Data analysis for a rotating quarter-wave, far-infrared Stokes polarimeter

Data analysis techniques are reviewed and extended for the measurement of the Stokes vector of partially or completely polarized radiation by the rotating quarter-wave method. It is shown that the conventional technique, based on the Fourier analysis of the recorded signal, can be efficiently replaced by a weighted least-squares best fit, so that the different accuracy of the measured data can be taken into account to calculate the measurement errors of the Stokes vector elements. Measurement errors for the polarization index P and for the azimuth and ellipticity angles psi and chi of the radiation are also calculated by propagation error theory. For those cases in which the above technique gives a nonphysical Stokes vector (i.e., with a polarization degree of P>1) a constrained least-squares best fit is introduced, and it is shown that in this way a Stokes vector with P = 1 (rather than P相似文献   

On the algebraic characterization of a Mueller matrix in polarization optics. II. Necessary and sufficient conditions for Jones-derived Mueller matrices

Abstract

We show that every Mueller matrix, that is a real 4 × 4 matrix M which transforms Stokes vectors into Stokes vectors, may be factored as M = L ₂ KL ₁ where L ₁ and L ₂ are orthochronous proper Lorentz matrices and K is a canonical Mueller matrix having only two different forms, namely a diagonal form for type-I Mueller matrices and a non-diagonal form (with only one non-zero off-diagonal element) for type-II Mueller matrices. Using the general forms of Mueller matrices so derived, we then obtain the necessary and sufficient conditions for a Mueller matrix M to be Jones derived. These conditions for Jones derivability, unlike the Cloude conditions which are expressed in terms of the eigenvalues of the Hermitian coherency matrix T associated with M, characterize a Jones-derived matrix M through the G eigenvalues and G eigenvectors of the real symmetric N matrix N = [Mtilde]GM associated with M. Appending the passivity conditions for a Mueller matrix onto these Jones-derivability conditions, we then arrive at an algebraic identification of the physically important class of passive Jones-derived Mueller matrices.     

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.     

Sensitivity of the backscattering Mueller matrix to particle shape and thermodynamic phase

The Mueller matrix (M) corresponding to the phase matrix in the backscattering region (scattering angles ranging from 175 degrees to 180 degrees) is investigated for light scattering at a 0.532-microm wavelength by hexagonal ice crystals, ice spheres, and water droplets. For hexagonal ice crystals we assume three aspect ratios (plates, compact columns, and columns). It is shown that the contour patterns of the backscattering Mueller matrix elements other than M11, M44, M14, and M41 depend on particle geometry; M22 and M33 are particularly sensitive to the aspect ratio of ice crystals. The Mueller matrix for spherical ice particles is different from those for nonspherical ice particles. In addition to discriminating between spherical and nonspherical particles, the Mueller matrix may offer some insight as to cloud thermodynamic phase. The contour patterns for large ice spheres with an effective size of 100 microm are substantially different from those associated with small water droplets with an effective size of 4 microm.     

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.     

Axially resolved complete mueller matrix confocal microscopy

We introduce a technique that is capable of obtaining complete polarization-sensitive three-dimensional images that could reveal unknown anatomical conditions of living tissue that possess polarization-dependent signatures. Previously, the 16 Mueller coefficients were measured independently only by use of two-dimensional imaging techniques. We also present the experimental combination of a depth-resolved confocal imaging system with a complete Mueller matrix polarimeter. To calibrate the system, a double-pass method had to be implemented. We also indicate, experimentally, that the confocal sectioning of the system has a degrading effect on axially resolved Mueller matrix measurements.     

Laboratory studies of angle- and polarization-dependent light scattering in sea ice

The angle- and polarization-dependent light scattering were measured for oriented first-year and multiyear sea ice taken from the Chukchi Sea near Pt. Barrow, Alaska. The entire Mueller matrix for these samples was determined at 532 nm. Mueller matrices were also determined for artificially grown saline ice samples and melted samples of the respective ice types. Phase functions for thin-slab samples are qualitatively consistent with calculations for scattering from brine inclusions in a solid ice medium and depend strongly on the shape of the scattering sample. Small orientation-dependent effects are observed for scattering from oriented sea ice. A simple model is used to describe qualitatively some features of the measured sea ice Mueller matrices. This model combines the effects of scattering from spherical inhomogeneities and the intrinsic birefringence of pure water ice. A set of Mueller matrix inequalities is presented and used to obtain physical insight into the measurement results.     

（广义）块对角占优矩阵的奇异与非奇异性

本文得到了块对角占优矩阵奇异与非奇异的几个充分必要条件,并由此得到了广义块对角占优矩阵奇异与非奇异的一些充分必要的判定条件.     

Non-oscillatory damped multi-degree-of-freedom systems

Summary An analysis of the conditions under which a symmetric damped linear system does not oscillate is presented. A necessary and sufficient condition is formulated in terms of the definiteness of a Hankel's matrix whose elements depend on the coefficients of the characteristic polynomial of the system. From a practical point of view it is of interest to find conditions which are related in a simple way to the properties of the system matrices. Such previously developed criteria are indicated and compared, and a new sufficient condition for non-oscillation is derived. Results obtained for symmetric systems are then generalized to asymmetric and symmetrizable systems. Several examples are used to illustrate the validity and application of the presented criteria.     

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.     

Scattering matrices for large ice crystal particles

The problem of light scattering by ice crystal particles whose sizes are essentially larger than the incident wavelength is divided into two parts. First, the scattered field is represented as a set of plane-parallel outgoing beams in the near zone of the particle. Then, in the far zone the scattered field is represented as a result of both diffraction and interference of these beams within the framework of physical optics. A proper ray-tracing algorithm for calculation of the amplitude (Jones) scattering matrix is developed and applied. For large particles, a number of reduced Mueller matrices are introduced and discussed, since the pure Mueller matrix obtained from the Jones matrix becomes a rather cumbersome and quickly oscillating value. Backscattering by hexagonal ice crystals, including polarization properties, is considered in detail.     

A Simple Necessary and Sufficient Condition on Physically Realizable Mueller Matrices

Abstract

Development of simple tools to test physical realizability of measured or computed Mueller matrices is the subject of this paper. In particular, the overpolarization problem, i.e., the problem of ensuring that the output degree of polarization does not exceed unity is solved by finding an easily implementable necessary and sufficient condition. With G being the Lorentz metric, it states that a given matrix M is not overpolarizing if and only if the spectrum of GM ^T GM is real and an eigenvector associated with the largest eigenvalue is a physical Stokes vector. This result is used to characterize some M classes of special interest, and is used to test several examples from recent literature.     

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.     

Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method

We have developed a powerful 3D Monte Carlo code, as part of the Radiance in a Dynamic Ocean (RaDyO) project, which can compute the complete effective Mueller matrix at any detector position in a completely inhomogeneous turbid medium, in particular, a coupled atmosphere-ocean system. The light source can be either passive or active. If the light source is a beam of light, the effective Mueller matrix can be viewed as the complete impulse response Green matrix for the turbid medium. The impulse response Green matrix gives us an insightful way to see how each region of a turbid medium affects every other region. The present code is validated with the multicomponent approach for a plane-parallel system and the spherical harmonic discrete ordinate method for the 3D scalar radiative transfer system. Furthermore, the impulse response relation for a box-type cloud model is studied. This 3D Monte Carlo code will be used to generate impulse response Green matrices for the atmosphere and ocean, which act as inputs to a hybrid matrix operator-Monte Carlo method. The hybrid matrix operator-Monte Carlo method will be presented in part II of this paper.     

Normal form for Mueller Matrices in Polarization Optics

Abstract

The normal (canonical) form for Mueller matrices in polarization optics is derived: it is shown that a non-singular real 4 × 4 matrix M qualifies to be the bona fide Mueller matrix of some physical system if and only if it has the canonical form M = L′ ΛL, where L and L′ are elements of the proper orthochronous Lorentz group L ^↑ ₊, and where Λ = diag (λ₀, λ₁, λ₂, λ₃) with λ₀ ≥ ¦λ_j¦ > 0. It is further shown that λ₁ and λ₂ can be taken to be positive so that the signature of λ₃ is the same as that of det M. Several experimentally measured Mueller matrices are analysed in the light of the normal form. The case of singular Mueller matrices is briefly discussed as a limiting case.     

Two-modulator generalized ellipsometry: theory

A new ellipsometer is described that uses two photoelastic modulator-polarizer pairs, where the photoelastic modulators are operating at differing resonant frequencies. The time-dependent intensity of the light beam is extremely complicated but can be analyzed so that all elements of the sample Mueller matrix are obtained. For a given configuration, nine of the Mueller matrix elements can be measured at any one time; the other seven elements are accessible when the azimuthal angles of the photoelastic modulators are changed. The single-configuration measurement is often sufficient to characterize a number of real situations completely, such as film growth in a vacuum environment, anisotropic samples, and simple depolarization.     

Space-bandwidth conditions for efficient phase-shifting digital holographic microscopy

Microscopy by holographic means is attractive because it permits true three-dimensional (3D) visualization and 3D display of the objects. We investigate the necessary condition on the object size and spatial bandwidth for complete 3D microscopic imaging with phase-shifting digital holography with various common arrangements. The cases for which a Fresnel holographic arrangement is sufficient and those for which object magnification is necessary are defined. Limitations set by digital sensors are analyzed in the Wigner domain. The trade-offs between the various holographic arrangements in terms of conditions on the object size and bandwidth, recording conditions required for complete representation, and complexity are discussed.     

Photopolarimetric measurement of single, intact pulp fibers by mueller matrix imaging polarimetry

A method based on Mueller matrix polarimetry is developed and demonstrated for determining the fibril angle and relative phase retardation of single, intact pulp fibers. The method permits quantitative and nondestructive determination of these parameters from measurements at one wavelength without any fiber alignment. The Mueller matrix of a pulp fiber and its relationship with the fibril angle and phase retardation are described. A nonmodulation method for determining the Mueller matrix is then proposed that is based on a set of intensity data registered by a single detector. Measurements were carried out with single pulp fibers as samples to test the theoretical prediction. The test measurements and results are described and presented.     

Remote sensing of penetrable objects buried beneath two-dimensional random rough surfaces by use of the Mueller matrix elements

The modified Mueller matrix elements for electromagnetic scattering from penetrable objects buried under two-dimensional random rough surfaces are investigated. This matrix relates the incident to the scattered waves, and it contains different combinations of the fully polarimetric scattering matrix elements. The statistical average of each Mueller matrix element is computed on the basis of the Monte Carlo simulations by exploiting the speed of the three-dimensional steepest-descent fast multipole method. The numerical results clearly show that relying only on the co-polarized or the cross-polarized intensities or both (i.e., vv, hh, vh, and hv) is not sufficient for sensing the buried objects. However, examining all 16 Mueller matrix elements significantly increases the possibility of detecting these objects. This technique can be used in remote sensing of scatterers buried beneath the rough ground.