斜程大气传输光束孔径平滑到达角与像点起伏

像面到达角起伏、波面抖动和像点抖动通常是研究大气干扰情况下高分辨成像系统波前特性的重要方法之一。采用Rytov近似、包含湍流内外尺度影响的修正von Karmam近似谱和接收光学系统孔径滤波函数和传输权重函数中的Airy函数的高斯函数近似,研究了斜程湍流大气中传输束状波的波面抖动、像面到达角起伏和像点抖动规律,导出了圆孔接收系统测量到的包含湍流内外尺度影响的束状波孔径平滑波面抖动、像点抖动和像面到达角方差理论模型。     

湍流大气中传输光波的波相位结构解析函数

在湍流大气对传输光波调制的双尺度湍涡(大尺度湍涡和小尺度湍涡)近似下,研究了用于计算描述湍流大气中传输光波相干长度变化的核心函数(互相干函数)的关键因子波结构函数(WSF),通过建立包含不同尺度湍流因子的折射率起伏谱密度函数,导出了可以用于精确理论分析平面波与球面波在湍流大气中传播时所产生的诸如到达角起伏和相干性变化等效应的波相位结构函数的精确解析式,同时给出了便于数值计算的近似误差在2%范围以内的波相位结构函数的精确渐近表达式。     

湍流变化对多孔径光学系统成像特性的影响

为了研究大气湍流变化对多孔径光学系统成像质量的影响,针对Golay3结构建立了一个理论分析模型,推导了湍流影响下望远系统的点扩散函数（point spread function, PSF）的表达式。分别针对近似圆形和近似长条状分布的湍流结构对成像特性的影响进行了讨论,具体构建了两种湍流影响下的光场相位计算模型,并计算比较了两种湍流的调制传递函数（modulation transfer function, MTF）。结果表明,光路中存在湍流将导致系统成像质量下降。在近似圆形湍流中,湍流强度越小,系统MTF影响越小。不同强度湍流影响的MTF在归一化空间频率0.16、0.45和0.69处均下降0.05左右。在近似长条状湍流中,对流湍流风速越小,系统MTF影响越小。不同风速的湍流影响的MTF在空间频率0.16、0.42和0.69处分别下降0.25、0.09和0.05左右。比较两种湍流表明,近似长条状湍流对成像系统MTF影响更为明显。     

湍流尺度对高斯谢尔光束闪烁孔径平滑的影响

通过运用包含湍流内、外尺度因子的调制折射谱和波场交叉谱密度函数的互相干函数近似,研究了大气湍流内、外尺度对高斯谢尔光束闪烁孔径平滑的影响,得出了弱大气湍流起伏环境下包含大气湍流外尺度因素的高斯谢尔光束闪烁孔径平滑因子。结果表明,随着湍流外尺度的减小,孔径对高斯谢尔光束的大气闪烁平滑作用减小,湍流外尺度对不相干光闪烁孔径平滑作用的影响可以忽略。     

湍流大气中空间部分相干奇异光波的传输

自由空间中带有光学涡的部分相干光的传输特性是影响大气光通信系统性能的关键因子之一.基于弱湍流大气中光波传输的Rytoy方法和部分相干光的互相干函数的交叉谱密度函数近似,研究了带有"光学涡"的空间部分相干拉盖尔一高斯光束在湍流大气中的传输特性,得出了弱湍流大气中传输的部分相干光束互相干函数和平均光强空间分布的解析关系.研究结果表明,弱湍流大气起伏仅仅影响这类光束相干函数的幅值,不改变光束光学涡的分布特征.     

湍流介质中光像抖动的频率相关

本文运用“马尔柯夫近似”获得了光在湍流大气中传输时,接收系统焦面上像斑抖动频率相关函数的一般关系式和弱光束湍流扩展区域内像斑抖动频率相关函数的解析式,同时讨论了光像抖动与光源波长的相关问题.     

斜程大气传输激光束的平均光强与短期光束扩展

基于广义惠更斯-菲涅耳原理、修正von Karman 湍谱、贝塞耳权重函数的高斯函数近似和误差小于4%的波结构函数平方近似,研究得出了包含湍流尺度影响的湍流大气中传输高斯光束的平均光强新关系和包含湍流外尺度影响的光束短期扩展因子。研究了高斯光束等效半径与传输距离、初始光束束径和光波波长间的关系,结果表明,在给定折射率结构参量和传输距离情况下,存在极小短期光束扩展对应的特征初始束径和特征光波波长。     

长曝光大气湍流退化图像点扩散函数估计

大气湍流能明显降低光学系统的成像质量,距离目标越远,曝光时间越长,受大气扰动越严重,图像越模糊。利用大气湍流退化点扩散函数可以对模糊图像进行复原,但实际自然条件下的点扩散函数往往难以准确获得。结合课题研究背景,针对长曝光大气湍流退化图像复原提出了近似等腰三角形模型,通过该模型能得到准确的大气湍流点扩散函数,并采用维纳滤波获得清晰复原图像。实验表明该方法能够对大视场、远距离条件下获得的长曝光大气湍流退化自然图像估计出准确的点扩散函数,复原图像拥有较好的视觉效果,通过计算灰度平均梯度值和拉普拉斯梯度模两个客观评价标准,进一步证实了该算法的有效性。     

弱湍流大气中Mathieu-Gauss束的传输

采用弱湍流大气光传输的Rytov近似和运用非衍射光束的平面波展开原理,研究并给出了弱湍流大气中Mathieu-Gauss束的场方程和平均光强解析表达式.研究表明:弱湍流大气中传输Mathieu-Gauss束由传输距离z函数的复振幅、高斯束包络、湍流引入的复相位和复标定横向非衍射束型四个因子构成,其归一化轴上平均光强随归一化距离z=z/zR和参量γ=1/2kpwO的变化与此类光束在自由空间传输的规律相同.     

基于激光雷达脉冲特性的湍流风速估计方法

提出了一种基于激光脉冲距离权重函数的湍流风场速度估计的方法,可以解决多普勒信息探测晴空湍流风场中精细化的风速测量问题。算法以划分的距离门为单位对速度值进行空间平均,将各距离单元速度与激光脉冲距离权重函数进行卷积运算得到风速的局部估计值。并考虑高斯激光脉冲在湍流风场中的有效空间展宽传输特性,根据直接选取距离门中心位置的速度估计方法和快速的线性平均近似方法的处理过程,引入激光脉冲的传输特性来表达湍流径向风速的统计平均值,以实现湍流风速的测量以及激光雷达在探测湍流上的应用。实验结果表明,在有明显湍流条件的风场环境中,脉冲距离权重方法比线性平均方法在保留真实风场属性的前提下具有相对更小的速度标准差,显示出较好的风速修正效果,提高了激光雷达对湍流风场的测速性能。     

关于前馈多层神经网络多维函数逼近能力的一个定理

本文首次证明了前馈神经网络多维函数逼近能力的一个重要定理:当隐层神经元数目足够多时,其多维函数逼近能力与维数无关.也就是说我们只需研究其一维函数逼近能力,所得的结论完全适合于多维情形,该定理大大简化了前馈多层神经网络函数逼近问题的分析难度。本文还给出了该定理的一个应用。     

A Basis-Function Canonical Piecewise-Linear Approximation

This paper proposes a basis-function canonical piecewise-linear (BF-CPWL) function, which can approximate any continuous function using a weighted sum of PWL BFs. The BF-CPWL approximation integrates Breiman's hinging hyperplane model and Julian's high-level canonical PWL approximation into a common theoretical framework. Moreover, an approximation algorithm is developed, which fits and adds the PWL BFs iteratively using a modified Gauss-Newton method. This algorithm guarantees a local convergence, while achieving a good tradeoff between computational simplicity and approximation accuracy. The BF-CPWL approximation can find applications in nonlinear circuit synthesis, dynamic system identification and control.     

An approximation with poles along the negative real axis of the complex frequency plane

A time domain approximation of the type e^-etis developed and shown to be a rational function of s in the frequency domain. This approximation is considered as a transfer function which may be realized with RC or RL elements. Two examples illustrate the approximation method.     

Complex polynomial phase integration

A previously published integration algorithm applicable to the numerical computation of integrals with rapidly oscillating integrands is generalized. The previous algorithm involved quadratic approximation of the phase function which was assumed to be real. The present generalization concerns approximation of a complex phase function by a polynomial of arbitrary degree. As before, the integrand is then written without approximation as a slowly varying function multiplied by the polynomial phase exponential and the slowly varying factor is approximated by a finite sum of Chebyshev polynomials. The integral is thus expressed as a sum of constituent integrals which are computed recursively via LU decomposition applied to a system of linear equations with a banded coefficients matrix. Examples are presented comparing various degree phase approximants.     

Approximation of multivariable functions by M-D transfer functions with separable denominator

The approximation of a given function by a rational function has been considered extensively by mathematicians. A particular result has been stated by Walsh that the best approximation of a given analytical function is one which interpolates the given function at several properly chosen points. In this paper, transfer functions of multidimensional digital filters with separable denominator are used for the approximation of given multivariate functions. It is shown that the result of Walsh can be generalized in a straightforward manner. By an example it is illustrated how the new result can be applied to, e.g., the order reduction of a higher-order system. In the conclusion we state the usefulness and the limitation of the result.     

Variational image segmentation using boundary functions

A general variational framework for image approximation and segmentation is introduced. By using a continuous "line-process" to represent edge boundaries, it is possible to formulate a variational theory of image segmentation and approximation in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general enough to include the most commonly used objective functions. Application is made to Mumford-Shah type functionals as well as those considered by Geman and others. Employing arbitrary L(p) norms to measure smoothness and approximation allows the user to alternate between a least squares approach and one based on total variation, depending on the needs of a particular image. Since the optimal boundary function that minimizes the associated objective functional for a given approximation function can be found explicitly, the objective functional can be expressed in a reduced form that depends only on the approximating function. From this a partial differential equation (PDE) descent method, aimed at minimizing the objective functional, is derived. The method is fast and produces excellent results as illustrated by a number of real and synthetic image problems.     

一维逆散射中Born近似公式的推广

本文借助于等效网络方法推广了用于重建3chrodinger方程中势函数的Born近似公式,同时还引入有效重建深度的概念,并导出它和势函数的约束关系。这个关系可作为Born近似及其推广和适用条件。     

Interference minimisation by autocorrelation shaping inasynchronous DS-CDMA systems: chaos-based spreading is nearly optimal

The classical estimation of co-channel interference in asynchronous direct sequence-code division multiple access (DS-CDMA) systems, obtained for a conventional receiver under the standard Gaussian approximation (SGA), is analytically minimised with respect to the auto-correlation function of spreading sequences. The optimum auto-correlation function is found to be real, with alternating signs, and extremely closely follows an exponential trend. A family of chaotic maps is presented which is able to generate sequences with exponential auto-correlation function with alternating signs. The resulting DS-CDMA system is an extremely good approximation of the optimum achievable system     

The circular homogeneous-ferrite microwave circulator - an asymptotic Green's function and impedance analysis

A detailed analysis of the circular, homogeneous ferrite microwave circulator is provided. Particular emphasis is on the circulator's Green's function and the impact of the asymptotic term within the Green's function on convergence, data quality, and design methodology. The asymptotic term is shown to be logarithmic, which suggests that the Green's function is weakly singular when the source and observation points occupy the same location. With the Green's function properly understood, two techniques - one analytical and one numerical - are then offered to integrate that function in order to obtain Z-parameter data and, subsequently, S-parameter data. Data are provided to show rapid convergence of all parameters of interest. A small coupling angle approximation is then given for the Z-parameters and, from that approximation, a first-order design equation is obtained that relates the coupling angle to circulator radius. A circulator design example is presented and compared to a design associated with the Wu and Rosenbaum method; the comparison substantiates the small coupling angle approximation and design formula.