Monostatic and bistatic statistical shadowing functions from a one-dimensional stationary randomly rough surface: II. Multiple scattering

The integral equation model (IEM) has been developed over the last decade and it has become one of the most widely used theoretical models for rough-surface scattering in microwave remote sensing. In the IEM model the shadowing function is typically either omitted or a form based on geometric optics with single reflection is used. In this paper, a shadowing function for one-dimensional rough surfaces which incorporates multiple scattering, finite surface length and both monostatic and bistatic configurations is developed. For any uncorrelated process, the resulting equation can be expressed in terms of the monostatic statistical shadowing function with single reflection, derived in the preceding companion paper. The effect of correlation between the surface slopes and heights for a Gaussian surface is studied to illuminate the range over which such correlations can be ignored. It is found that while the correlation between surface slopes and heights in the monostatic statistical shadowing function with single reflection can be ignored, when calculating the average shadowing function with double reflection the correlation between slopes and heights between points must be incorporated.     

Monostatic and bistatic statistical shadowing functions from a one-dimensional stationary randomly rough surface: II. Multiple scattering

Abstract

The integral equation model (IEM) has been developed over the last decade and it has become one of the most widely used theoretical models for rough-surface scattering in microwave remote sensing. In the IEM model the shadowing function is typically either omitted or a form based on geometric optics with single reflection is used. In this paper, a shadowing function for one-dimensional rough surfaces which incorporates multiple scattering, finite surface length and both monostatic and bistatic configurations is developed. For any uncorrelated process, the resulting equation can be expressed in terms of the monostatic statistical shadowing function with single reflection, derived in the preceding companion paper. The effect of correlation between the surface slopes and heights for a Gaussian surface is studied to illuminate the range over which such correlations can be ignored. It is found that while the correlation between surface slopes and heights in the monostatic statistical shadowing function with single reflection can be ignored, when calculating the average shadowing function with double reflection the correlation between slopes and heights between points must be incorporated.     

Theorems on symmetries and flux conservation in radiative transfer using the matrix operator theory

The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.     

基于微面斜率法的粗糙表面半透明介质层光谱散射特性分析

对具有一维高斯分布粗糙表面的半透明介质层光谱散射,基于微面斜率法建立了考虑遮蔽效应的粗糙表面光谱辐射传递概率模型,采用蒙特卡罗法模拟光谱辐射能束在粗糙表面、半透明介质层介质与镜反射基底之间的多次反射、折射和吸收等传递过程。通过数值模拟,分析了介质层表面粗糙度、光谱光学厚度、折射率和基底反射率对介质层双向反射分布函数(BRDF)的影响。结果表明,表面粗糙程度不同时,反射峰值随入射角度呈现不同的变化趋势;表面粗糙度增加或折射率增大都将导致漫反射份额增大;介质层光谱光学厚度和基底反射率主要影响BRDF的数值大小,而对BRDF的分布形态影响很小。     

光纤光栅法布里-珀罗腔中受激布里渊散射的理论研究

对光纤光栅法布里-珀罗腔中稳态受激布里渊散射模型进行了理论分析,在其耦合强度方程组基础上,推导出仅产生一阶斯托克斯波时,耦合强度方程组的解析表达式,由此计算出光纤光栅法布里-珀罗腔中抽运波与斯托克斯波透射功率和反射功率。对于光纤光栅法布里-珀罗腔中二阶斯托克斯波的产生,推导出光纤光栅法布里-珀罗腔入射端抽运波的解析表达式和忽略光纤损耗时能量守恒方程,利用Shooting和L-M算法数值求解出耦合强度方程组。分析讨论了抽运波,一阶斯托克斯波和二阶斯托克斯波的反射与透射功率随着入射波功率变化的情况。最后,仿真出光纤光栅法布里-珀罗腔中,抽运波与斯托克斯波沿腔长分布的情况。     

Bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase and scalar approximation with shadowing effect: comparisons with experiments and application to the sea surface

In this paper, the bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase method and scalar approximation with shadowing effect is investigated. Both of these approaches use the Kirchhoff integral. With the stationary phase, the bistatic cross section is formulated in terms of the surface height joint characteristic function where the shadowing effect is investigated. In the case of the scalar approximation, the scattering function is computed from the previous characteristic function and in terms of expected values for the integrations over the slopes, where the shadowing effect is analysed analytically. Both of these formulations are compared with experimental data obtained from a Gaussian one-dimensional randomly rough perfectly-conducting surface. With the stationary-phase method, the results are applied to a two-dimensional sea surface.     

Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system

Transfer of solar radiation in the combined atmosphere and ocean system is evaluated by the matrix operator method. Derivation of the reflection and transmission matrices required for applying the matrix method is discussed introducing the shadowing effect of light by the ocean waves. Spectral and total radiation fields just above and below the ocean surface, as well as the top of the atmosphere, are numerically calculated using several optical models of the atmosphere, ocean, and wind roughened ocean surface. Dependencies of radiance and flux reflectivity on the wind velocity and optical property of the ocean body are discussed in detail.     

Bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase and scalar approximation with shadowing effect: comparisons with experiments and application to the sea surface

Abstract

In this paper, the bistatic scattering coefficient from one- and two-dimensional random surfaces using the stationary phase method and scalar approximation with shadowing effect is investigated. Both of these approaches use the Kirchhoff integral. With the stationary phase, the bistatic cross section is formulated in terms of the surface height joint characteristic function where the shadowing effect is investigated. In the case of the scalar approximation, the scattering function is computed from the previous characteristic function and in terms of expected values for the integrations over the slopes, where the shadowing effect is analysed analytically. Both of these formulations are compared with experimental data obtained from a Gaussian one-dimensional randomly rough perfectly-conducting surface. With the stationary-phase method, the results are applied to a two-dimensional sea surface.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

负梯度水文环境下海山对声传播的影响

利用一次南海海山环境下的声传播实验数据,研究了负梯度水文环境下海底山对声传播的影响。针对实验数据中的传播损失异常,从射线声学角度给出了合理的解释,表明海底山的存在引起传播损失在距离上剧烈波动。在距离接收阵较近的7.6 km处,声源位于海山斜坡上,斜坡的反射使接收传播损失减小约8 dB,体现出斜坡增强特征。当声源位于海山后,海底山的遮蔽作用使23.8 km处的传播损失增加超过20 dB,不同位置处海山遮蔽效应的差异使传播损失随距离起伏。利用抛物模型对实验环境下的声传播进行了定量仿真,仿真传播损失同实验结果符合,验证了实验数据中海底山的反射和遮蔽作用。此外,对实验环境下海山的遮蔽损失进行分析,发现在不同声源位置处,海山遮蔽损失在特定频带上同频率对数具有线性关系。      

Coherent transmission and reflection of a two-dimensional planar photonic crystal

A method for modeling the radial distribution function for particles of a two-dimensional planar photonic crystal in the form of a monolayer of spatially ordered monodisperse spherical particles is proposed. The coherent transmission and reflection coefficients for layers under normal illumination are calculated in the quasi-crystalline approximation of the multiple wave scattering theory. The dependence of the coherent transmission and reflection of the layer on the degree of ordering of the spherical particles is investigated. The influence of the long-range order on the coherent transmission and reflection coefficients for layers with triangular, square, and hexagonal lattices is estimated. Monolayers of weakly absorbing dielectric and strongly absorbing metallic particles are considered.     

Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: application to the backscattering coefficient for a perfectly-conducting surface

Abstract

In this paper, the backscattering coefficient of a two-dimensional randomly rough perfectly-conducting surface is investigated using the Kirchhoff approach with a shadowing function. The rough surface height/slope correlations assumed to be Gaussian are accounted for in this analysis. The scattering coefficient is then formulated in terms of a characteristic function for the integrations over the surface heights, in terms of expected values for the integrations over the surface slopes. Numerical comparisons of Kirchhoff's approach (KA) with the stationary-phase (SP) approximation are made with respect to the choice of the one-dimensional surface height autocorrelation function and the shadowing effect. For an isotropic surface the results show that SP underestimated the incoherent backscattering coefficient compared with KA. Moreover, when the correlation between the slopes and the heights is neglected, the shadowing effect may be ignored.     

基于随机表面微面元理论的二向反射分布函数几何衰减因子修正

现有几何光学方法的二向反射分布函数BRDF (bidirectional reflection distribution function)模型在计算阴影遮蔽效应时普遍应用Blinn几何衰减效应假设, 其等倾角V形槽近似得出的分段折线形式的几何衰减因子导致BRDF曲线存在较大的误差. 基于倾斜角随机高斯分布的微面元理论提出了一种新的几何衰减模型, 得出了积分形式的几何衰减因子表达式, 数值模拟比较了Blinn几何衰减因子与修正后的积分型衰减因子以及对应的BRDF模型曲线. 结果表明: 提出的几何衰减因子在物理合理性以及模拟精度方面都有明显提升, 使BRDF模型曲线与已有BRDF 数据之间的标准误差由0.0636减小到0.0084.     

The reflection and transmission group delay times in an asymmetric single quantum barrier

The reflection and transmission group delay times are systematically investigated in an asymmetric single quantum barrier. It is reported that the reflection times in both evanescent and propagating cases can be either negative or positive, depending on the relative height of the potential energies on the two sides of the barrier. In the evanescent case where the energy of incident particles is less than the height of the barrier, the reflection and transmission times in the opaque limit are both independent of the barrier’s thickness, showing superluminality. On the other hand, in the propagating case where the energy of incident particles is larger than the height of the barrier, the reflection and transmission times as the periodical function of the barrier’s thickness can be greatly enhanced by the transmission resonance. It is also shown that the transmission time and the reflection times for the two propagation directions in the same asymmetric configuration satisfy the reciprocal relation, as consequence of time reversal invariance in quantum mechanics. These phenomena may lead to novel applications in electronic devices.     

A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface

We report on an exact vector (polarized) radiative transfer (VRT) model for coupled atmosphere and ocean systems. This VRT model is based on the successive order of scattering (SOS) method, which virtually takes all the multiple scattering processes into account, including atmospheric scattering, oceanic scattering, reflection and transmission through the rough ocean surface. The isotropic Cox–Munk wave model is used to derive the ref and transmission matrices for the rough ocean surface. Shadowing effects are included by the shadowing function. We validated the SOS results by comparing them with those calculated by two independent codes based on the doubling/adding and Monte Carlo methods. Two error analyses related to the ocean color remote sensing are performed in the coupled atmosphere and ocean systems. One is the scalar error caused by ignoring the polarization in the whole system. The other is the error introduced by ignoring the polarization of the light transmitted through the ocean interface. Both errors are significant for the cases studied. This code fits for the next generation of ocean color study because it converges fast for absorbing medium as, for instance, ocean.     

风驱粗糙海面背景下海雾对可见和红外光多次散射特性研究

通过测量空间辐射反演海雾气溶胶的微观特性是一种重要的遥感方法,但是海雾对辐射的反射会受到海面背景的影响。该工作研究了海雾与海面的耦合多次散射。利用Mie理论研究了海雾气溶胶的单次散射特性,利用辐射传输理论研究太阳光在无下垫面海雾中传输多次散射特性;在基尔霍夫近似下研究了风驱粗糙海面的散射特性,并考虑了海面的遮蔽效应,得到了风驱海面随风速的反射函数。根据累加法研究了海雾和海面的耦合散射,计算结果表明海雾在有粗糙海面作为背景的情况下,其整体反射有较大增强。     

Propagation of light in a structure with a regular magnetic inhomogeneity

The reflection and transmission of a light wave normally incident on a layer with a regular magnetic inhomogeneity described by a harmonic function are investigated. Solutions to the Maxwell equations for such a medium and the Jones matrices determining the magneto-optical characteristics of the structure under consideration (the coefficients of transmission and reflection and the degrees of polarization of transmitted and reflected waves) are obtained.     

Conservation laws and angular transverse shifts of the reflected and transmitted light beams

The relation between the angular transverse shifts of the beams reflected and transmitted at a plane interface of two isotropic transparent media is established. The derivation of this relation is based on the conservation law of the transverse component of the total Minkowski linear momentum, which takes place in the processes of the reflection and transmission of wave packets.     

基于多重散射的卷云辐射传输特性

采用空间离散化,并利用散射矩阵方法计算了卷云在3．72tim和6．85tim波长上的辐射传输特性,研究了卷云的冰晶粒子形状、组分和光学厚度等因素对卷云的辐射传榆特性的影响。仿真结果表明,随着平均冰晶尺度的增加,卷云的反射函数会逐渐减小;对于不同形状,但具有相同最大粒子尺寸的粒子组成的卷云,反射函数也会有所不同;随着光学厚度的增加,卷云的反射函数会逐渐增大,直至饱和,而透射函数逐渐减小;随着太阳天顶角的增大,卷云的反射函数逐渐增大。透射函数逐渐减小。     

On the theory of X-ray coherent reflection from a rough surface

A solution of the problem of X-ray specular reflection from a statistically rough surface is presented. It is based on using the Green function formalism. The Kirchhoff formula is used to describe the transmission of the wave field through a rough interface. Generally, microscopically exact expressions for the coefficients of transmission through a rough surface and reflection from it are obtained by taking multiple scattering effects into account. Averaging of the obtained expressions over possible realizations of random roughness of the interface between media allows to obtain rigorous expressions for specular reflection and transmission coefficients. The behavior of exact solutions in the limiting case of infinite correlation lengths is studied. It is shown that, in this case, the obtained solution corresponds to the Debye-Waller normalization. Expressions for the reflection and transmission coefficients making it possible to carry out numerical calculations are obtained in the Bourret approximation of multiple-scattering theory.