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).     

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.     

一种改进激光偏振主动成像的建模及理论分析

提出一种改进激光偏振主动成像的实验方法,给出实验装置原理图,详细分析实验装置的成像原理。在分析目标Mueller矩阵测量方法的基础上,给出改进后激光偏振成像装置偏振度和强度的计算公式,从理论上证明了该方法的可行性。然后针对实验仪器的要求分析了实验装置存在的误差,以及Cassegrain望远镜对目标散射光的消偏现象。该方法与利用双旋转波片技术（DRRT）测量目标散射光的偏振度和强度相比可以降低对实验装置的精度要求,同时可以提高测量速度,不需要进行16次测量,只需1次就可以测量出目标散射光的偏振度和强度,进而得到偏振度和强度图像。     

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.     

基于最大和最小光强图像的偏振去雾方法

相对于传统光学探测技术,偏振探测在目标探测、识别方面有着独特的优势。针对雾、霾等天气下图像退化的问题,提出一种利用偏振信息的图像去雾方法,通过获取3个角度下目标的偏振图像,求解出场景目标的斯托克斯矢量,从斯托克斯矢量与穆勒矩阵的关系出发,分析偏振图像光强随着偏振角度的变化规律,获取最大和最小光强下的正交偏振图像,利用偏振滤波和亮通道先验方法分别估算大气光偏振度和其无穷远处大气光强值,最终重构出无雾图像。实验结果表明,在雾霾天气下,利用获取的正交偏振图像能够重构出清晰的图像,且重构图像的平均梯度和边缘强度均提升了约3倍,灰度标准差提升了约88%。     

Polarization-based range-gated imaging in birefringent medium:Effect of size parameter

We have investigated the effect of size parameter of the scatterer on the image quality obtained with polarization-based range-gated imaging in birefringent turbid medium. Both linearly and circularly polarized light were utilized for imaging.The simulated results indicate that the improvement of visibility is more pronounced using circularly polarized light for the birefringent medium composed of smaller-sized scatterers at lower values of optical thickness and the birefringent medium comprising larger-sized scatterers. In contrast, linearly polarized light provides better image quality for the birefringent medium composed of smaller-sized scatterers at larger values of optical thickness. The evolution of the polarization characteristics of backscattered light and target light under the conditions mentioned above was measured to account for these numerical results.     

A hybrid model of polarized BRDF for rough surfaces

A new hybrid model of polarized bidirectional reflectance distribution function (p-BRDF) based on the micro-facet theory for painted rough surfaces combined by physics and statistical method is proposed. A 4 × 4 matrix (Mueller matrix) is used to describe the character of the polarized light scattered from the surface. The p-BRDF excellently represents the properties of the complex surfaces, playing a major role to evaluate and simulate signatures of the natural or artificial targets. In the model, genetic algorithm is employed to obtain key parameters derived from the experimental data. Comparisons between the model calculation and experimental data are also discussed in detail for several painted surfaces. This model agrees well with the experimental data, indicating great applicable to target polarization feature extraction.     

生物组织多光谱偏振特性研究

生物组织内部结构复杂且具有较强的散射特性,而光作为生物组织检测的重要信息载体,其自身特性包括颜色、幅值、偏振等都对信息获取有较大的影响.结合偏振成像,对生物组织多光谱偏振特性展开了研究,依据不同微粒尺寸的分布建立了均匀单层生物组织模型,结合瑞利和米氏散射理论模拟了基于单个微粒的两种散射事件.瑞利散射具有较好的前向后向散...     

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.     

用偏振荧光光谱表征乙醇-水团簇分子的取向行为

采用波长为236nm紫外光激励乙醇水溶液获得荧光光谱并对其偏振特性进行了研究.实验中分别改变入射光的偏振度，在300—400nm波段内进行荧光光谱、水平和垂直偏振荧光光谱检测.实验结果表明，当采用线偏振光照射乙醇水溶液时，其发射的荧光具有一定的偏振性，并计算了其偏振度.经理论分析得到了描述荧光偏振态的四个斯托克斯矢量，进而对该荧光的偏振状态进行了描述，通过对乙醇-水溶液的米勒矩阵的计算，对溶液中分子的取向特性进行了分析.本结果能对乙醇-水团簇分子的结构提供理论参考. 关键词： 荧光光谱 偏振光谱 斯托克斯矢量 米勒矩阵     

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.     

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.     

Mueller matrix polarimetry for the characterization of complex random medium like biological tissues

The polarization parameters of light scattered from biological tissues contain wealth of morphological and functional information of potential biomedical importance. But, in optically thick turbid media such as tissues, numerous complexities due to multiple scattering and simultaneous occurrences of many polarization events present formidable challenges, in terms of both accurate measurement and unique interpretation of the individual polarimetry characteristics. We have developed and validated an expanded Mueller matrix decomposition approach to overcome this problem. The approach was validated theoretically with a polarization-sensitive Monte Carlo light propagation model and experimentally by recording Mueller matrices from tissue-like complex random medium. In this paper, we discuss our comprehensive turbid polarimetry platform consisting of the experimental polarimetry system, forward Monte Carlo modelling and inverse polar decomposition analysis. Initial biomedical applications of this novel general method for polarimetry analysis in random media are also presented.     

Polarization Characteristics of Multiple Backscattering in Human Blood Cell Suspensions

The degree of polarization on normal and spiny red blood cell suspensions is analyzed by Mueller matrix measurement. Cells with spiny surface figures are prepared by adding salt to the suspension of diluted human blood cells to increase osmotic pressure. Fine structures on the cell surface cause differences in the degree of polarization in circular polarized light     

Effective dichroism in forward scattering by inhomogeneous birefringent medium

The Mueller matrix model for inhomogeneous medium characterized by simultaneous linear and circular birefringence for single scattering in the forward direction is derived. We find that the presence of inhomogeneity results in the occurrence of new polarization effects. In particular, forward scattering by inhomogeneous birefringent medium exhibits linear and circular dichroism. We show that in the case of weak depolarization (when Cloude's entropy is less than 0.5), the initial parameters for linear and circular birefringence can be obtained from deterministic Mueller matrix associated with the largest eigenvalue of Cloude's coherency matrix. Sample calculations are given for quartz.     

Imaging and multiple scattering through media containing optically active particles

This paper examines the behaviour of polarized light scattered by a medium containing small chiral spheroidal particles. We show that for single scattering the observed phenomena of optical activity may be interpreted in terms of an averaged Mueller matrix and describe how the degree of polarization is affected by such a medium. The polarization properties of multiply scattered light by chiral particles are considered through the use of Monte Carlo simulations. It is shown that the effects of chirality under multiple scattering can be interpreted as an order-preserving influence in a disordered system and that this influence can, in principle, be exploited for the purposes of imaging.     

Synchronization of optical polarization conversion and scattering in chiral fibers

We demonstrate that polarization transformation and scattering in adiabatically twisted single-mode birefringent optical fibers is synchronized so that light in one evolving elliptically polarized mode is freely transmitted while orthogonally polarized light is scattered out of the fiber. Thus, linearly polarized radiation initially oriented along the fast axis of the untwisted fiber is transformed to circularly polarized light with the same sense of rotation as the twisted fiber and is scattered out of the fiber. When the fiber twist is first accelerated and then decelerated, the fiber becomes a broadband, low-insertion-loss, linear polarizer.