Polarization characteristics of backscattering of turbid media based on Mueller matrix

Mueller matrix is one approach to characterizing optical polarization of the turbid media. We have simulated the two-dimensional images of Mueller matrix based on single-scattering approximation model and implemented experiments to verify the simulations. By comparing the experimental results to the theoretical simulations, we have obtained some conclusions. When the particle size is smaller than the wavelength, the linearly polarized light propagating through the turbid media of Rayleigh scatterers has better polarization-maintaining ability. Whereas when the particle size is larger than the wavelength, the circularly polarized light propagating through the turbid media of Mie scatterers has better polarization-maintaining ability. Moreover, the radial dependence of the element patterns becomes weak as the transport mean free path decreases. This study can help us understand to the fundamental principle of optical polarization.     

Measurements of diffuse backscattering Mueller matrices of turbid media

We report on the development of a method that records spatially dependent intensity patterns of polarized light that arise from illuminating a turbid media with a polarized laser beam and being diffusely backscattered. Our technique employs polarized light from a He-Ne laser () which is focused onto the surface of the scattering medium. A surface area of approximately 2×2 cm centered on the light input point is imaged through polarization analysis optics onto a CCD camera. The Mueller matrix is reconstructed by 49 intensity measurements with various orientations of polarizer and analyzer. The measured Mueller matrix of polystyrene spheres was compared with the theory result of incoherent scattering of light by spheres. The experimental and theory results are in excellent agreement. It appears that the azimuthal patterns of the Mueller matrix are determined by the symmetry of the turbid media.     

The temporal Mueller matrix solution for polarimetric scattering from a layer of random non-spherical scatterers

The Mueller matrix solution of the vector radiative transfer equation with time dependence is derived in this paper. It is applied to simulation of polarimetric bistatic scattering from a layer of non-uniformly oriented, random non-spherical scatterers when a Gaussian plane pulse is incident upon. Co-polarized and cross-polarized bistatic scattering are numerically calculated. The pulse echoes are compared with the incidence, and demonstrate its functional dependence on the physical parameters of random medium, such as spatial orientation and fractional volume of scatterers, incidence angle and polarization, the layer depth and others.     

Effects of modulation phase of ultrasound-modulated light on the ultrasound-modulated optical image in turbid media

In this paper, our investigations suggest that the modulation phase of ultrasound-modulated light escaping from the different locations in the ultrasonic field is different. In turbid media, the modulation phase causes the ultrasound-modulated light intensity collected outside the media to fluctuate. However, the ultrasound-modulated optical technology uses the ultrasound-modulated light signals to image. Consequently, the modulation phase affects the quality of ultrasound-modulated optical imaging.     

Determination of optical properties of slices of turbid media by diffuse CW laser light scattering profilometry

In this work we present a method for determining the optical parameters of turbid media, namely its absorption coefficient (μ_a) and its reduced scattering coefficient . It is based on the measurement of CW transmittance profiles and analysis of the experimental data by a theoretical model based on the diffusion approximation (DA) of the radiative transfer equation (RTE). The method developed has been investigated with solid polymer probes but it could be applied for liquid materials as well. Experimental results are presented and compared to those of other authors together with a discussion about the accuracy of measurements. In addition, measurements using integrating spheres as well as Monte Carlo simulations are also presented to validate these results.     

Influence of single scattering and multiple scattering on backscattered Mueller matrix in turbid media

Monte Carlo algorithm and Stokes-Mueller formalism are used to simulate the propagation behavior of polarized light in turbid media. The influence of single scattering and multiple scattering on backscattered Mueller matrix in turbid media is discussed. Single and double scattering photons form the major part of backscattered polarization patterns, while multiple scattering photons present more likely as background. Further quantitative analyses show that single scattering approximation and double scattering approximation are quite accurate when discussing the polarization patterns near the incident point.     

CW laser transilluminance in turbid media with cylindrical inclusions

The present work analyzes the process of detection of small diffusive inclusions in turbid hosts. Experiments were carried out using a transillumination geometry and continuous wave laser radiation, considering cylindrical inclusions in different environments. A comparison between experimental data, theoretical approaches for the radiative transfer equation in the diffusion approximation, and numerical Monte Carlo simulations, is 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.     

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%.     

随机非球形粒子全极化散射的时间相关Mueller矩阵解

从与时间相关的矢量辐射传输方程推导一阶Mueller矩阵解,用来模拟Gauss型平面脉冲波入射下,一层随机、非均匀取向非球形粒子的全极化双站散射.数值计算了同极化和去极化脉冲响应,与入射脉冲进行了比较,说明了随机介质的物理参数,如粒子的取向和占空比、入射角、极化以及层厚等对脉冲响应的影响 关键词： 平面脉冲波 非球形粒子 Mueller矩阵     

混浊介质二维后向漫散射穆勒矩阵的测量

研制了一套实验系统用于测量混浊介质的后向漫散射穆勒矩阵.在系统中,激光被调制成所需偏振态,聚焦于混浊介质表面.利用CCD相机配合相应的偏振元件,测量入射点周围区域的后向散射光中特定偏振态的能量空间分布,并由测量值计算出介质的后向漫散射穆勒矩阵.描述了系统的组成、测量原理以及方法,分别测量了消偏振分光棱镜的反射穆勒矩阵和浓度1.5％的脂肪乳溶液的后向漫散射穆勒矩阵.实验证明:该系统能够完全消除样品表面镜面反射光的干扰,精确的测量混浊介质的后向漫散射穆勒矩阵;并可望用于生物组织的研究中.     

Polarimetry group theory analysis in biological tissue phantoms by Mueller coherency matrix

The characterization of biological tissues by optical techniques provides several advantages over other techniques. Optical techniques enable to perform high resolution and contrast imaging, in a non-invasive way and with no-contact. Biological tissues are turbid media that strongly scatter light. The ultrastructure of some tissues makes them present a certain degree of anisotropy. Both scattering and anisotropy affect light polarization. Some pathologies alter these characteristics of the tissue. As a consequence polarized light can be used to extract additional information and achieve a better diagnosis.In this work, Group Theory is applied to analyse the polarization behavior of several samples. Firstly, the Mueller matrix for each sample is measured. Then, the Mueller Coherency matrix is obtained by means of the SU(4)-O + (6) homomorphism. Finally, the target decomposition theorem is applied by analyzing the eigenvalues and eigenvectors, and subsequently the different polarimetric effects are separated. In this way, the contrast of tissue imaging can be increased. This analysis is applied to biological tissue phantoms, which consisted on glucose suspensions of polystyrene spheres with different scatterer concentrations. Their behaviour can be modeled by means of single or multiple scattering depending on the concentration, either in the Rayleigh or Mie regimes. The same procedure could be used in a wide range of applications, like the study of cancerous cells that grow without control in cell cultures, or erythrocytes monitoring in anemia. The technique also has a great potential to be applied in Polarization Sensitive Optical Coherence Tomography (PS-OCT).     

手性介质中后向散射米勒矩阵特性及其在血糖无创检测中的应用初探

利用斯托克斯-米勒矩阵表述分析偏振光在手性介质中的传输规律,利用瑞利近似下的单次散射模型和基于米氏散射理论的多次散射的蒙特卡罗方法,探讨葡萄糖对后向散射偏振光传输特性的影响,计算了不同葡萄糖浓度下的后向散射米勒矩阵. 结果表明在含有葡萄糖的手性介质中后向散射米勒矩阵的若干矩阵元表现出微弱的旋光效应,旋光度随葡萄糖浓度增大而增大. 为了检测低浓度下微小的旋光变化,定义了函数对含-不含葡萄糖的米勒矩阵元图像进行处理,提取由葡萄糖引入的图像差异. 结合无创血糖检测应用要求,分析了葡萄糖生理浓度下的矩阵元图像,获 关键词： 医用光学与生物技术 偏振光 斯托克斯-米勒表述 蒙特卡罗模拟     

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.     

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.     

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.     

Structure of Deterministic Mueller Matrices and Their Reconstruction in the Method of Three Input Polarizations

The method of reconstruction of complete deterministic Mueller matrices for the structures of incomplete matrices, which are measured in the method of three input polarizations, has been developed. The method is based on reconstruction of the corresponding Jones matrices for the given structures of incomplete Mueller matrices.     

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.     

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.     

Study on photon migration path of ultrashort light pulse in turbid media by Monte Carlo method

The photon density and the photon weight density are obtained by a Monte Carlo method. Based on these two concepts the Gaussian peak value photon paths and the weight mean photon paths of ultrashort light pulse in turbid media are defined and studied. The width of the Gaussian peak value photon path is also given. The influence of the exit angle and time on the photon path and its width are discussed. The relative probability of the photon path is given by the sum of the photon weight densities along the photon path, which could be used to calculate the normalized diffusive intensity approximately. The diffusive reflective intensities will arrive at the maximum at some instant at the place where the photon path reaches on the entrance surface at the same instant. The absorption coefficient has small effect on the photon path and its width in the case of the photon weight density.