On the problem of the doppler spectrum of a microwave radar signal backscattered by the sea surface (transition region and bragg component)

We consider the problem of backscattering of a microwave radar signal by a perturbed water surface in the transition region of incidence angles (10°–25°). A theoretical model of the Doppler spectrum for the Bragg component of the reflected field is constructed within the framework of a two-scale model of the surface. Allowance for the large-scale component of waves indicates that the standard formulation of resonance scattering becomes invalid for small incidence angles. Large-scale waves restrict the power increase of the reflected signal prior to violation of the formal conditions for perturbation method applicability. It is shown that the new model is transformed to the known model of Doppler spectrum in the range of medium angles. Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 6, pp. 669–681, June, 1997.     

Correlation of Bragg scattering from the sea surface at different polarizations

The phase interference fading in Bragg backscattering from the sea surface at moderate incidence angles is considered using both moment method calculation of the scattering from measured water profiles and an implementation of the slightly rough, tilted facet model. The fading of the instantaneous scattering cross-section is shown to be independent of the instantaneous phase of the illuminating signal. The vertical and horizontal polarization fading responses are therefore strongly correlated when identical carrier frequencies and modulations are used at both polarizations since the electromagnetic energy is Bragg resonant with the same small-scale roughness in both cases, independent of whether the polarization channels are phase locked. Instantaneous horizontally polarized Bragg backscattering (HH) exceeding that at vertical polarization (VV) is extremely unlikely in this case. Use of an offset in the frequencies of monochromatic signals used at the two polarizations can lead to reduced correlation between the fading if the illumination footprint length is sufficiently large so that the frequency shift introduces a significant additional phase shift between the scattering from the leading and trailing edges of the footprint. The fading shows only a very weak correlation when this phase shift exceeds 400°. HH Bragg backscattering exceeding VV will be much more common under these specialized conditions.     

Radar backscattering from Gerstner's sea surface wave

In the framework of a two-scale scattering model, radar backscattering from the rough sea surface was considered. The sea surface was modelled as a superposition of a nonlinear, large-scale Gerstner's wave and small-scale resonant Bragg scattering ripples. The zero-order diffracted field was found by a geometrical optics approach, with shadowing taken into account, and by an 'exact' solution of the diffraction problem obtained numerically. For vertical and horizontal polarizations, the spatial distribution of specific scattering cross sections along the large-scale wave was obtained. The spatially averaged specific backscattering cross sections, as well as the mean Doppler frequency shifts at both polarizations, obtained by the geometrical optics approach are compared with those obtained by using the 'exact' solution of the large-scale diffraction problem. The roles of shadowing and multiple wave scattering processes are discussed, and qualitative explanations of the difference between these two approaches are given.     

双尺度动态分形粗糙海面的电磁散射及多普勒谱研究

利用更为符合海面实际散射场计算的双尺度法分析并计算了一维动态分形粗糙海面的后向散射截面，同时与微扰法有关结果进行了比较.研究了动态分形海面后向散射信号的多普勒谱分形特征，分析了不同极化状态下后向散射截面和多普勒谱谱宽随入射角及分维的变化规律，最后详细讨论了多普勒谱中心频率与海面Bragg谐振频率间的关系. 关键词： 双尺度模型 分形海面 电磁散射 多普勒谱     

Curvature effects in the composite model for low-grazing-angle rough-surface scatter

Abstract

The conventional composite surface model used for calculations of radar backscatter treats a large-scale surface component as an ensemble of tilted flat facets. This approach has limitations for low grazing angles. In the paper we develop a new composite model that takes into account the diffraction of an incident field on a curved, large-scale undulating surface. It is shown that, whereas corrections related to curvature effects are small for a steep incidence, those corrections for low-grazing-angle backscatter can be quite essential. Results of numerical simulations of radar backscattering cross sections for two polarizations are presented. Scattering from a surface with one-dimensionally varying roughness is considered. We have studied the role of undulating surface slopes and curvatures in the behaviour of the polarization ratio and found regimes in which the curvature influence on this ratio is more pronounced.     

Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

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.     

Behaviour of scattering from a rough surface at small grazing angles

The particular problem of wave scattering at low grazing angles is of great interest because of its importance for the long-distance propagation of radio waves along the Earth's surface, radar observation of near surface objects, as well as solving many other fundamental and applied problems of remote sensing. One of the main questions is: how do the scattering amplitude and specific cross section behave for extremely small grazing angles? We consider the process of wave scattering by a statistically rough surface with the Neumann boundary condition. This model corresponds to sound scattering from a perfectly 'hard' surface (for example, the interface between air and the sea surface) or 'vertically' polarized electromagnetic waves scattered by a perfectly conducting one-dimensional (i.e. cylindrical) surface when the magnetic field vector is directed along the generating line of this cylindrical surface. We assume that the surface roughness is sufficiently small (in the sense of the Rayleigh parameter) and the surface is rigorously statistically homogeneous and therefore, infinite. We confine ourselves only to the first-order approximation of small perturbation theory and therefore consider every act of wave scattering in the Born approximation when the Bragg scattering process takes place. Only one resonant Fourier component of surface roughness is responsible for the scattering in a given direction. However, we take into account the attenuation of incident and scattered waves due to the multiple scattering processes on the path 'before' and 'after' a scattering event in a given direction. Also we consider every one of these multiple scattering events only in the Born approximation. The main result we have obtained is that for small grazing angles the scattering cross section of the diffuse component decreases as the second power of the grazing angles with respect to the incident and scattered directions, and as the fourth power of the grazing angle for the backscattering (radar) situation. Generalizing our results from plane-wave scattering to finite beams allows us to obtain the criterion on the beamwidth. For sufficiently narrow beams the multiple scattering processes do not play any role because of a short 'interaction path', and only single Bragg scattering determines the scattering amplitude (which does not tend to zero for small grazing angles). However, for sufficiently wide beams the result obtained for infinite plane waves becomes valid: due to the above-mentioned multiple scattering processes, the scattering amplitude tends to zero for small grazing angles. Consequently, the behaviour of the scattering cross section for small grazing angles depends on the radiation pattern width of the transmitting and receiving antennae: for sufficiently wide beams the scattering cross section decreases to zero at small grazing angles, but for narrow beams it tends to the finite non-zero value.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Microwave sea return at moderate to high incidence angles

Abstract

Bragg scattering is widely recognized as the dominant mechanism by which the ocean surface backscatters microwave radiation, but efforts to identify other, non-Bragg sources of this scattering have been pursued for many years. Non-Bragg backscattering from the sea surface is known to occur at incidence angles close to 0° and 90°. In this paper Bragg scattering is shown to explain most features of sea surface backscatter for incidence angles between about 20° and 80°, except when it predicts very small mean cross sections. The often-quoted evidence for non-Bragg scattering in this incidence angle range is that σ _o (HH) is occasionally found to be larger than or equal to σ _o (VV) for short integration times. We show that because of fading this is not evidence of non-Bragg scattering. For incidence angles up to about 50°, standard Bragg/composite surface scattering theory yields probabilities of finding σ _o (HH)>σ _o (VV) that are only slightly smaller than those found experimentally. As the incidence angle increases, greater differences between theoretical and experimental probabilities are found. The addition of Bragg scattering from bound, tilted waves brings theory into excellent agreement with experiment at incidence angles near 45° but still cannot account adequately for the probability of σ _o (HH)>σ _o (VV) or observed σ _o (HH) cross sections at higher incidence angles. We show that the addition of a small, non-Bragg cross section that is independent of the incidence angle and polarization, brings simulated cross sections and probability distributions into good agreement with data. A possible source of this small, non-Bragg sea return is sea spray just above the air/sea interface.     

Anomalous sea surface reverberation scale model experiments

Low frequency sea surface sound backscattering from approximately 100 Hz to a few kHz observed from the 1960s broadband measurements using explosive charges to the Critical Sea Test measurements conducted in the 1990 s is substantially higher than explained by rough sea surface scattering theory. Alternative theories for explaining this difference range from scattering by bubble plumes/clouds formed by breaking waves to stochastic scattering from fluctuating bubble layers near the sea surface. In each case, theories focus on reverberation in the absence of the large-scale surface wave height fluctuations that are characteristic of a sea that produces bubble clouds and plumes. At shallow grazing angles, shadowing of bubble plumes and clouds caused by surface wave height fluctuations may induce first order changes in the backscattered signal strength. To understand the magnitude of shadowing effects under controlled and repeatable conditions, scale model experiments were performed in a 3 m x 1.5 m x 1.5 m tank at the Technical University of Denmark. The experiments used a 1 MHz transducer as the source and receiver, a computer controlled data acquisition system, a scale model target, and a surface wave generator. The scattered signal strength fluctuations observed at shallow angles are characteristic of the predicted ocean environment. These experiments demonstrate that shadowing has a first order impact on bubble plume and cloud scattering strength and emphasize the usefulness of model scale experiments for studying underwater acoustic events under controlled conditions.     

Study of scattering from turbulence structure generated by propeller with FLUENT

In this article, the turbulence structure generated by a propeller is simulated with the computational fluid dynamics (CFD) software FLUENT. With the method of moments, the backscattering radar cross sections (RCS) of the turbulence structure are calculated. The scattering results can reflect the turbulent intensity of the wave profiles. For the wake turbulence with low rotating speed, the scattering intensity of HH polarization is much smaller than VV polarization at large incident angles. When the turbulence becomes stronger with high rotating speed, the scattering intensity of HH polarization also becomes stronger at large incident angles, which is almost the same with VV polarization. And also, the bistatic scattering of the turbulence structure has the similar situation. These scattering results indicate that the turbulence structure can also give rise to an anomaly compared with traditional sea surface. The study of electromagnetic (EM) scattering from turbulence structure generated by the propeller can help in better understanding of the scattering from different kinds of waves and provide more bases to explain the anomalies of EM scattering from sea surfaces.     

畸形波电磁散射特性分析及其特征识别标识的研究

针对弱非线性的Longuet-Higgins模型在模拟强非线性畸形波海面时所存在的问题,采用修正的相位调制法模拟一维畸形波时间、空间波面,该方法能够实现畸形波的定时定点生成,并且其波形既能保持目标谱的频谱结构,又能较大程度地满足波浪序列的统计特性.同时,基于改进的双尺度(TSM)法及时域有限差分法建立畸形波的电磁散射模型,经过相对平均偏差和均方根偏差误差分析后,基于TSM法研究分析了畸形波及其背景海面波的归一化雷达散射截面(NRCS)的计算结果.实验表明,合成孔径雷达成像中畸形波的NRCS比背景波要小,即畸形波的合成孔径雷达图像成像比背景波要灰暗,因此可以将NRCS作为畸形波的特征识别标识.通过分析研究不同极化方式、入射角、入射频率条件下畸形波与背景波面的电磁散射特性实验数据得出:当二者的NRCS差值大于-11.8 dB及以上时,即认为产生畸形波,这为实际的工程应用提供了参照标准.     

阻抗劈绕射对破碎波后向散射特性的影响

海浪的破碎区会导致海面电磁散射特性发生很大改变,导致海尖峰现象的产生.本文结合阻抗劈结构模型分析了劈绕射对破碎波后向散射特性的影响.首先利用基尔霍夫近似求解破碎波的物理光学场;基于Maliuzhinets方法,从波动方程及精确阻抗边界条件出发,由谱函数的积分形式得到阻抗劈的一致性绕射系数,结合物理光学绕射系数导出阻抗劈等效边缘电磁流;利用边缘绕射场修正物理光学场,得到考虑劈绕射效应的破碎波散射总场.数值结果表明,阻抗劈的绕射场在Keller锥内出现HH极化大于VV极化的现象,因此计入绕射场的影响会使得破碎波生长到临近坍塌阶段时,小擦地角逆风观测出现总场的后向散射截面HH极化大于VV极化的现象,说明劈绕射是造成海尖峰现象产生的原因之一.     

浅海小掠射角的海底界面声反向散射模型的简化

在浅海,尤其是负梯度声速剖面和海面较为平静的浅海波导,海底界面反向散射是浅海混响的主要来源.经验散射模型只适用于分析浅海混响平均强度衰减特性,而基于物理机理建立的反向散射模型克服了这一缺陷,但同时也引入了其受地声模型约束的问题.本文结合了海底反射系数的三参数模型,对浅海远场海底反向散射模型进行了简化,以减少地声模型的输入参数.理论分析了海底反射系数的相移参数可以描述海底对声场的散射作用,无需任何海底地声参数的先验知识.通过对海底反向散射模型近似简化,结果表明在临界角附近和甚小掠射角范围内的海底粗糙界面反向散射模型的角度特性和强度特性受海底沉积层的影响不同:在临界角附近,海底反向散射的角度特性受海底反射系数的相移参数加权,而其散射系数则近似与相移参数无关;对于甚小掠射角,海底反向散射的角度特性近似与海底反射系数的相移参数无关,其散射系数则近似与相移参数的4次方成正比.     

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.     

A versatile composite surface model for electromagnetic backscattering from seas

A versatile composite surface model (VCSM) is presented for estimation of the electromagnetic backscattering coefficient of the sea. Taking into account the statistical characteristics of the sea surface and the validity conditions of component models for the small-scale and large-scale surfaces in the composite surface model (CSM), a method for the two-scale decomposition of sea surfaces is introduced. On this basis, the cutoff wavenumber with wind speed dependence and incident wave frequency dependence is applied to separate the sea spectrum into large- and small-scale components at different sea states with increased accuracy. Then, numerical results of the backscattering coefficient are evaluated and discussed in the case of different wind speeds, polarizations as well as incident frequencies. Finally, the VCSM is verified through the comparisons with the available experimental data, and the comparisons of the VCSM results and the classical CSM results also show that the VCSM behaves better.     

Experimentally validated Raman Monte Carlo simulation for a cuboid object to obtain Raman spectroscopic signatures for hidden material

In conventional Raman spectroscopic measurements of liquids or surfaces the preferred geometry for detection of the Raman signal is the backscattering (or reflection) mode. For non‐transparent layered materials, sub‐surface Raman signals have been retrieved using spatially offset Raman spectroscopy (SORS), usually with light collection in the same plane as the point of excitation. However, as a result of multiple scattering in a turbid medium, Raman photons will be emitted in all directions. In this study, Monte Carlo simulations for a three‐dimensional layered sample with finite geometry have been performed to confirm the detectability of Raman signals at all angles and at all sides of the object. We considered a non‐transparent cuboid container (high density polyethylene) with explosive material (ammonium nitrate) inside. The simulation results were validated with experimental Raman intensities. Monte Carlo simulation results reveal that the ratio of sub‐surface to surface signals improves at geometries other than backscattering. In addition, we demonstrate through simulations the effects of the absorption and scattering coefficients of the layers, and that of the diameter of the excitation beam. The advantage of collecting light from all possible 4π angles, over other collection modes, is that this technique is not geometry specific and molecular identification of layers underneath non‐transparent surfaces can be obtained with minimal interference from the surface layer. To what extent all sides of the object will contribute to the total signal will depend on the absorption and scattering coefficients and the physical dimensions. Copyright © 2015 John Wiley & Sons, Ltd.     

随机起伏冰面三维声散射的Kirchhoff近似数值计算模型

针对随机起伏冰面的声散射问题,建立了随机起伏冰面三维声散射的Kirchhoff近似数值计算模型。利用Delaunay三角剖分方法对随机起伏冰面进行三角面元剖分,然后采用Z-buffer算法进行面元的遮挡消隐,得到处于声波照射亮区的面元,最后采用Gordon面元积分的板块元方法计算得到随机起伏冰面的散射强度。数值计算模型中,将冰面认为是局部阻抗表面,直接代入起伏冰面局部反射系数进行散射声场的计算,避免了解析计算模型中对反射系数的近似处理。对比分析了数值和解析计算模型在小粗糙起伏冰面、大粗糙起伏冰面及不同声波入射角和不同声波频率时的散射强度。相比解析模型计算结果,数值模型计算结果与实测结果更吻合。