一维带限Weierstrass分形粗糙海面电磁后向散射的微扰法研究

On Electromagnetic Backscattering from 1D Band-limited Weierstrass Fractal Rough Sea Surface using the Small Perturbation Method

运用微扰法研究了平面电磁波入射随机粗糙海面的后向散射问题,结合一维带限Weier-strass分形粗糙海面的功率谱,导出了一维带限Weierstrass分形粗糙海面后向散射截面的数学表达式,进一步得出了不同极化状态下后向散射系数的计算公式。通过数值计算得到了两种情形下后向散射系数随入射角的变化曲线,讨论了粗糙面高度起伏均方根、分维、空间基频、标度区间、海水温度、入射波频率对后向散射系数的影响。得到了一维带限Weierstrass分形粗糙海面后向散射系数的基本特征、分形特征、随频率变化特征。

The electromagnetic backscattering of the random rough surface with plane electromagnetic wave incidence is studied by the Small Perturbation Method.Combined with the power spectral density of 1D band-limited weierstrass fractal rough sea surface,the mathematical expression of the backscattering cross section is derived.Based on the mathematical expression,the formulaes of the backscattering coefficient for the different polarized states are obtained.The curves of the backscattering coefficient of changing with the variation of the incident angle are obtained by numerical implementation.Further,the influence of the root mean square,the fractal dimension,special fundamental frequency scale interval,the temperature of seawater and the frequency of the incident wave on the backscattering coefficient is discussed.The basic characteristics,the fractal characteristics and the characteristics with varying frequency of the backscattering coefficient from 1D band-limited weierstrass fractal rough sea surface are obainted.