Antonello Tamburrino

Antonello Tamburrino, Vincenzo Mottola

This paper treats the inverse problem of retrieving the electrical conductivity of a material starting from boundary measurements in the framework of Electrical Resistance Tomography (ERT). In particular, the focus is on non-iterative reconstruction methods suitable for real-time applications. In this work, the Kernel Method, a new non-iterative reconstruction method for Electrical Resistance Tomography, is presented. The imaging algorithm addresses the problem of retrieving one or more anomalies of arbitrary shape, topology, and size embedded in a known background (the inverse obstacle problem). The foundation of the Kernel Method is based on the idea that if a proper current density applied at the boundary (Neumann data) of the domain exists such that it is able to produce the same measurements with and without the anomaly, then this boundary source produces a power density that vanishes in the region occupied by the anomaly, when applied to the problem involving the background material only. This new tomographic method has a simple numerical implementation that requires a very low computational cost. In this paper, the theoretical foundation of the Kernel Method is provided, and an extensive numerical campaign proves the effectiveness of this new imaging method.

Vincenzo Mottola, Luisa Faella, Carlo Forestiere et al.

The sharp increasing in fabrication capabilities of nanomaterials, and complex structures such as meta-surfaces and metalens, has opened to the possibility of employing them for accurately control the electromagnetic field, beyond the possibility ensured by traditional devices. The demand for large scale structures and more complex functionalities from meta-surfaces lead to the research for advanced techniques of inverse design, able to conjugate the ability to produce effective designs and limited computational cost. Among the various approaches for inverse design of large meta-surfaces, the ones based on the adjoint variable method are appealing since able to ensure a minimal computational cost for the gradient computation of the cost function. In this work, a systematic methodology for the application of the adjoint variable method for large meta-surface design is presented. The method is based on: (i) a parametrization of the relevant geometric parameters of the meta-atoms, (ii) the fast computation of the gradient with respect such parameters, allowing for the implementation of general affine transformations during the optimization process. The main findings are first theoretically justified and a numerical validation is provided to show the effectiveness of the proposed approach.