. The approach enabled tailoring of several exotic regimes of Fano resonance in a single device, including the complete reversal of the spectral asymmetry, and shows potential for applications involving control and manipulation of electromagnetic waves at the nanoscale.

Experimental study of thickness dependence of polarization and depolarization properties of anisotropic turbid media using Mueller matrix polarimetry and differential decomposition

We investigate the influence of sample thickness on the polarization and depolarization properties of light when it propagates through anisotropic turbid media using transmission Mueller matrix polarimetry. Since depolarization originates from light that has been multiply-scattered inside the sample, measurements were done by a polarimetric scatterometer equipped with large aperture optics to efficiently capture direct and scattered light. We made measurements in both, real and Fourier planes to study the distribution of polarization across the surface as well as their angular distribution respectively. We show that when properly averaged, the information obtained from images in both planes is equivalent. Rough stretched plastic sheets are used as model samples representing anisotropic turbid media which show both retardance and depolarization. The plastic sheets were stacked in different orientations to create different distributions of form birefringence, which in turn gave rise to different polarimetric properties such as linear (0°–90°, 45°–135°) and circular birefringence. We show that the dependency on the values of both, polarization properties and depolarization follows the theory of the fluctuating medium model, formulated in the framework of the differential Mueller matrix formalism. These results are used as a validation of the polarimetric scatterometer, and also, to show the interest of transmission Mueller matrix polarimetry to characterize samples showing scattering, which can be typically found in biomedicine and materials sciences.