Large Signal Analysis of the Michelson Interferometer with Gires-Tournois Interferometers in its Arms

A mathematical model for the transfer function of the Michelson interferometer with Gires-Tournois interferometers in its arms is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output when the input is formed of large-amplitude multisinusoidal voltage. The special case of two-tone equal-amplitude input voltage is considered in detail. The results show that the third-order intermodulation component is always higher than the third-harmonic component. The results also show that the linearity of the Michelson interferometer with Gires-Tournois interferometers in its arms improves with the increase of the front mirror reflectivity. Moreover, the results show that the third-order intermodulation exhibits a minimum for relatively large values of the front mirror reflectivity. Furthermore, compared with the traditional Mach-Zehnder interferometer, the results show that a reduction of 15 dB in the third-order intermodulation can be achieved even for relatively small values of the front mirror reflectivity.     

迈克尔逊干涉仪实验中最佳间隔条纹个数的探讨

用迈克尔逊干涉仪可以测量激光的波长,读取的干涉条纹个数较多时容易引起学生视力的疲劳。因此,本文测量了多组不同的间隔条纹个数时氦氖激光的波长,进而确定它们与波长理论值之间的误差大小,通过比较不同间隔条纹个数时百分差和相对不确定度的大小,最终确定最佳的间隔条纹个数。     

Introduction of the Impulse Response Function in Common-Path Interferometers with Fourier Plane Filters

In the present paper it will be shown how the introduction of a Fourier plane filter can create various types of common-path interferometers for measuring changes in surface tilt or curvature of an object surface. This is obtained by placing a holographic optical element in the Fourier plane of a 4-f optical system. The interferometers are analysed by using the paraxial approximation of the Huygens-Fresnel integral formalism, and the interferometer functions are given by a novel formalism using impulse response functions. Based on this technique, an interferometer for measuring dedicated changes in surface deflection is presented. This interferometer is insensitive to rigid surface rotations and displacements. The interferometer can be embedded in systems based on single point measurement of a time dependent deflection, i.e. vibrometers, as well as in full-field measurements such as electronic speckle interferometers.This paper was originally presented at the 2001 International Conference (2nd Joint OSJ-SPIE Conference) on Optical Engineering for Sensing and Nanotechnology, ICOSN 2001 which was held June 6-8, 2001 at the Pacifico-Yokohama Conference Center, Yokohama, Japan.     

迈克尔逊干涉仪测量空气折射率实验中最佳间隔条纹数的探讨

通过迈克尔逊干涉仪来研究压强对空气折射率的影响,通过Excel软件将实验数据进行线性拟合,得出了不同间隔条纹数下空气折射率随压强变化的拟合直线。当条纹间隔数取不同数值时,将测得的百分差和相对不确定度进行比较,最终确定最佳的间隔条纹数,提高了实验教学中测量空气折射率的精度。     

Hyperbolic Calorons, Monopoles, and Instantons

We construct families of SO(3)-symmetric charge 1 instantons and calorons on the space . We show how the calorons include instantons and hyperbolic monopoles as limiting cases. We show how Euclidean calorons are the flat space limit of this family. Supported by PPARC.     

Hyperbolic Bending of Vortex Lines with Finite Number and Length in Rotating Trapped Bose-Einstein Condensates

The minimal energy configurations of hyperbolic bending vortex lines in the rotating trapped Bose-Einstein condensates are investigated by using a variational ansatz and numerical simulation. The theoretical calculation of the energy of the vortex lines as a function of the rotation frequency gives self-consistently vortex number, curvature and configuration. The numerical results show that bending is more stable than straight vortex line along the z-axis, and the vortex configuration in the xy-plane has a little expansion by increasing z.     

All-reflective Michelson, Sagnac, and Fabry-Perot interferometers based on grating beam splitters

All-reflective Michelson, Sagnac, and Fabry-Perot interferometers based on grating beam splitters are experimentally demonstrated at a wavelength of 1064 nm. A 1200-groove/mm grating diffracting 0 and -1 orders with an efficiency of 48.2% for each order was used as a near-50/50 beam splitter. The all-reflective Sagnac and Michelson interferometers were formed by reintroducing both of the diffracted beams back to the grating. The Fabry-Perot interferometer was formed in a Littrow configuration by using a 1700-groove/mm grating with a blazing efficiency of 91% as a cavity coupler. These interferometers encompass all the fundamental configurations of all-reflective laser interferometric gravitational-wave detectors, promising improved wave-front quality by avoiding volume thermal effects in transmissive optics under high-power laser illumination.     

基于静态小波分解和能量函数优化的图像拼接

提出了一种基于静态小波分解和能量函数优化的全景图拼接算法.该算法首先使用静态小波分解初始图像,并利用序贯检验法对高频图像快速搜索计算粗略匹配序列,在此基础上对初始图像细致搜索计算精确匹配点;对于传统图像融合处理中采用的线性加权函数通常引起的重叠区域模糊问题,采用包含图像梯度的能量函数计算高频图像的全局最优融合因子进行融合,而低频图像则采用线性因子融合.实验表明,该算法在降低匹配运算时间的同时又能获得满意的视觉效果.     

A polarizing Michelson interferometer for the far-infrared and millimetre regions

A polarizing Michelson interferometer for the far-infrared and millimetre regions is described. It uses a simple mechanical drive to attain high-resolution spectra with excellent frequency accuracy, as evidenced by measurements of the rotational parameters for N₂O, for which the D parameter is measured with an uncertainty of ± 190 Hz; comparable with the accuracy of microwave techniques.     

Analysis of Multi-Path Fading and the Doppler Effect for Reconfigurable-Intelligent-Surface-Assisted Wireless Networks

The randomness property of wireless channels restricts the improvement of their performance in wireless networks. As a novel solution for overcoming this, a reconfigurable intelligent surface (RIS) was introduced to reshape wireless physical environments. Initially, the multi-path and Doppler effects are discussed in a case in which a reflector was considered to reflect the incident signal for wireless communication. Subsequently, the results for the transmission signal were analyzed when a reflector was coated with an RIS. Specifically, the multi-path fading stemming from the movement of the mobile transmitter was eliminated or mitigated by utilizing an RIS. Meanwhile, the Doppler effect was also reduced to restrain the rapid fluctuations in the transmission signal by using a tunable RIS in real time. The simulation results demonstrate that the magnitude and spectrum of the received signal can be regulated by an RIS. The multi-path fading and Doppler effect can be effectively mitigated when the reflector is coated with an RIS in wireless networks.     

迈克耳孙干涉仪白光等倾干涉的实现、条纹特征及形成机理

使用在迈克耳孙干涉仪的反射镜前插入附加玻璃板的方法实现了白光的等倾干涉,观察到干涉条纹在出现范围、衬比度、颜色等方面的基本特征;通过建立以色散为基础的理论模型,得到了条纹衬比度函数的简洁数值计算方法和近似解析表达式,并对这种白光等倾干涉的条纹特征和形成机理进行了全面解释.     

Hyperbolic lines and the stratospheric polar vortex

The necessary and sufficient conditions for Lagrangian hyperbolicity recently derived in the literature are reviewed in the light of older concepts of effective local rotation in strain coordinates. In particular, we introduce the simple interpretation of the necessary condition as a constraint on the local angular displacement in strain coordinates. These mathematically rigorous conditions are applied to the winter stratospheric circulation of the southern hemisphere, using analyzed wind data from the European Center for Medium-Range Weather Forecasts. Our results demonstrate that the sufficient condition is too strong and the necessary condition is too weak, so that both conditions fail to identify hyperbolic lines in the stratosphere. However a phenomenological, nonrigorous, criterion based on the necessary condition reveals the hyperbolic structure of the flow. Another (still nonrigorous) alternative is the finite-size Lyapunov exponent (FSLE) which is shown to produce good candidates for hyperbolic lines. In addition, we also tested the sufficient condition for Lagrangian ellipticity and found that it is too weak to detect elliptic coherent structures (ECS) in the stratosphere, of which the polar vortex is an obvious candidate. Yet, the FSLE method reveals a clear ECS-like barrier to mixing along the polar vortex edge. Further theoretical advancement is needed to explain the apparent success of nonrigorous methods, such as the FSLE approach, so as to achieve a sound kinematic understanding of chaotic mixing in the winter stratosphere and other geophysical flows. (c) 2002 American Institute of Physics.     

Products, Coproducts, and Singular Value Decomposition

Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, i.e. generalized eigenvalues, to these maps. We show, for the case of Grassmannand Clifford products, that twist maps significantly alter these data reducing degeneracies. Since non group like coproducts give rise to non classical behavior of the algebra of functions, makeing them noncommutative, we hope to be able to learn more about such geometries. A remarkabe thechnicallity is that the coproduct for positive singular values of eigenvectors in A yields directly corresponding eigenvectors in A⊗ A.     

6j Symbols for the Modular Double,Quantum Hyperbolic Geometry,and Supersymmetric Gauge Theories

We revisit the definition of the 6j symbols from the modular double of ${\mathcal{U}_q(\mathfrak{sl}(2, \mathbb{R}))}$ , referred to as b-6j symbols. Our new results are (1) the identification of particularly natural normalization conditions, and (2) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of non-abelian three-dimensional ${\mathcal{N}=2}$ supersymmetric gauge theories.     

大视场消色差温度补偿型风成像干涉仪调制度的分析与计算

简要论述了大视场、消色差、温度补偿型风成像干涉仪用于高层探测的基本原理.对自行设计的风成像干涉仪的调制度进行了理论分析与计算,推导了调制度的理论表达式.采用计算机模拟,分析了仪器调制度随入射角的变化关系.当调制度大于075时,风成像干涉仪视场角可达129°,充分显示了大视场、高调制度的显著特点.分析了玻璃折射率对调制度的影响,得到了调制度取得最大值时玻璃的优化组合;分析了温度对调制度的影响,得到了调制度随着温度变化的曲线.此研究为高层大气探测理论的发展、大气探测以及大视场、消色差、温度补偿型风成像干涉仪的研制提供了重要的理论依据及实践指导. 关键词： 干涉成像技术 迈克尔逊干涉仪 调制度 双光束干涉     

Effects of Field Fluctuations,Losses, and Aberrations on the Sensitivity of a Michelson GW Antenna Using Squeezed Radiation

The sensitivity of an interferometric gravitational wave (GW) antenna operating above a few hundred Hertz is shot-noise limited. Sub-shot-noise sensitivity can be achieved by superimposing squeezed light on the laser field. The benefits of this approach are reduced in nonideal interferometers having fringe visibility less than unity, as pointed out by Gea-Banacloche and Leuchs and recently discussed by Chickarmane. Here, we consider an interferometer described by a set of coefficients V_l^(k), V_sq^(k), V_lsq^(k) depending on the misalignment, mismatching, and aberrations of the optical systems, as well as on the asymmetry of the beam splitter and the two-arm losses. Due to the presence of terms proportional to the product of laser times squeezed fields, we have taken into account the amplitude fluctuations of a_l. A simple model of the squeezed vacuum light, produced by a degenerate optical parametric oscillator (OPO), is used for calculating the dependence of the spectral density of the output of a GW antenna on the fluctuations of the OPO-cavity resonance frequency, the pump amplitude fluctuation, and the nonlinear-crystal-temperature drift. A set of figures η_sq± and r_lsq±⁽²⁾ are introduced for describing the effects of the amplitude fluctuations and the relative line width γ_la on the spectral density of the quadrature phase operator X = a_la_sq⁺ h.c.     

Instabilities in the Chapman-Enskog Expansion and Hyperbolic Burnett Equations

It is well-known that the classical Chapman-Enskog procedure does not work at the level of Burnett equations (the next step after the Navier-Stokes equations). Roughly speaking, the reason is that the solutions of higher equations of hydrodynamics (Burnett's, etc.) become unstable with respect to short-wave perturbations. This problem was recently attacked by several authors who proposed different ways to deal with it. We present in this paper one of possible alternatives. First we deduce a criterion for hyperbolicity of Burnett equations for the general molecular model and show that this criterion is not fulfilled in most typical cases. Then we discuss in more detail the problem of truncation of the Chapman-Enskog expansion and show that the way of truncation is not unique. The general idea of changes of coordinates (based on analogy with the theory of dynamical systems) leads finally to nonlinear Hyperbolic Burnett Equations (HBEs) without using any information beyond the classical Burnett equations. It is proved that HBEs satisfy the linearized H-theorem. The linear version of the problem is studied in more detail, the complete Chapman-Enskog expansion is given for the linear case. A simplified proof of the Slemrod identity for Burnett coefficients is also given.     

主焦点式光学系统的光机结构设计与装调检测

针对应用在极轴式望远镜中的主焦点式光学系统,从主镜的支撑设计与分析、主镜的装调检测、校正镜组件的设计装调和系统的装调检测等方面进行了深入的研究.充分应用了有限元法分析主镜的支撑、定心仪检测光轴的同轴度、平行光管检测系统像质等,得出了主焦点式光学系统的一般装调检测方法.装调后的主镜面形检测结果均方根值达到0.042 8λ,校正镜组的光轴同轴误差达到12.4″.对系统的像质评价采用能量集中度法,成像在靶面上的星点80%能力集中度在24 μm×24 μm范围以内,达到设计指标要求,说明系统结构设计合理,装调检测方法可行.该方法和思路可推广至其他主焦点式光学系统的装调检测工作.     

Superposition, Entropy and Schmidt Decomposition of States

Superposition and entropy are compared using the language of the logic of quantum mechanics. It is pointed out that a finite value of the relative quantum entropy of states implies a superposition relation between the states themselves. The superposition relation is then studied by comparing the pure state of the compound system with the product of the reduced states and an intermediate Schmidt state. All the corresponding relative quantum entropies are evaluated in terms of the Schmidt coefficients of the global pure state. Some of the results are extended in case the compound system is in a state represented by a general density operator.