Solution of ۲-D Electromagnetic Problems for Inhomogeneous Objects using ۱-D FFT

This paper presents a novel solution of two dimensional (۲-D) method of moments (MoM) in Cartezian coordination to calculate the source-type electric field integral equations (EFIE) arising from electromagnetic inverse scattering problems in microwave imaging (MI). The main issue is to reduce the ۲-D problem into ۱-D case, using decomposition the electric-type Green’s function of inhomogeneous media. In this regard, recursive formulas in spatial frequency domain are derived for both TE and TM problems and the scattering field is rewritten into upward and downward components in a recursive form. It helps us to calculate a ۲-D problem using ۱-D stabilized biconjugate-gradient fast Fourier transform (BCGSFFT) of the induced source and save lots of memory and time for inhomogeneous objects in MI performance. The paper provides ۲-D TM and TE scattering examples for different scenarios and compares the proposed and conventional algorithms to demonstrate merits of the proposed formulas in terms of the accuracy and computational efficiency.