Influence of the order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex turbid media such as biological tissues

The influence of the multiplication order of the constituent basis matrices on the Mueller matrix decomposition-derived polarization parameters in complex tissue-like turbid media exhibiting simultaneous scattering and polarization effects are investigated. A polarization sensitive Monte Carlo (MC) simulation model was used to generate Mueller matrices from turbid media exhibiting simultaneous linear birefringence, optical activity and multiple scattering effects. Mueller matrix decomposition was performed with different selected multiplication orders of the constituent basis matrices, which were further analyzed to derive quantitative individual polarization medium properties. The results show that for turbid medium having weak diattenuation (differential attenuation of two orthogonal polarization states), the decomposition-derived polarization parameters are independent of the multiplication order. Importantly, the values for the extracted polarization parameters were found to be in excellent agreement with the controlled inputs, showing self-consistency in inverse decomposition analysis and successful decoupling of the individual polarization effects. These results were corroborated further by selected experimental results from phantoms having optical (scattering and polarization) properties similar to those used in the MC model. Results from tissue polarimetry confirm that the magnitude of diattenuation is generally lower compared to other polarization effects, so that the demonstrated self-consistency of the decomposition formalism with respect to the potential ambiguity of ordering of the constituent matrices should hold in biological applications.     

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.     

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     

Revisit to the symmetry relations in diffusely backscattered polarization patterns of turbid media

As there exists an inconsistency in claiming the symmetrical relations in the 16 Mueller matrix elements used to describe a turbid medium, the author restudies the symmetrical relationships between diffusely backscattered polarization patterns in isotropic turbid media and simulates all two-dimensional elements of diffusely backscattered Mueller matrix in both cases of Rayleigh and Mie scatterings using the doublescattering approximation and the Monte Carlo algorithm, respectively. The previous experimental observatious are compared with the numerically determined matrix elements, showing a good agreement in both double-scattering model and Monte Carlo simulation. The symmetrical relations between the Mueller matrix elements are clarified.     

Monte Carlo方法模拟光在生物组织中传播的新进展

Monte Carlo方法已被广泛用于模拟复杂的随机介质如生物组织中光的辐射传输.在生物光子应用中,早期的Monte Carlo模拟模型忽略了光在组织中传输的波动性,而用中性粒子光子包来模拟其传播过程.然而,许多光学诊断技术是基于光在组织中的偏振效应和多重散射的相干性来揭示组织的生理和病理信息,这就要涉及光辐射的波动性.本文阐述了用Monte Carlo方法模拟光在生物组织中传播的最新进展.     

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.     

含葡萄糖的混浊介质的Mueller矩阵模拟与分析

利用矢量Monte Carlo算法结合葡萄糖的旋光特性模拟了含糖混浊介质的背散射Mueller矩阵.数值模拟表明:含糖混浊介质的背散射Mueller矩阵元素中除Mll、M14、M41、M44外的其它元素花样均发生龙卷风状的不同程度的扭曲,其中M24、M34、M42、M43的扭曲程度更为显著.研究发现M24、M34、M4...     

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.     

混浊介质多光子激发荧光显微成像的蒙特卡罗模拟

将蒙特卡罗方法与几何光线追踪技术相结合用于研究样品混浊特性对多光子激发蒌光显微成像的影响。推导了模拟多层样品显微成像的数学模型,给出了用程序框图表示的基本仿真系统骨架,对传统蒙特卡罗方法的改进有效地增强了对聚焦光束的模拟能力,初步的模拟结果说明了混浊介质散射特性对显微成像的显著影响。     

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).     

Determination of the depth-resolved Stokes parameters of light backscattered from turbid media by use of polarization-sensitive optical coherence tomography

Polarization-sensitive optical coherence tomography (PS-OCT) was used to characterize completely the polarization state of light backscattered from turbid media. Using a low-coherence light source, one can determine the Stokes parameters of backscattered light as a function of optical path in turbid media. To demonstrate the application of this technique we determined the birefringence and the optical axis in fibrous tissue (rodent muscle) and in vivo rodent skin. PS-OCT has potentially useful applications in biomedical optics by imaging simultaneously the structural properties of turbid biological materials and their effects on the polarization state of backscattered light. This method may also find applications in material science for investigation of polarization properties (e.g., birefringence) in opaque media such as ceramics and crystals.     

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.     

Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium

The effect of preservation of the residual polarization of backscattered light in the case of multiply scattered disordered media illumination by a linearly polarized plane wave is examined using the path-integral approach and Monte Carlo simulation. Disordered ensembles of non-interacting dielectric particles are considered as the model of scattering media. The influence of the anisotropy parameter of the scattering system on the degree of residual polarization is analysed. Experimental results obtained for various scattering systems at different wavelengths of illuminating light are in satisfactory agreement with the results of theoretical analysis and Monte Carlo simulation. The dependence of statistical properties of the polarization states of backscattered field partial components, such as probability distributions of ellipticity, on the anisotropy parameter is studied.     

Optical diagnosis of dengue virus infected human blood using Mueller matrix polarimetry

Currently dengue fever diagnosis methods include capture ELISAs, immunofluorescence tests, and hemagglutination assays. In this study optical diagnosis of dengue virus infection in the whole blood is presented utilizing Mueller matrix polarimetry. Mueller matrices of about 50 dengue viral infected and 25 non-dengue healthy blood samples were recorded utilizing light source from 500 to 700 nm with scanning step of 10 nm. Polar decomposition of the Mueller matrices for all the blood samples was performed that yielded polarization properties including depolarization, diattenuation, degree of polarization, retardance and optical activity, out of which, depolarization index clusters up the diseased and healthy in to different separate groups. The average depolarized light in the case of dengue infection in the whole blood at 500 nm is 18%, whereas for the healthy blood samples it is 13.5%. This suggests that depolarization index of polarized light at the wavelengths of 500, 510, 520, 530 and 540 nm, we find that in case of depolarization index values are higher for dengue viral infection as compared to normal samples. This technique can effectively be used for the characterization of the dengue virus infected at an early stage of disease.     

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.     

Calculations of Backscattering Mueller Matrices for Turbid Media with a Sphere Queue Model

A sphere queue model is introduced to calculate Mueller matrices of turbid media. Combined with the single scattering approximation, the backscattering Mueller matrices of turbid media can be computed rapidly by Mie theory. The numerical results agree with the azimuthal dependences of backscattering Mueller matrices＇ patterns from turbid media, which indicates that the major contribution to the Mueller matrices＇ patterns comes from the single scattering of the sphere queue, and the multiple scattering considered as a high-order correction does not change the patterns. The numerical analysis reveals that the contrast of Mueller matrices＇ patterns will decrease with increase of the concentration of media and the distance from the incident point.     

High angle phase modulated low coherence interferometry for path length resolved Doppler measurements of multiply scattered light

We describe an improved method for coherence domain path length resolved measurements of multiply scattered photons in turbid media. An electro-optic phase modulator sinusoidally modulates the phase in the reference arm of a low coherence fiber optic Mach-Zehnder interferometer, at a high phase modulation angle. For dynamic turbid media this results in Doppler broadened phase modulation interference peaks at the modulation frequency and its multiples. The signal to noise ratio is increased by almost one order or magnitude for large modulation angles and the shape of the spectral peaks resulting from the interference of Doppler shifted sample waves and reference light is not changed. The path length dependent Doppler broadening is compared with the theoretical predictions in the single scattered and diffusive regimes. The experimentally measured optical path lengths are validated with the Monte Carlo technique.     

偏振门用于对散射介质成像的蒙特卡罗模拟研究

通过蒙特卡罗模拟研究偏振光在散射介质中的传播,对通过散射介质的偏振光的强度分布进行模拟,分析了偏振门和空间滤波对成像的影响.模拟结果表明,对于Rayleigh散射体,偏振门与空间滤波可以减小散射光的影响,提高图像对比度,圆偏振光入射比线偏振光具有更高的对比度.对于Mie散射粒子,偏振门的作用有限,不同偏振光的结果差别不大.对双组分的散射介质也进行了模拟,偏振门在这种体系中仍能提高图像对比度.     

Simulation of coherent properties of photons in scattering medium for optical coherence tomography

Monte Carlo model of optical coherence tomography is developed for simulation of photon transport in half infinite homogenous media. The procedure is accelerated by scaling the baseline data from standard Monte Carlo calculation in turbid media with arbitrary optical parameters. Gaussian beam is modeled by hyperboloid of one sheet for actual condition to obtain distribution of photons on sample surface. Depth dependence coherent signal and photons distribution are calculated in this way, which is important to reconstruction of optical parameters by inverse Monte Carlo. Numerical results have verified this method in turbid medium of different optical parameters with acceptable relative errors.     

Reconstruction of 3D light distribution produced by cylindrical diffuser in deep tissues based on photoacoustic imaging

Measurement of light distribution in biological tissue contributes to selecting strategy and optimizing dose for biomedical application. In this letter, a photoacoustic method combined with Monte Carlo simulation was used to estimate the three-dimensional light distribution in biological tissue. The light distribution was produced by a cylindrical diffuser which interposed into tissues. The light profiles obtained by the method were compared to those detected by photo diodes. The experimental results demonstrate the feasibility of this method. The approach can play a significant role for photo-dosimetry in biomedical phototherapy.