An Inverse Scattering Approach for Inspecting Dielectric Scatterers At Microwave Frequencies Without Phase Information Sandra Costanzo, Giuseppe Di Massa Department of Informatics, Modeling, Electronics and System Engineering University of Calabria Rende (CS), Italy {costanzo; dimassa}@deis.unical.it Matteo Pastorino, Andrea Randazzo Department of Electrical, Electronic, and Telecommunication Engineering, and Naval Architecture University of Genoa Genova, Italy {matteo.pastorino; andrea.randazzo}@unige.it Abstract—Microwave imaging techniques aim at inspecting targets by using interrogating microwaves. In recent years, several numerical inversion methods and prototypes of microwave imaging systems have been developed. In most cases, they consider an illuminating apparatus and one or more probes used to measure the field scattered by the target; usually, the values of the amplitudes and phases of the field samples are needed. In this work, a hybrid approach for phaseless imaging of dielectric targets is proposed. A two-probe measurement strategy with the related phase-retrieval method is adopted in conjunction with an inversion procedure based on an inexact-Newton method to give an efficient and low-cost imaging setup. Preliminary numerical and experimental validations are discussed. Keywords—Electromagnetic imaging; inverse scattering; dielectrics; phase retrieval I. INTRODUCTION Imaging systems based on microwaves have been studied for long time [1]–[18]. The research in this area follows essentially two directions. The first one is related to the development of apparatuses aimed at inspecting targets by illuminating the target of interest by using interrogating waves at microwave frequencies and efficiently measuring the field scattered by object [19]–[23]. The second one concerns the development of inversion procedures aimed at retrieving information about the target starting by the measured samples of the scattered field [24]–[32]. Both these research lines have so far produced very interesting results, and microwave imaging systems are now rather mature for practical applications. In particular, deterministic and stochastic procedure are now able to suitably face the ill-posedness of the relationships that relate the scattered field and the relevant properties of the target, such as the shape, the position and its dielectric parameters. In most cases, however, the system is rather complex and requires expensive circuitry. The need for simplified approach is relevant in several industrial area, e.g. for inspecting wood material. In this paper, the inspection of possibly inhomogeneous dielectric targets is considered. To this end, we propose a hybrid version of a previously developed reconstruction method, in which the “inversion” method (discussed later on) is combined with a procedure for the phase retrieval starting from amplitude- only measured data [33]–[38]. Therefore, the proposed solution results into a significant reduction of the measurement complexity. Two advantages can be obtained. The first one is related to a significant cost reduction of the apparatuses, with easier operation modalities. The second one is the corresponding computational time saving in the measurement stage. The considered inversion procedure is based on the solutions of the integral equations of the inverse scattering problem by an inexact-Newton method [39]–[44]. After discretization of the continuous model, two nested loops are considered. In the first one, the problem is linearized and the resulting linear equations are solved (in the second loop) in a regularization way. The inexact-Newton method has been found to be quite efficient in solving inverse problems in electromagnetics, also with specific reference to the retrieval of dielectric parameters in industrial applications. For the sake of simplicity, the approach is proposed for inspecting cylindrical targets under transverse-magnetic illumination, which results in a two-dimensional scalar inverse problem. The nonlinear nature of the problem is fully exploited and weakly scattering assumptions are not imposed. Concerning the treatment of phaseless data on the imaging acquisition domain, the two-probes measurement strategy proposed in [33]–[36] is followed. The phase reconstruction method discussed in [33]–[38] is then applied to obtain the complex field. Finally, the imaging procedure based on the inexact-Newton method is applied. In the following, the assumed imaging configuration will be discussed in Section II, together with the description of the considered hybrid inversion procedure. Some numerical results are then reported in Section III. They have been obtained in the case of scattering by inhomogeneous cylindrical targets. The synthetic data, at the measurement positions, are simulated by solving the electromagnetic forward problem by means of the moment method. A preliminary experimental result is reported in Section IV. It has been obtained by using real data collected inside the anechoic chamber of the Microwave Laboratory, University of Calabria, Italy. Finally, some conclusions are drawn in Section V.