Polarimetric Quantities Research Articles

The polarization of the boundary layer around weakly magnetized neutron stars in X-ray binaries

Context. X-ray binaries hosting a compact object have been among the main targets of the Imaging X-ray Polarimetry Explorer (IXPE) since its launch, due to their high brightness in the 2–8 keV energy band. The spectropolarimetric analysis performed so far has proved to be of great importance in providing constraints on the accretion geometry of these systems. However, the data statistics is not enough to unambiguously disentangle the contribution of the single components to the net observed polarimetric signal. Aims. In this work, we aim to present a model for computing the polarization degree and polarization angle of the boundary layer around weakly magnetized neutron stars in low-mass X-ray binaries in the soft state. The main motivation is to provide strong theoretical support to data interpretation of observations performed by IXPE or future satellites for X-ray polarimetry. Methods. The results were obtained by modeling the boundary layer as an equatorial belt around the compact object and locally approximating it as a plane-parallel scattering atmosphere, for which the associated radiative transfer equation for polarized radiation in the Thomson limit was solved. The polarimetric quantities were then transformed from the comoving frame to the observer frame using the numerical methods formerly developed for X-ray pulsars. Results. For typical values of the optical depth and electron temperature of the boundary layer of these systems in a soft state, the polarization degree was less then 0.5%, while the polarization angle was rotated by ≲5° with respect to the neutron star spin axis due to special and general relativistic effects for fast rotation, the amount progressively decreasing for lower spin frequencies. The derived quantities can be used to remove degeneracy when multicomponent spectropolarimetry is performed.

Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning

In biophotonics, novel techniques and approaches are being constantly sought to assist medical doctors and to increase both sensitivity and specificity of the existing diagnostic methods. In such context, tissue polarimetry holds promise to become a valuable optical diagnostic technique as it is sensitive to tissue alterations caused by different benign and malignant formations. In our studies, multiple Mueller matrices were recorded for formalin-fixed, human,ex vivocolon specimens containing healthy and tumor zones. The available data were pre-processed to filter noise and experimental errors, and then all Mueller matrices were decomposed to derive polarimetric quantities sensitive to malignant formations in tissues. In addition, the Poincaré sphere representation of the experimental results was implemented. We also used the canonical and natural indices of polarimetric purity depolarization spaces for plotting our experimental data. A feature selection was used to perform a statistical analysis and normalization procedure on the available data, in order to create a polarimetric model for colon cancer assessment with strong predictors. Both unsupervised (principal component analysis) and supervised (logistic regression, random forest, and support vector machines) machine learning algorithms were used to extract particular features from the model and for classification purposes. The results from logistic regression allowed to evaluate the best polarimetric quantities for tumor detection, while the use of random forest yielded the highest accuracy values. Attention was paid to the correlation between the predictors in the model as well as both losses and relative risk of misclassification. Apart from the mathematical interpretation of the polarimetric quantities, the presented polarimetric model was able to support the physical interpretation of the results from previous studies and relate the latter to the samples’ health condition, respectively.

Experimental validation of depolarizing Mueller matrix model via ex vivo colon samples

Experimental validation of a previously reported depolarizing Mueller matrix model is crucial to understanding the light-tissue interactions and the morphological alterations originating in malignant tissue zones in terms of their optical properties. This manuscript is a continuation of a previously reported case study, where a theoretical model was introduced with an additional Monte Carlo simulation. The main aim of this study is to empirically validate both theory and modelling. Once extracted from an experimental Mueller matrix via symmetric decomposition, the polarimetric quantities were compared with the corresponding parameters previously determined from polarized Monte Carlo simulations. Our results were obtained from an ex vivo colon sample and indicate a potential capability to provide supplementary polarimetric data to physicians and the gold standard histopathology analysis.

Dynamically important magnetic fields near the event horizon of Sgr A*

We study the time-variable linear polarisation of Sgr A* during a bright near-infrared flare observed with the GRAVITY instrument on July 28, 2018. Motivated by the time evolution of both the observed astrometric and polarimetric signatures, we interpret the data in terms of the polarised emission of a compact region (“hotspot”) orbiting a black hole in a fixed, background magnetic field geometry. We calculated a grid of general relativistic ray-tracing models, created mock observations by simulating the instrumental response, and compared predicted polarimetric quantities directly to the measurements. We take into account an improved instrument calibration that now includes the instrument’s response as a function of time, and we explore a variety of idealised magnetic field configurations. We find that the linear polarisation angle rotates during the flare, which is consistent with previous results. The hotspot model can explain the observed evolution of the linear polarisation. In order to match the astrometric period of this flare, the near horizon magnetic field is required to have a significant poloidal component, which is associated with strong and dynamically important fields. The observed linear polarisation fraction of ≃30% is smaller than the one predicted by our model (≃50%). The emission is likely beam depolarised, indicating that the flaring emission region resolves the magnetic field structure close to the black hole.

Visible and near-infrared spectro-interferometric analysis of the edge-on Be star o Aquarii

Aims. We present a detailed visible and near-infrared spectro-interferometric analysis of the Be-shell star o Aquarii from quasi-contemporaneous CHARA/VEGA and VLTI/AMBER observations. Methods. We analyzed spectro-interferometric data in the Hα (VEGA) and Brγ (AMBER) lines using models of increasing complexity: simple geometric models, kinematic models, and radiative transfer models computed with the 3D non-LTE code HDUST. Results. We measured the stellar radius of o Aquarii in the visible with a precision of 8%: 4.0 ± 0.3 R⊙. We constrained the circumstellar disk geometry and kinematics using a kinematic model and a MCMC fitting procedure. The emitting disk sizes in the Hα and Brγ lines were found to be similar, at ~10–12 stellar diameters, which is uncommon since most results for Be stars indicate a larger extension in Hα than in Brγ. We found that the inclination angle i derived from Hα is significantly lower (~15°) than the one derived from Brγ: i ~ 61.2° and 75.9°, respectively. While the two lines originate from a similar region of the disk, the disk kinematics were found to be near to the Keplerian rotation (i.e., β = −0.5) in Brγ (β ~ −0.43), but not in Hα (β ~ −0.30). After analyzing all our data using a grid of HDUST models (BeAtlas), we found a common physical description for the circumstellar disk in both lines: a base disk surface density Σ0 = 0.12 g cm−2 and a radial density law exponent m = 3.0. The same kind of discrepancy, as with the kinematic model, is found in the determination of i using the BeAtlas grid. The stellar rotational rate was found to be very close (~96%) to the critical value. Despite being derived purely from the fit to interferometric data, our best-fit HDUST model provides a very reasonable match to non-interferometric observables of o Aquarii: the observed spectral energy distribution, Hα and Brγ line profiles, and polarimetric quantities. Finally, our analysis of multi-epoch Hα profiles and imaging polarimetry indicates that the disk structure has been (globally) stable for at least 20 yr. Conclusions. Looking at the visible continuum and Brγ emission line only, o Aquarii fits in the global scheme of Be stars and their circumstellar disk: a (nearly) Keplerian rotating disk well described by the viscous decretion disk (VDD) model. However, the data in the Hα line shows a substantially different picture that cannot fully be understood using the current generation of physical models of Be star disks. The Be star o Aquarii presents a stable disk (close to the steady-state), but, as in previous analyses, the measured m is lower than the standard value in the VDD model for the steady-state regime (m = 3.5). This suggests that some assumptions of this model should be reconsidered. Also, such long-term disk stability could be understood in terms of the high rotational rate that we measured for this star, the rate being a main source for the mass injection in the disk. Our results on the stellar rotation and disk stability are consistent with results in the literature showing that late-type Be stars are more likely to be fast rotators and have stable disks.

SAR Imagery for Detecting Sea Surface Slicks: Performance Assessment of Polarization-Dependent Parameters

Remote sensing technology is an essential link in the global monitoring of the ocean surface, and radars are efficient sensors for detecting marine pollution. When used operationally by authorities, a tradeoff must usually be made between the covered area and the quantity of information collected by the radar. To identify the most appropriate imaging mode, a methodology based on receiver operating characteristic curve analysis has been applied to an original data set collected by two airborne systems operating at L-band, both characterized by a very low instrument noise floor. The data set was acquired during controlled releases of mineral and vegetable oil at sea. Various polarization-dependent quantities are investigated, and their ability to detect slick-covered areas is assessed. A relative ordering of the main polarimetric parameters is reported in this paper. When the sensor has a sufficiently low noise floor, HV is recommended because it provides the strongest slick-sea contrast. Otherwise, VV is found to be the most relevant parameter for detecting slicks on the ocean surface. Among all the investigated quad-polarimetric settings, no significant added value compared to single-polarized data was found. More specifically, it is demonstrated, by increasing the instrument noise level, that the studied polarimetric quantities which combine the four polarimetric channels have performances of detection mainly driven by the instrument noise floor, namely, the noise equivalent sigma zero. This result, obtained by progressively adding noise to the raw synthetic aperture radar (SAR) data, indicates that the polarimetric discrimination between clean sea and polluted area results mainly from the differentiated behavior between single-bounce scattering and noise. It is thus demonstrated, using SAR data collected with a low instrument noise floor, that there is no deviation from Bragg scattering for radar scattering from ocean surface covered by mineral and vegetable oil.

Simulated Polarimetric Fields of Ice Vapor Growth Using the Adaptive Habit Model. Part I: Large-Eddy Simulations

Abstract The bulk adaptive habit model (AHM) explicitly predicts ice particle aspect ratio, improving the representation of microphysical processes and properties, including ice–liquid-phase partitioning. With the unique ability to predict ice particle shape and density, the AHM is combined with an offline forward operator to produce fields of simulated polarimetric variables. An evaluation of AHM-forward-simulated dual-polarization radar signatures in an idealized Arctic mixed-phase cloud is presented. Interpretations of those signatures are provided through microphysical model output using the large-eddy simulation mode of the Weather Research and Forecasting Model. Vapor-grown ice properties are associated with distinct observable signatures in polarimetric radar variables, with clear sensitivities to the simulated ice particle properties, including ice number, size, and distribution shape. In contrast, the liquid droplet number has little influence on both polarimetric and microphysical variables in the case presented herein. Polarimetric quantities are sensitive to the dominating crystal habit type in a volume, with enhancements for aspect ratios much lower or higher than unity. This synthesis of a microphysical model and a polarimetric forward simulator is a first step in the evaluation of detailed AHM microphysics.

Simulated Polarimetric Fields of Ice Vapor Growth Using the Adaptive Habit Model. Part II: A Case Study from the FROST Experiment

Abstract A new adaptive habit model (AHM) grows ice crystals through vapor deposition while evolving ice particle properties, including shape and effective density. The AHM provides an opportunity to investigate observed microphysical processes through the computation of polarimetric variables and corroboration with microphysical model output. This study is unique because the polarimetric scattering calculations are computed using predicted microphysical parameters rather than a priori assumptions that are imposed within the scattering calculations in the forward simulator, allowing for a more effective comparison to radar observations. Through the simulation of a case in the Front Range of the Rocky Mountains in Colorado using the Advanced Research version of the Weather Research and Forecasting Model, it is found that the AHM approximates ice mass, shape, cloud vertical structure, and temporal evolution as reflected through polarimetric quantities compared to observations. AHM reflectivity magnitudes are similar to those observed with radar and are an improvement over spherical ice crystal assumptions. Further analyses are completed to examine the effect of microphysical processes on the evolution of the differential reflectivity and specific differential phase, both of which are simulated using the AHM. Simulations reveal a polarimetric response to ice crystal mass, number, size, density, and aspect ratio. While results reveal the need for model improvements (e.g., parameterizations for aggregation rate), testing forward-simulated radar fields against observations is a first step in the validation of model microphysical and precipitation processes.

Dual‐polarization radar products for biological applications

AbstractThe upgrade of the national network of next‐generation weather surveillance radars (NEXRAD) in the United States to dual polarizations has been completed, providing three additional routine data products: total differential phase (ψDP), differential reflectivity (ZDR), and copolar correlation coefficient (ρHV). The application and interpretation of these products in the context of aerial bird, bat, and insect movements is an actively developing research front, with potential implications for ecological and conservation studies. The following conceptually derives the definition of these products specifically for NEXRAD weather surveillance radars in the case of biological scatterers. Several cases are presented that illustrate characteristic values and variability of polarimetric quantities for birds and insects, and highlight site‐specific differences within the NEXRAD network. Finally, a short prospectus of future directions and applications within the field of polarimetric radar aeroecology is outlined.

Invariant quantities of a Mueller matrix under rotation and retarder transformations

Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic probe beams. The polarimetric quantities that are invariant under rotations of the said reference frames about the respective directions of propagation (rotation transformations) provide particularly interesting physical information. Moreover, certain properties are also invariant with respect to the action of birefringent devices located on both sides of the medium under consideration (retarder transformations). The polarimetric properties that remain invariant under rotation and retarder transformations are calculated from any given Mueller matrix and are then analyzed and interpreted, providing significant parameterizations of Mueller matrices in terms of meaningful physical quantities.

Detection of ice types in the Eastern Weddell Sea by fusing L- and C-band SIR-C polarimetric quantities

This article discusses the use of spaceborne polarimetric L-band and C-band synthetic aperture radar (SAR) data for sea-ice detection and classification. The benefits of combining L-band with C-band polarimetric quantities for supervised sea-ice classification in the Eastern Weddell Sea, Antarctica, are investigated. In the experiments, we compared the performance of a maximum likelihood (ML) classifier when used with the combined preferred polarimetric parameters and the individual ones, respectively. The relation between the classification accuracy and the preferred number of polarimetric parameters for classification was examined as well as whether principal component analysis (PCA) and locally linear embedding (LLE) can be used to reduce the dimensionality of the parameter sets. Combining dual-frequency polarimetric quantities improves classification accuracy compared to using individual single-frequency polarimetric quantities. By increasing the dimensionality of the preferred polarimetric parameter sets, the classification using high dimensionality can either result in improvements over the smaller subsets or result in no significant differences. Therefore, using all available polarimetric quantities over the study region is recommended. Further, data fusion with a PCA-based approach is found to be beneficial for sea-ice detection and classification, and poor results have been produced with an LLE-based approach.

DYNAMICAL EVOLUTION OF VISCOUS DISKS AROUND BE STARS. II. POLARIMETRY

Be stars exhibit variability for a great number of observables. Putting the pieces together of the disk dynamics is not an easy task and requires arduous modeling before achieving a good fit of the observational data. In order to guide the modeling process and make it more efficient, it is very instructive to investigate reference dynamical cases. This paper focuses on continuum polarimetric quantities and is the second of a series that aims to demonstrate the capacity of deriving the dynamical history and fundamental parameters of a classical Be star through the follow-up of various observables. After a detailed study of the different opacities at play in the formation of polarized spectra, we investigate predictions of polarimetric observables in the continuum for different dynamical scenarios. Our models are based on a coupling of a hydrodynamic viscous decretion simulations in a disk and a 3-D non-LTE radiative transfer code. Introducing the polarization color diagram (PCD), we show that certain combinations of polarimetric observables exhibit features that are characteristic of a mass loss history. This diagram also enables to estimate fundamental parameters such as the inclination angle, the disk density scale and the $\alpha$ viscous diffusion parameter. We present the PCD as a powerful diagnosis tool to track the dynamical phases of a Be star such as disk building-up, dissipation, periodic and episodic outbursts. Finally we confront our models with observations of 4 Be stars that exhibited long-term polarimetric activity.

Review on Mueller matrix algebra for the analysis of polarimetric measurements

The measured Mueller matrices contain up to 16 independent parameters for each measurement configuration (spectral profile of the wave probe of the polarimeter, angle of inci- dence, observation direction, etc.) and for each spatially resolved element of the sample (imaging polarimetry). Thus, the polarimetric techniques are widely used for the study of a great variety of material samples in optics and remote sensing. Nevertheless, the relevant physical information does not appear explicitly in the measured parameters, and thus, the best knowledge of the struc- ture of the physical information contained in a Mueller matrix is required in order to develop appropriate procedures for the polarimetric analysis. The main approaches for serial and parallel decompositions as well as for the geometric representation of measured Mueller matrices are reviewed. Furthermore, the physically invariant polarimetric quantities are identified and decoupled. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the origi- nal publication, including its DOI. (DOI: 10.1117/1.JRS.8.081599)

A Polarimetric Radar Forward Operator for Model Evaluation

Abstract A polarimetric radar forward operator has been developed as a tool for the systematic evaluation of microphysical parameterization schemes in high-resolution numerical weather prediction (NWP) models. The application of such a forward operator allows a direct comparison of the model simulations to polarimetric radar observations. While the comparison of observed and synthetic reflectivity gives information on the quality of quantitative precipitation forecasts, the information from the polarimetric quantities allows for a direct evaluation of the capacity of the NWP model to realistically describe the processes involved in the formation and interactions of the hydrometeors and, hence, the performance of the microphysical parameterization scheme. This information is expected to be valuable for detecting systematic model errors and hence improve model physics. This paper summarizes the technical characteristics of the synthetic polarimetric radar (SynPolRad). Different polarimetric radar quantities are computed from model forecasts using a T-matrix scattering code and ice phase hydrometeors are explicitly considered. To do so, the sensitivities of the scattering processes to the microphysical characteristics of different ice hydrometeors are investigated using sensitivity studies. Furthermore, beam propagation effects are considered, including attenuation and beam bending. The performance of SynPolRad and the consistence of the assumptions made in the derivation of the input parameters are illustrated in a case study. The resulting synthetic quantities as well as hydrometeor classification are compared with observations and are shown to be consistent with the model assumptions.

Improvement of Microphysical Parameterization through Observational Verification Experiment

Despite continual increases in numerical model resolution and significant improvements in the forecasting of many meteorological parameters, progress in quantitative precipitation forecasting (QPF) has been slow. This is attributable in part to deficiencies in the bulk microphysical parameterization (BMP) schemes used in mesoscale models to simulate cloud and precipitation processes. These deficiencies have become more apparent as model resolution has increased. To address these problems requires comprehensive data that can be used to isolate errors in QPF due to BMP schemes from those due to other sources. These same data can then be used to evaluate and improve the microphysical processes and hydrometeor fields simulated by BMP schemes. In response to the need for such data, a group of researchers is collaborating on a study titled the Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE). IMPROVE has included two field campaigns carried out in the Pacific Northwest: an offshore frontal precipitation study off the Washington coast in January–February 2001, and an orographic precipitation study in the Oregon Cascade Mountains in November–December 2001. Twenty-eight intensive observation periods yielded a uniquely comprehensive dataset that includes in situ airborne observations of cloud and precipitation microphysical parameters; remotely sensed reflectivity, dual-Doppler, and polarimetric quantities; upper-air wind, temperature, and humidity data; and a wide variety of surface-based meteorological, precipitation, and microphysical data. These data are being used to test mesoscale model simulations of the observed storm systems and, in particular, to evaluate and improve the BMP schemes used in such models. These studies should lead to improved QPF in operational forecast models.

Fourier analysis near-field polarimetry for measurement of local optical properties of thin films.

We present measurements of the local diattenuation and retardance of thin-film specimens by using techniques that combine near-field scanning optical microscopy (NSOM) and a novel polarization-modulation (PM) polarimetry utilizing Fourier analysis of the detected intensity signal. Generally, quantitative near-field polarimetry is hampered by the optical anisotropy of NSOM probes. For example, widely used aluminum-coated pulled-fiber aperture probes typically exhibit a diattenuation near 10%. Our analysis of aperture diattenuation demonstrates that the usual techniques for nulling a PM polarimeter result in a nonzero residual probe retardance in the presence of a diattenuating tip. However, we show that both diattenuation and retardance of the sample can be determined if the corresponding tip properties are explicitly measured and accounted for in the data. In addition, in thin films (<100 nm thick), where the sample retardance and diattenuation are often small, we show how to determine these polarimetric quantities without requiring alignment of the fast and diattenuating axes, which is a more general case than has been previously discussed. We demonstrate our techniques by using two types of polymer-film specimens: ultrahigh molecular weight block copolymers (recently noted for their photonic activity) and isotactic polystyrene spherulites. Finally, we discuss how changes in the tip diattenuation during data collection can limit the accuracy of near-field polarimetry and what steps can be taken to improve these techniques.

Restoration of polarimetric SAR images using simulated annealing

Filtering synthetic aperture radar (SAR) images ideally results in better estimates of the parameters characterizing the distributed targets in the images while preserving the structures of the nondistributed targets. However, these objectives are normally conflicting, often leading to a filtering approach favoring one of the objectives. An algorithm for estimating the radar cross-section (RCS) for intensity SAR images has previously been proposed in the literature based on Markov random fields and the stochastic optimization method simulated annealing. A new version of the algorithm is presented applicable to multilook polarimetric SAR images, resulting in an estimate of the mean covariance matrix rather than the RCS. Small windows are applied in the filtering, and due to the iterative nature of the approach, reasonable estimates of the polarimetric quantities characterizing the distributed targets are obtained while at the same time preserving most of the structures in the image. The algorithm is evaluated using multilook polarimetric L-band data from the Danish airborne EMISAR system, and the impact of the algorithm on the unsupervised H-/spl alpha/ classification is demonstrated.

A fully polarimetric multiple scattering model for crops

This article describes an electromagnetic model which simulates the microwave polarimetric backscatter of agricultural fields. The model is based on radiative transfer theory and solves the relevant equation by means of a numerical algorithm, namely matrix doubling, which includes multiple scattering effects. The backscatter coefficient may be simulated for any pair of incidence and scattering elliptical polarizations; also, the phase difference between VV and HH channels is computed. Model simulations are compared with experimental results obtained at L band (1.2 GHz) by the NASA-JPL AIRSAR, in the framework of the MAC Europe '91 campaign, over sunflower fields belonging to an Italian site named Montespertoli. A satisfactory agreement is observed between predicted and measured polarimetric quantities of vegetated fields, while for bare soils (particularly at VV polarization) backscatter coefficients are overestimated, due to inaccuracies of surface models available at present.

Millimeter-wave radars for remotely sensing clouds and precipitation

Millimeter-wave radars have been used since the early 1950s to study clouds and precipitation, but until recently these early instruments were limited to simple backscatter power measurements and were plagued by hardware problems. However, development of solid-state millimeter-wave componentry and high-power klystron amplifiers has spurred the evolution of reliable, coherent radars operating up to 95 GHz. In addition, advances in digital signal processing technology have resulted in single-card processors that can simultaneously execute algorithms to compute reflectivity, Doppler, and polarimetric quantities in real time. A review of the current state of the art in millimeter-wave cloud radars is presented, including a discussion of transmitters, antennas, and receiver components. Two radar systems built by the University of Massachusetts are described, including a mobile, dual-frequency (33- and 95-GHz) polarimetric radar, and an airborne 95-GHz polarimetric radar that was recently flown in a cooperative experiment with the University of Wyoming. Spaceborne applications are also discussed, especially the use of satellite-based 95-GHz radars for measuring the vertical distribution of clouds. >