多维梯度折射率介质内辐射传递的扩散近似

推导多维梯度折射率介质内稳态辐射传递的扩散近似方程.使用有限元法对扩散近似进行离散和求解,利用两个二维半透明介质的稳态辐射传递问题验证该扩散近似的精度及适用性.算例考虑介质为均匀折射率及梯度折射率两种情况.利用扩散近似分别求解辐射平衡时的边界热流、介质内温度场分布,并与辐射传递方程的求解结果进行对比分析.结果表明:介质折射率变化、散射特性、光学厚度及散射反照率均直接影响扩散近似的精度;在光学厚及强散射条件下,该扩散近似可以作为一种快速算法应用于梯度折射率介质稳态辐射传递的求解.     

Analysis of Light Propagation in a Realistic Head Model by a Hybrid Method for Optical Brain Function Measurement

Near infrared spectroscopy (NIRS) is used to measure the change in blood volume and oxygenation in the brain cortex induced by functional brain activation. The development of an adequate model to calculate light propagation in the head is very important because the light is strongly scattered in the tissue and this causes ambiguity in the volume of tissue interrogated with a source–detector pair of the NIRS instrument. In this study, a two-dimensional realistic head model is generated from a MRI scan of a human adult head. The light propagation in the head model is calculated by the hybrid Monte Carlo–diffusion method to obtain the change in detected intensity caused by a focal absorption change in the grey matter or in the white matter to discuss the relationship between the depth of the activated region and the sensitivity of the NIRS signal. The sensitivity to the activated region in the white matter steeply decreases with an increase of the depth of the activated region because the spatial sensitivity profile is mainly confined to the grey matter. The contribution of the focal brain activity to the NIRS signal is determined by not only the depth of the activated region from the head surface but also the depth of the activated region from the brain surface.     

Light propagation for time-domain fluorescence diffuse optical tomography by convolution using lifetime function

Time-domain light propagation in biological tissue is studied by solving the forward problem for fluorescence diffuse optical tomography using a convolution of the zero-lifetime emission light and the exponential function for a finite lifetime. We firstly formulate the fundamental equations in a time-domain assuming that the fluorescence lifetime is equal to zero, and then the solution including the lifetime is obtained by convolving the emission light and the lifetime function. The model is a two-dimensional (2-D) 10 mm-radius circle with the optical properties simulating biological tissue for the near infrared light, and contains some inclusions with fluorophores. Temporal and spatial profiles of excitation and emission light are calculated and discussed for several models with different inclusions. The results are physically reasonable and will be used for the inverse problem of fluorescence diffuse optical tomography.     

综合核方法求解辐射输运问题的求积组选取

简要介绍求解辐射输运方程的综合核方法,分析计算误差和收敛性,提出新的求积组和误差修正方法,提高综合核方法的计算精度.通过对基准问题的计算比对表明,采用提出的求积组并通过误差修正,综合核方法在低阶时的结果具有较高的计算精度.     

球谐函数法解点源辐射传输方程的P3近似及其在生物组织中的应用

辐射传输方程在球坐标下的P3近似是一个非线性微分方程组,其齐次解为球Bessel函数.需要将球Bessel函数分解为指数函数,才能用参数变异法求出它的特解.由于球Bessel函数在r=0的奇异性,无法利用Marshak和其它近似边界条件,因此直接利用能量守恒,和当介质的吸收系数比约化散射系数小得多时P3近似等于P1近似这个特点,确定全解中的常数.比较Monte Carolo模拟和P3近似理论的解析解发现,P3近似能处理约化散射系数与吸收系数之比介于2~10之间的生物组织.     

Analysis of Light Propagation in a Three-Dimensional Realistic Head Model for Topographic Imaging by Finite Difference Method

Near infrared topographic imaging is a novel non-invasive technique to obtain the activated region in the brain cortex. The light propagation in the head is strongly scattered and this causes results in poor spatial resolution and contrast in the topographic images. Adequate modelling of light propagation in the head in order to deduce the volume of tissue interrogated by a source-detector pair for topographic imaging is very important to improve the quality of image of brain activity. In this study, the light propagation in a three-dimensional realistic head model is calculated by the finite difference method. The geometry of the model is generated from axial slices of an MRI scan. The topographic image is obtained from the change in intensity detected by source-detector pairs caused by the brain activity. The images obtained by two types of source-detector arrangement are compared to evaluate the efficiency of source-detector arrangement. The results show that the double-density arrangement improves the quality of the topographic image of the brain activity.     

New Models for the Solution of Intermediate Regimes in Transport Theory and Radiative Transfer: Existence Theory, Positivity, Asymptotic Analysis, and Approximations

In this paper we propose, derive, and establish the mathematical foundations of new models for the solution of intermediate regimes in transport theory and radiative transfer. These new models consist of coupling the transport equations with their diffusion approximations. Our mathematical theory includes the existence theory, the positivity of the solutions, and the asymptotic analysis. We also give the rate of the asymptotic decay. In order to solve the new coupled problem we propose to use the transmission time marching algorithm introduced and studied in refs. 10, 13–15. We then study the convergence of the resulting algorithm. These studies are based in an essential way on the methods we introduced in refs. 14, 15.     

多光谱辐射层析重建三维火焰温度场

提出一种基于多光谱辐射测温理论及光学层析技术的三维温度场重建方法。建立了基于参考温度的多光谱测温法数学模型，提出了一种基于模拟退火理论的变松弛因子的光学层析技术新算法，通过计算机数值模拟，详细考察了该算法对非对称温度场分布的重建效果并与传统的代数迭代重建算法及滤波反投影算法进行比较。计算结果表明，变弛豫因子重建算法重建精度最高。作为一个应用实例，用多光谱辐射变弛豫因子重建层析方法重建了四峰蜡烛火焰某一截面的温度分布。     

Numerical Simulation of Bessel-Gauss Light Beams in Crystals with Quadratic Nonlinearity

With the developed method of numerical simulation, the dynamics of formation of the spatial structure of interacting wave fields in the process of generation of the sum-frequency radiation was investigated. Radial intensity profiles and angular spectra of diffracting light beams with varied restriction and focusing parameters at different stages of energy exchange in the KTP crystal have been calculated. It is shown that with weak focusing, a self-channeling wave structure of soliton type with angular divergence of the second-harmonic component at the level close to the diffraction limit is formed in the field of the wide Bessel-Gauss pumping beam. Moreover, in the far-field zone complete spatial separation of the light fluxes corresponding to the fundamental and second harmonics occurs. Comparison of the efficiencies of conversion on pumping by Gauss and Bessel-Gauss light beams is made. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 358–365, May–June, 2005.     

Finite Difference Time Domain Analysis of Diffusion Equations with Nonuniform Grids for Time-Resolved Reflectance of an Optical Pulse in Three-Dimensional Scattering Medium

An integral form of diffusion equations and their finite difference time domain (FDTD) analysis have been formulated. The analysis is extended to FDTD analysis with nonuniform grids in three-dimensional (3-D) scattering medium. It has been confirmed that 600 time steps in calculation sequences of the time-resolved reflectance for 3-D medium 80 × 80 × 30 mm³ in volume is completed within 4 seconds by utilizing 2³ and 4³ mm³ nonuniform cubic grids, when a conventional personal computer with 3 GHz CPU clock is used. The conditions for keeping numerical accuracies comparable to those in 2³ mm³ uniform grids are made clear. The proposed analysis greatly reduces time to run and memory space in 3-D scattering medium numerical analysis.