Physical optics theory of resistive surfaces

The physical optics current is obtained from the exact solution of the scattering problem of plane waves by a resistive surface. The edge point method is used for the determination of the physical optics surface current. The derived physical optics integral by considering the new surface current enables one to evaluate the scattering problems by various resistive surfaces with edge discontinuities. The method is applied to the diffraction problem of plane waves by a concave cylindrical reflector. The scattered fields are examined numerically.     

The method of the boundary diffraction wave for impedance surfaces

The line integral of the boundary diffraction wave theory is extended for the diffraction process of waves by the impedance surfaces with edge discontinuities. With this aim, the exact diffraction field expression of Maliuzhinets is transformed into a line integral. The method is applied to the scattering problems of waves by a spherical reflector with edge discontinuity and the diffracted fields are evaluated asymptotically. The resultant expressions of the waves are examined numerically.     

Boundary diffraction wave theory of junctions between two surfaces with different face impedances

The line integral of the boundary diffraction wave theory is derived for the diffraction process of waves by a junction between two surfaces with different face impedances. The exact solution of Maliuzhinets is used with this aim. The resultant integral is applied to the diffraction of waves by a circular junction between two impedance surfaces. The results are examined numerically.     

Structure of boundary diffraction wave revisited

The physically appealing boundary diffraction wave theory which suggests that diffraction patterns arise due to interference of an undisturbed (geometrical) wave and the boundary diffraction wave generated by edge of the diffracting aperture, simplifies the solution of diffraction problems by reducing the Fresnel–Kirchhoff surface integral into a line integral over the illuminated boundary of the diffracting aperture. The present work reports experimental investigations carried out on the structure of the boundary diffraction wave. It has been shown that the boundary diffraction wave is continuous behind the diffracting aperture and apparently there does not exist any discontinuity at the geometrically light to shadow transition boundary, as is required by the theory. PACS 42.25.-p; 42.25.Fx; 42.25.Hz     

The relation between the boundary diffraction wave theory and physical optics

The physical optics surface integral is asymptotically reduced to a line integral along the contour of the diffracting edge. It is shown that the resultant integral can be separated into two sub-integrals which represent the reflected and transmitted diffracted fields. The integrands are transformed into the same forms with the potential function of the boundary diffraction wave theory.     

Effect of diffraction of molecules on collisional line narrowing

A new model of line profile is proposed, which simultaneously takes into account hard and soft (in velocity) collisions leading to collisional line narrowing. It is shown that parameters of collisional narrowing and broadening obtained by processing experimental profiles on the basis of the standard model of hard collisions contain almost no contribution of diffraction scattering of molecules by buffer gas particles. The model proposed for the line profile makes possible a correct comparison of frequencies of the collision integral measured by methods of linear and nonlinear spectroscopy.     

用相因子判断法分析条形余弦光栅衍射场

基于波前相因子判断法并考虑到光栅孔径的影响,揭示了余弦光栅的衍射场所含基元成分．给出了各基元成分衍射场的积分表达式,进而导出了像面上光强分布的公式,并显示了相应的沿轴线的光强分布曲线,得到各焦斑的半值线宽公式．本研究为余弦光栅用于空间滤波和光学信息处理技术提供了一个理论基础．     

晶面偏角对利用Voigt函数法计算硅单晶本征晶格应变的影响

研究并制备了不同晶面偏角的Si(111)单晶,经过研磨和抛光使表面粗糙度低至3.4?达到超光滑水平,消除了表面和亚表面损伤层以及其所产生的应力变化.利用高精度X射线衍射仪分别测定了在不同晶面偏角条件下衍射曲线的半高全宽和积分宽度.应用Voigt函数法分析计算了微观应变,通过理论计算和实验对比可知,Si(111)单晶在晶面偏角达到0.749o时,偏角本身所带来的衍射峰半高全宽变化使计算出的应变值误差大于5%.研究结果为其他晶体类似研究提供了重要参考.     

An analytical technique for calculation of distributed resistance in a rectangular domain

A Green's function approach is used to obtain an integral representation for the electric potential in a multi-terminal distributed resistive structure. This integral representation for the potential is then used to formulate a coupled system of Fredholm integral equations of the first kind, in which the normal components of current density over the different terminal contacts are the unknowns. A procedure for solving this system of equations is presented and the obtained results for the unknown normal components of the current density are used to express the electric potential and current density vector at any point in the domain of the distributed resistive structure. The indefinite admittance matrix relating the terminal currents to the applied terminal voltages, is a by-product of the solution process. Explicit expressions for the Green's function and complete orthonormal sets of functions which are required to apply the solution to a rectangular domain are given. Applications to three-terminal structures are considered in order to illustrate the method.     

两级同轴Blumlein线理论及其模拟分析

利用拉普拉斯变换求解两级同轴Blumlein线对负载的放电过程,得到了纯电阻负载上理想输出电压的解析表达式。分析了开关电感、负载电感及回路电感对负载主脉冲的影响。对PSpice模拟的结果与推测的负载电压表达式进行对比,两者符合得较好。分析结果表明:脉冲的前沿主要是由开关电感决定,而平顶幅值的变化趋势主要是由回路电感决定;开关电感越小,上升沿越小,回路电感越大;脉冲输出电压和能量传输效率越高。     

一种用加权高斯-柯西组合函数拟合对称衍射线形测定晶粒大小的方法

本文提出了一种用加权的高斯-柯西组合函数来拟合衍射线形,并借助傅里叶变换方法不需假定物理宽化函数f(x)的线形而直接得到f(x)积分宽度以测定晶粒大小的方法。这种方法比常用的近似函数方法精确又快速简便,且避免了由于假定物理宽化函数f(x)的线形而带有的人为性和任意性。 关键词：     

激光束受限衍射对扫描系统分辨本领的影响

基于菲涅耳衍射积分公式推导出激光束经扫描元件衍射后场分布表达式,数值分析了激光束经扫描元件后衍射场振幅分布、激光束在扫描面上的光斑半径和激光扫描系统光学分辨本领的大小.结果表明,改变入射光束的束腰半径对激光扫描系统线分辨率、可分辨光点数和分辨容积产生不同的衍射影响.采用近似和拟合方法,分段给出不同衍射情况下激光扫描系统的线分辨率的函数表达式,并通过误差分析证明了近似和拟合函数表达式的精确性.     

Scattering of a spherical wave from the coupling of two half-planes

Summary  The diffraction of a spherical acoustic wave from the juncture of pressure release (soft) and locally reacting (absorbing) half-planes in a fluid moving at subsonic velocity is examined. This consideration is important because the point sources are regarded as better substitutes for real sources than line sources/plane waves. The integral representation of the field is obtained using integral transforms and the Wiener-Hopf technique. The factorization of the kernel function in the Wiener-Hopf functional equation is accomplished. The analytic solution of the integrals is obtained by employing asymptotic methods and the far field is presented. The effect of the Mach number is shown explicitly on the diffracted field.     

Optimization and analysis of multi-layer diffractive optical elements in visible waveband

An optimization for diffraction efficiency of the multi-layer diffractive optical elements (MLDOEs) is presented, then the construction process of optimization program is introduced in detail. A new optimization initial point is proposed, which contributes to analyze the relationship between the optimal relief heights and the base materials. Through the optimization examples, diffraction efficiency higher than 99.7% from F line (486.1327 nm) to C line (656.2725 nm) of visible waveband can be achieved, and the polychromatic integral diffraction efficiency (PIDE) over the entire waveband is 99.94%. Moreover, this paper compares and analyzes optimization results of different glass pairs, and the relationship between the optimal relief heights pairs and base materials pairs is obtained.     

Local magnetic field distributions in superconducting niobium at 4.2 K by neutron diffraction

Neutron diffraction experiments on flux line lattices in superconducting Nb are reported. From the integral reflectivities of the (10), (11), (20), (21) and (31) reflections the absolute values of the formfactors were obtained as a function of the flux density. Considering certain properties of the flux line lattice it is also possible to determine the phases of the formfactors. From this the local field distribution in the mixed state could be calculated by Fourier-transformation. The dependence of the resulting maximum, minimum, and saddle point fields on the flux density and on the impurity parameter is discussed and compared with theory.     

Acoustic diffraction by deformed edges of finite length: theory and experiment

The acoustic diffraction by deformed edges of finite length is described analytically and in the frequency domain through use of an approximate line-integral formulation. The formulation is based on the diffraction per unit length of an infinitely long straight edge, which inherently limits the accuracy of the approach. The line integral is written in terms of the diffraction by a generalized edge, in that the "edge" can be a single edge or multiple closely spaced edges. Predictions based on an exact solution to the impenetrable infinite knife edge are used to estimate diffraction by the edge of a thin disk and compared with calculations based on the T-matrix approach. Predictions are then made for the more complex geometry involving an impenetrable thick disk. These latter predictions are based on an approximate formula for double-edge diffraction [Chu et al., J. Acoust. Soc. Am. 122, 3177 (2007)] and are compared with laboratory data involving individual elastic (aluminum) disks spanning a range of diameters and submerged in water. The results of this study show this approximate line-integral approach to be versatile and applicable over a range of conditions.     

Diffraction of spherical waves at an annular aperture in the use of the boundary diffraction wave theory: A comparison of different diffraction integral approaches

The integral expression for divergent spherical waves diffracted at an annular aperture is derived based on the theory of the boundary diffraction wave. The expressions for divergent spherical waves diffracted at a circular aperture and a disk, and the axial field are treated as the special cases of our general one. Numerical calculation results for axial and transversal intensity distributions are given to compare our results with the Kirchhoff diffraction integral, first and second Rayleigh diffraction integrals. As expected, our results are in agreement with those in the use of the Kirchhoff diffraction integral, but the computer time is reduced greatly by using the boundary diffraction wave theory. The four diffraction formulae are shown to be consistent for axial and transversal intensity distributions, if the source and observation points are positioned equally from the aperture, or the observation point is located enough far from the aperture. Otherwise, the mean value of the first and second Rayleigh diffraction integrals is equal to the result of the boundary diffraction wave theory.     

New line integral expressions for Fraunhofer diffraction

New expressions for Fraunhofer diffraction at an arbitrary shape aperture are presented. These are expressed in the simple form of the line integral over the rim of the aperture. Far field patterns for various shaped apertures are easily derived from these expressions which are well suited for numerical calculation. As examples, Fraunhofer diffraction fields for elliptical, polygonal, and sinusoidal apertures are shown.     

菲涅耳-基尔霍夫积分与半波带法分析衍射光谱

惠更斯菲 涅耳原理指出光的衍射本质是无穷多次波的相干叠加.在研究衍射光谱的强度时可使用菲涅耳-基尔霍夫衍射积分进行计算,但该积分的计算较为复杂.为了简化计算而引入菲涅耳半波带的概念,把积分运算简化为振幅矢量的叠加,从而在研究衍射时由菲涅耳-基尔霍夫衍射积分过渡到菲涅耳半波带法.在菲涅耳半波带法中波前上相邻两个半波带到达叠加点的光程差为半个波长,从而导致相位差π.因此相邻两个半波带引起的振动在叠加点发生相消,最终叠加点的光强由发出次波的半波带数目的奇偶性决定.奇数个半波带在叠加点的光强得到加强,偶数个半波带在叠加点的光强发生相消.     

Diffraction effects on bulk-wave ultrasonic velocity and attenuation measurements

The loss and phase advance due to diffraction are experimentally observed by measuring the amplitude and phase of radio frequency (rf) tone burst signals in the VHF range, in an ultrasonic transmission line consisting of a buffer rod with an ultrasonic transducer on one end, a couplant of water, and a solid specimen of synthetic silica glass. The measured results agree well with the calculated results from the exact integral expression of diffraction. The diffraction effects on the velocity and attenuation measured in this frequency range and their corrections are investigated to realize more accurate measurements. It is shown that attenuation measurements are influenced by diffraction losses and can be corrected by numerical calculations, and that velocity measurements are affected by the phase advance caused by diffraction. This investigation demonstrates that, in complex-mode velocity measurements, in which the velocity is determined from the measured phase of the signals, the true velocity at each frequency can be obtained by correction using the numerical calculation of diffraction. Based on this result, a new correction method in amplitude-mode velocity measurements is also proposed. In this new method, the velocity is determined from the intervals of interference output obtained by sweeping the ultrasonic frequency for the superposed signals generated by the double-pulse method. Velocity may be measured accurately at frequencies in the Fresnel region, and diffraction correction is essential to obtain highly accurate values with five significant figures or more.