Study of the Electromagnetic Scattering from the Very Rough Fractal Sea Surface

In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approx-imation and with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional veryrough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximationat microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation andintegral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancementon the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.     

改进的二维分形模型在海面电磁散射中的应用

提出了一种改进的二维分形海面模型，其表面谱函数在空间波数小于基波波数及大于基波波数时分别满足正幂率关系和负幂率关系.通过比较可以发现在不同风速时，改进模型的空间自相关函数及表面轮廓谱和有关文献结果有较好的吻合.在满足Kirchhoff近似条件下推导了改进分形模型的散射系数及散射强度系数的计算公式并进行了数值计算，比较了改进模型和经典模型的后向散射强度系数角分布并详细讨论了它们随入射频率、海上风速和风向的变化. 关键词： 改进分形模型 粗糙海面 电磁散射 Kirchhoff近似     

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.     

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.     

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.     

Analysis of multiple scattering from two-dimensional dielectric sea surface with iterative Kirchhoff approximation

<正>An iterative method in the Kirchhoff approximation is proposed for high frequency multiple electromagnetic scattering from two-dimensional dielectric sea surface.The multiple interaction of the scattering field is characterized with the corrected electromagnetic currents of the wind-driven sea surface.The actual surface currents are approximated with the iterative solution of the corrected currents.A newly developed sea spectrum,Elfouhaily spectrum,is utilized to build the sea surface model.The shadowing correction is improved by the Depth-Buffer algorithm.The validity of the iterative Kirchhoff approximation is verified by the agreement of backscattering coefficients with the measured data.     

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.     

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.     

Analytical comparison between the surface current integral equation and the second-order small-slope approximation

Abstract

This paper is the third in a series discussing a new approximate bistatic model for electromagnetic scattering from perfectly conducting rough surfaces. Our previous approach supplemented the Kirchhoff model through the addition of new terms involving linear orders in slope and surface elevation differences that arise naturally from a second iteration of the surface current integral equation. This completion of the Kirchhoff was shown to provide the correct first-order small perturbation method (SPM-1) in the general bistatic context. The agreement with SPM-1 was achieved because differences of surface heights are no longer expanded in powers of surface slope. While consistent with SPM, our previous formulation fails to reconverge toward the Kirchhoff model, at some incidence and scattered angles, when the illuminated surface satisfies the high frequency roughness condition. This weakness is also shared with the first-order small slope approximation (SSA-1) which is structurally equivalent to our previous formulation where the polarization is independent of surface roughness. The second-order small slope approximation (SSA-2), which satisfies the SPM-1 and second-order small perturbation method (SPM-2) limits by construction, was shown by Voronovich to converge toward the tangent plane approximation of the Kirchhoff model under high frequency conditions. In the present paper, we show that, in addition to the linear orders in our previous model, one must now include cross-terms between slope and surface elevation to ensure convergence toward both high frequency and small perturbation limits. With the inclusion of these terms, our new formulation becomes comparable to the SSA-2 (second-order kernel) without the need to evaluate all the quadratic order slope and elevations terms. SSA-2 is more complete, however, in the sense that it guarantees convergence toward the second-order Bragg limit (SPM-2) in the fully dielectric case in addition to both SPM-1 and Kirchhoff. Our new generalization is shown to explain correctly extra depolarization in specular conditions to be caused by surface curvature and surface autocorrelation for incoherent and coherent scattering, respectively. This result will have large repercussions on the interpretation of bistatically reflected signals such as those from GPS.     

Three dimensional analyses of scattering by pressure-release sinusoidal surfaces

Scattering by pressure-release sinusoidal surfaces in three dimensions is analyzed using the Fresnel phase approximation and realistic source and receiver directivity approximations. Geometrical shadowing and second-order scattering are explicitly included to explore the validity of the Kirchhoff approximation. No restrictions on the surface heights and slopes are made. The "goodness" of the resulting expressions is verified by requiring the pressure scattered by a sinusoidal surface to reduce to the image solution as the surface amplitude goes to zero. The first-order scattered pressure achieves a very good approximation to the image solution, and the second-order scattered pressure goes to zero, as expected, under this requirement. The theory is compared with available experimental scattering measurements, and the agreement is good. Because the slopes on the experimental surface are very steep, shadowing corrections are indispensible to achieving accurate first and second order scattering results. Shadowing has a greater impact on the scattering prediction than the second-order scattering contribution. This suggests that the Kirchhoff approximation may be more robust when incorporated into a theory including a detailed shadowing treatment as well as the Fresnel phase approximation and a good directivity approximation.     

Analytical comparison between the surface current integral equation and the second-order small-slope approximation

This paper is the third in a series discussing a new approximate bistatic model for electromagnetic scattering from perfectly conducting rough surfaces. Our previous approach supplemented the Kirchhoff model through the addition of new terms involving linear orders in slope and surface elevation differences that arise naturally from a second iteration of the surface current integral equation. This completion of the Kirchhoff was shown to provide the correct first-order small perturbation method (SPM-1) in the general bistatic context. The agreement with SPM-1 was achieved because differences of surface heights are no longer expanded in powers of surface slope. While consistent with SPM, our previous formulation fails to reconverge toward the Kirchhoff model, at some incidence and scattered angles, when the illuminated surface satisfies the high frequency roughness condition. This weakness is also shared with the first-order small slope approximation (SSA-1) which is structurally equivalent to our previous formulation where the polarization is independent of surface roughness. The second-order small slope approximation (SSA-2), which satisfies the SPM-1 and second-order small perturbation method (SPM-2) limits by construction, was shown by Voronovich to converge toward the tangent plane approximation of the Kirchhoff model under high frequency conditions. In the present paper, we show that, in addition to the linear orders in our previous model, one must now include cross-terms between slope and surface elevation to ensure convergence toward both high frequency and small perturbation limits. With the inclusion of these terms, our new formulation becomes comparable to the SSA-2 (second-order kernel) without the need to evaluate all the quadratic order slope and elevations terms. SSA-2 is more complete, however, in the sense that it guarantees convergence toward the second-order Bragg limit (SPM-2) in the fully dielectric case in addition to both SPM-1 and Kirchhoff. Our new generalization is shown to explain correctly extra depolarization in specular conditions to be caused by surface curvature and surface autocorrelation for incoherent and coherent scattering, respectively. This result will have large repercussions on the interpretation of bistatically reflected signals such as those from GPS.     

Study on electromagnetic backscattering and Doppler spectrum of a moving spherical target above time-varying sea surface

The surface electric current of the sea surface and the first-order scattering field from the spherical target were obtained by employing Physical Optics method and Mie theory, respectively. The backscattering field of the time-evolving sea surface was calculated by using Kirchhoff Approximation. Meanwhile, by taking the advantage of a newly developed technique that utilizes the reciprocity theorem, the difficulty in formulating the secondary coupling scattering fields from the spherical target above the sea surface was reduced. The dependence of the secondary coupling backscattering field on the size and the position of the spherical target was discussed, and the characteristic of the Doppler spectrum of the composite backscattering field with different incident angles was analyzed in detail. Supported by the National Natural Science Foundation of China (Grant No. 60571058) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070701010)     

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: I. Theoretical study

Abstract

In this paper the first- and second-order Kirchhoff approximation is applied to study the backscattering enhancement phenomenon, which appears when the surface rms slope is greater than 0.5. The formulation is reduced to the geometric optics approximation in which the second-order illumination function is taken into account. This study is developed for a two-dimensional (2D) anisotropic stationary rough dielectric surface and for any surface slope and height distributions assumed to be statistically even. Using the Weyl representation of the Green function (which introduces an absolute value over the surface elevation in the phase term), the incoherent scattering coefficient under the stationary phase assumption is expressed as the sum of three terms. The incoherent scattering coefficient then requires the numerical computation of a ten- dimensional integral. To reduce the number of numerical integrations, the geometric optics approximation is applied, which assumes that the correlation between two adjacent points is very strong. The model is then proportional to two surface slope probabilities, for which the slopes would specularly reflect the beams in the double scattering process. In addition, the slope distributions are related with each other by a propagating function, which accounts for the second-order illumination function. The companion paper is devoted to the simulation of this model and comparisons with an ‘exact’ numerical method.     

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: I. Theoretical study

In this paper the first- and second-order Kirchhoff approximation is applied to study the backscattering enhancement phenomenon, which appears when the surface rms slope is greater than 0.5. The formulation is reduced to the geometric optics approximation in which the second-order illumination function is taken into account. This study is developed for a two-dimensional (2D) anisotropic stationary rough dielectric surface and for any surface slope and height distributions assumed to be statistically even. Using the Weyl representation of the Green function (which introduces an absolute value over the surface elevation in the phase term), the incoherent scattering coefficient under the stationary phase assumption is expressed as the sum of three terms. The incoherent scattering coefficient then requires the numerical computation of a ten- dimensional integral. To reduce the number of numerical integrations, the geometric optics approximation is applied, which assumes that the correlation between two adjacent points is very strong. The model is then proportional to two surface slope probabilities, for which the slopes would specularly reflect the beams in the double scattering process. In addition, the slope distributions are related with each other by a propagating function, which accounts for the second-order illumination function. The companion paper is devoted to the simulation of this model and comparisons with an 'exact' numerical method.     

一维随机粗糙面后向增强效应的蒙特-卡罗方法研究

根据基尔霍夫近似方法,用蒙特－卡罗方法模拟随机粗糙面,观测到了随机粗糙面的后向增强效应。分别研究了高斯粗糙面及分形粗糙面,讨论了统计特性相同的粗糙面在不同小波尺度的电磁（光）波散射特性。所得结果与实验事实相当吻合     

Polarimetric scattering from a two-dimensional improved sea fractal surface

This paper studies the influence of wind parameters and fractal dimension from an improved two-dimensional sea fractal surface on the polarimetric scattering by using facet integration.A two-dimensional improved sea surface simulated is discretized into three matrices of sea surface facets including a height matrix and two slope matrices on orthogonal directions.Based on the Kirchhoff approximation,the polarimetric scattered field is derived in the Cartesian coordinate system by integration of three matrices mentioned above.Finally,the fully polarised radar cross section is numerically simulated and the dependence of the polarimetric scattering on the sea fractal surface,such as the wind speed,the wind direction,as well as the fractal dimension,is discussed in detail.     

分形海面的微波电磁散射计算模型

利用2维Weierstrass带限函数建立了模拟粗糙海面形状的模型,讨论了分形维数、频率幅度尺度因子等分形参数对海面形状的影响。以粗糙海面形状模型为基础,针对模拟的分形海面形状,从亥姆霍兹积分出发,利用基尔霍夫近似推导出2维分形海面的电磁散射系数,并进行了数值模拟。对微波电磁散射特性随分形维数、频率幅度尺度因子、入射波入射角变化的规律做了进一步讨论分析。在低掠射角时电波会受海面的遮挡,用遮挡函数对散射系数进行修正。研究表明:随着分形维数的增大,散射峰分布变均匀。频率幅度尺度因子越大,散射也越分散。随着入射角的增大,后向散射也逐渐增强,而前向散射逐渐减弱。     

基尔霍夫近似下激光海面漫反射组网通信特性

 针对激光点对点通信方式的不足,根据舰艇编队通信的实际需要,提出了利用海面作为激光漫反射媒介的一对多的组网通信方法,并且采用基尔霍夫近似的方法对激光海面漫反射通信的特性进行了研究。通过对激光光束入射海面后产生的散射场的分析计算,采用遮蔽函数对计算过程中的阴影效应加以修正,得出了较为准确的2维激光海面双站散射系数和后向散射系数,并进行了实验验证,说明了激光海面漫反射组网通信方法的可行性。     

Electromagnetic backscattering from one-dimensional drifting fractal sea surface Ⅱ:Electromagnetic backscattering model

Sea surface current has a significant influence on electromagnetic(EM) backscattering signals and may constitute a dominant synthetic aperture radar(SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section(NRCS) discrepancies between the model for a coupled wavecurrent fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle,as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface.