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.     

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.     

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.     

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.     

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.     

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.     

Angularly resolved backscattering of light from turbid suspensions of dielectric spheres

An analytic expression for the angular dependency of light backscattered from turbid suspensions of dielectric spheres that accounts for multiple-scattering effects is developed. The multiple-scattering model expresses backscattered light as a convolution of the phase function and a kernel representing the effects of forward scattering, multiplied by the optical thickness of the slab. Excellent agreement between Monte Carlo simulations and the analytic expressions is demonstrated for optical thicknesses of 0.1-4. The results are important for goniometric sizing measurements of biological cells and cellular organelles using elastically backscattered light.     

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.     

多分散高浓度介质偏振光后向扩散散射的Monte Carlo仿真

建立了针对多分散高浓度介质偏振光后向扩散散射的Monte Carlo仿真模型，导出了多分散 系统的有效自由程分布函数. 给出了半径为50nm与550nm及其三种不同体积浓度比混合的聚 苯乙烯微球作为散射粒子的高浓度介质的仿真结果. 定性地分析了多分散介质偏振光后向扩 散散射的光强空间分布特征与粒子的体积浓度比的关系. 关键词： 后向扩散散射 偏振光 多分散高浓度介质 Monte Carlo仿真     

Measurements of optical parameters of phantom solution and bulk animal tissues in vitro at 650 nm

Optical parameters of bulk animal tissue in vitro, including absorption coefficient (μ_a), reduced scattering coefficient (μ′_s) or scattering coefficient (μ_s), total attenuation coefficient (μ_t), anisotropy factor (g) and refractive index (n) are measured at wavelength of 650 nm. Clinical Intralipid-10% is diluted in distilled water into different concentrations to use as tissue phantoms. Four types of animal tissues in vitro are studied. The relationships among the optical parameters are analyzed systemically. For animal tissues, μ_a, μ′_s or μ_s and n rely on muscle fiber orientations. μ_s and μ_t range from 10 to 20 mm⁻¹, μ_a from 10⁻² to 10⁻³ mm⁻¹ and g from 0.95 to 0.99.     

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.     

混浊介质中线偏振光和圆偏振光的后向漫散射特征

以标准的组织模型Intralipid脂肪乳溶液为研究对象,采用CCD偏振成像系统,通过测量该混浊介质的后向漫散射光的斯托克斯矢量,深入研究了不同方位的线偏振光及不同旋向的圆偏振光入射时,后向漫散射光的特征.研究结果表明：对不同的入射偏振态,后向漫散射强度、偏振度的空间分布具有方位选择性,强度和偏振度的大小随距离入射点的距离增加而减小;介质浓度增加,后向散射强度增加,偏振度减小,且同一浓度下,圆偏振光的偏振度总是高于线偏振光.     

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.     

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.     

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.     

Noninvasive detection of inhomogeneities in turbid media with time-resolved log-slope analysis

Detecting foreign objects embedded in turbid media using noninvasive optical tomography techniques is of great importance in many practical applications, such as in biomedical imaging and diagnosis, safety inspection on aircrafts and submarines, and LIDAR techniques. In this paper we develop a novel optical tomography approach based on slope analysis of time-resolved back-scattered signals collected at the medium boundaries where the light source is an ultrafast, short-pulse laser. As the optical field induced by the laser-pulse propagates, the detected temporal signals are influenced by the optical properties of the medium traversed. The detected temporal signatures therefore contain information that can indicate the presence of an inhomogeneity as well as its size and location relative to the laser source and detection systems. The log-slope analysis of the time-resolved back-scattered intensity is shown to be an effective method for extracting the information contained in the signal. The technique is validated by experimental results and by Monte Carlo simulations.     

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.     

混沌介质光学常数测量

对基于漫射理论并应用CCD相机测量混沌介质的光学常数进行了实验研究.提出采用漫射中心环带约束法来提高逆向求解光学常数的精确性,以及采用在通过光的入射点和漫射中心的直线上截取一维原始数据的方法来提高算法的计算效率.以Intralipid脂肪乳剂作为混沌介质,对方法进行了实验验证.结果表明,本文提出的方法是可行的.     

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).     

Optical Mueller matrices in terms of geometric algebra

Connection between optical Mueller matrices and geometrical (Clifford) algebra multivectors is established. It is shown that starting from 3-dimensional (3D) Cl_3,0 algebra and using isomorphism between Cl_3,0 and even Cl_3,1⁺ subalgebra one can generate canonical Mueller matrices and their combinations that describe an optical system. It appears that representation of polarization devices in terms of geometric algebra is very compact and, in contrast to Mueller matrix approach, there is no need for speculative physical restrictions. If needed, properties of media can be logically introduced into Maxwell equation in a form of Clifford algebra via constitutive relations. Since representation of polarization by Cl_3,1 algebra is Lorentz invariant it allows to include relativistic effects of moving bodies on light polarization as well. In this paper only simple examples of connection between Mueller matrices and geometric algebra multivectors is presented.