Infrared Mueller matrix acquisition and preprocessing system

An analog Mueller matrix acquisition and preprocessing system (AMMS) was developed for a photopolarimetric-based sensor with 9.1-12.0 microm optical bandwidth, which is the middle infrared wavelength-tunable region of sensor transmitter and "fingerprint" spectral band for chemical-biological (analyte) standoff detection. AMMS facilitates delivery of two alternate polarization-modulated CO(2) laser beams onto subject analyte that excite/relax molecular vibrational resonance in its analytic mass, primes the photoelastic-modulation engine of the sensor, establishes optimum throughput radiance per backscattering cross section, acquires Mueller elements modulo two laser beams in hexadecimal format, preprocesses (normalize, subtract, filter) these data, and formats the results into digitized identification metrics. Feed forwarding of formatted Mueller matrix metrics through an optimally trained and validated neural network provides pattern recognition and type classification of interrogated analyte.     

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.     

Mueller matrix imaging of targets in turbid media: effect of the volume scattering function

Detecting objects in turbid media by use of just radiance signals has been a subject of study for many years. The use of Mueller matrix imaging methods has only recently been used as a tool for target detection. We will show not only that can targets still be detected by Mueller matrix methods even after their detection has escaped normal radiance schemes but also that their surface features can also still be distinguished. We will also show how the shape of the volume scattering function as well as the target and medium albedo strongly influences various elements of the Mueller matrix. One of the more interesting features of Mueller matrix imaging is that the diagonal elements are sensitive to perturbations in the environment surrounding the target. This implies that targets can be detected far beyond their geometric cross section. The methods presented here will have applications to submersible object detection, remote sensing in the atmosphere, and the detection of inhomogeneities in tissue.     

Interpretation of nondepolarizing Mueller matrices based on singular-value decomposition

A product decomposition of a nondepolarizing Mueller matrix consisting of the sequence of three factors--a first linear retarder, a horizontal or vertical "retarding diattenuator," and a second linear retarder--is proposed. Each matrix factor can be readily identified with one or two basic polarization devices such as partial polarizers and retardation waveplates. The decomposition allows for a straightforward interpretation and parameterization of an experimentally determined Mueller matrix in terms of an arrangement of polarization devices and their characteristic parameters: diattenuations, retardances, and axis azimuths. Its application is illustrated on an experimentally determined Mueller matrix.     

Characteristic properties of Mueller matrices

A complete and minimum set of necessary and sufficient conditions for a real 4 x 4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely, the four conditions obtained from the nonnegativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the transmittance condition. Using the properties of H, a demonstration is also presented of Tr(M(T)M) = 4m(2)00 as being a necessary and sufficient condition for a physical Mueller matrix to be a pure 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.     

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.     

Differential absorption mueller matrix spectroscopy and the infrared detection of crystalline organics

The complete 16-element Mueller matrices for backscattering from amino acids, sugars, and other enantiomorphic compounds pressed into wafer form were measured at infrared wavelengths. For each compound a pair of CO(2) laser lines was selected from the 9.1-11.6-mum region such that one line excited an absorption band in the compound, whereas the other did not. It was observed that at least some of the matrix elements differed significantly depending on which of the two wavelengths was used in the measurement. We propose that a neural network pattern recognition system can be trained to detect the presence of specific compounds based on multiwavelength backscatter Mueller matrix measurements.     

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.     

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.     

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.     

Neural network pattern recognition of thermal-signature spectra for chemical defense

We treat infrared patterns of absorption or emission by nerve and blister agent compounds (and simulants of this chemical group) as features for the training of neural networks to detect the compounds' liquid layers on the ground or their vapor plumes during evaporation by external heating. Training of a four-layer network architecture is composed of a backward-error-propagation algorithm and a gradient-descent paradigm. We conduct testing by feed-forwarding preprocessed spectra through the network in a scaled format consistent with the structure of the training-data-set representation. The bestperformance weight matrix (spectral filter) evolved from final network training and testing with software simulation trials is electronically transferred to a set of eight artificial intelligence integrated circuits (ICs') in specific modular form (splitting of weight matrices). This form makes full use of all input-output IC nodes. This neural network computer serves an important real-time detection function when it is integrated into pre- and postprocessing data-handling units of a tactical prototype thermoluminescence sensor now under development at the Edgewood Research, Development, and Engineering Center.     

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.     

Error analysis for Mueller matrix measurement

The linear errors of Mueller matrix measurements are formulated for misalignment, depolarization, and incorrect retardation of the polarimetric components. The measured errors of a Mueller matrix depend not only on the imperfections of the measuring system but also on the Mueller matrix itself. The error matrices for different polarimetric systems are derived and also evaluated for the straight-through case. The error matrix for a polarizer-sample-analyzer system is much simpler than those for more complicated systems. The general error matrix is applied to null ellipsometry, and the obtained errors in ellipsometric parameters psi and delta are identical to the errors specifically derived for null ellipsometry with depolarization.     

Treatment of polarization in laser remote sensing of ocean water

We review existing experimental data and methods for calculating the Mueller matrix of ocean water for use as input in a simulation model applicable to laser remote sensing. Calculations of the Mueller matrix are made for scattering media of different refractive indices, shapes, and size distributions. Dependencies of the backscattering depolarization ratio as a function of the particle refractive index are presented, and we demonstrate the potential importance of polarization in bathymetric sensing.     

Components of purity of a Mueller matrix

The degree of polarimetric purity of a Mueller matrix, also called "depolarization index" [Opt. Acta 33, 185 (1986)] is expressed as a quadratic average of two contributions of different nature. The contribution due to the polarizance and diattenuation properties is given by a unique parameter called "degree of polarizance," and the complementary contribution due to nonpolarizing properties is given by a parameter called "degree of spherical purity." These two intrinsic quantities are useful in order to analyze the sources of the polarimetric purity of a material sample whose Mueller matrix has been measured and provide criteria for the classification of Mueller matrices.     

Mueller Matrices and Depolarization Criteria

Abstract

The question of whether a given Mueller matrix represents a deterministic or a non-deterministic system is analysed by means of a matrix condition. The possibility of replacing this matrix condition by a scalar condition is examined. It is shown that this is permissible only for those cases where a Hermitian matrix constructed from the Mueller matrix is positive semidefinite.     

Electro-optic coefficient spectrum of cadmium telluride

A spectrum for the electro-optic coefficient of cadmium telluride measured from 3 to 14 μm is reported. The spectrum shows that the quantity n(3)r(41) has a nearly constant value of 1.09 × 10(-10) m/V over this spectral band, with a slight (5%) dip at the weak absorption band centered at 6 μm. Measurements were performed with an infrared Mueller matrix spectropolarimeter. Transmission spectra of the Mueller matrix were acquired at a set of applied voltages. Retardance spectra were calculated from Mueller matrix spectra, and then the electro-optic coefficient was calculated at each wavelength by a least-squares fit to the resulting retardance as a function of voltage.     

Polarimetric characterization of liquid-crystal-on-silicon panels

Mueller matrix imaging polarimetry of liquid-crystal-on-silicon (LCoS) panels provides detailed information useful for the diagnosis of LCoS problems and to understand the interaction of LCoS panels with other projector components. Data reduction methods are presented for the analysis of LCoS Mueller matrix images yielding contrast ratio, efficiency, spatial uniformity, and the calculation of optimum trim retarders. The effects of nonideal retardance, retardance orientation, and depolarization on LCoS system performance are described. The white-state and dark-state Mueller matrix images of an example LCoS panel are analyzed in terms of LCoS performance metrics typical for red-green-blue wavelengths of 470, 550, and 640 nm. Variations of retardance, retardance orientation, and depolarization are shown to have different effects on contrast ratio, efficiency, and brightness. Thus Mueller matrix images can diagnose LCoS problems in a way different from radiometric testing. The calculation of optimum trim retarders in the presence of spatial variations is discussed. The relationship of the LCoS retardance in single-pass (from front to back) to the double-pass retardance (from entrance to exit) is established and used to clarify coordinate system issues related to Mueller matrices for reflection devices.     

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.