Radar cross sections of a random medium layer

Abstract

Analytic expressions are derived for the normalized radar cross sections (NRCS) of a random medium layer. These are calculated from the first-order solutions for diffuse intensities which are based on a multiple-scattering wave theoretical analysis. The permittivity fluctuations are assumed to be small and to obey stationary Gaussian statistics. On studying the expressions for the NRCS, some of their characteristics are pointed out. Three different correlation functions are considered and expressions for the coherent propagation constants are provided. Numerical examples are used to verify theoretical results and highlight some interesting characteristics of NRCS.     

Numerical study of electromagnetic scattering from one-dimensional nonlinear fractal sea surface

In recent years, linear fractal sea surface models have been developed for the sea surface in order to establish an electromagnetic backscattering model. Unfortunately, the sea surface is always nonlinear, particularly at high sea states. We present a nonlinear fractal sea surface model and derive an electromagnetic backscattering model. Using this model, we numerically calculate the normalized radar cross section (NRCS) of a nonlinear sea surface. Comparing the averaged NRCS between linear and nonlinear fractal models, we show that the NRCS of a linear fractal sea surface underestimates the NRCS of the real sea surface, especially for sea states with high fractal dimensions, and for dominant ocean surface gravity waves that are either very short or extremely long.     

Application of the Tikhonov regularization method to wind retrieval from scatterometer data I. Sensitivity analysis and simulation experiments

Scatterometer is an instrument which provides all-day and large-scale wind field information, and its application especially to wind retrieval always attracts meteorologists. Certain reasons cause large direction error, so it is important to find where the error mainly comes. Does it mainly result from the background field, the normalized radar cross-section (NRCS) or the method of wind retrieval? It is valuable to research. First, depending on SDP2.0, the simulated `true' NRCS is calculated from the simulated 'true' wind through the geophysical model function NSCAT2. The simulated background field is configured by adding a noise to the simulated 'true' wind with the non-divergence constraint. Also, the simulated 'measured' NRCS is formed by adding a noise to the simulated 'true' NRCS. Then, the sensitivity experiments are taken, and the new method of regularization is used to improve the ambiguity removal with simulation experiments. The results show that the accuracy of wind retrieval is more sensitive to the noise in the background than in the measured NRCS; compared with the two-dimensional variational (2DVAR) ambiguity removal method, the accuracy of wind retrieval can be improved with the new method of Tikhonov regularization through choosing an appropriate regularization parameter, especially for the case of large error in the background. The work will provide important information and a new method for the wind retrieval with real data.     

Electromagnetic backscattering from freak waves in(1+1)-dimensional deep-water

To study the electromagnetic (EM) backscatter characteristics of freak waves at moderate incidence angles, we establish an EM backscattering model for freak waves in (1+1)-dimensional deep water. The nonlinear interaction between freak waves and Bragg short waves is considered to be the basic hydrodynamic spectra modulation mechanism in the model. Numerical results suggest that the EM backscattering intensities of freak waves are less than those from the background sea surface at moderate incidence angles. The normalised radar cross sections (NRCSs) from freak waves are highly polarisation dependent, even at low incidence angles, which is different from the situation for normal sea waves; moreover, the NRCS of freak waves is more polarisation dependent than the background sea surface. NRCS discrepancies between freak waves and the background sea surface with using horizontal transmitting horizomtal (HH) polarisation are larger than those with using vertical transmitting vertical (VV) polarisation, at moderate incident angles. NRCS discrepancies between freak waves and background sea surface decreases with the increase of incidence angle, in both HH and VV polarisation radars. As an application, in the synthetic-aperture radar (SAR) imaging of freak waves, we suggest that freak waves should have extremely low backscatter NRCSs for the freak wave facet with the strongest slope. Compared with the background sea surface, the freak waves should be darker in HH polarisation echo images than in VV echo images, in SAR images. Freak waves can be more easily detected from the background sea surface in HH polarisation images than in VV polarisation images. The possibility of detection of freak waves at low incidence angles is much higher than at high incidence angles.     

Probabilistic characteristics of signal detection by a spatial correlation filter

Results of theoretical and model studies of the probabilistic characteristics of signal detection by a spatial correlation filter are described. A mathematical model of signal processing in the spatial correlation filter is presented. Expressions for estimating the detection probability, missed detection probability, false alarm probability, and threshold level, as well as expressions for choosing the optimal filter parameters to obtain preset probability characteristics, are derived on the basis of this model. Results of computer simulation of the probabilistic characteristics of signal detection by spatial correlation filters with random arrays are shown to corroborate the theoretical findings obtained within the model.     

Introduction to imaging from scattered fields

In the context of electromagnetic wave backscattering from ocean-like surfaces, by using the lowest order of the SSA (SSA-1) model, Bourlier et al. proposed an original technique to reduce the number of numerical integrations to two for easier numerical implementation. To be consistent with microwave measurements, closed-form expressions of the Fourier coefficients with respect to the wind direction of the backscattering normalized radar cross-section (NRCS) are obtained. For Gaussian statistics, previous work is extended in this paper to kernels of unified models expanded up to second order, like full SSA and full LCA. Thus, with the help of Bessel functions and by analytical integrations over the azimuthal angles, the second-order backscattering (BNRCS) is expressed in terms of two-fold integrations and another independent integration instead of four-fold integrations, if no analytical integration is made. This approach allows us to obtain fast results (less than one second). Numerical results are then presented for different microwave frequencies and wind speeds.     

The weighted curvature approximation in scattering from sea surfaces

A family of unified models in scattering from rough surfaces is based on local corrections of the tangent plane approximation through higher-order derivatives of the surface. We revisit these methods in a common framework when the correction is limited to the curvature, that is essentially the second-order derivative. The resulting expression is formally identical to the weighted curvature approximation, with several admissible kernels, however. For sea surfaces under the Gaussian assumption, we show that the weighted curvature approximation reduces to a universal and simple expression for the off-specular normalized radar cross-section (NRCS), regardless of the chosen kernel. The formula involves merely the sum of the NRCS in the classical Kirchhoff approximation and the NRCS in the small perturbation method, except that the Bragg kernel in the latter has to be replaced by the difference of a Bragg and a Kirchhoff kernel. This result is consistently compared with the resonant curvature approximation. Some numerical comparisons with the method of moments and other classical approximate methods are performed at various bands and sea states. For the copolarized components, the weighted curvature approximation is found numerically very close to the cut-off invariant two-scale model, while bringing substantial improvement to both the Kirchhoff and small-slope approximation. However, the model is unable to predict cross-polarization in the plane of incidence. The simplicity of the formulation opens new perspectives in sea state inversion from remote sensing data.     

Universal LCAO parameters for III–V compound semiconductors

A set of semi-empirical expressions for the two-center integrals which enter the Slater-Koster parameters are constructed for Group III–V compound semiconductors These expressions show their explicit dependence on the atomic characteristics, on the dielectric constant, on the lomcity of solids, and also on the interatomic separations, and they are valid for atomic separations as far as second-neighbor distances For zero ionicity they reduce to those obtained previously by us for Group IV semiconductors The Slater-Koster parameters are then constructed from these expressions for the two-center integrals The band structures of various gallium and indium compounds are obtained and are compared with other theoretical calculations and with experimental photoemission results     

Probability distributions of the fractional differences of the structure amplitudes and intensities of two related crystals

The probability distributions of the fractional intensities and amplitudes of x-ray reflections from a pair of imperfectly related structures are derived when both the structures satisfy the requirements of a given type of basic Wilson distribution. These two distributions are used to obtain theoretical expressions for 2 new fractional type ofR-indices which are expected to be useful in the final stages of refinement. The theoretical distributions are also used to deduce some theoretical distributions which are useful as tests for centrosymmetry via the random permutation method. The theoretical values of the relevant semi-cumulative functions are also tabulated.     

Application of the temperature distribution formula for the photoacoustic investigations of layer systems

This paper presents results of theoretical investigations of layer structures of the type: a thin semitransparent layer on the thick semitransparent substrate. Considerations presented in the paper comprise a derivation of the analytical expressions for the spatial distributions of the instantaneous temperature in the surface layer and the thermally semi infinitive substrate. These analytical expressions are of great importance as they enable computations of both frequency and spectral photoacoustic characteristics of several layer systems.     

阶梯槽交错双栅慢波结构高频特性理论和模拟

本文基于一种阶梯槽交错双栅周期慢波结构模型,获得了该结构中的电磁场分布公式.通过场匹配方法,求出了该结构的高频色散方程和耦合阻抗表达式.以W波段行波管用的阶梯槽交错双栅为例,利用本文公式和CST-MWS电磁软件比较计算了色散和耦合阻抗特性,分析了阶梯尺寸参数对高频特性(基模色散、+1次空间谐波归一化相速和耦合阻抗)的影响.结果表明,理论和CST-MWS软件模拟有很好的一致性;相对矩形交错双栅,改善了色散特性,拓展了基模带宽,同时具有足够大的耦合阻抗和适合工程应用的机械强度,在一定程度上可以弥补矩形交错双栅周期慢波结构的不足.     

Photon time-interval statistics of laser light scattered by brownian particles

Measurements are reported and some theoretical expressions are given for half-open photon time-interval statistics of laser light scattered by particles in brownian motion. Expressions in terms of cumulants are shown not to be valid in general.     

Correct determination of net gain in Er-doped optical waveguide amplifier from pump-on/off measurement

Starting with evolution equation of signal optical power in an Er-doped channel waveguide, rigorous theoretical expressions used for correct determination of net gain from signal enhancement measured by using pump-on/off method are derived. These expressions allow to clarify the argument on relationships between net gain, internal gain and signal enhancement in some earlier literatures. Physical implications of net gain, internal gain and signal enhancement expressions are analyzed. Standardized definitions for the three physical quantities are proposed. The definition for net gain is proposed on the basis of practical application of an EDWA in optical fiber communication and the definitions for the latter two are suggested based on the physical implication analysis of their expressions.     

周期场透镜的成象特性

由三个或五个透镜元素组成的周期场,可以作为离子透镜使离子束成象。通常它具有比单个透镜元素强得多的聚焦能力(在相同的电压比下)。这种周期场透镜曾用于静电加速器离子源初聚系统中,但它的成象特性尚未有详细的分析。本文提出一种研究这类透镜特性的方法。将周期场看作由若干个透镜元素合成的组合透镜,然后以Ferraris特征行列式求它的基点表示式。作为普遍情况,以浸没透镜作为透镜元素,导得了三个和五个透镜元素的周期场透镜基点表示式。式中只包含透镜元素的基点参量和电极系统的几何参量。式子十分简洁,便于计算,并有足够的精确度。通过解析表示式中各个因子的分析,可以方便地掌握透镜的特性。由短磁透镜组合的周期磁场是上述普遍情况的一个特例。文中以等径小间隙双圆筒透镜为浸没透镜元素,对周期场透镜的特性用导得的基点表示式进行了计算和分析。     

无源谐振腔激光陀螺中的闭锁效应

从谐振腔的谐振特性出发，严格地推导出无源谐振腔激光陀螺中由腔镜背散射引起的闭锁效应关系式及闭锁阈值表达式。实验观察结果证实了理论推导的正确性。     

A simplified asymptotic theory for ocean surface electromagnetic wave scattering

The normalized radar cross-section (NRCS) expression of the Local Curvature Approximation (LCA-1) is derived to first order. The polarization sensitivity of this model is compared to the Kirchhoff Approximation (KA), Two-Scale Model (TSM), Small Slope Approximation (SSA-1) and Small Perturbation Method (SPM-1) to first order in the backscattering configuration. Analytical comparisons and numerical simulations show that LCA-1 and TSM could be rewritten with the same formulation and that their polarization sensitivities are comparable. Comparisons with experimental data acquired in C- and Ku-band reveal that the polarization sensitivities of these models are not adequate. However, the NRCS azimuth modulation predicted by LCA-1 is found to be dependent on polarization and sea surface roughness. This property of the LCA-1 model yields to an azimuth modulation for the polarization ratio. Based on the surface curvature correction concept, a simplified electromagnetic model is proposed. The curvature correction is restricted to the resonant wave-number of the sea roughness spectrum. This is found to reproduce the polarization ratio given by experimental data versus incidence angle and wind speed.     

A unified study on the output probability distribution of arbitrary linear vibratory systems with arbitrary random excitation

New theoretical expressions of probability density and cumulative distribution functions for the output response are exactly derived without any simplification of the problem and any approximation of analysis in the case when a general random signal with arbitrary probability distribution and correlation functions is passed through an arbitrary linear vibratory system with finite order. The result is given as an explicit solution of expansion series in a functional form of input statistics and vibratory system parameters, and not given as a mere numerical solution by use of a recurrence algorithm. An effect of random input and system characteristics is concretely reflected in the expansion coefficients. The experimental results obtained by digital simulation are in good agreement with the theory. Thus, the above theory is experimentally confirmed for some typical examples by the method of digital simulation.     

A bow-tie shaped optical fiber loop and ring with double couplers

A theoretical study of a bow-tie shaped optical fiber loop and a ring with double couplers is carried out. The expressions for the circulating (resonant) intensity and the two output (reflected and transmitted) intensities are derived and the computed results are presented as graphs. The special characteristics, advantages, and possible applications of this type of fiber loop and ring, in comparison with other types, are discussed.     

A bow-tie shaped optical fiber loop and ring with double couplers

A theoretical study of a bow-tie shaped optical fiber loop and a ring with double couplers is carried out. The expressions for the circulating (resonant) intensity and the two output (reflected and transmitted) intensities are derived and the computed results are presented as graphs. The special characteristics, advantages, and possible applications of this type of fiber loop and ring, in comparison with other types, are discussed.     

双近贴聚焦微光像增强器分辨力理论极限问题研究

分辨力和MTF是微光像增强器的2个重要参数。根据线性系统傅里叶频谱理论,分析了微光像增强器的MTF和分辨力特性。 计算出理想条件下,基于光阴极/MCP/荧光屏3部件结构以及带内电子增益机制的光阴极/荧光屏2部件结构的近贴聚焦像管的理论极限分辨力。它们分别是96.6lp/mm和98.1lp/mm。该结果可供人们改进像管MTF及分辨力特性时参考。