光栅衍射型超广角激光告警系统光斑定位方法

成像光斑中心精确定位是光栅衍射型超广角激光告警系统具有高定向准确度和高波长分辨能力的基础.本文分析了光栅衍射型超广角激光告警系统成像光斑特点.针对随激光入射角增大,系统成像光斑畸变为强度近似高斯分布倾斜光斑的问题,提出一种改进型高斯拟合法计算光斑中心,通过仿真模拟和实验测试研究了新方法的定位性能.模拟结果表明,高斯噪音标准差为0.01情况下,光斑长轴与x轴夹角由0°逐渐增大为90°过程中,本文方法的定位误差平均值小于0.005像素,误差标准差小于0.02像素.实验测试表明,实验图像经帧相减和高斯平滑滤波预处理后,光斑长轴与坐标轴方向一致时,本文方法与高斯拟合法的定位结果非常接近,明显优于灰度重心法.光斑倾斜时,本文方法求得的激光入射方向角的误差均值和标准差明显小于灰度重心法和普通高斯拟法.     

Experimental measurement of covariance matrix of two-mode entangled state

A two-mode entangled state was generated experimentally through mixing two squeezed lights from two optical parametric amplifiers on a 50/50 beam splitter.The entangled beams were measured by means of two pairs of balanced homodyne detection systems respectively.The relative phases between the local beams and the detected beams can be locked by using the optical phase modulation technique.The covariance matrix of the two-mode entangled state was obtained when the relative phase of the local beam and the detected beam in one homodyne detection system is locked and the other is scanned.This method provides a way by which one can extract the covariance matrix of any selected quadrature components of two-mode Gaussian state.     

Weber and Beltrami integrals of squared spherical Bessel functions: finite series evaluation and high‐index asymptotics

Weber integrals and Beltrami integrals are studied, which arise in the multipole expansions of spherical random fields. These integrals define spectral averages of squared spherical Bessel functions with Gaussian or exponentially cut power‐law densities. Finite series representations of the integrals are derived for integer power‐law index μ, which admit high‐precision evaluation at low and moderate Bessel index n. At high n, numerically tractable uniform asymptotic approximations are obtained on the basis of the Debye expansion of modified spherical Bessel functions in the case of Weber integrals. The high‐n approximation of Beltrami integrals can be reduced to Legendre asymptotics. The Airy approximation of Weber and Beltrami integrals is derived as well, and numerical tests are performed over a wide range of Bessel indices by comparing the exact finite series expansions of the integrals with their high‐index asymptotics. Copyright © 2013 John Wiley & Sons, Ltd.     

Entropy and the fourth moment phenomenon

We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for the score function of smoothly perturbed random variables, as well as on the de Bruijn?s formula of information theory. When applied to sequences of functionals of a general Gaussian field, our results can be combined with the Carbery–Wright inequality in order to yield multidimensional entropic rates of convergence that coincide, up to a logarithmic factor, with those achievable in smooth distances (such as the 1-Wasserstein distance). In particular, our findings settle the open problem of proving a quantitative version of the multidimensional fourth moment theorem for random vectors having chaotic components, with explicit rates of convergence in total variation that are independent of the order of the associated Wiener chaoses. The results proved in the present paper are outside the scope of other existing techniques, such as for instance the multidimensional Stein?s method for normal approximations.     

On Piterbarg’s max-discretisation theorem for multivariate stationary Gaussian processes

Let {X(t),t≥0}$\{X\left(t\right),t\ge 0\}$ be a stationary Gaussian process with zero-mean and unit variance. A deep result derived in Piterbarg (2004)  [23], which we refer to as Piterbarg’s max-discretisation theorem gives the joint asymptotic behaviour (T→∞$T\to \infty$) of the continuous time maximum M(T)=_maxt∈[0,T]X(t)$M\left(T\right)={max}_{t\in [0,T]}X\left(t\right)$, and the maximum M^δ(T)=_maxt∈R(δ)X(t)$M^{\delta }\left(T\right)={max}_{t\in \mathfrak{R}\left(\delta \right)}X\left(t\right)$, with R(δ)⊂[0,T]$\mathfrak{R}\left(\delta \right)\subset [0,T]$ a uniform grid of points of distance δ=δ(T)$\delta =\delta \left(T\right)$. Under some asymptotic restrictions on the correlation function Piterbarg’s max-discretisation theorem shows that for the limit result it is important to know the speed δ(T)$\delta \left(T\right)$ approaches 0 as T→∞$T\to \infty$. The present contribution derives the aforementioned theorem for multivariate stationary Gaussian processes.