Contrast mechanisms in polarization-sensitive Mueller-matrix optical coherence tomography and application in burn imaging

We investigate the various contrast mechanisms provided by polarization-sensitive (PS) Mueller-matrix optical coherence tomography (OCT). Our PS multichannel Mueller-matrix OCT is the first, to our knowledge, to offer simultaneously comprehensive polarization-contrast mechanisms, including the amplitude of birefringence, the orientation of birefringence, and the diattenuation in addition to the polarization-independent intensity contrast, all of which can be extracted from the measured Jones or the equivalent Mueller matrix. Theoretical analysis shows that when diattenuation is negligible, the round-trip Jones matrix represents a linear retarder, which is the foundation of conventional PS-OCT, and can be calculated with a single incident polarization state, although the one-way Jones matrix generally represents an elliptical retarder; otherwise, two incident polarization states are needed. The experimental results obtained from rat skin samples, which conform well with the histology, show that Mueller OCT provides complementary structural and functional information on biological samples and reveal that polarization contrast is more sensitive to thermal degeneration of biological tissue than amplitude-based contrast. Thus, Mueller OCT has significant potential for application in the noninvasive assessment of burn depth.     

Depolarization of diffusely reflecting man-made objects

The polarization properties of light scattered or diffusely reflected from seven different man-made samples are studied. For each diffusely reflecting sample an in-plane Mueller matrix bidirectional reflectance distribution function is measured at a fixed bistatic angle using a Mueller matrix imaging polarimeter. The measured profile of depolarization index with changing scattering geometry for most samples is well approximated by an inverted Gaussian function. Depolarization is minimum for specular reflection and increases asymptotically in a Gaussian fashion as the angles of incidence and scatter increase. Parameters of the Gaussian profiles fitted to the depolarization data are used to compare samples. The dependence of depolarization on the incident polarization state is compared for each Stokes basis vector: horizontal, vertical, 45 degrees, 135 degrees, and right- and left-circular polarized light. Linear states exhibit similar depolarization profiles that typically differ in value by less than 0.06 (where 1.0 indicates complete depolarization). Circular polarization states are depolarized more than linear states for all samples tested, with the output degree of polarization reduced from that of linear states by as much as 0.15. The depolarization difference between linear and circular states varies significantly between samples.     

Propagation of polarized light through textile material

In this paper a detailed investigation, based on simulations and experiments of polarized light propagation through textile material, is presented. The fibers in textile material are generally anisotropic with axisymmetric structure. The formalism of anisotropic fiber scattering (AFS) at oblique incidence is first deduced and then, based on this formalism and considered multiscattering, a polarization-dependent Monte Carlo method is employed to simulate the propagation of polarized light in textile material. Taking cotton fiber assemblies as samples, the forward-scattering Mueller matrices are calculated theoretically through the AFS-based simulations and measured experimentally by an improved Mueller matrix polarimeter. Their variations according to sample thickness are discussed primarily. With these matrices polar-decomposed, a further discussion on the optical polarization properties of cotton fiber assemblies (i.e., depolarization Δ, diattenuation D, optical rotation ψ and linear retardance δ) versus the thickness is held. Simultaneously, a meaningful comparison of both the matrices and their polar decomposition, generated from the simulations based on isotropic fiber scattering (IFS), with those simulated based on AFS is made. Results show that the IFS-derived values are strikingly different from those that are AFS-derived due to ignoring the fiber anisotropy. Furthermore, all the AFS-derived results are perfectly consistent with those obtained experimentally, which suggests that the Monte Carlo simulation based on AFS has potential applications for light scattering and propagation in textile material.     

Degree of polarization as a criterion to obtain the nine bilinear constraints between the Mueller-Jones matrix elements

The degree of polarization is employed as a criterion to find the nine independent relations among the elements of the Mueller-Jones matrix. This procedure is applied by considering a previously determined, physically realizable Mueller matrix. On the other hand, the nine bilinear constrains are obtained by directly measuring the degree of polarization from an outgoing beam of light from an optical system by considering nine incident states of light taken from the Poincaré sphere. For practical purposes, all the incident polarization states must be scanned from the Poincaré sphere in order to satisfy the over-polarization and the over-gain conditions, respectively, for the physical realizability of the Mueller matrix.     

Use of polar decomposition for the diagnosis of oral precancer

The Mueller matrix describes all the polarizing properties of a sample and, therefore, the optical differences between noncancerous and precancerous tissue that may be present within the matrix elements. A high-speed polarimetry system that generates 16 (4x4) full Mueller matrices to characterize tissues is presented. Feature extraction is done on the Mueller matrix elements resulting in depolarization and retardance images by polar decomposition. These are used to detect and classify early oral cancers and precancerous changes in epithelium such as dysplasia. These images are compared with orthogonal polarization images and analyzed in an attempt to identity useful factors for the differentiation between cancerous lesions and their benign counterparts. Our results indicate that polarimetry has potential as a method for the in vivo early detection and diagnosis of oral premalignancy.     

Positive-operator-valued-measure view of the ensemble approach to polarization optics

The statistical ensemble formalism of Kim et al [J. Opt. Soc. Am. A4, 433 (1987)] offers a realistic model for characterizing the effect of stochastic nonimage-forming optical media on the state of polarization of transmitted light. With suitable choice of the Jones ensemble, various Mueller transformations-some of which are hitherto unknown-are deduced. It is observed that the ensemble approach is formally identical to the positive-operator-valued measures (POVMs) on the quantum density matrix. This observation, in combination with the recent suggestion by Ahnert and Payne [Phys. Rev. A71, 012330-1 (2005)]-in the context of generalized quantum measurement on single photon polarization states-that linear optics elements can be employed in setting up all possible POVMs enables us to propose a way of realizing different types of Mueller devices.     

Polarization characterization of biological tissues using Stokes vector decomposition

A method is proposed for characterizing the polarization properties of a depolarizing anisotropic medium based on decomposition of the Stokes vector representing the light emerging from the medium. The exiting Stokes vector can be considered as being decomposed into two parts, namely a completely unpolarized and a completely polarized part. Then, the Mueller matrix representing the sample can be extracted as a superposition of two distinguishable parts. The differential Mueller formalism is applied to one part of the Muller matrix. Here, explicit expressions are presented for the extraction of polarization properties of the medium. Results indicate that the proposed method is a promising method for characterization of complicated media such as biological tissues.     

Measurement of the complex refractive index of isotropic materials with mueller matrix polarimetry

The complex refractive index of materials at infrared wavelengths is often determined when absorption measurements are made at selected wavelengths, and then the Kramers-Kronig relationship is used to calculate the real part of the index. Because many organic materials are highly absorbing in the infrared, absorption measurements require a short path length. We report on the use of an attenuated total internal reflection (TIR) method in combination with an infrared Mueller matrix spectropolarimeter to measure the Mueller matrix spectrum of samples from 3 to 14 mum. From the elements of the Mueller matrix the complex refractive index is determined for materials whose TIR interfaces are eigenstates of s and p polarization. The calculated index for water compares well with data found in the literature.     

Mueller matrix roots depolarization parameters

The Mueller matrix roots decomposition recently proposed by Chipman in [1] and its three associated families of depolarization (amplitude depolarization, phase depolarization, and diagonal depolarization) are explored. Degree of polarization maps are used to differentiate among the three families and demonstrate the unity between phase and diagonal depolarization, while amplitude depolarization remains a distinct class. Three families of depolarization are generated via the averaging of different forms of two nondepolarizing Mueller matrices. The orientation of the resulting depolarization follows the cyclic permutations of the Pauli spin matrices. The depolarization forms of Mueller matrices from two scattering measurements are analyzed with the matrix roots decomposition-a sample of ground glass and a graphite and wood pencil tip.     

Mueller matrices and information derived from linear polarization lidar measurements: theory

A Mueller matrix M is developed for a single-scattering process such that G(theta, phi) = T (phi(a))M T (phi(p))u, where u is the incident irradiance Stokes vector transmitted through a linear polarizer at azimuthal angle phi(p), with transmission Mueller matrix T (phi(p)), and G(theta, phi) is the polarized irradiance Stokes vector measured by a detector with a field of view F, placed after an analyzer with transmission Mueller matrix T (phi(a)) at angle phi(a). The Mueller matrix M is a function of the Mueller matrix S (theta) of the scattering medium, the scattering angle (theta, phi), and the detector field of view F. The Mueller matrixM is derived for backscattering and forward scattering, along with equations for the detector polarized irradiance measurements (e.g., cross polarization and copolarization) and the depolarization ratio. The information that can be derived from the Mueller matrix M on the scattering Mueller matrixS (theta) is limited because the detector integrates the cone of incoming radiance over a range of azimuths of 2pi for forward scattering and backscattering. However, all nine Mueller matrix elements that affect linearly polarized radiation can be derived if a spatial filter in the form of a pie-slice slit is placed in the focal plane of the detector and azimuthally dependent polarized measurements and azimuthally integrated polarized measurements are combined.     

3 x 3 matrix for unitary optical systems

We introduce a 3 x 3 matrix for the study of unitary optical systems. This 3 x 3 matrix is a submatrix of the 4 x 4 Mueller matrix. The elements of this 3 x 3 matrix are real, and thus complex-number calculations can be avoided. The 3 x 3 matrix is useful for illustrating the polarization state of an optical system. One can also use it to derive the conditions for linear and circular polarization output for a general optical system. New characterization methods for unitary optical systems are introduced. It is shown that the trajectory of the Stokes vector on a Poincaré sphere is either a circle or an ellipse as the optical system or input polarizer is rotated. One can use this characteristic circle or ellipse to measure the equivalent optical retardation and rotation of any lossless optical system.     

Transmitted and reflected scattering matrices from an English oak leaf

The complete Mueller matrix for an English oak (Quercus robur) leaf for a fixed azimuth angle (90 degrees) was determined immediately after plucking and a day following exposure to normal room temperature and pressures. The Mueller matrices were determined for transmitted light at observation angles ranging from 0 degrees to 24 degrees and for reflected backscattering angles from 153 degrees to 170 degrees. All the measurements were taken with a He-Ne laser light source at 0.63 microm. Since positive eigenvalues were obtained for the coherence matrix, the polarimetric measurements were physically realizable. The anisotropy parameters were determined from the Jones matrices by use of the decomposition theorem. From the M33 and M44 components of the Mueller matrices, it was found that nonspherical structures within the leaf were primarily responsible for observed transmitted light scatter, and spherical structures were mostly responsible for observed backscatter. Variations in backscatter Mueller matrix elements from a fresh leaf to a second day of observation were assumed because of changes to water vapor concentration in the leaf.     

A comparison of wavelength dependent polarization dependent lossmeasurements in fiber gratings

We have measured wavelength dependent Polarization Dependent Loss (PDL) in chirped fiber Bragg gratings for dispersion compensation, grating filters for wavelength add/drop multiplexing and long period gratings for EDFA gain flattening. The PDL is measured in devices used in reflection and in transmission by applying the Jones matrix method, the Mueller matrix method and the polarization scanning method. A comparison of the experimental results and an analysis of the sources of errors are presented     

Normal-incidence generalized ellipsometry using the two-modulator generalized ellipsometry microscope

A new microscope is described that is capable of measuring the polarization characteristics of materials in normal-incidence reflection with a demonstrated lateral resolution of 4 microm. The instrument measures eight parameters of the sample Mueller matrix, which can be related to the diattenuation, retardation, circular diattenuation, direction of the principal axis, and the polarization factor. With proper calibration, the eight elements of the sample Mueller matrix can be determined to better than 0.001-0.002 for small values. Examples are given for aluminum, rutile (TiO2), and calcite (CaCO3).     

State of Polarization in Open- and Closed-loop Helices of Single-mode Fibres

Abstract

The state of polarization in helically wound single-mode fibres is described in terms of coupled-mode equations and the Mueller matrix for an elliptically birefringent single-mode fibre in the quasi-monochromatic case. Possible depolarization has been accounted for by means of the mutual correlation function |γ| between eigenpolarization modes. The polarization state in closed-loop fibre-optic helices has been studied experimentally under single- and dual-mode operation. It has been shown that the closed-loop set-up can be used for the development of compact fibre-optic sensors.     

Real-time measurement of the polarization transfer function

We present a simple method for measuring the Mueller matrix associated with a scattering medium. Without involving moving parts, four input states of polarization are generated sequentially, and for each of them all four Stokes vector parameters are simultaneously measured for the complete determination of the Mueller matrix. Two liquid-crystal variable retarders are used for controlling the input state of polarization, whereas the measurement of the state of polarization involves phase modulation with a single-pass photoelastic modulator, and Fourier analysis in two polarization channels. The setup is controlled by a computer, allowing for real-time measurement of the Mueller matrix. The method is tested on standard elements such as polarizers and quarter-wave plates, as well as on inhomogeneous particulate systems.     

Structure of a general pure Mueller matrix

Changes in the radiance and state of polarization of a beam of radiation can often be described by means of a pure Mueller matrix. Such a 4 × 4 matrix transforms Stokes parameters and can be expressed in terms of the elements of a 2 × 2 Jones matrix. Relations between the two types of matrix are discussed. Explicit expressions are given for changes of a pure Mueller matrix that are caused by certain elementary changes of its Jones matrix, such as when its transpose, complex conjugate, or Hermitian conjugate are taken. It is shown that every pure Mueller matrix has a simple and elegant structure, which is embodied by interrelations that involve either only squares of the elements or only products of different elements. All possible interrelations for the elements of a general pure Mueller matrix are derived from this simple structure.     

Changes in Polarization of a Light Beam with Arbitrary Autocoherence Propagating in a Birefringent Crystal

Based on the Mueller-Stokes matrix formalism and the Wolf autocorrelation functions, a general approach is developed for studying the polarization characteristics of a light beam with arbitrary autocoherence during its interaction with various media. This makes it possible to take into account the dispersion of the medium and the coherence properties of the light field. It is shown that the propagation of a polychromatic light beam with spectrally pure polarization in a certain medium can be described by an integrated Mueller matrix. For a linear phase plate, the matrix elements can be expressed by means of the modulus and the phase of the complex degree of autocoherence. The polarization of a light beam emitted by a black-body radiator and the influence of the dispersion in a KDP crystal in quasi-monochromatic light are discussed as applications.     

Anisotropic incoherent reflection model for spectroscopic ellipsometry of a thick semitransparent anisotropic substrate

An anisotropic incoherent reflection model for the Mueller matrix elements of an optically thick uniaxial anisotropic semitransparent substrate with its anisotropy axis along its surface normal is developed. The Mueller matrix elements are measured by phase-modulated spectroscopic ellipsometry (SE) and compared with incoherent reflection model simulations. In the case of a sapphire substrate the oscillations observed are accurately modeled, and, in addition, the oscillating degree of polarization is correctly predicted. A straightforward generalization of the optical model, in the case of an arbitrary stack of layers containing a thick anisotropic semitransparent substrate, is also proposed and experimentally validated. The model is further applied to study the anisotropic dielectric function of a semi-insulating 4H-SiC wafer. An approximation based on a simple variation in the optical transition element is proposed to model the SiC birefringence. In conclusion, SE is shown to be a powerful alternative for investigating and predicting the behavior of optically thick birefringent materials.     

Definition of a parametric form of nonsingular Mueller matrices

The goal of this paper is to propose a mathematical framework to define and analyze a general parametric form of an arbitrary nonsingular Mueller matrix. Starting from previous results about nondepolarizing matrices, we generalize the method to any nonsingular Mueller matrix. We address this problem in a six-dimensional space in order to introduce a transformation group with the same number of degrees of freedom and explain why subsets of O(5,1), the orthogonal group associated with six-dimensional Minkowski space, is a physically admissible solution to this question. Generators of this group are used to define possible expressions of an arbitrary nonsingular Mueller matrix. Ultimately, the problem of decomposition of these matrices is addressed, and we point out that the "reverse" and "forward" decomposition concepts recently introduced may be inferred from the formalism we propose.