Three-dimensional vector radiative transfer in a semi-infinite, Rayleigh scattering medium exposed to a polarized laser beam: spatially varying reflection matrix

Three-dimensional vector radiative transfer in a semi-infinite, Rayleigh scattering medium exposed to a polarized, Gaussian laser beam directed perpendicular to the surface is studied. The focus of this investigation is the 4×4, spatially varying reflection matrix that can be used to determine the normally backscattered radiation when the polarization of the incident radiation is specified. An inverse integral transform is used to construct the spatially varying reflection matrix from the generalized reflection matrix found in a previous study. The elements of this matrix depend on location specified by optical radius and azimuthal angle. The azimuthal variation is found by performing part of the inverse transform analytically, while the radial variation is described by five functions that are calculated numerically via an inverse Hankel transform. Benchmark numerical results for these five functions are presented, and the effects of beam radius and particle concentration are discussed. Expressions that describe the behavior of the reflection functions at small and large optical radii are developed, and comparisons are made to the one-dimensional and scalar situations. The scalar approximation fails to predict the three-dimensional effects produced by the polarized beam, and even when the incident radiation is unpolarized, the error in the scalar reflection function can be as high as 20%.     

Three-dimensional radiative transfer in an anisotropically scattering, plane-parallel medium: generalized reflection and transmission functions

The problem of spatially varying, collimated radiation incident on an anisotropically scattering, plane-parallel medium is considered. A very general phase function is allowed. An integral transform is used to reduce the three-dimensional radiative transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to derive nonlinear integral and integro-differential equations for the generalized reflection and transmission functions. The integration is over the polar and azimuthal angles—this formulation is referred to as the double-integral formulation. The integral equations are used to illustrate symmetry relationships and to obtain single- and double-scattering approximations. The generalized reflection and transmission functions are important in the construction of the solutions to many multidimensional problems. Coupled integral equations for the interior and emergent intensities are developed and, for the case of two identical homogeneous layers, used to formulate a doubling procedure. Results for an isotropic and Rayleigh scattering medium are presented to illustrate the computational characteristics of the formulation.     

Three-dimensional vector radiative transfer in a semi-infinite, Rayleigh scattering medium exposed to spatially varying polarized radiation: generalized reflection matrix

Three-dimensional vector radiative transfer in a semi-infinite medium exposed to spatially varying, polarized radiation is studied. The problem is to determine the generalized reflection matrix for a multiple scattering medium characterized by a 4×4 scattering matrix. A double integral transform is used to convert the three-dimensional vector radiative transfer equation to a one-dimensional form, and a modified Ambarzumian's method is then applied to derive a nonlinear integral equation for the generalized reflection matrix. The spatially varying backscattered radiation for an arbitrarily polarized incident beam can be found from the generalized reflection matrix. For Rayleigh scattering and normal incidence and emergence, the generalized reflection matrix is shown to have five non-zero elements. Benchmark results for these five elements are presented and compared to asymptotic results. When the incident radiation is polarized, the vector approach used in this study correctly predicts three-dimensional behavior, while the scalar approach does not. When the incident radiation is unpolarized, both the vector and scalar approaches predict a two-dimensional distribution of the intensity, but the error in the scalar prediction can be as high as 20%.     

Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: generalized reflection function

Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large.     

Probability density function of the intensity scattered by Rayleigh-particle aggregates. Evolution with optical properties

We study the probability density function of the statistical fluctuations of the intensity scattered by an aggregate freely floating in space and constituted by Rayleigh particles under the dipole approximation. Its evolution as a function of the optical properties of the particles (polarizability) and their separation distance is analyzed. Aggregate geometries with two and three particles will be considered. The influence of the multiple scattering effect on the statistics of the scattered intensity is especially studied.     

分布式光纤布里渊散射温度传感实验系统

提出一种基于布里渊光时域反射计法的分布式光纤布里渊散射温度传感系统.光源采用窄谱半导体激光器.声光调制器将光源调制成窄脉冲,并由高增益光纤放大器放大,产生高功率光脉冲信号,提高了自发布里渊散射信号的强度.采用双通马赫-曾德干涉仪将布里渊散射从瑞利散射中分离出来,在一段4.25 km长的光纤上进行分布式温度传感的实验研究.双通马赫-曾德干涉仪对瑞利散射进行了很好的抑制,得到了比较纯净的随温度变化的布里渊散射信号.     

Two-dimensional isotropic scattering in a finite thick cylindrical medium exposed to a laser beam

Graphical and tabular results are presented for the back-scattered intensity from a finite two-dimensional cylindrical medium exposed to a Gaussian beam of radiation. Also, results for the source function and flux at the boundaries are presented. The influence of optical thickness and albedo are most pronounced at large optical radii. The semi-infinite results can be used to approximate the finite case for small optical radii. Ranges for single, double, and multiple scattering are discussed. For locations far from the incident beam, the results can be expressed in terms of universal functions independent of beam size. A method is presented for extending the isotropic results to the anisotropic case where the phase function is made up of a spike superimposed on an otherwise isotropic phase function.     

Phenomenology of collinear photon emission from quark–gluon plasma in <Emphasis Type="Italic">AA</Emphasis> collisions

Multiple backscattering from layers with various thicknesses, including the case of half-space, is numerically simulated and a comparative analysis is performed for systems with the anisotropy of scattering described by the Henyey–Greenstein and Rayleigh–Gans phase functions. It is shown that the intensity of backscattering depends on the form of the phase function; the difference between the intensities obtained within the two models increases with anisotropy.     

Stimulated Brillouin scattering as the referencing mechanism of an optical fibre intensity sensor

An optical fibre intensity sensor referenced by stimulated Brillouin scattering is presented. The optical sensor uses Fresnel reflection signal at the sensor fibre end and employs an adequate relationship between Brillouin and Rayleigh scattering and Fresnel reflection to have a referenced optical fibre intensity sensor addressed in reflection.     

Interlocked multiplets in anisotropically scattering medium with exponential Planck function

The equation of transfer for interlocked multiplets in anisotropically scattering atmosphere with planetary phase function has been considered. The Planck function is considered as exponential function of optical depth. The diffusely reflected intensity and emergent intensity in nth approximation has been obtained. Attempt has been made to get exact diffusely reflected intensity and emergent intensity.     

非球形大气粒子对任意波束的电磁散射特性

研究大气中变形球状的气象粒子对电磁波以及激光的散射特性,采用广义米氏(Mie)理论,精确地求解在任意波束中大气粒子的散射强度,数值计算激光束腰位置对散射强度分布的影响,分析彩虹强度和散射角与变形球状粒子偏心率的关系,研究随着长短轴比例增加,彩虹强度峰值的偏移。计算结果表明雨滴在下降过程中,它在各个方向的光散射强度逐步减弱,即随着雨滴偏心率的增大,散射强度减少,彩虹角变大。对于激光入射,当粒子距离波束中心位置越远,粒子的散射就越弱,并且随尺寸参量增加,后向散射振荡的频率要大于前向散射,当束腰位置矢径的大小增加时,后向散射和前向散射强度均变小。     

沙尘天气下激光信号的传输特性

以小角度近似为条件,利用逐级递归的方法推导了激光信号在沙尘天气下的辐射传输方程,得到了多次散射下的光强分布函数,以及波长和不对称因子对光强的影响。同时,通过比较不同散射相位函数及沙尘粒子的散射特性,采用了修正的TTHG(Two Term Henyey-Greenstein)散射相位函数,更加全面地反映了沙粒散射后光强的变化规律。研究结果表明,随着光学厚度的增加,散射光强呈现出先增大后减小的趋势,且多次散射的比重相比于单次散射而言逐渐增大。当散射次数超过3次以上时,接收光强的变化可以忽略不计。相对于Mie理论下的结果而言,采用小角度近似理论,从辐射传输的角度分析沙粒的散射特性误差更小,实现了准确描述沙尘天气下激光信号传输特性的目的。     

多层球对高斯波束散射的德拜级数研究

基于广义洛伦兹-米氏理论,利用多层球粒子散射系数的德拜级数展开公式,提出了一种新的研究多层球粒子对高斯波束散射的方法。计算结果与已有的广义洛伦兹-米氏理论算法的计算结果吻合得很好。利用该方法有效分离了折射率分布满足指数变化规律的多层球粒子对高斯波束散射的远区散射场中多阶彩虹的干涉强度分布。数值模拟了双层球的归一化双一阶彩虹强度分布以及各层的一阶彩虹艾里结构。最后分析讨论了高斯波束的入射位置和束腰半径对多层球单阶彩虹强度分布的影响。     

超衍射极限相干反斯托克斯拉曼散射显微成像技术中空心光束的形成

空心光束的质量是超衍射极限相干反斯托克斯拉曼散射显微成像技术中决定成像质量的一个至关重要的因素. 本文基于菲涅耳衍射理论,分析了螺旋相位片法产生空心光束的物理机理,并且模拟了不同的入射条件对产生的空心光束的影响. 模拟结果表明:波长与相位片中心波长匹配且光强呈圆对称分布的高斯光垂直入射到相位片上,当高斯光束中心与相位片中心完全对准时,可获得较理想的空心光束;入射光光强分布的圆对称性以及入射光中心与相位片中心的对准程度都会影响产生的空心光束的强度分布;同时,高斯光束小角度倾斜入射时,空心光的强度分布仍呈圆对称,却在观察面发生一定的位移;此外,入射光中心波长偏离相位片中心波长不大时,对产生的空心光束的强度分布几乎没有影响. 上述分析结果对用于超衍射相干反斯托克斯拉曼散射显微成像技术中理想空心光束的获取具有重要的指导意义. 关键词： 空心光束 超衍射极限 相干反斯托克斯拉曼散射 螺旋相位片     

Formation of the Intensity Distribution in Laser Beams due to Difraction on Structures of Small-Size Optical Inhomogeneities

The possibilities of formation of the intensity distribution in laser beams due to diffraction of radiation on spatial structures of small-size optical inhomogeneities are considered. Computer modeling of beam profile formation by plates-apodizers containing two-dimensional structures of discrete amplitude or phase scatterers is performed. The results presented testify to the prospects of optical elements with scattering centers for laser beam shaping in UV, visible, and IR spectral ranges.     

环形光束的非线性传输及聚焦特性研究

针对用于产生光镊的环形光束,利用分步傅里叶-贝塞尔变换算法,对二维环形超高斯光束的非线性传输及聚焦过程进行了数值模拟,给出了环形光束聚焦场附近的光强分布,并分析了非线性调制对聚焦性质(包括焦面中心光强、焦面光强的横向分布、轴上光强和光束质量)的影响.研究表明,从聚焦角度来看,非线性调制中的位相调制比振幅调制对环形光束聚焦性质的影响程度要大;从非线性传输角度来看,随着非线性介质长度的增加,位相调制和振幅调制对环形光束聚焦性质各有不同程度的加剧,其中非线性作用对振幅调制的影响要比位相调制明显.     

相干瑞利散射海水水下温度测量技术的理论研究

海水水下温度的快速大范围测量是海洋监测的重要内容,在民用和军事领域都有着至关重要的意义,本文提出了采用相干瑞利散射方法测量海水水下温度的新方法:用宽带高速光电探测器接收本振激光和海水后向瑞利散射光相干产生的差频信号,进行傅里叶变换分析获取海水瑞利散射展宽谱,从而反演海水温度,首先从海水的热力学特性出发,对利用瑞利散射谱测量海水水下温度的基本原理进行了理论研究和软件模拟;然后对采用相干探测测量海水瑞利散射谱的测量方法进行了理论分析和软件模拟;在此基础上对瑞利散射海水水下温度测量精度进行了分析,得出当水体瑞利散射频谱半宽度测量精度为1 MHz时,测温精度约为0.35 K。     

The propagation dynamics of ultraviolet light filament with Rayleigh scattering in air

In this paper we present for the first time the effects of Rayleigh scattering on the long distance propagation of ultraviolet （UV） light filament in air based on the stationary analysis. The simulation results show that the effects of Rayleigh scattering on the propagation of UV laser filaments may not be ignored. These influences are slightly dependent on the laser wavelength. We also compare the UV filament propagations at different input powers in the presence and the absence of the Rayleigh scattering and discuss the mechanisms of power loss and beam defocusing. In the absence of Rayleigh scattering, the filament propagation is determined by the oscillating behaviour of the beam size. In the presence of the scattering, the propagation lengths of filament are close to each other at different initial powers and determined by the Rayleigh scattering.     

Direct solution of the radiative transfer equation for plane-parallel atmospheres

A method is described for solving the monochromatic radiative transfer equation for the case of inhomogeneous, plane-parallel scattering and absorbing atmospheres illuminated by external as well as internal sources. The solution procedure, which is based on a series expansion of the radiation intensity with respect to the angular and spatial coordinates, is analytical in nature and can thus be implemented on small computing facilites. Test calculations were performed for isotropic and Rayleigh scattering atmospheres of various optical thicknesses and single scattering albedos. The results coincide well with data from other methods given in the literature.     

光纤背向激光自发喇曼散射的温度效应研究

从理论和实验上研究了光纤背向激光自发喇曼散射的温度效应.光纤背向激光自发反斯托克斯喇曼散射、斯托克斯喇曼散射光的相对强度正比于光纤分子上、下能级粒子数的布居,依赖于温度.由于实际系统中,作为分光用的干涉滤光片不可能完全隔离背向瑞利散射光,因此,实际系统温度曲线比理论曲线低,本文给出了理论修正公式,提出了附加修正项,它与隔离度和波长有关.