Sensitivity analysis of electrically small objects in lossy inhomogeneous structures

Accurate response Jacobians can significantly improve the convergence and the resolution of the reconstruction algorithms used in inverse microwave imaging. As the electrical size of an object decreases, however, the accuracy of the computed Jacobians with respect to its shape and constitutive parameters deteriorates. This is especially valid if finite-difference (FD) approximations are used. In this paper, we investigate the accuracy of the Jacobians provided by our self-adjoint sensitivity analysis (SASA) of lossy dielectric structures. We focus on time-domain solutions. The accuracy of the response gradients is investigated for electrically small objects. Recommendations are given for a proper choice of shape parameters when the object's size becomes smaller than certain limits. We show that our approach yields accurate Jacobians even for objects as small as one grid cell while the FD approximations are prone to numerical noise.