Small-angle Light Scattering by Spherulites in the Anomalous Diffraction Approximation

Using the anomalous-diffraction (AD) light-scattering approximation, a relationship is derived between the scattering matrix of an object and its full Jones' matrix. This allows scattering to be calculated for dielectric objects having any kind of optical anisotropy, e.g. birefringent or optically active particles. The theory is used to calculate the small-angle light scattering (SALS) by a spherulite placed between two linear polarizers. Serious disagreements are found between the AD theory and the currently accepted theory of SALS based on the Rayleigh-Gans-Debye approximation.     

A Comparison of Extinction Efficiencies in the Eikonal and the Anomalous Diffraction Approximations for Spheres

Abstract

Extinction curves in the eikonal approximation and the anomalous diffraction approximation have been compared with exact extinction curves for homogeneous spheres of various refractive indices. Our results show the anomalous diffraction approximation to be more suitable for extinction calculations.     

中子衍射应力测量试验中赝偏移现象的影响

主要介绍了中子衍射应力谱仪试验过程中,由非应力原因引起的衍射偏移的各种因素的影响。讨论了样品的定位与样品测量体积的选择对衍射峰赝偏移的影响,最后给出了赝偏移校正方法与试验过程中减小赝偏移的有效技术手段,使试验数据得到有效的处理,从而得到样品内部应力的真实信息。     

On the Diffraction Limit for Lensless Imaging

The diffraction limit for lensless imaging, defined as the sharpest possible point image obtainable with a pinhole aperture, is analyzed and compared to the corresponding limit for imaging with lenses by means of theoretical considerations and numerical computations using the Fresnel-Lommel diffraction theory for circular apertures. The numerical result (u = π) obtained for the best configuration parameter u which defines the optical setup is consistent with the quarter-wave criterion, and is the same as the value reported in a classical paper by Petzval but smaller than the value (u = 1.8π) found by Lord Rayleigh. The smallest discernible detail (pixel) in a composite image is defined by an expression found by Rayleigh on applying the half-wave criterion and is shown to be consistent with the Sparrow criterion of resolution. The numerical values of other measures of image size are reported and compared to equivalent parameters of the Fraunhofer-Airy profile that governs imaging with lenses.     

On the Study of Partial Coherence via Diffraction Experiments

The radiation pattern of a circular aperture illuminated both uniformly and non-uniformly by partially coherent light is calculated in the diffraction limit. Furthermore, the angular resolution of a circular lens is examined for four reasonable correlation functions. Also the effects of the parameters—partial coherence, misalignment, and non-uniform illumination—on the diffraction pattern of a double slit are considered for a particular mathematical model of the radiation field. The results of this analysis are used to discuss the the use of diffraction experiments in the study of the coherence properties of light.     

关于Bernstein多项式的同时逼近

本文研究函数f的Bernstein多项式Bn（f，X）对函数及其导数的同时逼近，对于fP≥1，给出的渐近展开式．     

Investigation of Domains of Validity of Approximation Methods in Forward Light Scattering from Long Cylinders

Domains of validity of approximation methods in light scattering from non-absorbing transparent long cylinders of diameter h 5 w m have been clearly identified. Numerical comparisons between these methods and the exact theory for various values of the refractive index and size parameter of the cylinder are presented. The utility of the eikonal approximation and the corrections to this approximation is emphasized.     

模糊环境下粗糙近似算子的表示

给出了在一般的模糊环境下各种粗糙近似算子的定义，得到了这些近似算子的经典表示。     

On the Numerical Study of Deep Conducting Lamellar Diffraction Gratings

A root-finding algorithm for the solution of the eigenvalue equation linked with the theoretical study of lossy lamellar gratings is outlined. The computation time seems to be shorter than required when using a method proposed by Botten et al. (1981). The agreement is found to be excellent.     

Investigation of Domains of Validity of Corrections to the Eikonal Approximation in Forward Light Scattering from Homogeneous Spheres

Corrections to the eikonal approximation in light scattering from non-absorbing, transparent homogeneous spheres are considered. Numerical comparisons with the exact theory for various values of relative refractive index m and diameter d are presented. Of particular interest are the results in the diameter range 0·2 μm ? d ? 5·0 μm where it has been shown that for m? 1·15, predictions of diameters from the eikonal approximation and Mie theory agree to within 6 per cent.     

On High-Frequency Asymptotics in Diffraction by Finite-Length

The paper is concerned with high-frequency diffraction by open finite-length waveguides. The problem is reduced to an integral equation of the first kind over a finite interval, with its kernel depending on the difference of the arguments only. A new asymptotic approach is developed that permits explicit analytical representation of the solution.     

论标准信息的有效性管理

一、加强标准信息有效性管理的必要性国家标准GB/T4894-1985《情报与文献工作词基本术语》对标准文献工作所下的定义是“:持续系统地收集、整理、传递与利用书面(及其他记录形式的)情报的活动与过程”。按照这个定义,标准化信息管理工作的内容可归纳为标准信息的收集、整理、传递和服务。国家标准GB/T15496-2003《企业标准体系要求》,也对企业标准化信息管理工作提出了基本要求,即标准信息管理必须具有完整性、有效性、准确性和及时性。标准信息的最基本作用在于能够引导用户准确地了解标准,并正确地选择和使用标准,防止误用作废或失效的…     

有理插值算子对连续函数的逼近

本文给出了有理插值算子当1＜S＜Z及S＞2时的Timan型逼近阶，从而推广了已有的S＞3的结果．     

On the Validity of the Method of Depolarization Factors an Analytical Study

A comparison between two alternative scattering theories, the approximate method of depolarization factors and the exact Mie theory, is performed on a pure analytical basis for the case of spherical particles. It is shown that the usual assumption requiring that the radius be small compared with the interacting wavelength is insufficient to ensure the validity of the approximate method. The complete set of conditions are provided for both the scattered and absorbed fields.     

Anomalous Depression of the Debye-Waller Factor and Observations of the Laue Spots Only at Forward X-ray Diffraction in the Light Atom Crystals as Quantum Solid

The ratio of 6·(1/2m)·(E ₀/c)² of 12.9 meV at E ₀=4 keV to k _{B D} of 2.27 meV for hcp-⁴He in the exponent 2M=[6·(1/2m)·(E ₀/c)²/k _{B D} ]·(t)sin² _B of the Debye-Waller factor D=exp(–2M) becomes 5.7, because of the small atomic mass m and the low Debye temperature _D . Conversely that of the heavy atom crystals becomes smaller than 1. An experiment on hcp-⁴He as an example of a light atom crystal at low temperature limit of (t)1 reveals that not only the maximum value of D is significantly reduced below 0.249 (=e ^–1.395) but also the values of D for all other Laue spots except the following observed six spots are crowded into a range of D<0.05. Therefore, only the six Laue spots of at 11.2 keV, (0002) at 20.3 keV, and at 14.4 keV and and at 23.9 keV in a low angular range of _B10.22° were observed over low values of e ^–1.395>De ^–3. At high angle of _B 45°, the values of E ₀ for the above six Laue spots are assigned to the region below 4.07 keV from the Bragg condition under constant values of D. Therefore, detection of them over the higher angular range of _B 45° is not impossible but quite difficult at low temperature X-ray diffraction, considering X-ray absorption by multi-thermal shields of the refrigerator, the thick sample holder as a pressure vessel and massive air in space. Generally this means that the large reduction of the Debye-Waller factor of hydrogen and helium drastically encloses the diffraction intensity and the number of observable Laue spots within lower bounds. This is the reason why definite Laue spots in the light atom crystals of hcp-⁴He could be observed only by forward X-ray diffraction. Conversely the recoil fraction of the diffuse scattering expressed by 1–D concomitantly increases as a major part of the total scattering. A proposal to measure thermal diffuse scattering as well as pressure experiments will provide insight into the wave-like character of constituent atom in solid helium.     

On the Possibility of Approximation of Irregular Porous Microstructure by Isolated Spheroidal Pores

Calculation of the effective elastic constants of a material with irregularly shaped porous space is discussed. It is shown that isolated pores of irregular shapes may be approximated, with good accuracy, by the spheroidal ones. Procedure of evaluation of the average aspect ratio from the photomicrograph is described. Several commonly used approximate schemes are applied to predict effective Young’s and shear moduli of a material with spheroidal pores. Comparisons of these predictions with the experimentally measured elastic constants for completely sintered hydroxyapatite exhibit reasonably good accuracy. The best agreement is given by self-consistent and effective field methods.     

X射线衍射法测定Fe-Mn-Si形状记忆合金层错几率的研究

Ｆｅ－Ｍｎ－Ｓｉ合金的形状记忆效应来源于马氏体相变,而马氏体相变则通过奥氏体内形成每隔一层｛１１１｝面上的堆垛层错来完成。与层错能相关的层错几率可能控制马氏体的相变机制。本文根据Ｗａｒｅｎ的衍射理论,用Ｘ射线衍射峰位移和峰宽化两种方法测定了Ｆｅ－Ｍｎ－Ｓｉ合金的层错几率,其结果表明随锰含量增加,层错几率降低。本文着重对提高衍射峰位移和峰宽化两种测定方法的精度及其影响因素进行详细的研究,并认为峰位移法更简便     

On a Simple and Accurate Approximation of Control Chart Constants

A simple and accurate approximation of control chart constants forx and x charts is given. The computation is easily performed on an electronic calculator. The maximum magnitude of the error which can result from the use of the approximation for any of the control chart constants is .0046.     

The Solution of Some Inverse Diffraction Problems in Terms of the Diffraction Coefficients

The form of the recently developed series representation of the axially symmetrical diffraction fields enables us to establish the pupil function from the series coefficients _γk (u). A new interpretation of the Strehl intensity ratio is given. It represents the ratio of the energy coming to the image focus and that coming to the other foci of the filter. Further, by the use of the three-term approximation, the transmissivity of the filter giving the desired two-point resolution and attaining the maximum value of the Strehl criterion is found and compared with the exact solution proposed by Luneberg. Finally, it is shown that the Luneberg filter transmissivity represents a common approximative solution of the apodization problems that utilize the integral criteria of apodization.     

函数最佳平方逼近多项式是否唯一

本文对最佳一致逼近多项式与最佳平方逼近多项式相互比较,给出了相同的内积和基函数最佳平方逼近多项式是唯一,并且验证了勒让德展开部分和得到的最佳平方逼近多项式与Hn中的最佳平方逼近多项式是一致的.