随机分布多导体圆柱目标散射的快速计算及其成像模拟

用二维迭代方法快速地解析计算多导体圆柱目标的散射场,其中各圆柱目标自身的一次散射以各自中心为原点的柱面波函数叠加,匹配各圆柱表面的边界条件获得展开系数;各圆柱间的散射相互作用由坐标变换实现,具体体现在圆柱中心偏移产生的初始相位上.为考虑各个柱目标间的二次散射,将每个柱目标自身的一次散射看成另一柱目标的激励场,利用柱面波函数的加法定理和边界条件匹配来计算各柱目标间的二次散射贡献.类似的处理可获得三次或更高次的散射计算.与矩量法(MoM)的数值结果比较,验证了该方法的有效性,明显提高了后向散射的计算速度.对于随机生成的多个圆柱目标模型,解析计算一定频带f和360°方位角θ范围内均匀离散样点的后向散射场.为抑制数据截断产生的振铃效应,对频率向的散射数据用Hamming窗实现平滑过渡.为充分利用快速Fourier变换(FFT)的高效计算,对f－θ平面上的离散散射数据用二维的三次样条插值处理,得到X－Y平面的均匀离散数据.最后,用FFT方法快速实现逆合成孔径雷达(ISAR)成像模拟,很好地重构了各圆柱体目标的位置和大小尺寸.

Analytical iterative algorithm for fast computation of scattering from multiple conductive cylinders and the image reconstruction

An analytical iterative algorithm for fast computation of scattering from multiple conductive cylinders is developed. It takes account of the independent 1-st order, coupling 2-nd and higher order scattering of multiple objects. The 1-st order scattering, as independent scattering of a single object self, is derived by using the expansion of cylindrical waves in local coordinate of the object, which are solved by the boundary conditions. Exciting by the 1-st order scattering from one object, the 2-nd order scattering of multi-objects are obtained iteratively using the addition theorem of Hankel function and the boundary conditions. The same approach is applicable to calculations of the 3-rd order and higher order scattering. It is found that the phase differences caused by the cylinder centers indicate the scattering wave interferences of multi-objects. Comparison with numerical MoM results well vailidates the analytical iterative algorithm, which significantly accelerates the scattering computation for wide-band frequency f and overall azimuth angles θ over 360°. In order to depress the ringing effect caused by the abrupt change of scattering field in computed region to zero field in uncomputed region, the Hamming window is used to make gradual change of the scattering field to zero. Using FFT and 2D 3-order spline interpolation, discrete scattering data over f－θ plane yield uniform discrete data over X－Y plane. The image reconstruction is finally performed for multiple conductive cylinders. The image can well identify the positions and sizes of multi-objects.