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.     

Size determination by use of two-dimensional Mueller matrices backscattered by optically thick random media

Here we are concerned with the systematic study of polarized light transport in thick, isotropic, homogeneous random media and of the associated inverse problem. An original spatial and intensity rescaling of the polarization transport allows one to account implicitly for the volume fraction. This parameter elimination permits a complete exploration, by means of Monte Carlo simulations of the dependence of polarized light transport on microscopic parameters. Analysis of the Mueller matrices obtained from the simulations show that additional correlations (with respect to scalar transport) are obtained between the microscopic parameters and the spatial distribution of specific elements of the Mueller matrix. As a consequence, using carefully chosen polarization states, one can determine an average particle size independently of the volume fraction of particles, with only the knowledge of the refractive-index ratio being required. This analysis is validated with experimental Mueller matrices obtained for emulsions of various size, concentration, and polydispersity.     

Virtues of mueller matrix imaging for underwater target detection

We present a theoretical analysis on use of polarized light in the detection of a model target in a scattering and absorbing medium similar to seawater. Monte Carlo numerical simulations are used in the calculation of the effective Mueller matrix which describes the scattering process. A target in the shape of a disk is divided into three regions, each of which has the same albedo but different reduced Mueller matrices. Contrast between various parts of the target and background is analyzed in the images created by ordinary radiance, by various elements of the Mueller matrix, and by certain suitable combinations of these elements. It is shown that the application of polarized light has distinct advantages in target detection and characterization when compared with use of unpolarized light.     

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.     

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   

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.     

Mueller calculus of polarization change in the cube-corner retroreflector

The optical ray properties of the cube-corner retroreflector (CCR) are first recalled. The change of polarization of the radiation due to CCR reflection is then derived by use of the Mueller matrix calculus. It is found that, in general, when the faces are not ideal reflectors, the useful cross section of the CCR consists of six zones, each of which produces a different change of polarization, i.e., it gives a different Mueller matrix. All the Mueller matrices depend on wavelength. The results are quite general and can be used directly also for partially polarized radiation.     

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.     

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.     

Investigation of Mueller matrices of anisotropic nonhomogeneous layers in application to an optical model of the cornea

We consider a system of anisotropic layers as an optical model of the eye cornea. Effective refraction indices for normally incident light are calculated with the assumption that each layer consists of closely packed uniform cylinders (fibrils). Jones matrix formalism is used to describe light propagation through the cornea. We calculate the Jones matrices from the experimentally measured Mueller matrices. Two algorithms are used for this purpose. The experiments have shown that ~20% of cornea area studied had the structure well described by the helical model proposed.     

Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error

The relationship between system condition and signal-to-noise ratio (SNR) in reconstructed Stokes parameter images is investigated for rotating compensator, variable retardance, and rotating analyzer Stokes vector (SV) polarimeters. A variety of optimal configurations are presented for each class of systems. The operation of polarimeters is discussed in terms of a four-dimensional conical vector space; and the concept of nonorthogonal bases, frames, and tight frames is introduced to describe the operation of SV polarimeters. Although SNR is an important consideration, performance of a polarimeter in the presence of errors in the calibration and alignment of the optical components is also important. The relationship between system condition and error performance is investigated, and it is shown that an optimum system from the point of view of SNR is not always an optimum system with respect to error performance. A detailed theory of error performance is presented, and the error of a SV polarimeter is shown to be related to the stability and condition number of the polarization processing matrices. The rms error is found to fall off as the inverse of the number of measurements taken. Finally, the concepts used to optimize SV polarimeters are extended to be useful for full Mueller matrix polarimeters.     

Optical Transmission in Polycrystals

Optical transmission in a polycrystalline aggregate consisting of randomly oriented anisotropic transparent crystals has been worked using Mueller matrices. The interesting results are: (1) A completely polarized beam of light emerges as partially polarized light. (2) The completely polarized part of the emergent beam is in the same state of polarization as the incident light for optically inactive crystallites. (3) The intensity of the completely polarized part not only depends on the optical and the geometrical parameters of the crystallite but also on the polarization state of the incident light. (4) For optically active crystallites the medium behaves as an isotropic optically active solid with a rotatory power equal to the mean rotatory power of the single crystal. This helps one in extracting most of the gyration tensor components in enantiomorphic optically active crystals.     

Polarization and retinal image quality estimates in the human eye

We have previously studied how polarization affects the double-pass estimates of the retinal image quality by using an imaging polarimeter [Opt. Lett. 24, 64 (1999)]. A series of 16 images for independent combinations of polarization states in the polarimeter were recorded to obtain the spatially resolved Mueller matrices of the eye. From these matrices, double-pass images of a point source for light with different combinations of incoming (first-pass) and outcoming (second-pass) polarization states were reconstructed and their corresponding modulation transfer functions were calculated. We found that the retinal image or, alternatively, the ocular aberrations, are nearly independent of the state of polarization of the incident light (in the first pass). This means that a significant improvement in the ocular optics by using a specific type of polarized light could not be achieved. However, quite different estimates of the retinal image quality are obtained for combinations of polarization states in both the first and the second passes in the double-pass apparatus.     

Neural network pattern recognition by means of differential absorption Mueller matrix spectroscopy

Artificial neural network systems were built for detecting amino acids, sugars, and other solid organic matter by pattern recognition of their polarized light scattering signatures in the form of a Mueller matrix. Backward-error propagation and adaptive gradient descent methods perform network training. The product of the training is a weight matrix that, when applied as a filter, discerns the presence of the analytes on the basis of their cued susceptive Mueller matrix difference elements. This filter function can be implemented as a software or a hardware module to a future differential absorption Mueller matrix spectrometer.     

Properties of light reflected from road signs in active imaging

Night vision systems in vehicles are a new emerging technology. A crucial problem in active (laser-based) systems is distortion of images by saturation and blooming due to strong retroreflections from road signs. We quantify this phenomenon. We measure the Mueller matrices and the polarization state of the reflected light from three different types of road sign commonly used. Measurements of the reflected intensity are also taken with respect to the angle of reflection. We find that different types of sign have different reflection properties. It is concluded that the optimal solution for attenuating the retroreflected intensity is using a linear polarized light source and a linear polarizer with perpendicular orientation (with regard to the source) at the detector. Unfortunately, while this solution performs well for two types of road sign, it is less efficient for the third sign type.     

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.     

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.     

Linear dichroism of the retinal nerve fiber layer expressed with Mueller matrices

An electro-optic device is used that permits the measurement of polarized absorption spectra (linear dichroism). The change of the polarization state of a light beam brought about by passage through the optic elements of a dichrograph are described mathematically by a transformation of the Stokes vector. The polarization or absorption properties of the optical elements are described by the Mueller matrices. The dichroic properties of sheep retina and cornea are studied in vitro.     

Formulation of a Mueller matrix for modeling of depolarization and scattering of nitrobenzene in a Kerr cell

We have studied the depolarization of light from nitrobenzene in a Kerr cell. We observed that absorption in nitrobenzene is electric-field dependent. For modeling a nitrobenzene device we formulated a Mueller matrix for the Kerr-cell assembly, and by operating it on a Stokes vector of the input light we obtained a corresponding Stokes vector for the output light. The first parameter of the output Stokes vector corresponds to the intensity transmittance. It was simulated and compared with the measured intensity transmittance for several orientations of the polarizer-analyzer pair with respect to the applied voltages. The measurement of all unknown coefficients in a Mueller matrix consisting of the superposition of nondepolarizing and depolarizing components predicts the depolarization, scattering, and absorption in the nitrobenzene electro-optic device. The output intensities of the orthogonally polarized and cross-coupled depolarizing coefficients are in good agreement for a semi-isotropic medium. The formulated Mueller matrix agrees with the experimentally measured transmittance.     

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.