A non-canonical inhomogeneous background medium is one whose Green's function cannot be obtained by an analytical method. Electromagnetic scattering from objects embedded in a non-canonical inhomogeneous background medium is very challenging because of the computational complexity with the calculation of its Green's function and the multiple scattering between objects and the background. This work applies the Diagonal Tensor Approximation (DTA) to calculate the scattering from arbitrary objects in a noncanonical inhomogeneous background. Previously, the DTA has only been applied to a canonical background such as a homogeneous or layered background media. This approach employs a numerical method to obtain all Green's functions required in the calculation; an accurate DTA is used to calculate the scattering properties. In order to reduce the large number of simulations, we employ the symmetry and reciprocity in the Green's function calculation. Furthermore, considering that most realistic imaging measurements are made through a voltage probe usually represented by a wave port, we develop a method to convert the scattered field on the probe (the antenna) to the measured wave port voltage. Numerical results show that this method can obtain accurate scattering characteristics from arbitrary objects in a non-canonical inhomogeneous background medium in a microwave imaging system.
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