Abstract
An approach is presented to combine the response of a two-dimensionally inhomogeneous dielectric object in a homogeneous environment with that of an empty inhomogeneous environment. This allows an efficient computation of the scattering behavior of the dielectric cylinder with the aid of the CGFFT method and a dedicated extrapolation procedure. Since a circular observation contour is adopted, an angular spectral representation can be employed for the embedding. Implementation details are discussed for the case of a closed 434 MHz microwave scanner, and the accuracy and efficiency of all steps in the numerical procedure are investigated. Guidelines are proposed for choosing computational parameters such as truncation limits and tolerances. We show that the embedding approach does not increase the CPU time with respect to the forward problem solution in a homogeneous environment, if only the fields on the observation contour are computed, and that it leads to a relatively small increase when the fields on the mesh are computed as well.
Highlights
In almost any computational approach to solving nonlinear inverse-scattering problems, a discretized configuration is introduced that depends on a fixed number of parameters
An approach is presented to combine the response of a two-dimensionally inhomogeneous dielectric object in a homogeneous environment with that of an empty inhomogeneous environment. This allows an efficient computation of the scattering behavior of the dielectric cylinder with the aid of the conjugate-gradient FFT (CGFFT) method and a dedicated extrapolation procedure
We show that the embedding approach does not increase the CPU time with respect to the forward problem solution in a homogeneous environment, if only the fields on the observation contour are computed, and that it leads to a relatively small increase when the fields on the mesh are computed as well
Summary
In almost any computational approach to solving nonlinear inverse-scattering problems, a discretized configuration is introduced that depends on a fixed number of parameters. For the case of an inhomogeneous, lossy dielectric cylinder in a homogeneous surrounding medium, it was demonstrated that a highly efficient implementation is obtained when the fields are computed by solving a contrast-source integral equation with a combination of the conjugate-gradient FFT (CGFFT) method and a special extrapolation procedure [12]. With well-chosen values for these parameters, the embedding approach does not increase the CPU time as compared to the forward problem solution in a homogeneous environment, if only the fields on the observation contour are computed, and that it leads to a relatively small increase in CPU time, when the fields in the object are needed as well, for example, to compute the Jacobian matrix in a Newton-type inversion scheme.
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