基于Clean算法的离子束抛光技术的驻留时间求法

离子束抛光技术的关键在于对驻留时间进行求解,通常通过反卷积运算来完成.这在理论上可以实现,但是当需要加工量很小或趋于零时,加工时间就变为无穷大,此时变成一个病态问题.因此驻留时间的求解变得困难,出现的奇异值使加工难以实现.以Clean算法为基础提出了天文望远镜离子束抛光技术中对驻留时间求解的一种新的有效方法,并通过拟合来处理数据,理论上可以实现任何精度.更好地方便计算机控制的实现,为加工提供了基础.仿真结果表明,此方法所求驻留时间符合天文光学镜面离子束抛光技术的要求.     

离轴二次曲面面型参数测量归算方法的研究

为了在制造过程中保证离轴非球面的光学特性,需要对其主要的面型参数进行严格控制,除了常规形式的顶点曲率半径和非球面系数外,还需要控制镜面的离轴量和离轴角.本文基于普通的二次曲面方程,推导了在新坐标系下的二次曲面表达式,并在这个坐标系下,利用Powell共轭方向法求取镜面的顶点曲率半径、二次曲面系数、离轴量和离轴角.通过对抛物面和双曲面两种形式不同外形的镜面数据的计算,拟合的RMS值可以达到10nm的精度,从而表明该测量计算方法可以有效地控制离轴面加工时的参数误差.     

稀疏矩阵技术及其在天测与测地VLBI数据处理中的应用

介绍了稀疏矩阵的四种常见形式以及稀疏矩阵技术在天测与测地VLBI数据处理中的应用。推演了天测与测地VLBI数据综合解算中所用稀疏矩阵形式下待估参数求解和协方差矩阵估算的算法。通过对是否采用稀疏矩阵技术时方程求解 (乘法和加法 )运算对数的估算和比较 ,表明普通最小二乘方法的运算对数约为参数总数的 3次方 ,而采用稀疏矩阵技术时的运算对数近似与参数总数成线性关系 ,从而能够在现代空间对地观测技术的大样本数据处理中显著缩短计算时间。     

射电天文图像的反卷积算法研究

在射电天文干涉测量中,测量的图像包含设备点扩展函数的影响. CLEAN反卷积算法是移去点扩展函数旁瓣影响的最常用算法.自适应尺度像素分解算法是一种尺度敏感的CLEAN反卷积算法,适合于延展源的重建.然而这种算法是耗时的.实现了一种尺度敏感的反卷积算法.它使用若干高斯函数来逼近潜在的真实天空图像,同时用新的方法估计较小的初始分量.实验表明,算法在获得高质量重建结果的同时,速度提高3倍左右.     

卫星定位中的一种分步加权解算方法

卫星定位中,当可视卫星数目多于4颗时常采用加权最小二乘(Web Login Server,WLS)算法,对各卫星解算权重进行重新评估而获得最优解。然而由于受到多重因素的影响,权矩阵W的构造与确定一直是各类加权算法中的重点和难点。从线性测量方程组出发,通过研究迭代解算过程中用户等效伪距测量误差对坐标位置误差的传递与放大规律,提出了一种新的加权最小二乘解算方法,及其权矩阵的具体构造与实现方法,从而对各未知数进行分步加权与分离解算。通过全球定位系统(Global Positioning System,GPS)实测实验,对方法的可行性和精度水平进行了分析与验证。结果表明,使用该分步加权方法进行定位,解算结果准确度更高、稳定性更好。     

稀疏矩阵技术及其在天测与测地VLBI数据处理中的应用

介绍了稀疏矩阵的四种常见形式以及稀疏矩阵技术在天测与测地VLBI数据处理中的应用。推演了天测与测地VLBI数据综合解算中所用稀疏矩阵形式下待估参数求解和协方差矩阵估算的算法。通过对是否采用稀疏矩阵技术时方程求解(乘法和加法)运算对数的估算和比较，表明普通最小二乘方法的运算对数约为参数总数的3次方，而采用稀疏矩阵技术时的运算对数近似与参数总数成线性关系，从而能够在现代空间对地观测技术的大样本数据处理中显著缩短计算时间。     

利用正交变换方法计算协方差分析的统计量

证明用Givens—Gentleman正交变换给出的加仅最小二乘解与统计定轨理论求得的解一致．采用正交变换方法计算其它的一些重要的统计量,如考察协方差矩阵、摄动矩阵等,并计算这些量随时间的传播．这种算法的优点是通过降低法方程的条件数提高计算的稳定性,同时可以方便地对不同的参数组合情况求解而不需多次解算法方程．     

辛算法的分类与发展

辛算法作为研究哈密顿系统长期定性演化的最佳积分工具,自问世以来就受到了很大的关注。通过对哈密顿函数的截断误差分析,可以从不同角度构造出较高精度的辛算法,也可以通过引入正规化技术实现自动调整积分步长和改善数值稳定性。从辛算法的表现形式可以将它分为显式和隐式两种。当哈密顿系统能够分解为几个可积部分且每部分的解能用时间显函数来表示时,可以构造显式算法。显式算法有非力梯度显式辛算法、力梯度辛算法、辛校正、类高阶辛算法四种。当哈密顿系统变量不能分离时,适合应用隐式辛算法和扩充相空间对称算法求解。分别对这些算法的构造方法及其适用的物理模型进行归纳对比,分析了各种辛算法的优劣性和发展趋势,对如何选择辛算法高效高精度地解决实际问题提供了一定的理论和数值计算依据。     

大口径离轴非球面镜预应力环抛方法研究

提出了一种加工离轴非球面的预应力环抛方法,基于预应力加工方法的基本原理,利用环抛机来磨制离轴非球面.设计了一套专门的加载装置,将拼接镜面中具有不同离轴量的非球面子镜转化成曲率半径相同的球面子镜进行磨制,可以在同一台环抛机上进行抛光.利用这种方法,花费连续40 h的时间,磨制了一块按照中国30 m极大口径望远镜(CFGT)主镜参数比例缩小的离轴抛物面,顶点曲率半径21.6 m,离轴量3.6 m,离轴口径为330 mm,最大非球面度为16μm.试验表明该方法效率高,适用于批量加工,特别是极大口径天文望远镜拼接主镜的大批量非球面子镜研制.     

用改进的SPEA求解轨道转移的时间-能量极小化问题

提出了改进的SPEA，这是一种多目标进化算法，适于求解大尺度空间的多目标优化的Pareto最优解，并应用于求解轨道转移的时间—能量极小化问题，计算结果表明算法的有效性。     

An improved technique for preparing polished thin sections of stony-iron meteorites

Abstract— Polished thin sections of stony-iron meteorites can be prepared easily and quickly using a new technique in which the cooling water to the polishing machine is refrigerated. When using this technique, the silicate and sulfide phases do not heat up and expand differentially, as is often the case when normal procedures are used, and do not pluck out during the polishing process.     

Preliminary orbit-determination method having no co-planar singularity

It has long been recognized and demonstrated in the astrodynamic literature that three observations of angular position are not always sufficient to determine a preliminary orbit. One reason for this is due to the fact that as the plane of the observer's motion approaches the plane of the orbit of the observed object, the determination of the orbit of the object becomes indeterminant. Merely changing the coordinate system will not eliminate the inherent indeterminacy or singularity. When the observed object is moving in the same plane as the observer, their relative motion is described in two dimensions rather than three. The problem reduces to defining two components of position and two of velocity given only three angular measures and no solution is possible. Although this singularity is a rather old, albeit infrequently arising problem in celestial mechanics, it has received renewed interest due to the advent of satellite observatories that observe other spacecraft. In this new circumstance the plane of the observer's motion is rather frequently near the plane of the object (12% to 35% of the time) and the co-planar singularity becomes a subject that deserves additional attention.It is the purpose of this paper to develop a practical and simple method of orbit determination using four observations. This method also allows one to avoid the problem of multiple orbit-determination solution roots, and provides numerical indices that are useful in assessing the degree of indeterminacy in any given observer/object geometry. This paper does not dwell at length on the theory of orbital singularities, since they have been already treated in celestial mechanics literature. Instead, the emphasis is on the details of a new computational technique, which has been found to be computationally more efficient than previous four-observation methods, and which is unique in being formulated in the geocentric system and involves only one scalar quantity in the correction process.The equations for the new method are developed and a numerical example is presented that demonstrates the efficiency of the method.     

A new way to conserve total energy for Eulerian hydrodynamic simulations with self-gravity

We propose a new method to conserve the total energy to round-off error in grid-based codes for hydrodynamic simulations with self-gravity. A formula for the energy flux due to the work done by the self-gravitational force is given, so the change in total energy can be written in conservative form. Numerical experiments with the code Athena show that the total energy is indeed conserved with our new algorithm and the new algorithm is second order accurate. We have performed a set of tests that show the numerical errors in the traditional, non-conservative algorithm can affect the dynamics of the system. The new algorithm only requires one extra solution of the Poisson equation, as compared to the traditional algorithm which includes self-gravity as a source term. If the Poisson solver takes a negligible fraction of the total simulation time, such as when FFTs are used, the new algorithm is almost as efficient as the original method. This new algorithm is useful in Eulerian hydrodynamic simulations with self-gravity, especially when results are sensitive to small energy errors, as for radiation pressure dominated flow.     

Gamma-ray burst afterglows: effects of radiative corrections and non-uniformity of the surrounding medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be the result of continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, i.e. n _ext ∝  R ^{− k} , we study the effects of the first-order radiative correction and the non-uniformity of the medium on a GRB afterglow analytically. We first derive a new relation among the observed time, the shock radius and the Lorentz factor of the fireball: t _⊕ =  R /4(4− k ) γ²c, and also derive a new relation among the comoving time, the shock radius and the Lorentz factor of the fireball: t _co = 2 R /(5− k ) γc. We next study the evolution of the fireball by using the analytic solution of Blandford &38; McKee. The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is p  = 2.5, implied from the spectra of GRBs, the X-ray afterglow of GRB 970616 is well fitted by assuming k  = 2.     

Satellite prediction formulae for Vinti's model

For Vinti's dynamical problem, there is proposed a new form of solution wherein all three coordinates are expressed in terms of one independent variable. The formulae for the three co-ordinates are clear generalizations of the corresponding formulae for the Kepler problem while the independent variable corresponds to the true anomaly. The solution is completed by the relation connecting the independent variable with time: the latter is a generalization of the well known Kepler time-angle relationship. From the form and method of solution the main qualitative features of the motion are readily derived.     

大面积硅微条探测器在轨数据压缩算法的设计与实现

硅微条探测器具有位置分辨高、响应快、低噪声、低功耗等优点,广泛应用在各大加速器试验中,测量粒子径迹.新世纪以来,逐渐应用于空间探测领域.计划中的"悟空"2号暗物质粒子探测卫星的硅微条探测器将至数十万计,将产生海量的原始数据.如何实现探测器快速实时的数据压缩,是其需要解决的一大难题.立足于面向空间应用的硅微条探测器在轨实时压缩算法,算法采用FPGA (Field-programmable Gate Array)搭建流水线结构的方式实现,在提高系统集成度、节省逻辑资源的同时,批量数据处理时最高可将数据压缩率提升至38.4 M通道/s.算法结构具有通用性,设计思想和方案将为"悟空"2号的径迹探测器的研制提供参考.     

Phasing of segmented mirrors: a new algorithm for piston detection

The point spread function of a segmented-mirror telescope is severely affected by segment misalignment, which can nullify the performance of adaptive optics systems. The piston and tilt of each segment must be precisely adjusted in relation to the other segments. Furthermore, the direct detection of the alignment error with natural stars would be desirable in order to monitor the errors during astronomical observation.
We have studied the lost information of the piston error caused by the presence of atmospheric turbulence in the measurements of curvature, and present a new algorithm for obtaining the local piston using the curvature sensor. A phase-wrapping effect is shown as responsible for the loss of curvature information and so the piston errors can no longer adequately be mapped; this happens not only in the presence of atmospheric turbulence, but also in its absence.
Good results are obtained using a new iterative method for obtaining the local piston error map. In the presence of atmospheric perturbation, the turbulent phase information obtained from a Shack–Hartmann sensor is introduced in our new iterative method. We propose a hybrid sensor composed of a curvature sensor and a Shack–Hartmann sensor, in order to complete all the information for the phasing. This design takes a short computation time and could be used in real time inside an adaptive optics system, where tilt and piston errors must be corrected.     

A new algorithm for the Lie transformation

Following Hori, the Lie transformation is presented in a form that is independent of any extraneous parameters. The transformation is canonical, and its inverse is obtained by changing the sign of the generating function. The introduction of a small parameter into the generating function and the Hamiltonian then yields a recursive, triangular algorithm. The case of a Hamiltonian containing the time explicitly is included by adjoining an additional pair of conjugate variables. The necessary and sufficient condition that this transformation be identical to Deprit's transformation is given as a recursive relation between successive terms in the generating functions. Explicit formulas are obtained through the sixth order.After submitting the present paper the author learned of similar and independent work by Campbell and Jefferys and by Kamel (Ph.D. thesis).     

截短后平衡的扩频码搜索方法

为了能够高效地找出平衡的扩频码(平衡性的扩频码有较好地抑制载波的性能),研究了一种不交叠平衡性扩频码字的搜索方法。在这种方法中,首先生成母码,然后计算、查找平衡不交叠的子码。该方法在计算平衡码时与其它方法有相同的时间复杂度。计算机仿真表明,该母码生成方法较为高效。在采用分割方法后,搜索过程得到了进一步的优化。