Determination of the Polarization Characteristics of Objects by the Method of Three Probing Polarizations

A method of three probing polarizations for determining the polarization characteristics of objects by measuring their Mueller complete and incomplete matrices has been developed. The conditions of optimal implementation of the method from the viewpoint of minimizing the error in measurement of the Mueller matrix elements have been investigated.     

Spectroscopic Mueller matrix polarimeter using four-channeled spectra

A Mueller matrix polarimeter acquired for four-channeled spectra is proposed. Both the polarizing and analyzing optics of this system consist of a linear polarizer and a high-order retarder. The polarizing elements can modulate the polarization states in the wavenumber space. By applying a Fourier transform method to a single-channeled spectrum, nine elements of the Mueller matrix can be deconvoluted without modifying the configuration of either the polarizing or analyzing optics. It is thus possible to determine the wavelength dependence of all the Mueller matrix elements from four-channeled spectra obtained using four different configurations for the polarizing and analyzing optics. The performance of this method is evaluated by measuring polarization properties, such as retardance, azimuthal angle, and linear diattenuation, from the obtained Mueller matrix in wavenumber space.     

Three linear probe polarization method in Mueller polarimetry with a source of arbitrary ellipticity

This is a study of the effect of the ellipticity of the polarization of radiation at the inlet of the shaping polarizer in the probe channel of a Mueller polarimeter operating with three linear probe polarizations on the accuracy with which the incomplete Mueller matrix is determined (without a fourth beam). It is shown that the appearance of and variations in the ellipticity cause a change in the conditions for optimization of the set of polarizations of the probe radiation from the standpoint of minimizing the measurement error. In the case of linear polarization (zero ellipticity), the measurement error is the same as the error when four probe polarizations are used. This allows measurement of the complete Mueller matrix and makes this version of the polarimeter especially promising, because in the input channel of the polarimeter, a single polarizing element, i.e., a linear polarizer with a controllable azimuthal orientation, can be used as the polarization transducer. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 875–880, November–December, 2008.     

旋转波片偏振仪波片方位误差研究

旋转波片Stokes偏振仪是最常用的测量光束偏振态的仪器。波片快轴方位误差是影响旋转波片Stokes偏振仪的主要误差源之一。为了研究波片方位偏差对测量精度的影响,提出了一种描述波片快轴方位误差向最终的偏振测量误差传递的数学模型,并引入协方差矩阵法表征偏振测量误差。根据这一模型,获得最优的偏振仪配置参数。在推导过程中,假设波片方位误差服从同一高斯分布。基于此误差模型,得到如下结论：(1)由波片方位误差引入的测量误差与光强测量次数N成反比;(2)测量误差独立于入射光强度,但是依赖于入射光偏振态(s₁, s₂, s₃)和波片的位相延迟量δ;(3)波片位相延迟量在(103.22°, 116.13°)范围内时波片方位误差引入的测量误差最小。最后,经过仿真实验证明,所得解析结果与仿真模拟结果相一致。     

Observation of the circular polarization correlation of the positron-electron annihilation quanta

The circular polarization-circular polarization angular correlation of annihilation quanta has been measured unambiguously by use of two backscattering Compton polarimeters in coincidence. The interpretation of the measurement required a quantum mechanical calculation of the circular polarization detection probability for coincident annihilation quanta. This calculation showed that the most favourable geometry for detecting a circular polarization correlation is the backscattering geometry because here, in contrast to forward scattering and transmission geometries, strong perturbations by the linear polarization correlation are not present. By using the polarization efficiencyη=4.7% for a single polarimeter, which was derived from a Monte Carlo calculation, the measured effect for the circular polarization-circular polarization correlation showed good agreement with theory.     

Polarimetric characterization of ultra-high molecular weight polyethylene (UHMWPE) for bone substitute biomaterials

In this work the UHMWPE is characterized for their optical properties with Mueller matrix polarimeter. The transmittance birefringence, retardance, polarizance, linear and circular polarization and absorbance of polarized light at different wavelengths ranging 400-800 nm are measured. The presented Mueller matrix elements along with depth resolve polarization decrease in intensity with the change in the wavelength. Linear retardance increases compared to circular through highly scattering polyethylene. High refractive index and low mean free path; and close bonding of particles of material rotates the incoming photons and circular polarization which is dominant as compared to the linear one. Therefore the average intensity increases with both the optical depth and the scattered concentration in UHMWPE, which would accordingly decrease the apparent degree of polarization.The extracted results in terms of linear and circular retardances prove that UHMWPE is compatible, strong, and compact. This research work provides an optical characterization technique for bone substitute biomaterial in the health care industry.     

Role of the null space of the DRM in the performance of modulated polarimeters

Imaging polarimeters infer the spatial distribution of the polarization state of the optical field as a function of time and/or wavelength. A polarimeter indirectly determines the polarization state by first modulating the intensity of the light field and then demodulating the measured data to infer the polarization parameters. This Letter considers passive Stokes parameter polarimeters and their inversion methods. The most widely used method is the data reduction matrix (DRM), which builds up a matrix equation that can be inverted to find the polarization state from a set of intensity measurements. An alternate strategy uses linear system formulations that allow band limited reconstruction through a filtering perspective. Here we compare these two strategies for overdetermined polarimeters and find that design of the null space of the inversion operator provides degrees of freedom to optimize the trade off between accuracy and signal-to-noise ratio. We further describe adaptive filtering techniques that could optimize the reconstruction for a particular experimental configuration. This Letter considers time-varying Stokes parameters, but the methods apply equally to polarimeters that are modulated in space or in wavelength.     

Measurements of structure-induced polarization features in forward scattering from collections of cylindrical fibers

Many applications in remote sensing, material sciences and biomedical field are characterized by a transition domain between single scattering and multiple-scattering regimes. This regime is described by typical polarization features which can be used to retrieve structural information. An electronically agile technique was used for measuring in real time the Stokes vectors of light incident on and emerging from an inhomogeneous medium. Subsequently, the Mueller matrix associated with the scattering medium is determined. We focus our attention on forward scattering from systems consisting of random as well as partially oriented long cylindrical fibers. We discuss the effects of: (1) shape of individual scattering centers, (2) structure parameter, and (3) optical density of the scattering medium. The anisotropic behavior of the structure function at different packing fractions determines nontrivial characteristics of the polarization transfer. The complex effective index of refraction can be polarization dependent as a result of the optical anisotropy due to both the shape of the individual scatterers and the structure characteristics of the scattering system. Some of the Mueller matrix elements are shown to be related to the optical anisotropy of the system for the case of long cylindrical fibers. The polarization efficiency, the structure parameter, and the packing fraction are used to quantify this relationship. We also found that some of the matrix elements are more sensitive to the degree of structural anisotropy and the packing fraction, while other elements are sensitive to structural non-uniformities across the investigated area.     

Test of a symmetrical four-detector compton polarimeter using low temperature nuclear orientation

A symmetrical four-detector Compton polarimeter was used to measure the linear polarization of gamma-rays emitted from nuclei oriented by the hyperfine interaction at low temperature. Its polarization detection efficiency was determined in the range 0.3–1.4 MeV and compared with some other polarimeters.     

基于双折射晶体的快拍穆勒矩阵成像测偏原理分析

针对传统穆勒矩阵成像测偏仪包含活动部件,需进行多次测量,容易产生测量误差,不能对运动目标或动态场景进行同时、实时测量等问题,提出了一种以改进型萨瓦偏光镜为核心分光器件的快拍Mueller矩阵成像测偏技术(MSP-SMMIP).它不含任何活动部件,能通过单次快拍测量获取目标强度图像和全部16个穆勒矩阵阵元图像.它主要由偏振态产生和偏振态分析两部分组成,偏振干涉条纹通过偏振态产生光路后定位于测试样品上,随后这些条纹通过空间载频将样品的Mueller矩阵分量编码,经偏振态分析光路成像于焦平面上.采用斯托克斯矢量-穆勒矩阵形式阐明了光场偏振态被MSP-SMMIP调制的过程,给出了其像面干涉图表达式,讨论了Mueller矩阵反演和系统定标的方法.基于CCD相机参数分析了系统的光学指标.通过数值模拟实验给出模拟测量结果,通过定性和定量评价测量结果表明该系统的可行性.MSP-SMMIP技术具有稳态、快拍、结构简洁、易定标、可同时实时获取目标强度图像和全部Mueller矩阵阵元图像的显著特点.     

Calculation of Systematic Errors in Determining Light‐Scattering Matrix Elements

We consider systematic errors in determining lightscattering matrix elements by a device in which the polarization properties of probing radiation change depending on different angular positionings of the principal directions of the first phase plate, and we perform polarization analysis of scattered radiation using the Fourier expansion of the signal from a photodetector that records the intensity of radiation passed through the rotating second phase plate and a stationary analyzer. Formulas estimating the errors arising in separate deviation of the axes of the anisotropic optical elements in the illuminating and lightreceiving channels of the measuring device were derived. Using the method of mathematical simulation, we consider the combined influence of various inaccuracies in positioning anisotropic elements.     

Mueller matrix differential decomposition

We present a Mueller matrix decomposition based on the differential formulation of the Mueller calculus. The differential Mueller matrix is obtained from the macroscopic matrix through an eigenanalysis. It is subsequently resolved into the complete set of 16 differential matrices that correspond to the basic types of optical behavior for depolarizing anisotropic media. The method is successfully applied to the polarimetric analysis of several samples. The differential parameters enable one to perform an exhaustive characterization of anisotropy and depolarization. This decomposition is particularly appropriate for studying media in which several polarization effects take place simultaneously.     

Optimization of a snapshot Mueller matrix polarimeter

We report on the optimization of a snapshot Mueller matrix polarimeter performed by using singular-value decomposition. The snapshot technique relies on wavelength polarization coding by four wave plates. The statistical noise on Mueller components is minimized through adjustment of the thickness of each plate. The spectrometer response and its cutoff frequency were considered to find the optimal configurations described here.     

Random error of determining light scattering matrix elements at various polarization states of probing radiation

Using the method of mathematical modeling, we consider the transformation of a random error of light intensity measurement into an error of determining elements of the light scattering matrix. We consider a device in which the polarization properties of probing radiation change depending on the setting of the phase plate and polarization analysis of scattered radiation is performed while the second phase plate located ahead of a stationary analyzer is rotated. A set of settings of the first phase plate has been revealed, which provides a minimum random error in determining the scattered light matrix elements. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 4, pp. 520–523, July–August, 2000.     

Measurement of optical rotation and phase retardance of optical samples with depolarization effects using linearly and circularly polarized probe lights

This paper presents an experimental technique for measuring the optical rotation, depolarization, and phase retardance of optical samples. In the proposed approach, the optical properties of the sample are derived using a Stokes–Mueller matrix formalism in conjunction with linearly and circularly polarized probe lights. For a compound sample comprising a half-wave plate positioned in front of glucose solutions with concentrations ranging from 0 to 1.2 g/dl, the average normalized error in the measured rotation angle is determined to be 3.11% when using a linearly polarized light. The average surviving linear and circular polarization fractions of the glucose solutions are determined to be 1.0252 and 0.9945. The average normalized error in the measured retardance of the half-wave plate is 3.45%. When measuring a compound sample comprising a half-wave plate positioned in front of the scattered glucose solutions with turbidities from 0% to 50% by the addition of milk, experimental results show that the induced rotation angle increased as the turbidity increased, whereas both surviving linear and circular polarization fractions decreased as the turbidity increased. The effect of the turbidity on rotation angle is more significant than that on both surviving linear and circular polarization fractions. The average normalized error in the measured retardance of the half-wave plate is 1.43%. Consequently, a simplified geometry of the polarimeter is proposed to independently estimate the rotation angle, surviving linear and circular polarization fractions, and retardance from the derived viable algorithm.     

Snapshot imaging Mueller matrix polarimeter using polarization gratings

A snapshot imaging Mueller matrix polarimeter (SIMMP) is theoretically described and empirically demonstrated through simulation. Spatial polarization fringes are localized onto a sample by incorporating polarization gratings (PGs) into a polarization generator module. These fringes modulate the Mueller matrix (MM) components of the sample, which are subsequently isolated with PGs in an analyzer module. The MM components are amplitude modulated onto spatial carrier frequencies which, due to the PGs, maintain high visibility in spectrally broadband illumination. An interference model of the SIMMP is provided, followed by methods of reconstruction and calibration. Lastly, a numerical simulation is used to demonstrate the system's performance in the presence of noise.     

The possibility of measuring linear and quadratic magnetooptical effects in magnetic field under conditions of magnetomechanical resonance

We have considered the possibility of measuring the linear and quadratic (in magnetic field) magnetooptical effects in magnetooptical crystals that are simultaneously exposed to a constant (polarizing) magnetic field and to an alternating magnetic field under conditions of magnetomechanical resonance. The use of a Mueller polarimeter in combination with spectral analysis of the intensity of the light wave at the output of the polarimeter makes it possible to selectively determine elements of the Mueller matrix and minimize the amount of measurements. We have shown that there is a possibility of solving the inverse problem on finding two components of the alternating magnetic field in which a magnetooptical crystal is placed.     

Polarimetric target detection in the presence of spatially fluctuating Mueller matrices

In polarimetric imaging systems, the main source of perturbations may not be detection noise but fluctuations of the Mueller matrices in the scene. In this case, we propose a method for determining the illumination and analysis polarization states that allow reaching the highest target detection performance. We show with simulations and real-world images that, in practical applications, the statistics of Mueller matrix fluctuations have to be taken into account to optimize polarimetric imagery.     

Single-shot full-field interferometric polarimeter with an integrated calibration scheme

A simple interferometric polarimeter with an integrated calibration scheme is proposed for accurate and fast mapping of the state of polarization (SOP). Conventional single-shot polarimeters that detect the amplitude and phase of orthogonally polarized field components by interferometry using Fourier fringe analysis suffers from errors caused by the imperfect reference beam and ambiguity in the spatial carrier frequency in the fringe pattern. In the proposed system, the integrated calibration scheme eliminates those error sources and enables accurate measurement of SOP without prior knowledge of the reference beam and the spatial carrier frequency.     

Hybrid complete Mueller polarimeter based on phase modulators

Optical properties of matter as diattenuation, retardance and depolarization can be evaluated using polarimetric techniques. In this paper, the analysis and implementation of a complete Mueller polarimeter is presented. The system is constituted of a polarization state generator (PSG) and a polarization state analyzer (PSA), which are controlled and synchronized through a computer program. The PSG comprises a dual liquid crystal variable retarder system while the PSA is based on a two-photoelastic modulator setup. Using air and common polarizing optics as test samples for calibration at 633 nm, the hybrid instrument met a good precision when the Mueller matrices of those optical elements were measured.