Physical spherical phase compensation in reflection digital holographic microscopy

Reflection configured digital holographic microscopy (DHM) can perform accurate optical topography measurements of reflecting objects, such as MEMs, MOEMs, and semiconductor wafer. It can provide non-destructive quantitative measurements of surface roughness and geometric pattern characterization with nanometric axial resolution in real-time. However, the measurement results may be affected by an additional phase curvature introduced by the microscope objective (MO) used in DHM. It needs to be removed either by numerical compensation or by physical compensation.We present a method of physical spherical phase compensation for reflection DHM in the Michelson configuration. In the object arm, collimated light is used for illumination. Due to the use of the MO, the object wavefront may have a spherical phase curvature. In the reference arm, a lens and mirror combination is used to generate a spherical recording reference wave in order to physically compensate the spherical phase curvature of the object wavefront. By controlling the position of the mirror and the sample stage, the compensation process has been demonstrated. The relative positions of the test specimen and the reference mirror must be fixed for the physical spherical phase to be totally compensated. A numerical plane reference wave is preferred for the numerical reconstruction of the phase introduced by the test specimen. Experimental results on wafer pattern recognition are also given.     

Capillary surfaces in a cone

We show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and for which the surface boundary meets the boundary of the cone at a constant angle, is radially graphical if the mean curvature is non-positive with respect to the Gauss map pointing towards the domain bounded by the surface and the boundary of the cone. In the particular case in which the cone is circular, we prove that the surface is a spherical cap or a planar disc. The proofs are based on an extension of the Alexandrov reflection method using inversions about spheres.     

Energy flux and Goos-Hänchen shift in frustrated total internal reflection

Using Yasumoto and ?ishi's energy flux method, a generalized analytical formulation for analyzing the Goos-H?nchen (GH) shift in frustrated total internal reflection is provided, from which the GH shift given by Artman's stationary phase method is shown to equal the GH calculated by Renard's conventional energy flux method plus a self-interference shift. The self-interference shift, originating from the interference between the incident and reflected beams, sheds light on the asymptotic behavior of the GH shift in such optical tunneling process in term of energy flux.     

A low-limit estimate of average distance between conjugate points on a geodesic with random curvature

The minimum distance between conjugate points on a geodesic with the curvature given by a random renewal process is estimated. It is shown that, in the zero-curvature limit, the problem is reduced to analysis of the intersection of the level by a certain diffusion process with reflection.     

Total internal reflection of a Gaussian light beam

An approximate theoretical model for calculating the reflected and refracted fields of a Gaussian light beam at a plane interface between two isotropic media is formulated on the basis of a Fourier integral. In the vicinity of the critical angle of incidence (for total internal reflection) the model predicts the presence of two refracted beams, one displaced along the interface by an amount equal to the Goos-Hänchen shift; curvature of the phase fronts and nonalignment of the effective directions of energy and phase propagation occur for each beam, as in an anisotropic medium.     

Beam couplings and phase conjugate effects in reflection and transmission in BaTiO3

The details of experiments showing the effects of self-pumped phase conjugation on reflection and on transmission in barium titanate crystal are given. The specular reflection and the second-surface reflection of an extraordinary polarized beam, incident on the face of the crystal parallel to itsc-axis, get reduced in intensity as the phase conjugation develops. It has been found that parts of the self-pumped phase conjugate beam emerge out of the crystal as additional transmission beams. They grow in intensity as the phase conjugation develops. Other measurements which combine coherent or incoherent coupling beams are presented and used to explain the observations.     

Understanding of surface pit formation mechanism of GaN grown in MOCVD based on local thermodynamic equilibrium assumption

Frank's theory describes that a screw dislocation will produce a pit on the surface,and has been evidenced in many material systems including GaN.However,the size of the pit calculated from the theory deviates significantly from experimental result.Through a careful observation of the variations of surface pits and local surface morphology with growing temperature and V/III ratio for c-plane GaN,we believe that Frank's model is valid only in a small local surface area where thermodynamic equilibrium state can be assumed to stay the same.If the kinetic process is too vigorous or too slow to reach a balance,the local equilibrium range will be too small for the center and edge of the screw dislocation spiral to be kept in the same equilibrium state.When the curvature at the center of the dislocation core reaches the critical value 1/r_0,at the edge of the spiral,the accelerating rate of the curvature may not fall to zero,so the pit cannot reach a stationary shape and will keep enlarging under the control of minimization of surface energy to result in a large-sized surface pit.     

Localization of nonlinear excitations in curved waveguides and chains of nonlinear oscillators

It is shown that the interplay of curvature and nonlinearity in systems with finite curvature: bent waveguides, curved chains of nonlinear oscillators, etc can lead to the qualitative effects, such as symmetry breaking of the nonlinear excitations and their trapping by the bending. The finite curvature of the waveguide with infinite hard walls (Dirichlet boundary conditions) provides a stabilizing effect on otherwise unstable localized states of repelling nonlinear Schr?dinger excitations. The number of quanta which the curved waveguide can bind monotonically increases when the radius of curvature decreases. In the waveguides with Neumann boundary conditions at the confining walls the curved region might manifest itself as a two-hump potential barrier with interbarrier space acting as a potential valley. A threshold character of the scattering process, i.e. transmission, trapping, or reflection of the moving nonlinear excitation passing through the bending, is demonstrated.     

Shape instabilities in vesicles: A phase-field model

A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also derived. With this model it is possible to see the vesicle shape deformation dynamically, when some external agent instabilizes the membrane, for instance, inducing an inhomogeneous spontaneous curvature. The numerical scheme used is detailed and some stationary shapes are shown together with a shape diagram for vesicles of spherical topology and no spontaneous curvature, in agreement with known results.     

基于鬼像和像差分析的高功率激光装置透镜设计

为了设计能够满足高功率固体激光装置需求的空间滤波器透镜,采用矩阵光学方法,分析光束经过单透镜传输时剩余反射形成各阶鬼像的过程,得到鬼像位置与透镜曲率半径的关系式.该关系式表明,透镜的曲率半径设计可以控制鬼像所在的区域.根据高功率激光装置光路排布的特点简化鬼像分析,利用自行开发的鬼像追迹软件分析了主放大级鬼像分布特点.通过改变透镜的曲率半径和倾斜透镜这两种方式,基于鬼像规避和像差最小化两种原则,最终确定主放大级透镜曲率半径的最优选择为1:3弯月型,凸面朗向光学元件集中的方向.该方法可普遍应用于指导高通量复杂光学系统的透镜设计.     

Theory of chirped gratings in broad band filters

Closed form expressions for the reflection of light in a dielectric waveguide incident on a grating with a nonlinear chirp are presented. The method is based on a direct integration of the coupled mode equations using the method of stationary phase.     

一种新型的低散射微带天线阵设计

本文将电磁表面(electromagnetic surface, EMS)的设计思想引入到微带天线阵的设计中,在设计天线单元的同时,也将其作为EMS单元兼顾其反射特性.通过在矩形辐射贴片上开弧形缺口,得到一种新的单元结构,该单元可与原始EMS单元之间形成180°±30°有效相位差,且作为天线单元时与原始天线工作在相同谐振模式、相同频带.将两种单元以棋盘形式构成组合天线阵,在两个极化下分别基于相位对消原理和吸波原理实现了雷达散射截面(radar cross section, RCS)减缩.实测与仿真结果表明:相较于等大小的金属板,在x极化波照射下,天线阵在5.6—6.0 GHz实现了6 dB以上的RCS减缩,相对带宽为10.1%;在y极化波照射下,天线阵在5.0—7.2 GHz实现了6 dB以上的RCS减缩,相对带宽为24%.同时由于两种单元在辐射上具有较好的一致性,使得组合天线阵的辐射性能得以保持.该方法有效解决了天线阵辐射和散射难以兼顾的矛盾,为其他形式的低散射天线阵的设计提供了新的方法与思路.     

Laue case reflection curves of deformed crystals

The stationary phase method is used for the calculation of the reflection curves in the case of elastically bent crystals. This method, based on the Takagi s equations, enables us to estimate the widths of these curves and to compare them with the experimentally measured ones.     

Relaxation of physical systems in relative-number state representation

The relaxation properties of physical systems in the Liouville space are investigated in terms of the relative-number state representation. An arbitrary state can be expressed by superposition of relative-number states. In the absence of an time-dependent external field, all components with non-zero relative-numbers decay to zero with time, and any stationary state can be expressed only in terms of zero relative-number states. The phase canonically conjugate to the relative-number is completely uncertain in a stationary state. It is thought that relaxation from an arbitrary initial state to a stationary state is described as some kind of phase relaxation process. Such a phase relaxation process is explicitly described by the phase operator formalism within the framework of the relative-number state representation.     

Stress pulse dispersion in helical springs

This paper presents the results of investigating the effect of curvature and pitch on stress-wave propagation in helical springs. It supplements a previous paper in which the work carried out on a single spring of fixed curvature and pitch was described and the experimental results compared with theory. A short duration, wide-band pulse technique, described in the first paper, was used to investigate the nature of the propagation. Theoretical dispersion curves, appropriate to the springs used, were computed for comparison with the experimental results which were interpreted according to Kelvin's principle of stationary phase.     

数字全息显微术中重建物场波前的相位校正

数字全息显微术克服了传统光学显微术无法直接提取样品相位信息的缺点,可以对活体细胞组织等相位型生物样品进行定量测量和有效观察。但在数字全息显微成像过程中,像场弯曲会对再现像相位分布的测量和观察产生影响。提出一种采用相位相减来校正数字全息再现像像场弯曲的方法。通过在样品加入前后两次拍摄全息图,并对数值重建像分别进行去包裹运算再令其相减,即可实现对像场弯曲的有效校正,对蝉翼和大蒜表皮细胞等相位型物体进行测量,并采用数值校正和相位相减两种方法对像场弯曲进行校正。与现有的数值校正方法相比,利用相位相减获得样品三维相位信息的方法更为简单、可靠,是校正像数字全息再现场弯曲的有效方法。     

Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

<正>In this paper,an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface,where the surface tension is implemented.The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid,an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface,and an indicator function is introduced to update the fluid properties accurately.The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points,and then the surface tension is directly computed by using the normal vector and curvature of the interface.Two benchmark problems,including Laplace’s law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation.Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.     

Curvature measurement of optical surface using digital holography

In this paper, an optical surface curvature measurement technique based on digital holography is proposed. Unlike the previous digital holographic methods, which only involve a small part of the measured data for parameter estimation, the proposed method adopts more of them using least square method. Hence, the analyzed result is not affected by data extraction direction and less sensitive to imperfect phase compensation. The proposed method is demonstrated with a sample of reflection mirror in laser resonator, and verified by comparing the measurement result with that of the white light interferometer.     

Geometrothermodynamics of higher dimensional black holes

We study the thermodynamics and geometrothermodynamics of different black hole configurations in more than four spacetime dimensions. We use the response functions to find the conditions under which second order phase transitions occur in higher-dimensional static Reissner–Nordström and stationary Kerr black holes. Our results indicate that the equilibrium manifold of all these black hole configurations is in general curved and that curvature singularities appear exactly at those places where second order phase transitions occur.     

Phenomenological diffusion laws in solids

A method is considered for study of diffusion in the solid phase, free of the shortcomings of Fick's equations. For the stationary case analytical expressions are obtained for the probability of transmission, reflection, and absorption of diffusing particles by a layer of specified thickness. Principles are formulated for reduction of the nonstationary problem to the stationary case. The results obtained are applied to a study of the kinetics of oxidation processes. A generalization of Fick's first law to the nonstationary case is presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 31–36, April, 1979.