The Role of the Plane Wave Excitations in the Number of Degrees of Freedom and Resolution for Scattering Strip Objects

In the linear inverse scattering problem, if the system is a multi-view configuration, it is required to consider multiple Plane Waves(PWs) and observation points from different directions to achieve sufficient information about the unknown object with multiple transmitters and receivers. The sensing modality can be chosen according to the application of interest, and the multi-view configurations give more information. However, considering multi-view configurations requires spending much time and cost to establish the experimental set-up. One solution can be reducing the number of incident PWs to a minimum. However, this reduction can affect the reconstruction quality and it might be impossible to reconstruct the unknown object perfectly. Therefore, it arises the important question of how many independent PWs are needed to reconstruct the object reliably. Thus, we investigate the role of the PW excitations for different scattering strip objects on the Number of Degrees of Freedom (NDF) and the achievable resolution by using the Point Spread Function (PSF) for the single frequency case and multi-view sensing configuration in the far zone. In addition, an analytical approximated PSF is introduced to be compared with the exact one and to assess its efficiency. We show how the NDF and resolution change by considering different numbers of PWs and different angles. Moreover, a minimum number of PWs and their direction are introduced to achieve the estimated NDF and resolution for different scattering strip geometries, and it is confirmed that they depend on the shape of the object. The theoretical results are validated through numerical examples.