Radiative transfer in a two-dimensional rectangular medium exposed to diffuse radiation

The integral equation for radiative transfer in a two-dimensional rectangular scattering medium exposed to diffuse radiation is solved numerically by removing the singularity. This method yielded accurate results except at very large optical thicknesses. Graphical and tabular results for the source function, flux, and intensity are presented. The source function is also calculated using the first term of a Taylor series expansion. The Taylor series is fairly accurate for small optical thicknesses and columnar geometries. A method is presented for extending these results to the problem of a strongly anisotropic scattering phase function which is made up of a spike in the forward direction superimposed on an isotropic phase function.     

Two-dimensional isotropic scattering in a semi-infinite cylindrical medium

Beginning with the integral equation for the source function, the solutions for the source function, flux and intensity at the boundary of a two-dimensional, isotropically scattering cylindrical medium are found. The incident radiation is collimated and normal to the surface of the medium and depends only on the radial coordinate. For a Bessel function boundary condition, separation of variables is used to reduce the source function integral equation to a one-dimensional equation. The resulting integral equation is shown to be the same as that for the two-dimensional planar case. Solutions for other boundary conditions are then shown to be superpositions of the Bessel function solution. Numerical results are presented for a Gaussian distribution of incident radiation which closely models a laser beam. These multiple scattering results are compared to the single scattering approximation. Also, the solution for a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on an otherwise isotropic phase function is expressed in terms of the isotropic results.     

Scattering contributions to the internal partition function of a diatomic molecular system

An analytical expression for the phase shift contribution to the internal partition function for the Morse potential is derived by using an approximate Jost function. This function is shown to be a convergent sum. The numerical results obtained for H₂ and HCl show the partition function to be a monotonically increasing function of temperature. This observation agrees with the results of Rogers and co-workers. Work supported in part by the Department of Atomic Energy, Government of India.     

采样窗口对光学系统MTF测量影响的研究

对光学系统MTF测试中采样窗口对其测量影响进行了研究。在对标准镜头MTF测试时,采用离散傅里叶变换计算,线扩散函数扫描方向长度为所选针孔像线扩散函数半高宽的5倍左右时,MTF测试结果与设计值差异极值为0．011;采用快速傅里叶变换计算,线扩散函数扫描方向长度为所选针孔像线扩散函数半高宽的5倍左右时,同时采样点数要满足2^N,测试结果与设计值差异极值为0．010。为了证明此结论的普适性,按所提的采样窗口选取原则,对大像差镜头轴上和轴外的MTF进行了试验,并将测试结果与OPTIKOS的测试结果进行对比,最大极差为0．013。试验结果表明,此结论能够为光学系统MTF测试时采样窗口选择提供依据。     

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.     

基于谱线线型函数的气体浓度检测技术

快速、精确地测量微量气体浓度的技术在大气质量分析、环境污染检测等领域具有广泛的用途。在红外光谱检测技术中,气体吸收光谱的谱线线型函数是定量测量气体浓度的一个重要参量,而如何准确和快速地得到气体谱线线型函数值是气体浓度测量中的一个关键问题。首先从理论上分析了谱线线型函数,得出计算谱线线型函数的一般方法及探讨了气体浓度与谱线线型函数峰值之间的关系。然后,利用可调激光器及光谱仪检测系统测量了乙炔在1 515～1 545 nm波长范围内的吸收光谱,再通过Lambert-Beer定律计算得到在不同频率下的谱线线型函数峰值,最后利用程序拟合出该波段内气体的谱线线型函数峰值分布曲线,并与Voigt线型函数理论计算值进行了比较,发现理论计算的谱线线型函数峰值仍存在一定的偏差。相比理论计算结果,所提出的检测方法得到的乙炔浓度与真实的乙炔浓度值更加吻合,表明了通过实验确定的谱线线型函数的经验公式可以更好地用于气体浓度的检测。由于利用实验测量值获得了谱线线型函数峰值分布的拟合曲线,因此可以快速准确地计算出所对应的谱线线型函数峰值,从而大大地简化了线型函数的计算过程。实验所获得的数据可应用于光学遥测乙炔气体浓度,且提供的方法也可以应用到其他气体的谱线线型函数峰值的测量中。     

Analytical evaluation of the plasma dispersion function for a Fermi—Dirac distribution

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.     

二氧化钒的电子结构及光学性质计算

本文使用基于量子力学第一性原理的CASTEP程序包,计算了单斜结构和金红石结构的二氧化钒(VO2)的电子结构、介电常数、吸收系数、折射率等光学性质。介电函数的虚部、吸收光谱、折射率等它们的峰值位置存在一一对应关系,这表明了它们之间存在着内在的联系,它们都与电子从价带到导带的跃迁吸收有关,这为从物理本质上理解二氧化钒的光学性质提供了重要的依据。计算结果与实验结果符合得很好。     

Theoretical Investigation of Uniform and Non-uniform Penetrable Sphere Fluid

A bridge function approximation is proposed for a single-component fluid consisting of penetrable sphere interacting via a potential that remains finite and constant for center-center distance smaller than the particle diameter and is zero otherwise. The radial distribution function from the Ornstein-Zernike integral equation combined with the present bridge function approximation is in satisfactory agreement with the corresponding simulation data for all of the investigated state points. The presently calculated excess Helmholtz free energy respectively based on virial route and compressibility route is highly self-consistent, and is in very good agreement with simulational results for the case of low temperatures. The present bridge function approximation, combined with the bridge density functional approximation,can reproduce very accurately density profiles of the penetrable sphere fluid confined in a hard spherical cavity for all the cases where simulational results are available.     

Theoretical Investigation of Uniform and Non-uniform Penetrable Sphere Fluid

A bridge function approximation is proposed for a single-component fluid consisting of penetrable sphere interacting via a potential that remains finite and constant for center-center distance smaller than the particle diameter and is zero otherwise. The radial distribution function from the Ornstein-Zernike integral equation combined with the present bridge function approximation is in satisfactory agreement with the corresponding simulation data for all of the investigated state points. The presently calculated excess Helmholtz free energy respectively based on virial route and compressibility route is highly self-consistent, and is in very good agreement with simulational results for the case of low temperatures. The present bridge function approximation, combined with the bridge density functional approximation, can reproduce very accurately density profiles of the penetrable sphere fluid confined in a hard spherical cavity for all the cases where simulational results are available.     

A new method for analyzing the collimation angle of a neutron Soller collimator

A new method for analyzing the collimation angle of a neutron Soller collimator is described. A Gaussian distribution formula is used to define the angular distribution function of the neutron source and the neutron transmission function of the Soller collimator. A relationship between the FWHM of the collimator rocking curve and the collimation angle is derived. Using this method, some rocking curve experiment results are analyzed. The results show that the new function can be a good theoretical model for fitting the experimental data, especially for the data of two collimators with different collimation angles.     

δ函数SN方法求解含各向异性散射输运方程的本征值问题

将角通量分解成一个δ函数和一个低阶函数,分别采用解析方法和求积组来计算源项.利用δ函数S_N方法,计算了平几何条件下含各向异性散射单速输运方程的临界问题.分析和数值结果表明,采用数量较少的离散方向,能够达到较高计算精度.     

铝表面的电子关联函数

根据金属表面的多体波函数,建立了非均匀电子关联函数的积分方程,对此方程消除了因长程关联而出现的发散。在第一次迭代下求得了铝表面的电子关联函数的数值结果。 关键词：     

高效双螺旋点扩展函数相位片的设计与实验研究

双螺旋点扩展函数具有随离焦连续旋转变化的特性, 结合单分子定位方法可用于厚样品三维超分辨成像及分子定位追踪研究. 但双螺旋点扩展函数不足之处是光能利用率低, 对于光子数受限的荧光显微成像而言其应用受限. 本文通过对双螺旋点扩展函数在空域、频域和拉盖尔-高斯模式面等三个不同域中进行约束优化. 模拟结果表明, 优化后的双螺旋点扩展函数的光能效率提高了30多倍. 同时, 基于最优设计方案制备了相位片, 并实验验证了该设计的正确性. 与文献报道相比较, 本文结果在成像深度和光能利用率方面都有所改善. 关键词： 双螺旋点扩展函数 超分辨成像 轴向定位 优化算法     

Study on Properties of Intensity Profiles Scattered from the Self-Affine Fractal Random Surfaces: an Approximate Theory and Simulations

We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces. Weuse the mathematical decay function to approximate the duple negative exponent function in the rigorous theory ofscattering, by letting them have the same maximum value and half-width, and the expression for the half-widths of theintensity profiles in the whole range of the perpendicular wave vector component is obtained. The previous results in thetwo extreme cases are included in the results of this paper. In the simulational verification, we propose a method for thegeneration of self-affine fractal random surfaces, using the square-root of Fourier transform of the correlation function ofthe surface height. The simulated results conform well with the theory.     

轴对称收敛型电子枪设计方法再讨论

 对轴对称收敛型电子枪设计方法进行了整理分析,就阴极半锥角的初始值对迭代综合法的收敛性能所产生的影响进行了讨论,针对低压缩比条件下原来的Vaughan公式失效的问题进行了分析,给出了更为合理的初始值计算公式。采用修正后的公式和迭代综合法对电子枪进行设计,在高压缩比情况下的设计结果与采用原来Vaughan方法的结果完全一致;而对于低压缩比的情况,也得到了合理的设计,从而解决了原来的Vaughan方法在低压缩比情况下失效的问题,扩大了迭代综合法的应用范围。     

Two-dimensional linearly anisotropic scattering in a semi-infinite cylindrical medium exposed to a laser beam

A modification of Ambarzumian's method is used to develop the integro-differential equations for the source function, flux, and intensity at the boundary of a two-dimensional, semi-infinite cylindrical medium which scatters linearly. The incident radiation is collimated, normal to the top surface of the medium, and is dependent only on the radial coordinate. The radial variation is assumed to be a Bessel function or a Gaussian distribution. The Gaussian boundary condition is used to simulate a laser beam. Numerical results are presented in graphical and tabular forms for both boundary conditions. Results for forward and backward scattering phase functions are compared with those for isotropic scattering. A method is presented for extending these results to the problem of a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on a linear phase function.     

Variational method for spin waves in disordered ferromagnets

A variational method for spin waves in a disordered ferromagnet is described and is shown to give same results as obtained by a Green function method. The results of this calculation are applied to rare earth di-aluminium alloys. The spin wave dispersion relations in these alloys as a function of concentration are predicted.     

Solutions of the Percus-Yevick and hyper-netted chain equations near the gas-liquid critical point

An intuitive approach is used to develop a theory of the transverse current correlation function in simple liquids. The memory function obtained on the basis of this approach is expressed in terms of the velocity autocorrelation function for the kinetic part and in terms of the radial distribution function, the interatomic potential and a time-dependent term which describes the relative motion of two atoms in the liquid for the potential part. The results for the memory function and the frequency spectrum are found to be in satisfactory agreement with the computer simulation studies of Levesque et al.