Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

随机粗糙表面激光散射后向增强效应实验研究

随机粗糙表面激光散射后向增强效应实验研究吴振森（西安电子科技大学物理系西安７１００７１）ＥｘｐｅｒｉｍｅｎｔＲｅｓｅａｒｃｈｏｎＥｎｈａｎｃｅｄＢａｃｋｓｃａｔｅｒｉｎｇｏｆＲａｎｄｏｍＲｏｕｇｈＳｕｒｆａｃｅｓＷｕＺｈｅｎｓｅｎ（Ｄｅｐａｒｔｍｅｎ...     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

分形分层粗糙面电磁波透射特性的混合算法

运用基于矩量法(method of moment,MoM)结合基尔霍夫近似(Kirchhoff approximation,KA)的混合算法研究一维带限Weierstrass分形分层介质粗糙面的电磁波透射问题.在混合算法中将上层粗糙面和下层粗糙面分别划分到MoM区域和KA区域,数值计算得到透射系数随透射波的散射角的变化,讨论粗糙面分维数、高度起伏均方根、底层介质介电常数、中间层介质介电常数和厚度、入射波频率对透射系数的影响,结果表明上层粗糙面参数对透射系数有显著影响,而下层粗糙面参数对透射系数影响较小.     

Absolute backscatter coefficient estimates of tissue-mimicking phantoms in the 5-50 MHz frequency range

Absolute backscatter coefficients in tissue-mimicking phantoms were experimentally determined in the 5-50 MHz frequency range using a broadband technique. A focused broadband transducer from a commercial research system, the VisualSonics Vevo 770, was used with two tissue-mimicking phantoms. The phantoms differed regarding the thin layers covering their surfaces to prevent desiccation and regarding glass bead concentrations and diameter distributions. Ultrasound scanning of these phantoms was performed through the thin layer. To avoid signal saturation, the power spectra obtained from the backscattered radio frequency signals were calibrated by using the signal from a liquid planar reflector, a water-brominated hydrocarbon interface with acoustic impedance close to that of water. Experimental values of absolute backscatter coefficients were compared with those predicted by the Faran scattering model over the frequency range 5-50 MHz. The mean percent difference and standard deviation was 54%?±?45% for the phantom with a mean glass bead diameter of 5.40 μm and was 47%?±?28% for the phantom with 5.16 μm mean diameter beads.     

Pulse broadening of enhanced backscattering from rough surfaces

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l≳λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

Pulse broadening of enhanced backscattering from rough surfaces

Abstract

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l?λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

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.     

FDTD Investigation on Electromagnetic Scattering from Two-Layered Rough Surfaces under UPML Absorbing Condition

Electromagnetic scattering from one-dimensional two-layered rough surfaces is investigated by using finite-difference time-domain algorithm （FDTD）. The uniaxial perfectly matched layer （UPML） medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. The rough surfaces are characterized with Gaussian statistics for the height and the autocorrelation function. The angular distribution of bistatic scattering coefficient from single-layered perfect electric conducting and dielectric rough surface is calculated and it is in good agreement with the numerical result with the conventional method of moments. The influence of the relative permittivity, the incident angle, and the correlative length of two-layered rough surfaces on the bistatic scattering coefficient with different polarizations are presented and discussed in detail.     

不稳定表面粗糙目标的太赫兹波段散射特性分析

研究了不同粗糙度下的非均匀和分区均匀不稳定表面粗糙导体目标在太赫兹波段的散射特性。区别于采用经验公式的建模方法,提出把随机粗糙面的建模理念应用到太赫兹波段的非均匀和分区均匀不稳定表面粗糙导体目标的建模中,用描述粗糙面的均方根高度和相关长度两个物理量来调节目标表面的粗糙度变化。提出表面粗糙目标的分类形式并给出具体模型,然后用随机高斯粗糙面来模拟非均匀和分区均匀不稳定粗糙目标的表面,再采用物理光学和等效电流相结合的方法来进行仿真计算,分别对不同入射角、不同频率和不同粗糙度的非均匀和分区均匀不稳定表面粗糙导体目标的太赫兹波散射特性进行分析,最后得出了相关的结论。     

Investigation on electromagnetic scattering from rough soil surface of layered medium using the small perturbation method

Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

A Study of Optical Backscattering Enhancement from One-Dimensional Rough Surface Using Monte Carlo Method

In this paper, according to Kirchhoff approximation, the optical backscattering enhancement of one-dimensional random rough surface, which includes fractal rough surfaces and random rough surfaces with Gaussian and exponential correlation simulated by Monte Carlo method, is obtained. It is shown that backscattering enhancement of random rough surfaces will increase with increasing the rms height of rough surface for a given correlation length. The angle width of backscattering enhancement is directly proportional to incident wavelength and inverse proportional to correlation length of rough surface. Complex phase of scattering field from superposed rough surface is uniformly distributed, none of the directions is of more overweight. The backscattering enhancement is also studied by wavelet analysis. The numerical results show good consistent with that of the relative references.     

Electromagnetic scattering from two-layer rough interfaces in the Kirchhoff approximation

Electromagnetic wave scattering from multilayers consisting of two two-layer Gaussian rough surfaces with lossless media is investigated in the Kirchhoff approximation (KA), with consideration of the shadowing effects. The tapered incident wave is introduced into the classic KA, and the bistatic scattering coefficient is redetermined. The advantage of this method is that it is faster in computation than the exact numerical methods. The numerical results show that the bistatic scattering coefficient calculated in the KA is in good agreement with that obtained by using the method of moment (MOM) over a most angular range, which indicates the validity of the KA proposed in our paper. Finally, the effects of the relative permittivity, the root-mean-square (RMS) height, the correlative length, and the average height between the two interfaces on the bistatic scattering coefficient are discussed in detail.     

Height distribution on a rough plane and specularly diffracted light amplitude are Fourier transform pair

In this report we show that the amplitude of specularly diffracted light from a plane rough surface as a function of incident angle cosine is Fourier transform of the height distribution on the surface. Therefore, an even height distribution function, which is the case for many rough surfaces, can be obtained by measuring the specularly diffracted light intensities. Also, it is observed that for polychromatic illumination the spectrum of the specularly diffracted light is modified and the modification depends on roughness, incident angle, and wavelength. It is also shown that, for a fixed incident angle, the height distribution on the rough plane is Fourier transform of the spectral modifying function. Experimental studies on some surfaces of different roughnesses, prepared by grinding sheet-glasses by powders of different grain sizes, show that the corresponding height distributions are Gaussian and the rms heights obtained by the two approaches are quite consistent.     

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.     

Polarization ratio characteristics of electromagnetic scattering from sea ice in polar areas

In the global climate system, the polar regions are sensitive indicators of climate change, in which sea ice plays an important role. Satellite remote sensing is a significant tool for monitoring sea ice. The use of synthetic aperture radar(SAR) images to distinguish sea ice from sea water is one of the current research hotspots in this topic. To distinguish sea ice from the open sea, the polarization ratio characteristics of sea ice and sea water are studied for L-band and C-band radars, based on an electromagnetic scattering model of sea ice derived from the integral equation method(IEM) and the radiative transfer(RT) model. Numerical experiments are carried out based on the model and the results are given as follows. For L-band, the polarization ratio for sea water depends only on the incident angle, while the polarization ratio for sea ice is related to the incident angle and the ice thickness. For C-band, the sea water polarization ratio is influenced by the incident angle and the root mean square(RMS) height of the sea surface. For C-band, for small to medium incident angles,the polarization ratio for bare sea ice is mainly determined by the incident angle and ice thickness. When the incident angle increases, the RMS height will also affect the polarization ratio for bare sea ice. If snow covers the sea ice, then the polarization ratio for sea ice decreases and is affected by the RMS height of snow surface, snow thickness, volume fraction and the radius of scatterers. The results show that the sea ice and the open sea can be distinguished by using either L-band or C-band radar according to their polarization ratio difference. However, the ability of L-band to make this differentiation is higher than that of C-band.     

修正反射系数的Kirchhoff近似方法计算高斯起伏冰面三维声散射

针对随机起伏冰面的声散射计算问题,利用修正反射系数的Kirchhoff近似方法计算了高斯起伏冰面的三维声散射。在计算模型中引入了冰面局部统计平均反射系数的概念,将二维高斯起伏冰面的散射分为相干散射和非相干散射,分别得到两类散射成分的散射系数公式,计算了高斯起伏冰面三维声散射的散射强度。分析了散射强度与随机起伏冰面的均方根高度、声波入射角度及频率的关系。通过实验室水池中高斯起伏冰面的散射强度测量实验,对理论模型的计算结果进行了验证。将实验结果分别与采用冰面局部统计平均反射系数的模型计算结果和文献中采用平整冰面镜反射系数的模型计算结果进行了对比,采用冰面局部统计平均反射系数的模型计算结果与实验测量值吻合较好。      

Acoustic scattering by a three-dimensional elastic object near a rough surface

The ensemble-averaged field scattered by a smooth, bounded, elastic object near a penetrable surface with small-scale random roughness is formulated. The formulation consists of combining a perturbative solution for modeling propagation through the rough surface with a transition (T-) matrix solution for scattering by the object near a planar surface. All media bounding the rough surface are assumed to be fluids. By applying the results to a spherical steel shell buried within a rough sediment bottom, it is demonstrated that the ensemble-averaged "incoherent" intensity backscattered by buried objects illuminated with shallow-grazing-angle acoustic sources can be well enhanced at high frequencies over field predictions based on scattering models where all environmental surfaces are planar. However, this intensity must compete with the incoherent intensity scattered back from the interface itself, which can defeat detection attempts. The averaged "coherent" component of the field maintains the strong evanescent spectral decay exhibited by flat interface predictions of shallow-angle measurements but with small deviations. Nevertheless, bistatic calculations of the coherent field suggest useful strategies for improving long-range detection and identification of buried objects.