脑组织漫反射光谱与约化散射系数的斜率估算法

约化散射系数是生物组织光学研究中的一个重要的组织光学参数。利用微光纤探头与光纤光谱仪组成漫反射光谱采集系统对脑组织约化散射系数的实时在位测量进行研究。通过悬乳液与模拟胶模型实验推导了700～850nm波段约化散射系数与漫反射光谱斜率绝对值的关系式,用模型对公式的计算精度进行验证,利用该系统实时在位测量了20只大鼠脑组织在700nm、750nm和800nm处的约化散射系数。经统计分析,大鼠脑白质约化散射系数在上述波长处分别为30±5cm-1、28±5cm-1和25±6cm-1,脑灰质约化散射系数则分别为14±3cm-1、13±3cm-1和12±3cm-1。脑组织约化散射系数实时在位测量对脑外科微创手术中的组织识别具有重要的参考意义。     

无限介质中近场辐射率的P5近似

针对辐射率的漫射近似、P3近似等正向模型在描述小源探距离及低约化反照率介质下光子传输时存在的局限性,推导了用于小源探距离低反照率无限媒质中各向同性稳态点光源下辐射传输方程在P5近似下的解析解,并将P3近似、P5近似计算的辐射率分别和蒙特卡洛模拟结果进行对比.结果表明:在高约化反照率(0.97)条件下,P5近似和蒙特卡洛模拟结果的最大相对误差为13.17%,而P3为41.57%.在低约化反照率(0.69)条件下,最大相对误差分别为27.78%,286.70%.在其他光学参数下,P5近似与蒙特卡洛模拟的最大相对误差均小于P3.在P5适用的范围内舍弃最大特征根相关项,可以简化解析表达式,提高计算速度,且对P5的计算结果影响甚微.稳态辐射率测量系统仿体验证表明,在高、低约化反照率介质中的小源探距离下,由P5近似计算得到的辐射率和实验测量结果相符.     

热作用致良性前列腺增生组织的光学特性变化

研究了热作用下的良性前列腺增生(BPH)组织对808和980 nm的半导体激光的光学特性的变化及其差异。实验采用双积分球测量系统以及反向倍增法获取良性前列腺增生组织的光学特性。结果表明,热作用下的良性前列腺增生组织对808 nm和980 nm的吸收系数、约化散射系数和光学穿透深度都是随着加热温度的变化而变化的,在20~80℃的温度范围内,良性前列腺增生组织对808 nm的吸收系数和约化散射系数都分别明显地较其对980 nm的吸收系数和约化散射系数要大,而其对808 nm的光学穿透深度却明显地较其对980 nm的光学穿透深度要小,吸收系数的最大值都在20℃,分别为0.528 mm-1和0.448 mm-1;最小值分别在50℃和70℃,分别为0.436 mm-1和0.326 mm-1,吸收系数的最大差异在70℃,其值为34.1%;约化散射系数的最大值都在80℃,其值分别为1.45 mm-1和1.43 mm-1,最小值分别在20℃和70℃,分别为1.15 mm-1和0.973 mm-1,最大差异在70℃,其值为24.4%;光学穿透深度的最大值分别在50℃和70℃,其值分别为0.684 mm和0.887 mm,最小值都在80℃,其值分别为0.608 mm和0.696 mm,最大差异在70℃,其值为30.4%。在70℃的热作用下良性前列腺增生组织达到完全热凝固,吸收系数、散射系数和光学穿透深度的差异达到最大值。     

良性前列腺增生组织对钛宝石激光的吸收和散射特性

研究了经尿道等离子体双极电切除术(PKRP)切除和经尿道前列腺电切术(TURP)切除的前列腺增生(BPH)组织对640, 660, 680, 700, 720, 740, 760, 780, 800, 820, 840, 860和880 nm波长的钛宝石激光的光学特性及其差异,实验采用双积分球测量系统以及反向倍增法获取BPH组织的吸收和散射特性参数。结果表明：PKRP和TURP切除的BPH组织对这1３个不同波长的激光的吸收系数和约化散射系数都是随着激光波长增大而明显减小的,PKRP切除的BPH组织对这同一波长的激光的吸收系数和约化散射系数都明显较TURP切除的BPH组织对相应的波长的激光的吸收系数和约化散射系数要小,PKRP和TURP切除的BPH组织的吸收系数以及约化散射系数的最大值都在640 nm,其值分别为(0.885±0.022)和(0.955±0.024)mm-1以及(1.564±0.039)和(1.658±0.042)mm-1,其差异分别为7.91%以及6.01%,其最小值都在880 nm,其值分别为(0.443±0.011)和(0.455±0.011)mm-1以及(1.117±0.028)和(1.197±0.030)mm-1,其差异分别为2.71%以及7.16%。PKRP和TURP切除的BPH组织对660 nm的吸收系数的差异最大,其值为8.95%,其差异最小在860 nm,其值为1.75%,PKRP和TURP切除的BPH组织对800 nm的约化散射系数的差异最大,其值为9.13%,其差异最小在640 nm,其值为6.01%。     

热凝固致良性前列腺增生组织在590～1 064 nm的吸收和散射特性的变化

研究了自然的和热凝固的良性前列腺增生(BPH)组织在590～1 064 nm光谱范围的光学特性及其差异,实验采用带积分球附件的分光光度计以及反向倍增法获取组织样品的吸收和散射特性参数。结果表明：热凝固导致BPH组织在590～1 064 nm光谱范围的吸收系数明显地减小的,自然的和热凝固的BPH组织的吸收系数都有一个峰值在990 nm处,其值分别为0.438和0.416 mm-1,自然的和热凝固的BPH组织的吸收系数的最大差异在1 064 nm,其值为86.79%,其最小差异在920 nm,其值为4.74%。热凝固导致BPH组织在600～1 064 nm光谱范围的约化散射系数明显地增大,而在590 nm处,热凝固导致BPH组织的约化散射系数却是明显地减小,自然的和热凝固的BPH组织的约化散射系数都有一个峰值在970 nm处,其值分别为1.090和1.449 mm-1,其另一个峰值都在1 050 nm处,其值分别为1.116和1.627 mm-1,自然的和热凝固的BPH组织的约化散射系数的最大差异在1 060 nm,其值为47.73%,其最小差异在600 nm,其值为4.86%。     

吸收介质中微椭球体颗粒光学参数的研究

本文应用Eikonal近似将微椭球用其等效的球来近似, 结合Mie理论对吸收介质中微椭球体颗粒光学参数进行了数值计算。 结果表明, 椭球位置变化时, 散射和吸收性能发生变化。离心率增大时, 散射和吸收系数都增大, 离心率越大增大的越明显。波长增大时, 在紫光波长为0.4 μm和近红外区波长为1.58 μm处散射系数出现了峰值, 而吸收系数单调增大。相对折射率实部以及虚部变化对光学参数均有影响, 颗粒的吸收性越强, 散射相应地减弱。结果表明这种数值解析方法能有效地计算椭球体颗粒的光学参数。     

基于积分球试验的粉体材料辐射特性分析研究

为了获取准确的粉体材料红外辐射特性参数,本文对Al_2O_3粉体材料的红外辐射特性进行了以下研究:对粉末样品进行积分球反射率和透射率的测量试验,利用三热流近似法求解辐射传输方程,结合粒子群算法反演粉末的散射系数和吸收系数。Al_2O_3粉体材料的辐射特性研究结果显示,在4~7μm波段散射系数和吸收系数均随波长和厚度的增加而减小,且粉末层厚度越小,粒子散射越强烈。该方法适用于获取常温下各种粉体材料的辐射特性参数,并分析粉体材料的辐射特性参数及其与厚度等因素的关系。     

Broer-Kau-Kupershmidt方程组的对称、约化和精确解

利用修正的CK直接方法得到了Broer-Kau-Kupershmidt (简写为BKK)方程组的对称、约化, 通过解约化方程得到了该方程组的一些精确解, 包括双曲函数解、 三角函数解、 有理函数解、 艾里函数解、 幂级数解和 孤立子解等. 关键词： 修正的CK直接方法 BKK方程组 对称、约化 精确解     

水下任意刚性散射体对Bessel波的散射特性分析

本文利用Bessel波的谐波展开式, 采用T矩阵方法的推导思路, 建立了水下任意刚性散射体在Bessel波照射下的声散射场计算公式. 以水下刚性椭球体和两端附连半球的刚性圆柱体为例, 计算了在不同波锥角β 下的反向散射形态函数, 同时, 依据镜反射波和绕行波的干涉物理模型, 给出了预报Bessel波照射下的反向散射形态函数峰峰间隔值的计算模型. 仿真结果表明本文提出的Bessel波照射下反向散射形态函数峰峰间隔值预报方法是准确有效的, 同时也说明, 本文建立的基于T矩阵法计算水下任意刚性散射体在Bessel波束下的声散射场方法是有效的, 这拓展了T矩阵法的应用领域.     

Bessel光束经椭圆环形孔径后的衍射光场

基于菲涅耳衍射积分理论及硬边孔径的复高斯函数展开法导出了Bessel光束经椭圆环形孔径后的光场表达式, 数值模拟了其光场的强度分布. 研究了Bessel光束经椭圆环形孔径后的光场变化及其传播过程; 在实验上利用轴棱锥输出的近似无衍射Bessel光, 通过椭圆环形孔径, 使用电荷耦合器件拍摄得到不同传播距离处的光强分布. 理论结果和实验结果均表明无衍射光束经椭圆环形孔径后会产生空心光束.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

Abstract

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Analytic description of critical point nuclei in a spherical-axially deformed shape phase transition

An approximate solution at the critical point of the spherical to axially deformed shape phase transition in nuclei is presented. The eigenvalues of the Hamiltonian are expressed in terms of zeroes of Bessel functions of irrational order.     

A New Spherical Bessel Function Result Related to Quantum Mechanical Scattering Theory

The authors present a derivative formula for the square of a spherical Bessel function in terms of the spherical Bessel function of twice the argument. This derivative formula is then applied in an inversion problem for the partial-wave Born approximation in quantum mechanical scattering theory. Several other closely related results and derivative formulas are also considered.     

Localization of Spherical Particles under the Action of Gradient Forces in the Field of a Zero-Order Bessel Beam. Rayleigh–Gans Approximation

The amplitude of the gradient force acting on a transparent spherical particle in the field of a zero-order Bessel beam has been calculated in the Rayleigh–Gans approximation. The expression obtained for the gradient-force amplitude takes into account the heterogeneity of the acting radiation in the volume of the particle. The optimal conditions of trapping and transportation of the particle (parameters of the particle, liquid, and of the Bessel beam) to the localization region have been determined using the solution of the kinetic equation of particle motion in a liquid. It is shown that for certain relationships between the particle radius and the Bessel beam width the localization region is shifted relative to the central maximum of the beam. This is due to the equal action of the gradient forces caused by the central maximum and the first interference ring of the Bessel beam. A qualitative comparison of the results obtained with the known experimental data has been performed.     

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.     

Solitary Waves in Spherical Bessel Lattice

The analytical solitary waves solution to (3+1)-dimensional Gross-Pitaevskii equation with varying coefficients and an spherical Bessel lattice potential is obtained, which is in the form of self-similar solitary waves. The properties and the stability of the solitary waves family are discussed in detail.     

Transient response of a spherical shell in an acoustic medium—Comparison of exact and approximate solutions

The transient response of a spherical shell in an acoustic medium is studied. The exact solution is obtained by expressing the classical spherical wave equation in terms of a residual potential. Approximate solutions are obtained from the use of eight functions; namely, doubly asymptotic approximations, δ-sequence functions, and spherical wave approximations. The advantages and disadvantages of these approximate solutions are pointed out. The third member of the class of the modal doubly asymptotic approximations for a spherical surface and an improved spherical wave approximation are introduced.     

Frequency-radial duality based photoacoustic image reconstruction

Photoacoustic image reconstruction algorithms are usually slow due to the large sizes of data that are processed. This paper proposes a method for exact photoacoustic reconstruction for the spherical geometry in the limiting case of a continuous aperture and infinite measurement bandwidth that is faster than existing methods namely (1) backprojection method and (2) the Norton-Linzer method [S. J. Norton and M. Linzer, "Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solution for plane, cylindrical and spherical apertures," Biomedical Engineering, IEEE Trans. BME 28, 202-220 (1981)]. The initial pressure distribution is expanded using a spherical Fourier Bessel series. The proposed method estimates the Fourier Bessel coefficients and subsequently recovers the pressure distribution. A concept of frequency-radial duality is introduced that separates the information from the different radial basis functions by using frequencies corresponding to the Bessel zeros. This approach provides a means to analyze the information obtained given a measurement bandwidth. Using order analysis and numerical experiments, the proposed method is shown to be faster than both the backprojection and the Norton-Linzer methods. Further, the reconstructed images using the proposed methodology were of similar quality to the Norton-Linzer method and were better than the approximate backprojection method.