基于傅里叶变换的光纤法布里-珀罗传感器解调研究

从双光束干涉的基本原理出发,分析了高斯分布光源条件下利用傅里叶变换解调光纤法布里-珀罗传感器的原理。针对高斯分布光源特点,提出直接对波长均匀采样得到的光谱数据进行快速傅里叶变换,然后利用传感器腔长与频域中峰值频率之间的关系求解传感器腔长的可行性。在此基础上,采用频谱插值技术提高了系统解调精度,并利用宽带光源和光谱仪等组成的解调系统,对所提出的方法进行了实验验证。结果表明,从实验中测得的数据与理论计算值能较好地吻合。     

高斯光束斜入射非平行法布里-珀罗干涉仪后的透射光强分布

基于多光束干涉原理,推导出了高斯光束斜入射非平行法布里-珀罗干涉仪射后的透射光强表达式,在此基础上,着重研究了高斯光束入射角的大小以及法布里-珀罗干涉仪两反射端面的不平行度对透射光强分布的影响。研究结果表明：入射角的大小和干涉仪的不平行度对透射光的强度分布、峰值强度的大小和峰值强度的位置有很大的影响;在入射高斯光束具有较小的腰斑半径或法布里-珀罗干涉仪的两端面的反射率较大时,必须考虑高斯光束沿传输轴线的衍射效应;楔角为负的非平行法布里珀罗出射光斑的光强在“反跳”处急剧下降到零,可利用这一特点对距离进行精确测量。     

带形状参数的二次三角多项式Bézier曲线形状分析

对一类二次三角多项式Bézier曲线的形状及其控制多边形之间的关系进行了研究.根据控制多边形边之间的相对位置关系,先通过计算推理得到有关空间二次三角多项式Bézier曲线奇、拐点的一个结论;再利用包络理论和拓扑映射的方法,分别得到平面二次三角多项式Bézier曲线上含有尖点、拐点、重结点和曲线为全局凸、局部凸的充分必要条件,并给出了曲线具有尖点、重结点和拐点的数值例子;最后,讨论了形状参数对形状分区的影响.     

基于时域位相分析的云纹法形貌测量技术研究

采用影像云纹法和时域相位分析技术研究了物体形貌测量的新方法.通过研制高精度旋转平台,利用栅线旋转的方式使栅线的空间频率以一定的规律变化,使物体的离面高度与该点的灰度变化率有关.在利用FFT确定灰度变化频率时,采用补零的方法提高了频率的确定精度,从而有效地提高了物面形貌测量的精度.实验发现:当补零倍数达到原始长度的128倍时,使用空间频率为5 l/mm的栅线精度可以达到0.02mm.本文讨论了该方法相关技术参数的选取方法,给出了标定实验和利用该测量系统实际测量门齿生长发育沟的实例,阐述了牙齿表面形貌数字化在牙科修复手术中的意义.通过具体标定过程与应用实例,证明了本文提出的测量方法提高了测量精度,简化了测量过程,在云纹干涉形貌测量领域有了新的突破.     

基于空芯光子晶体光纤的微小型非本征光纤法布里-珀罗干涉应变传感器

报道了一种用空芯光子晶体光纤制作的法布里-珀罗腔体,利用光纤熔接方法将该法布里-珀罗腔体和两根普通通信单模光纤熔接起来构成的微小型光纤法布里-珀罗干涉应变传感器。这种干涉传感器制作过程仅应用了切割和熔接手段,光纤材料单一,因此受温度变化的影响小。另外,该类型传感器的干涉腔长度对干涉信号强度影响不大,其干涉腔长度可至数厘米。因此,这类传感器将在大容量、准分布式传感系统中具有极大的潜在应用价值。     

10 GHz全光帧时钟提取的理论和实验研究

提出了一种新型的10 GHz全光帧时钟提取的提取方案。采用低精细度的法布里-珀罗(F-P)滤波器直接提出帧时钟,保证帧时钟的快速建立和快速消失。利用半导体光放大器(SOA)的自增益调制效应(SGM)对法布里-珀罗滤波器提取的帧时钟进行整形,降低帧时钟的幅度噪声。并推导了法布里-珀罗滤波器的精细度和半导体光放大器的自增益调制效应对帧时钟建立时间、消失时间的影响。通过理论分析表明,利用半导体光放大器的自增益调制效应可以降低帧时钟的幅度噪声并加快帧时钟建立速度。实验中,用上述方案对10.075 GHz的帧信号进行了全光帧时钟提取,得到了建立时间为8个信号周期,消失时间为22个信号周期,抖动为2.35 ps的帧时钟信号。     

Phragmén-Lindel(o)f and continuous dependence type results in a Stokes flow

This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder.With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder,solutions either grow or decay exponentially in the distance from the finite end of the cylinder.In the case of decay,the effect of perturbing the equation parameters is also investigated.     

A Statistical Mechanical Analysis on the Bound State Solution of an Energy-Dependent Deformed Hulthén Potential Energy *

In this article, we investigate the bound state solution of the Klein Gordon equation under mixed vector and scalar coupling of an energy-dependent deformed Hulthén potential in D dimensions. We obtain a transcendental equation after we impose the boundary conditions. We calculate energy spectra in four different limits and in arbitrary dimension via the Newton-Raphson method. Then, we use a statistical method, namely canonical partition function, and discuss the thermodynamic properties of the system in a comprehensive way. We find out that some of the thermodynamic properties overlap with each other, some of them do not.     

Locally risk-minimizing hedging strategies for unit-linked life insurance contracts under a regime switching L��vy model

This paper extends the model and analysis in that of Vandaele and Vanmaele [Insurance: Mathematics and Economics, 2008, 42: 1128–1137]. We assume that parameters of the Lévy process which models the dynamic of risky asset in the financial market depend on a finite state Markov chain. The state of the Markov chain can be interpreted as the state of the economy. Under the regime switching Lévy model, we obtain the locally risk-minimizing hedging strategies for some unit-linked life insurance products, including both the pure endowment policy and the term insurance contract.     

Oblique Derivative Problem for Quasilinear Mixed (Lavrentév-Bitsadze) Equations of Second Order in Two Connected Domains

In this article, we first give the representation of solutions for the oblique derivative problem of mixed (Lavrentév-Bitsadze) equations in two connected domains, afterwards prove the uniqueness of solutions of the above problem. Moreover, we prove the solvability of oblique derivative problem for quasilinear mixed (Lavrentév-Bitsadze) equations of second order, and obtain a priori estimates of solutions of the above problem. The above problem is an open problem proposed by Rassias.