Calculation of Photon Path Distribution Based on Photon Behavior Analysis in a Scattering Medium

We calculated the photon path distribution (PPD) in a scattering medium based on a theoretical analysis, which utilizes the relationship between the photon intensity and photon pathlength. This PPD is defined by local photon pathlengths for photons having total pathlengths of l between the light input points and detection points. The PPD of photons that consist of the impulse response at time t (= l/c) was calculated for a 2-D model. Precise analysis of photon migration in the scattering medium is essential in order to carry out image reconstruction of diffuse optical tomography (DOT). We show the PPD at time t (the total pathlength l = ct) and demonstrate its effectiveness. Our method for describing photon migration is intuitive and allows finding weight functions in DOT.     

Diffuse Optical Tomography using Time-resolved Photon Path Distribution

Our research goal is to develop diffuse optical tomography (DOT) capable of quantitative measurement. Information on optical pathlength is essential for reconstructing images with quantitative properties, and we have performed image reconstruction with a simulation model using a time-resolved photon path distribution (time-resolved PPD). The results showed that a DOT image reconstruction algorithm using this PPD is effective in quantifying the absorbers in a scattering medium such as human tissue. This algorithm uses a photon distribution independent of absorption by simply assuming that the measurement object is homogeneous, which means that PPD needs to be calculated only once. Our technique is therefore applicable to short-time imaging of measurement objects for which absorption changes flatness such as that in human tissue.     

偏振相移与相位共轭结合的散射光聚焦技术研究

散射介质对光的随机散射作用是制约其光学聚焦和成像的重要因素，光学相位共轭技术能够通过对散射光场共轭还原实现透过散射介质的光学聚焦和成像，其中散射光场相位的获取是共轭还原的核心。阐述了偏振相移的基本原理，将偏振相移与相位共轭技术相结合，设计了新的基于偏振相移的数字光学相位共轭系统。采用633 nm的HeNe激光器作为系统光源，毛玻璃作为散射介质开展散射光聚焦实验研究。实验结果表明:该装置能够成功实现透过散射介质的光学聚焦，其中聚焦点与背景光强的比值可达约400倍。     

快速多极边界元法用于扩散光学断层成像研究

在求解扩散光学断层成像中的正向问题时, 目前普遍采用有限元法, 但是随着实际模型规模的增大, 有限元法的计算量问题日益显著, 而边界元法则由于可以降低计算维度使计算量减少而备受关注. 本文以均匀的高散射介质为模型, 研究了将快速多极边界元法用于扩散光学断层成像的正向问题. 快速多极边界元法利用核函数的多极展开, 将常规边界元法中系数矩阵和迭代矢量的乘积项等价为相应四叉树结构的一次递归, 再结合广义最小残量法进行迭代求解. 将计算结果和蒙特卡罗法的模拟结果进行了比较, 表明利用快速多极边界元法的模拟结果和蒙特卡罗法的结果有很好的一致性. 研究结果验证了快速多极边界元法可以用于扩散光学断层成像, 为其大规模和实时成像带来可观的前景. 关键词： 扩散光学断层成像 边界元法 快速多极边界元法     

光学厚度对颗粒媒质的多重散射的影响

基于辐射传播方程及多重散射基础理论,利用Fraunhofer近似,对颗粒媒质的多重散射光强进行了计算。研究了光学厚度对多重散射的影响,揭示了多重光散射的角分布特征,光强大小随光学厚度的变化,以及单散射引起的误差等方面的规律。为实际的颗粒媒质的光学测量等提供了理论根据。     

A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser

A novel circular polarized optical heterodyne interferometer using a Zeeman laser to measure optical rotation both in nonscattered and scattered chiral medium is proposed. A pair of correlated orthogonal circular polarized light waves of different temporal frequency propagating in the chiral medium at different speed is studied. This results in phase retardation between circular polarized light waves of which the phase difference is proportional to the optical rotation angle of a linear polarized light in a chiral medium. In the mean time, two orthogonal circular polarized light waves can be treated as a circular polarized photon pair that is able to reduce the scattering effect in a scattered chiral medium. Then the optical rotation angle can be measured in the scattering medium. In addition, a common-path configuration with respect to circular polarized light waves immune the background noise. This further improves the sensitivity on optical rotation measurement based on phase difference detection.     

Optical Computed Tomography Based on Extraction of Quasi-Straight forward Propagating Photons Using Sum-Frequency Generation Technique

Aiming at the realization of optical computed tomography (optical CT), a compact system comprised of two cw-lasers and a detector was proposed for the extraction of quasi-straightforward propagating photons from scattered light transmitting through a scattering medium. The extraction ability of the system based on the sum-frequency generation technique was investigated using a standard scattering medium of Intralipid-10% aqueous solution and was found to be 78 dB in dynamic range. The optical CT image of absorbers placed in the scattering medium was successfully obtained with high contrast using the proposed system.     

The estimation of a unique solution for steady-state diffuse optical tomography by applying mechanical pressure

The accuracy of diffuse optical tomography (DOT) highly depends on two important factors: first, the knowledge of the tissue optical heterogeneities for accurate modeling of light propagation, and second, the uniqueness of reconstructed values of optical properties. Previous studies illustrated that the inverse problem associated with steady-state DOT does not have unique solutions. In this study, we propose a simple method that can be applied to improve this challenging problem of steady-state DOT. In this method, we study the propagation of photons through compressed breast phantoms. The applied mechanical pressure can change the values of optical properties and this pressure dependence of optical properties as a set of constraint equations can be used to improve the inverse problem. The applied pressure can help us to restrict the distribution of possible values of depth and radius of defect inside breast phantom reconstructed by inverse problem.     

Determination of g and mu using multiply scattered light in turbid media

We propose an inversion scheme to reconstruct the scattering coefficient mu and the anisotropy factor g that characterize the optical properties of a turbid medium. It is based on a theory for the scattering of light inside the medium from an angularly collimated light source. We demonstrate the feasibility of this method using light scattering data obtained from a Monte Carlo simulation.     

Effect of absorption of multiply scattering media on the degree of residual polarization of backscattered light

The effect of absorption in a scattering medium on the degree of residual polarization of backscattered radiation is studied in the case of probing of multiply scattering media by a linearly polarized light. An approximate expression describing the dependence of the degree of residual linear polarization of the backscattered radiation on the optical characteristics of a multiply scattering medium is derived within the framework of the phenomenological approach, based on the concept of the distribution of the optical paths of partial components of the scattered optical field under the conditions of multiple scattering, and with the use of the ideas about the similarity of statistical moments of the multiply scattered optical fields. The cut-off of the partial components, characterized by a large value of the optical path, because of their absorption, results in a substantial increase of the degree of residual polarization for the bands of the selective absorption caused by the presence of chromophores in the scattering medium. The results of experiments with model scattering media (whole milk) and biological tissues (human skin in vivo) are presented.     

微纳粒子光学散射分析

为实现利用光学方式对微纳尺度粒子性质的研究,探讨了亚微米线及亚微米球对光电磁波的散射效应.微纳米尺度粒子的光学散射,散射粒子尺寸与入射光波长尺寸可满足米氏(Mie)散射条件.利用Matlab数值模拟的方式,将分析结果以模拟图的形式清晰地展现出来.满足尺寸条件的层状粒子以及任意多个散射粒子存在时对电磁波的散射都可采用Mie散射分析方法,并且针对多粒子散射,分析了散射体位于不同位置时对散射造成的影响.通过分析光学散射光场相关的微分散射截面及近场散射电磁场分布,可得出散射光场随散射角度的变化趋势,以及散射光场受各类因素的影响,包括入射光偏振态、散射粒子尺寸、散射粒子结构及粒子构成层数、散射粒子数量等的影响,也包括一些隐含因素对散射光场的影响,如散射粒子与周围介质的相对折射率.本文的科学意义体现在:与入射光波长尺寸可比的亚微米尺度的粒子,可用作传感器,对于其位移的探测可通过光学方式来实现,而由于粒子本身特性对散射光的影响具有一定的参考价值,从而使通过光学方式对机械位移的读出具有更高准确度.研究结果对于光学方式探测亚微米线机械振动具有指导意义.     

Frequency-swept ultrasound-modulated optical tomography of scattering media

A novel frequency-swept ultrasound-modulated optical tomography technique was developed to image scattering media. A frequency-swept ultrasonic wave was used to modulate the laser light passing through a scattering medium. The modulated light was received by an optical detector and was heterodyned with a reference frequency sweep. The heterodyned signal was recorded in the time domain and was then analyzed in the frequency domain to yield a one-dimensional image along the ultrasonic axis. Multiple one-dimensional images obtained at various positions perpendicular to the ultrasonic axis were combined to yield a two-dimensional tomographic image of the medium.     

Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model

Optical tomography is a novel imaging modality that is employed to reconstruct cross-sectional images of the optical properties of highly scattering media given measurements performed on the surface of the medium. Recent advances in this field have mainly been driven by biomedical applications in which near-infrared light is used for transillumination and reflectance measurements of highly scattering biological tissues. Many of the reconstruction algorithms currently utilized for optical tomography make use of model-based iterative image reconstruction (MOBIIR) schemes. The imaging problem is formulated as an optimization problem, in which an objective function is minimized. In the simplest case the objective function is a normalized-squared error between measured and predicted data. The predicted data are obtained by using a forward model that describes light propagation in the scattering medium given a certain distribution of optical properties.In part I of this two-part study, we presented a forward model that is based on the time-independent equation of radiative transfer. Using experimental data we showed that this transport-theory-based forward model can accurately predict light propagation in highly scattering media that contain void-like inclusions. In part II we focus on the details of our image reconstruction scheme (inverse model). A crucial component of this scheme involves the efficient and accurate determination of the gradient of the objective function with respect to all optical properties. This calculation is performed using an adjoint differentiation algorithm that allows for fast calculation of this gradient. Having calculated this gradient, we minimize the objective function with a gradient-based optimization method, which results in the reconstruction of the spatial distribution of scattering and absorption coefficients inside the medium. In addition to presenting the mathematical and numerical background of our code, we present reconstruction results based on experimentally obtained data from highly scattering media that contain void-like regions. These types of media play an important role in optical tomographic imaging of the human brain and joints.     

Diffuse optical tomography: Present status and its future

Diffuse optical tomography (DOT) is one of the emerging modalities for the non-invasive imaging of thick biological tissues using near-infrared (NIR) light. This article reviews the fundamentals and development of DOT technology since its advent in the early 1990s, including the modeling of light propagation in biological tissues which strongly scatter and weakly absorb NIR light, the optical properties of biological tissues in the NIR wavelength range, three typical measurement methods, image reconstruction algorithms, and so forth. Then various studies are referred to for improvement of the DOT images, which are essentially low in quality due to the ill-conditioned and underdetermined problem. Studies and clinical applications presently attracting much attention are discussed in some detail. Finally, the expected future developments are summarized.     

Improving depth resolution of diffuse optical tomography with an exponential adjustment method based on maximum singular value of layered sensitivity

The sensitivity of diffuse optical tomography (DOT) imaging exponentially decreases with the increase of photon penetration depth, which leads to a poor depth resolution for DOT. In this letter, an exponential adjustment method (EAM) based on maximum singular value of layered sensitivity is proposed. Optimal depth resolution can be achieved by compensating the reduced sensitivity in the deep medium. Simulations are performed using a semi-infinite model and the simulation results show that the EAM method can substantially improve the depth resolution of deeply embedded objects in the medium. Consequently, the image quality and the reconstruction accuracy for these objects have been largely improved.     

Correlation transfer and diffusion of ultrasound-modulated multiply scattered light

We develop a temporal correlation transfer equation (CTE) and a temporal correlation diffusion equation (CDE) for ultrasound-modulated multiply scattered light. These equations can be applied to an optically scattering medium with embedded optically scattering and absorbing objects to calculate the power spectrum of light modulated by a nonuniform ultrasound field. We present an analytical solution based on the CDE and Monte Carlo simulation results for light modulated by a cylinder of ultrasound in an optically scattering slab. We further validate with experimental measurements the numerical calculations for an actual ultrasound field. The CTE and CDE are valid for moderate ultrasound pressures and on a length scale comparable with the optical transport mean-free path. These equations should be applicable to a wide spectrum of conditions for ultrasound-modulated optical tomography of soft biological tissues.     

Time-reversed ultrasonically encoded optical focusing into scattering media

Light focusing plays a central role in biomedical imaging, manipulation, and therapy. In scattering media, direct light focusing becomes infeasible beyond one transport mean free path. All previous methods1-3 to overcome this diffusion limit lack a practical internal "guide star."4 Here we proposed and experimentally validated a novel concept, called Time-Reversed Ultrasonically Encoded (TRUE) optical focusing, to deliver light into any dynamically defined location inside a scattering medium. First, diffused coherent light is encoded by a focused ultrasonic wave to provide a virtual internal "guide star"; then, only the encoded light is time-reversed and transmitted back to the ultrasonic focus. The TRUE optical focus-defined by the ultrasonic wave-is unaffected by multiple scattering of light. Such focusing is especially desirable in biological tissue where ultrasonic scattering is ~1000 times weaker than optical scattering. Various fields including biomedical and colloidal optics can benefit from TRUE optical focusing.     

Ultimate degree of residual polarization of incoherently backscattered light for multiple scattering of linearly polarized light

By invoking ideas about the distribution of the optical paths of partial components of the scattered field, we obtain an expression for estimating the degree of residual polarization of light that is incoherently backscattered from a disordered multiply scattering semi-infinite medium illuminated by linearly polarized light. In the backscattering regime, the depolarization length of the linearly polarized light in the disordered medium becomes smaller with the passage from the isotropic to anisotropic scattering. Experiments with model media featuring substantially anisotropic scattering (the anisotropy parameter of 0.90 ≤ g ≤ 0.95) demonstrated that for backscattering of linearly polarized light, the depolarization length is close to the transport length of the scattering medium.     

聚焦光在亚表面损伤介质中的散射特性

针对光学元件的亚表面缺陷,结合基于激光共焦层析的亚表层检测方法,建立聚焦光束在亚表面损伤介质中的传输模型,并采用有限元分析方法,仿真研究K9玻璃光学元件亚表层缺陷对聚焦光束的散射调制特性,特别对颗粒状和微裂纹两类特殊缺陷的光学调制特性进行研究和分析,探索了波长、缺陷大小、缺陷折射率及缺陷方向对聚焦光束散射特性的影响规律,通过分析包含亚表面损伤缺陷信息的光场分布图和强度变化曲线,获得了亚表面损伤缺陷的信息,并对其进行评价。     

透过散射介质对直线运动目标的全光成像及追踪技术

光散射是限制光传输以及降低和破坏光学成像性能的主要因素,透过复杂散射介质对运动目标的全光成像是光学领域极具挑战性的技术之一.本文提出一种利用散斑差值自相关透过散射介质对运动目标进行实时追踪的方法.采用赝热光照明,基于光学记忆效应理论,通过对运动目标采集的两帧散斑做差值,然后做自相关运算,计算目标移动的距离,实现对目标的实时追踪,并且利用相位恢复算法进行简单处理就可以重建隐藏目标.对该方法进行了实验验证,成功地对隐藏的运动目标实现了成像与追踪.这种透过散射介质对运动目标的全光成像及实时追踪技术,在生物医学等领域具有重要应用潜力.