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 1st-order, coupling 2nd-order and higher-order scattering of multiple objects. The 1st-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 1st-order scattering from one object, the 2nd-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 3rd-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 validates the analytical iterative algorithm, which significantly accelerates the scattering computation for wide-band frequencies f and overall azimuth angles theta over 360 degrees. 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 spline interpolation, discrete scattering data over the f - theta plane yield uniform discrete data over the 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.