Numerical reconstruction stability of fiber Bragg gratings

Traditional algorithms for solving the inverse scattering problem for a fiber Bragg grating are described, and a new numerical method for this problem is developed. The method is based on the fast inversion of a matrix using its Toeplitz symmetry and on a special “inner-bordering” procedure. It is shown that the method is equally efficient as the well-known discrete layer peeling method but exceeds the latter in accuracy, especially for high-reflectance gratings. The stability of the proposed method with respect to initial data errors is demonstrated.     

Surface currents of a superconducting axisymmetric body that screen an external coaxial magnetic field

A time-saving method to find currents on the surface of a superconducting axisymmetric body is suggested for the case when the axis of the body and the symmetry axis of an external magnetic field coincide. The method is based on solving a one-dimensional integral equation. Analytical solutions are derived for the superconductor in the form of an ellipsoid of revolution that is placed in a uniform magnetic field and in the form of a sphere placed in a magnetic field varying as a polynominal at the symmetry axis. To find the current density on the surface of an arbitrarily shaped axisymmetric body placed in an arbitrarily varying magnetic field, a method of numerically solving the integral equation is proposed. It is a combination of the iterative regularization method and the projective method with a projector in the form of B splines. The results of numerical reconstruction of the sought functions by the latter method for a number of particular cases are presented.     

A new volume-of-fluid method with a constructed distance function on general structured grids

A second-order volume-of-fluid method (VOF) is presented for interface tracking and sharp interface treatment on general structured grids. Central to the new method is a second-order distance function construction scheme on a general structured grid based on the reconstructed interface. A novel technique is developed for evaluating the interface normal vector using the distance function. With the normal vector, the interface is reconstructed from the volume fraction function via a piecewise linear interface calculation (PLIC) scheme on the computational domain. Several numerical tests are conducted to demonstrate the accuracy and efficiency of the present method. In general, the new VOF method is more efficient than both the high-order level set and the coupled level set and volume-of-fluid (CLSVOF) methods. The results from the new method are better than those from the benchmark VOF method, particularly in the under-resolved regions, and are comparable to those from the CLSVOF method. Breaking waves over a submerged bump and around a wedge-shaped bow are simulated to demonstrate the application of the new method and sharp interface treatment in a two-phase flow solver on curvilinear grids. The computational results are in good agreement with the available experimental measurements.     

Optical method for measuring structural parameters of island films

An optical method for determining characteristics of the submicron structure in island films is proposed. The method is based on the measurements of fluctuations of optical properties of a film detected when a focused laser beam is scanned over it. It is shown that the island size distribution can be determined in principle by the method proposed. Structural inhomogeneity of a Cs film on sapphire is revealed experimentally. Parameters of these inhomogeneities are measured as functions of the film thickness. The correspondence of the results of the optical method and the data of electron microscopy is tested for a In film on glass.     

Lattice Boltzmann method on quadtree grids for simulating fluid flow through porous media: A new automatic algorithm

During the past two decades, the lattice Boltzmann (LB) method has been introduced as a class of computational fluid dynamic methods for fluid flow simulations. In this method, instead of solving the Navier Stocks equation, the Boltzmann equation is solved to simulate the flow of a fluid. This method was originally developed based on uniform grids. However, in order to model complex geometries such as porous media, it can be very slow in comparison with other techniques such as finite differences and finite elements. To eliminate this limitation, a number of studies have aimed to formulate the lattice Boltzmann on the unstructured grids. This paper deals with simulating fluid flow through a synthetic porous medium using the LB method and on the quadtree grid structure. To this end, the LB method was used on nonuniform grids coupled with a technique for image reconstruction which resulted in the quadtree grids for simulation of fluid flow through porous media. Accuracy and efficiency of this algorithm is compared against the conventional LB method based on uniform grids. While the decrease in computational time in the proposed LB method on nonuniform grids is found to be significant regarding the size of the initial and reconstructed images, the same level of accuracy is obtained when compared with the conventional LB method on uniform grids.     

Phase-only hologram generation based on integral imaging and its enhancement in depth resolution

We introduce a phase-only hologram generation method based on an integral imaging,and propose an enhancement method in representable depth interval.The computational integral imaging reconstruction method is modified based on optical flow to obtain depth-slice images for the focused objects only.A phaseonly hologram for multiple plane images is generated using the iterative Fresnel transform algorithm.In addition,a division method in hologram plane is proposed for enhancement in the representable minimum depth interval.     

基于界面捕捉的三维多介质辐射流体力学方程MMALE计算方法

针对界面重构产生的混合介质网格,建立基于能量守恒的子网格封闭模型,给出基于混合介质网格上的三维扩散方程求解方法.在此基础上,结合界面重构和流体力学方程MMALE （multi-material arbitrary Lagrangian-Eulerian）算法,给出一种针对三维辐射流体力学的MMALE计算方法.采用解析解算例,验证算法的正确性和精度.通过对典型辐射驱动问题的模拟,展示方法的健壮性.     

Estimating the amplitude of measurement noise present in chaotic time series

We propose a method for estimating the amplitude of measurement noise present in chaotic time series. This method is based on the evaluation of initial errors for a given time series and for a new one synthesized by adding an adequate amount of noise to the given one. The method is valid over a much wider range of noise levels than the previous methods are because it is not based on the detail of dynamical structure which generates the data. In addition, it is possible to check if the method is valid for the given data prior to its application. To confirm the effectiveness of the method we show the results of numerical experiments and apply the method to chaotic data obtained from an electrochemical experiment. (c) 1999 American Institute of Physics.     

Method for the determination of dopant concentrations of luminescent ions

We report on a new method for determining dopant ion concentrations in laser materials. This method is based on optical absorption spectroscopy. In contrast to other methods used to measure the dopant concentration that are based on absorption measurements, this method does not require the knowledge of the absorption cross sections. An advantage of this method compared to the micro probe analysis is that only concentrations of dopant ions of a certain valency, which are luminescent, are detected. The method is sensitive especially for small doping concentrations of ions with high absorption cross sections. Another application of this method is the determination of the ratio between luminescent dopant ions to the total number of dopant ions in the case that not all dopant ions are on crystal sites that allow for optical transitions.     

Scattering of light by axially symmetric particles: Modification of the point-matching method

The approach based on the separation of the fields into two parts with definite properties and the proper choice of special scalar potentials for each of them is applied to the point-matching method. Earlier, such a procedure carried out within the framework of the method of separation of variables for spheroids allowed us to obtain a solution that is considerably more efficient for strongly prolate and strongly oblate particles than solutions obtained with other versions of this method. It was found that the replacement of the summation over points on the particle surface in the point-matching method by the corresponding integral leads to a faster and more exact algorithm. The applicability of the proposed method is considered in comparison with the related method of extended boundary conditions. For spheroids and Chebyshev particles with a maximum-to-minimum-size ratio exceeding 1.5–2, the efficiency of the point-matching method is not high. For other Chebyshev particles, the point-matching method is undoubtedly preferable to the commonly used method of extended boundary conditions since it allows one to increase the accuracy of calculations by several orders of magnitude. Moreover, whereas the latter method is in principle inapplicable to certain Chebyshev particles, the former lacks this disadvantage.     

Computation of localized modes in a defect-containing photonic crystal by the method of periodic continuation of solution

The applicability of the method of periodic continuation of solution for computing the spatial distribution of an electromagnetic field in a photonic crystal with a defect is analyzed. The accuracy of the method is estimated. The crystal eigenmodes are classified, and the method is shown to be applicable only for states localized on the defect. The results of numerical calculations based on expansion of electromagnetic field in plane waves are presented, and the details of the expansion method are described.     

A Fourier-based elliptic solver for vortical flows with periodic and unbounded directions

We present a computationally efficient, adaptive solver for the solution of the Poisson and Helmholtz equation used in flow simulations in domains with combinations of unbounded and periodic directions. The method relies on using FFTs on an extended domain and it is based on the method proposed by Hockney and Eastwood for plasma simulations. The method is well-suited to problems with dynamically growing domains and in particular flow simulations using vortex particle methods. The efficiency of the method is demonstrated in simulations of trailing vortices.     

基于色貌的跨媒体颜色复制

介绍了一种基于视觉匹配的跨媒体颜色复制方法。通过视觉匹配将一个环境下的一些色貌因素"映射"到另一个环境,是一种基于色貌的CRT特性化方法。该方法复制的22个Munsell色卡的平均视觉评价为6分制的5.17分。其中,红色调的复制色块视觉评价较好,蓝色调或蓝色占有较大比例的复制色块误差较大。sRGB作为目前流行的用于颜色通讯的标准色空间,在实验中也进行了比较。实验证明这种基于视觉匹配的特性化方法,已经包含了一些色貌因素,可以满足一般的应用要求,有着广泛的应用前景。     

一阶不连续光学元件MRF流体动力学分析方法

一阶不连续光学元件的磁流变抛光问题是制约我国高精高效光学制造领域发展的难题之一,其涉及锥形、矩形等几何形貌元件的光学元件加工问题以及常见光学元件的边缘效应控制问题。提出了基于一阶不连续光学元件的磁流变抛光流体动力学方法,建立了该类元件抛光区域流体动力分析的理论方法和数值手段。首先,对磁流变抛光工况下的流场进行了合理假设,其次,从微元流体动力方程出发,建立了适用于一阶不连续面形的流场分析方法,最后,基于有限差分法和数值迭代方法建立了流场控制方程的数值计算方法。通过对切入距离为1~18 mm的抛光过程进行数值仿真,发现该方法所获取的一阶不连续面形的压力分布形态是正确的,产生的不连续压降与实验观测一致。     

插值法在低温温度测量中的应用

依托建立的低温精馏装置,针对低温环境中温度测量问题,提出一种基于LabVIEW的低温温度测量方法。该方法将插值法引入到数据分析中,通过软件编程实现数据处理、显示、存储等功能。经过理论分析与实验对比,该方法准确度提高到0.01 K,可移植性强,是低温环境中温度测量的可行方法。     

An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection(VP) method.Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection(IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method,without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio(SNR)for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.     

Swept source optical coherence tomography based on non-uniform discrete fourier transform

A high-speed high-sensitivity swept source optical coherence tomography （SSOCT） system using a high speed swept laser source is developed. Non-uniform discrete fourier transform （NDFT） method is introduced in the SSOCT system for data processing. Frequency calibration method based on a Mach-Zender interferometer （MZI） and conventional data interpolation method is also adopted in the system for comparison. Optical coherence tomography （OCT） images from SSOCT based on the NDFT method, the MZI method, and the interpolation method are illustrated. The axial resolution of the SSOCT based on the NDFT method is comparable to that of the SSOCT system using MZI calibration method and conventional data interpolation method. The SSOCT system based on the NDFT method can achieve higher signal intensity than that of the system based on the MZI calibration method and conventional data interpolation method because of the better utilization of the power of source.     

元胞方法与蒙特卡洛方法相结合的薄膜生长过程模拟

利用仿真方法从原子尺度研究薄膜生长过程是当前薄膜研究领域的热点. 目前, 仿真方法主要在纳米尺度模型实现, 时空需求很大. 针对这一问题, 本文提出元胞和蒙特卡洛相结合的模拟方法, 实现对微米尺度模型薄膜生长过程的模拟. 利用元胞方法来实现模型表示以及演化计算, 从而降低对内存空间的要求, 提高计算效率, 并使用蒙特卡洛方法计算粒子的扩散概率. 通过对氮化硅薄膜生长过程进行具体研究, 将模拟结果与实际实验结果和分子动力学演化结果进行表面形貌和成分的比较, 验证了该方法的有效性.     

A plating method for metal coating of fiber Bragg grating

We present a method for metal coating optical fiber and in-fiber Bragg grating. The technology process which is based on electroless plating and electroplating method is described in detail. The fiber is firstly coated with a thin copper or nickel plate with electroless plating method. Then, a thicker nickel plate is coated on the surface of the conductive layer. Under the optimum conditions, the surfaces of chemical plating and electroplating coatings are all smooth and compact. There is no visible defect found in the cross-section. Using this two-step metallization method, the in-fiber Bragg grating can be well protected and its thermal sensitivity can be enhanced. After the metallization process, the fiber sensor is successfully embedded in the 42CrMo steel by brazing method. Thus a smart metal structure is achieved. The embedding results show that the plating method for metallization protection of in-fiber Bragg grating is effective.     

Determination of surface flatness by spectral interferometric method

In this study a novel method for determining surface flatness based on spectral interferometry is reported. In the traditional method a laser is used to produce intensity interference fringes and by measuring the shift in the position of a fringe when a test plate is put on a reference plate, the surface flatness of the test plate is determined. In the present study we have used a broad-band source for determining the flatness of a test plate. By studying the changes in the spectrum of the source on interference that are produced when a test plate is put on a reference plate, the surface flatness is determined. It has been found that the surface flatness determined by spectral studies comes out to be of the same order as that with a quasi-monochromatic laser light. This method might provide an edge over the present method by reducing the time taken in the study and also provide a cost-effective solution.