A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x-and y-axis directions are obtained with a phaseshifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

Acoustic wave propagation through the boundary between a liquid and the Heusler ferromagnetic alloy

Incidence of an acoustic wave upon a plane boundary between a liquid and a ferromagnetic crystal is considered. The ferromagnet is the Ni_2+x+y Mn_1−x Ga_1−y Heusler alloy with a shape memory, which is in the region of the premartensite or martensite phase transition in temperature. The directions of propagation and polarization and the amplitudes of the reflected and transmitted quasilongitudinal and quasitransverse waves in the (110) plane of the crystal are determined. Starting from a certain critical angle of incidence, a longitudinal wave in the crystal becomes inhomogeneous and gliding along the boundary with an accompanying surface oscillation. In the vicinity of the phase transition point, this wave may be radiated into the crystal bulk. Proceeding from the experimental data by Trivisonno for ultrasonic velocities and absorption in a Ni₂MnGa crystal, numerical estimates are obtained for the aforementioned acoustic effects.     

A novel acoustic emission beamforming method with two uniform linear arrays on plate-like structures

A novel acoustic emission (AE) source localization approach based on beamforming with two uniform linear arrays is proposed, which can localize acoustic sources without accurate velocity, and is particularly suited for plate-like structures. Two uniform line arrays are distributed in the x-axis direction and y-axis direction. The accurate x and y coordinates of AE source are determined by the two arrays respectively. To verify the location accuracy and effectiveness of the proposed approach, the simulation of AE wave propagation in a steel plate based on the finite element method and the pencil-lead-broken experiment are conducted, and the AE signals obtained from the simulations and experiments are analyzed using the proposed method. Moreover, to study the ability of the proposed method more comprehensive, a plate of carbon fiber reinforced plastics is taken for the pencil-lead-broken test, and the AE source localization is also realized. The results indicate that the two uniform linear arrays can localize different sources accurately in two directions even though the localizing velocity is deviated from the real velocity, which demonstrates the effectiveness of the proposed method in AE source localization for plate-like structures.     

Temperature gradient mechanism in laser forming of thin plates

To obtain further insight into the deformation of a plate in the laser forming process, the temperature gradient mechanism (TGM) is studied. Through the investigation, it can be found that, under the processing conditions of TGM, the plate not only bends about the x-axis but also about the y-axis. An analytical model estimate of the bending angle about the y-axis is constructed based on the theories of heat transfer and the mechanics of elastoplasticity. Numerical simulations are carried out to investigate the deformation of the plate about the y-axis by choosing the different process parameters. The analytically based estimate is used to suggest suitable starting values for the simulation process of calculated results. The study of the bending about the y-axis may describe more fully the deformation of a plate, which is helpful in high-precision forming.     

Recovery of particle distribution function in four-dimensional phase space from measurements with pepper-pot method

The possibility of recovering the particle distribution function at any point of the four-dimensional transverse phase volume “x, x′, y, y′” using the results of measurements with the pepper-pot method is demonstrated. The proposed method for processing experimental data is based on the assumption that the one-to-one correspondence between holes in the mask and their images on the screen is established. Such a preliminary calibration should be experimentally performed on the measured ion beam. The method of moments is used for the recovery of the distribution function. Using Legendre polynomials for processing experimental results reduces the problem to a sequence of recurrence relations. A numerical simulation of the measurement process demonstrated that the recovery accuracy of the particle distribution function is about ±10%.     

Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry

Phase unwrapping is a task common to many applications like interferometry imaging, medical magnetic resonance imaging, solid-state physics, etc. Fourier transform profilometry (FTP) values the height distribution of object, elaborating the interference between a plane reference grating and a deformed object grating. Since the height information is extracted from the phase of a complex function, the phase unwrapping is a critical step of the process. Several unwrapping algorithms are proposed in literature, but applied to measurement technologies different from FTP. The purpose of this paper is to define the performances of eight different unwrapping algorithms applied to FTP optical scan method and to define the best one. The algorithms chosen are: Goldstein's algorithm, quality guided path following method, Mask cut method, Flynn's method, multi-grid method, weighted multi-grid method, preconditioned conjugate gradient method and minimum L_p-norm method. The methods were tested on real images acquired by a FTP scanner developed and calibrated for these experiments. The objects used vary from simple geometries, like planes and cylinders, to complex shapes of common use objects. Algorithms were qualified considering the phase unwrapping errors, execution time and accuracy of the shape of objects obtained from the scan method in comparison with real ones. The results show that quality guided algorithm best fits in FTP application.     

Non-equilibrium phase transitions in the two-temperature Ising model with Kawasaki dynamics

Phase transitions of the two-finite temperature Ising model on a square lattice are investigated by using a position space renormalization group (PSRG) transformation. Different finite temperatures, T _x ?and?T _y , and also different time-scale constants, ?? _x and ?? _y for spin exchanges in the x and y directions define the dynamics of the non-equilibrium system. The critical surface of the system is determined by RG flows as a function of these exchange parameters. The Onsager critical point (when the two temperatures are equal) and the critical temperature for the limit when the other temperature is infinite, previously studied by the Monte Carlo method, are obtained. In addition, two steady-state fixed points which correspond to the non-equilibrium phase transition are presented. These fixed points yield the different universality class properties of the non-equilibrium phase transitions.     

双波长数字全息相位解包裹方法研究

使用两个不同的波长分别记录数字全息图,分别由数值再现得到每个波长对应的包裹相位图,再求得两者的相位差得到等效波长的相位图,通过此双波长相位解包裹方法得到连续的相位分布以消除相位包裹。通过数值模拟研究了双波长相位解包裹方法,搭建了双波长数字全息实验系统,并利用660nm和671nm两个波长的激光对标准石英平片和平凹透镜进行了相衬成像。通过双波长相位解包裹方法得到了连续的相位分布,实验结果与数值模拟结果具有较好的一致性,证明了双波长相位解包裹方法的有效性。     

用多项式和阶跃函数构造网格多涡卷混沌吸引子及其电路实现

提出一种利用多项式和阶跃函数构造N×M涡卷的构造方法.利用蔡氏电路,传统的利用多项式函数只能产生双涡卷、三涡卷,在此基础上,通过多项式平移得到相空间x方向的多涡卷,再通过多项式与阶跃函数组合来扩展相空间中指标2的鞍焦平衡点,使得多涡卷向y方向延伸,从而生成网格多涡卷混沌吸引子.该构造方法的主要特征是通过光滑曲线和非光滑曲线的组合生成网格多涡卷混沌吸引子,能通过调整自然数N和M的值实现平面网格任意涡卷混沌吸引子阵列.理论分析、数值模拟和电路仿真证实了方法的可行性. 关键词： 网格多涡卷混沌吸引子 蔡氏电路 阶跃函数 电路实现     

Transformation of phase to (x,y,z)-coordinates for the calibration of a fringe projection profilometer

In this work we present a phase to (x,y,z)-coordinates transformation method for the calibration of a fringe projection profilometer. Our technique is divided in two parts: (1) phase to z transformation (for axial calibration) based on the typical polynomial fitting which uses a flat plane placed at several z positions to measure the phase of the projected fringes. (2) Phase to x and y transformation (for transverse calibration) based on the use of a crossed gratings pattern and a Fourier phase measurement method to determine x and y coordinates at several z positions. As will be shown the use of the crossed gratings pattern and the Fourier phase measurement method for transverse calibration is advantageous in several aspects: an unique image can give us x and y information at once. It provides x and y coordinates at each pixel in the image avoiding the use of interpolation methods. We present some experimental results and explain the viability of the proposed technique.     

从一幅载频全息图中实现相位重构的新算法

为了实现对单幅载频下涉图进行相位重构.提出了一种避免相位"解包裹"的简易算法.该算法从载频干涉图中解出所求相位的两个偏导数,然后对两个偏导数积分从而得到所求的相位.利用该算法分别对计算机模拟的干涉图和实验所得干涉图进行相位重构,重构结果均表明该算法能够很好地从载频干涉图样中实现相化重构.并且由于避免了相位"解包裹"的过程,从而简化了相位重构的流程,同时也避免了由相位解包带来的错误或误差.此外,该方法在重构相位时,对干涉图中强度分布的不均匀性不敏感.     

Measurement of object height in emission electron microscopy

The possibility of measuring the height of an object in emission electron microscopy (EEM) is investigated. If the specimen is characterized by an equipotential surface with the relief h(x,y), the image is equivalent to a specimen with an ideal flat surface and a corresponding distribution of the electric potential φ(x,y)=−E _ext h(x,y). As a consequence of the interaction with the microfields grad φ(x,y), the trajectories of electrons forming the image become deformed, which leads to characteristic image distortion. From EEM, images obtained at different voltages of the extractor V _ext,φ(x,y) can be derived and thereby h(x,y) is reconstructed. If the surface of the specimen is characterized both by a distribution of the potential and in addition by a relief h(x,y), then for the reconstruction one needs an additional EEM image taken at a different voltage of the extractor. The maximal sensitivity to microfields/relief is exploited when using the electron microscope in the mirror operation mode. We illustrate the performance of the method by means of a test pattern of Au on Si. For quantitative comparison, the same structure was investigated by atomic force microscope.     

Interpretation of neutron scattering and μSR data on paramagnetic Gd in terms of magnetic clusters and coherent dissipative structures

Fullyc-axis oriented thin films of YBa₂(Cu_1−x ⁵⁷Fe _x )₃O_7−y were studied by varying the Fe- and O-content and the substrate. For the two substrates MgO and SrTiO₃ no difference in the CEMS spectra was observed. Measurements for differentx andy values and their comparison with results from powder samples proved that the solubility of iron is the same in the films and powders. The substitution of Cu(2) by Fe in the films is the highest ever reported. The CEMS spectrum of a reduced film shows that the direction of the magnetic hyperfine field for doubletC is perpendicular to thec-axis.     

倾斜入射的波前编码系统的点扩散函数扩大效应分析

通过对坐标系统进行旋转,计算得到了三次型波前编码系统的倾斜入射的光瞳函数,并给出了近似表达式. 分析表明倾斜入射会产生三次相位扩大效应和离焦扩大效应,它们和入射角的正负无关,且随着入射角绝对值的增大而增大. 这表现在点扩散函数(point spread function, PSF)上会扩展PSF包络的两条直角边,表现在调制传递函数(modulation transfer function, MTF)上会降低MTF值. 子午面倾斜入射时,子午方向的三次相位扩大效应和离焦放大效应大于弧矢方向,从而导致子午方向 关键词： 倾斜入射 波前编码 三次相位扩大效应 离焦扩大效应     

具有极化选择特性的超材料频率选择表面的设计

基于超材料结构的设计理论,通过长金属线周期阵列和具有Lorentz谐振形式等效介电常数的金属短线的组合可频率选通特性.由不同周期排布和结构尺寸的长金属线和金属短线组合而成的频率选择表面具有不同频段的选通特性.文章提出了双层及单面两种具有极化选择特性的频率选择表面,两种结构均可实现对特定频段TE及TM波选通.具有极化选择特性的超材料频率选择表面的设计为极化滤波器以及极化波产生器的设计提供了借鉴. 关键词： 频率选择表面 超材料 极化选择     

Bose-Einstein condensates with vortices in rotating traps

We investigate minimal energy solutions with vortices for an interacting Bose-Einstein condensate in a rotating trap. The atoms are strongly confined along the axis of rotation z, leading to an effective 2D situation in the x-y plane. We first use a simple numerical algorithm converging to local minima of energy. Inspired by the numerical results we present a variational ansatz in the regime where the interaction energy per particle is stronger than the quantum of vibration in the harmonic trap in the x-y plane, the so-called Thomas-Fermi regime. This ansatz allows an easy calculation of the energy of the vortices as function of the rotation frequency of the trap; it gives a physical understanding of the stabilisation of vortices by rotation of the trap and of the spatial arrangement of vortex cores. We also present analytical results concerning the possibility of detecting vortices by a time-of-flight measurement or by interference effects. In the final section we give numerical results for a 3D configuration. Received 16 December 1998 and Received in final form 18 March 1999     

倾斜入射的波前编码系统的点扩散函数扩大效应分析

通过对坐标系统进行旋转，计算得到了三次型波前编码系统的倾斜入射的光瞳函数，并给出了近似表达式. 分析表明倾斜入射会产生三次相位扩大效应和离焦扩大效应，它们和入射角的正负无关，且随着入射角绝对值的增大而增大. 这表现在点扩散函数(point spread function, PSF)上会扩展PSF包络的两条直角边，表现在调制传递函数(modulation transfer function, MTF)上会降低MTF值. 子午面倾斜入射时，子午方向的三次相位扩大效应和离焦放大效应大于弧矢方向，从而导致子午方向     

Study on Fourier transforms profilometry based on bi-color projecting

Projecting a bicolor sinusoidal fringe pattern consisting of two interlaced RGB format base color fringe patterns with π phase difference onto an object thought digital light projector, we can capture a deformed color pattern by color digital camera, then decode two individual sinusoidal fringe patterns with π phase difference by color-separating technique. Accessing these two fringe patterns, not only are zero-order spectra eliminated, but mask function is also built to mark valid unwrapping area in FTP, automatically.Moreover, because the wrapped phase just inside the valid areas is needed unwrapping, we can mark these areas with mask function, which avoids the error transferring resulting from unwrapping the invalid areas and shortens the unwrapping time. Furthermore, in Fourier transform processing, the full-field deformed fringe pattern generally needed to guarantee measurement precision can be formed by expanding non-full-field fringe pattern captured using the mask function.     

Phase diagram of Fe(1−x)CoxCl2; a random mixture of two antiferromagnets with competing spin anisotropies

Concentration vs transition temperature phase diagram of a random mixture of two anisotropic antiferromagnets, FeCl₂ and CoCl₂, is obtained from the measurement of the susceptibility on the single crystals. Two distinct critical points, one along the c-axis and the other in the c-plane, are observed for the respective concentrations between x = 0.264 and x = 0.481. Three kinds of ordered phases, namely, Fe-rich and Co-rich antiferromagnetic phases and a new phase are found. The phase diagram shows a tetracritical point as well.A hump is observed in the temperature dependence of the susceptibility along the c-axis (c-plane for x ? 0.3) near the ordering temperature occuring in the c-plane (c-axis for x ? 0.3).     

Simultaneous dual directional strain measurement using spatial phase-shift digital shearography

This paper presents a Dual Directional Sheared Spatial Phase-Shift Digital Shearography (DDS-SPS-DS) system for simultaneous measurement of strains/displacement derivative in two directions. Two Michelson Interferometers are used as the shearing device to create two shearograms, one in the x-shearing direction and one in the y-shearing direction, which are recorded by a single CCD camera. Two lasers with different wavelengths are used for illumination, and corresponding band pass filters are applied in front of each Michelson Interferometer to avoid cross-interference between the two shearing direction channels. Two perpendicular shearing directions in the two measurement channels introduce two different spatial frequency carriers whose spectrums are orientated in different directions after Fourier Transform. Phase maps of the recorded two shearograms can be obtained by applying a windowed inverse Fourier transform, which enables simultaneous measurement of dual directional strains/displacement derivatives. The new system is well suited for nondestructive testing and strain measurement with a continuous or dynamic load. The capability of the dual directional spatial phase-shift digital shearography system is described by theoretical discussions as well as experiments.