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.     

Product decompositions of depolarizing Mueller matrices with negative determinants

We show that the product decomposition of a depolarizing Mueller matrix (S.-Y. Lu, R.A. Chipman, J. Opt. Soc. Am. A 13 (1996) 1106) as well as the recently proposed reverse decomposition (R. Ossikovski, A. De Martino, Opt. Lett. 32 (2007) 689) need to be extended in order to account for Mueller matrices with negative determinants. The necessity of such an extension of the formalism is illustrated on experimentally determined Mueller matrices. The procedure of the modified decomposition formalism is explicitly described.     

Numerical study of the characterization of forward scattering Mueller matrix patterns of turbid media with triple forward scattering assumption

We propose a triple forward scattering model to numerically investigate the forward scattering Mueller matrix of a turbid medium. The calculated results show that the Mueller matrix based on the triple scattering model can completely describe the basic symmetries and azimuthal structures of the forward scattering Mueller matrix of a turbid medium. The results show that the forward scattering Mueller matrix is characterized with special symmetric structure compared with backscattering Mueller matrix patterns. The method will extend the investigation to light scattering mechanism from cells and to diagnosis of diabetes and other blood related diseases.     

基于Mueller矩阵椭偏仪的纳米压印模板与光刻胶光栅结构准确测量

在纳米压印工艺中,对模板和压印结构的几何参数进行快速、低成本、非破坏性地准确测量具有非常重要的意义.与传统光谱椭偏仪只能改变波长和入射角2个测量条件并且在每一组测量条件下只能获得振幅比和相位差2个测量参数相比,Mueller矩阵椭偏仪可以改变波长、入射角和方位角3个测量条件,而且在每一组测量条件下都可以获得一个4×4阶Mueller矩阵共16个参数,因此可以获得更为丰富的测量信息.通过选择合适的测量条件配置,充分利用Mueller矩阵中的测量信息,有望实现更为准确的纳米结构测量.基于此,本文利用自主研制的Mueller矩阵椭偏仪对硅基光栅模板和纳米压印光刻胶光栅结构进行了测量.实验结果表明,通过对Mueller矩阵椭偏仪进行测量条件优化配置,并且在光学特性建模时考虑测量过程中出现的退偏效应,可以实现压印工艺中纳米结构线宽、线高、侧壁角以及残胶厚度等几何参数更为准确的测量,同时对于纳米压印光刻胶光栅结构还可以直接得到光斑照射区域内残胶厚度的不均匀性参数.     

Mueller matrix-based optimization of reflective type twisted nematic liquid crystal SLM at oblique incidences

Mueller matrix measurements were used to characterize the polarization properties of liquid crystal-based reflective type twisted nematic (TN) special light modulator (SLM) at oblique incidence of the laser beam. The experimentally obtained Mueller matrices were used to obtain the combination of polarization optics required to optimize it for phase only modulation. The results indicate that minimum intensity modulation is obtained with the use of a polarizer followed by a quarter wave plate (QWP) in polarization state generator (PSG) arm and a QWP followed by an analyzer in polarization state analyzer arm (PSA). Polarization parameters such as retardance, rotation and depolarization were calculated from the experimentally obtained Mueller matrices using polar decomposition method at different angle of incidences of the laser beam and the results has been discussed. The similarity between retardance and depolarization curve as a function of address voltage of TNSLM indicated that depolarization is mainly associated with errors in retardance values. Further, spectral Mueller matrix measurements were used to obtain intensity modulation response in the range of wavelengths 450-700 nm for broadband applications.     

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.     

基于穆勒矩阵的模拟溢油样品荧光偏振特性研究

为了对模拟溢油样品在不同偏振态激发下诱导荧光的偏振特性进行研究,借鉴了穆勒矩阵椭偏仪的原理和结构,搭建了基于旋转波片原理的模拟溢油样品激光诱导荧光椭偏实验装置。通过特征值校准方法对该装置进行校准,获得了宽波段下偏振状态调制矩阵W(λ)和偏振状态分析矩阵A(λ)的确切调制状态,并基于荧光光谱强度矩阵Flu(λ)分别建立了轻、中、重质原油样品和柴油样品的荧光穆勒矩阵。通过极化分解方法对荧光穆勒矩阵进行分解后发现,不同样品荧光光谱的退偏振性质差异十分显著。柴油样品荧光穆勒矩阵的退偏振系数Δ(λ)没有明显的波长响应性,在荧光光谱范围内始终保持较高的退偏值,而三种原油样品的退偏系数Δ(λ)则随波长增大逐渐上升,其中,中质原油样品退偏系数随波长的变化幅度小于重质样品,超过轻质样品;就不同样品的退偏值来看,轻质原油样品最高,重质样品最低,中质原油样品介于二者之间,柴油样品的荧光退偏值略低于轻质原油样品,介于轻质和中质原油样品之间。将基于荧光穆勒矩阵极化分解后的结果与线偏振激发下样品荧光光谱的正交偏振实验结果进行对比,发现两种实验方法获得的退偏系数具有较高的吻合程度。实验还发现,四种模拟溢油样品荧光穆勒矩阵所包含的双向衰减和相位延迟性质都很微弱,不具有明显的差异。     

Mueller Matrix Analysis of PDL Components

A detailed Mueller-Stokes analysis of an arbitrary elliptical dichroic polarizer is presented. Explicit expressions for the Jones matrix, the Stokes parameters, and the Mueller matrix for a distributed and localized dichroic polarizer acting as a polarization-dependent loss (PDL) element are derived. Application to wavelength-dependent PDL elements is discussed. The Poincare sphere representation and the application of the Mueller matrices for the study of randomly oriented concatenated PDL elements and PDL vector measurement are addressed.     

Mueller-Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator

In the twisted nematic liquid crystal spatial light modulators (TN-LCSLM), distortion of uniform twist and decrease in tilt angle of liquid crystal molecules on application of an electric field lead to amplitude and phase modulations of the transmitted or reflected wavefront, respectively. The amplitude and phase modulation characterization of TN-LCSLM using Jones calculi is simple and extensively used but does not give any information about important polarimetric parameters such as diattenuation and depolarizance. On the other hand, the characterization using Mueller calculi provides all information in terms of polarimetric properties such as diattenuation, retardance (birefringence) and depolarization. In this paper, polarimetric properties of the transmissive TN-LCSLM (HOLOEYE LC2002) are characterized measuring 17 different Mueller matrices at different addressed gray scale through Mueller Matrix Imaging Polarimeter (MMIP) at 530 nm wavelength. Lu-Chipman polar decomposition for Mueller matrix is utilized to separate out three independent Mueller matrices for diattenuation, depolarization and retardance as a function of addressed gray scale. Further, Mueller-Stokes combined formulation is used to examine the effect of depolarization present in the TN-LCSLM on six different states of polarization and evaluation of eigenpolarization states for the TN-LCSLM has been presented.     

Iterative approach of high-order scattering solution for vector radiative transfer of inhomogeneous random media

By stratifying a random scatter media into multiple thin layers in the vertical z direction, the first-order scattering solution of each thin layer is employed to derive high-order scattering solution of whole random media. Using the Fourier transform and Mueller matrices in discrete ordinates, an iterative approach to solve high-order scattering solution of vector radiative transfer (VRT) equation is newly developed. Numerical results are well compared with the Mueller matrix solutions of the first order for a single layer medium, second order for a half-space, and the results of the discrete ordinate and eigen analysis method. It demonstrates our approach as feasible, effective and especially applicable to high-order solution of VRT for both bistatic scattering and thermal emission of inhomogeneous non-spherical scatter media.     

Use of Dirac matrices in polarization optics

Several matrix methods have been developed for studying polarization properties of light. Jones was the first to apply the matrix method to the study of polarization optics. In Jones matrix formalism the polarized wave field is represented by 2-element column matrix known as Jones Vector and the polarization device encountered by light is represented by a 2×2 matrix, known as the characteristic Jones matrix of the device. Mueller introduced a new matrix method where the wave field is represented by a 4-dimensional vector. The elements of the vector are the Stokes parameters of the beam. In Mueller matrix formalism the optical device is represented by a 4×4 real matrix known as ‘Mueller Matrix’ of the device. The use of coherency matrix also proves to the useful in the study of partially polarized light. Pauli spin matrices have been used to unify the different matrix treatments of polarization optical phenomena. The present article is an attempt to unify the analysis of polarization phenomena using Dirac matrices used by Dirac in quantum mechanics. We have however redefined the set of Dirac matrices in terms of the Kronecher product of Pauli spin matrices.     

Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy

We derive the complete formulae governing the polarization state measurement in terahertz-time domain spectroscopy (THz-TDS) by using a rotatable THz polarizer. Four Stokes parameters can be uniquely obtained by spectrally-resolved measurement in THz-TDS. Further, we propose a new approach to measure the Mueller matrix of a pure birefringent material, using THz-TDS, by rotating the material under test. Based on the above techniques, we successfully measured the Mueller matrices of a quartz crystal in the frequency domain.     

掺杂对随机分布团簇粒子缪勒矩阵的影响

文章分析了不同含量的杂质对随机分布团簇粒子缪勒矩阵的影响.利用Bruggeman有效介质理论得到了含有不同体积份额杂质的硅酸盐粒子的等效复折射率.采用离散偶极子近似方法对包含有不同化学成分的随机分布团簇粒子的缪勒矩阵进行了数值计算,给出了各个缪勒矩阵元素的散射角分布曲线,探讨了不同含量的杂质对随机分布团簇粒子缪勒矩阵的影响.研究表明,掺杂对随机分布团簇粒子的缪勒矩阵存在着不同程度的影响,并且此影响随着粒子尺度参数的变化而显著变化. 关键词： 团簇粒子 缪勒矩阵 Bruggeman有效介质理论 离散偶极子近似方法     

偏振器的物理意义及圆偏振器的Jones矩阵--评《关于圆偏振器》一文

从正交完备系及Mueller矩阵等角度阐明了理想圆偏振器的物理意义,指出已有文献中其Jones矩阵描述的正确性,而《关于圆偏振器》一文对诸多文献的批评是错误的。     

基于Mueller矩阵成像椭偏仪的纳米结构几何参数大面积测量

为了实现有效的工艺监控, 在批量化纳米制造中对纳米结构的关键尺寸等几何参数进行快速、低成本、非破坏性的精确测量具有十分重要的意义. 光学散射仪目前已经发展成为批量化纳米制造中纳米结构几何参数在线测量的一种重要手段. 传统光学散射测量技术只能获得光斑照射区内待测参数的平均值, 而对小于光斑照射区内样品的微小变化难以准确分析. 此外, 由于其只能进行单点测试, 必须要移动样品台进行扫描才能获得大面积区域内待测参数的分布信息, 从而严重影响测试效率. 为此, 本文将传统光学散射测量技术与显微成像技术相结合, 提出利用Mueller矩阵成像椭偏仪实现纳米结构几何参数的大面积快速准确测量. Mueller矩阵成像椭偏仪具有传统Mueller矩阵椭偏仪测量信息全、光谱灵敏度高的优势, 同时又有显微成像技术高空间分辨率的优点, 有望为批量化纳米制造中纳米结构几何参数提供一种大面积、快速、低成本、非破坏性的精确测量新途径.     

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.     

Differentiating characteristic microstructural features of cancerous tissues using Mueller matrix microscope

Polarized light imaging can provide rich microstructural information of samples, and has been applied to the detections of various abnormal tissues. In this paper, we report a polarized light microscope based on Mueller matrix imaging by adding the polarization state generator and analyzer (PSG and PSA) to a commercial transmission optical microscope. The maximum errors for the absolute values of Mueller matrix elements are reduced to 0.01 after calibration. This Mueller matrix microscope has been used to examine human cervical and liver cancerous tissues with fibrosis. Images of the transformed Mueller matrix parameters provide quantitative assessment on the characteristic features of the pathological tissues. Contrast mechanism of the experimental results are backed up by Monte Carlo simulations based on the sphere–cylinder birefringence model, which reveal the relationship between the pathological features in the cancerous tissues at the cellular level and the polarization parameters. Both the experimental and simulated data indicate that the microscopic transformed Mueller matrix parameters can distinguish the breaking down of birefringent normal tissues for cervical cancer, or the formation of birefringent surrounding structures accompanying the inflammatory reaction for liver cancer. With its simple structure, fast measurement and high precision, polarized light microscope based on Mueller matrix shows a good diagnosis application prospect.     

Incomplete active polarimetry: Measurement of the block-diagonal scattering matrix

The problem of measurement of block-diagonal scattering matrix as being part of the so-called incomplete or partial Mueller polarimetry is addressed. It has been shown that non-zero elements of the scattering matrix with block-diagonal structure can be measured using only two elliptical polarizations of input light. Optimal pairs of these polarizations are derived. Utilization of the optimal input polarizations results in halving measurement time and decreasing measurement errors by 30%.     

Recovery of the Complete Mueller Matrix of an Arbitrary Object in the Method of Three Input Polarizations

The problem of the recovery of the complete Mueller matrix of an arbitrary object by additionally measuring the matrix elements whose values are not determined in base measuring cycles of the method of three input polarizations is considered. We suggest a number of methods for recovering the complete matrix of dependent and independent recovery and for carrying out two base measuring cycles of the method of three input polarizations. A comparative analysis of the accuracy characteristics of the proposed methods has been performed.     

Calculation of Birefringence Distribution in Optical Fiber Based on Analysis of Angle Between States of Polarization

A method of the calculation of spatial birefringence distribution in an optical fiber link is presented. This method is based on analysis of the polarization properties of the backscattered optical signal. The analytical results are compared with numerical results. This comparison gives excellent agreement. The spatial birefringence distribution is evaluated from the measurement of the round-trip Mueller matrices derived from calculation of the angles between the input and output state of polarization.