Analysis of a Nonlinear Technique for Microwave Imaging of Targets Inside Conducting Cylinders

Microwave imaging of targets enclosed in circular metallic cylinders represents an interesting scenario, whose applications range from biomedical diagnostics to nondestructive testing. In this paper, the theoretical bases of microwave tomographic imaging inside circular metallic pipes are reviewed and discussed. A nonlinear quantitative inversion technique in non-Hilbertian Lebesgue spaces is then applied to this kind of problem for the first time. The accuracy of the obtained dielectric reconstructions is assessed by numerical simulations in canonical cases, aimed at verifying the dependence of the result on the size of the conducting enclosure and comparing results with the conventional free space case. Numerical results show benefits in lossy environments, although the presence and the type of resonances should be carefully taken into account.

Four solutions of a two-cylinder electrostatic problem, and identities resulting from their equivalence

Summary Four distinct solutions exist for the potential distribution around two equal circular parallel conducting cylinders, charged to the same potential. Their equivalence is demonstrated, and the resulting analytical identities are discussed. The identities relate the Jacobi elliptic function $sn$, the Jacobi theta functions $\theta _1 ,~\theta _2 $ and infinite series over trigonometric and hyperbolic functions.