Study on the Degrees of Freedom of Scattered Fields in Nonlinear Inverse Scattering Problems

In this work, we study the impact of contrast of scatterers on the degrees of freedom (DoF) of scattered fields in nonlinear inverse scattering problems (ISPs), and two numerical methods for calculating DoF are proposed. The number of DoF are proportional to the spatial bandwidth of the scattered field, which is affected by the electromagnetic properties of scatterers in the domain of investigation (DoI). Based on the discretized volume integral equations, an accurate numerical method for calculating the DoF is proposed by taking the maximum contrast of DoI into account. Furthermore, assuming that the contrast of DoI tends to infinity, the upper bound of DoF independent of contrast is obtained. Frequency-domain zero-padding method is applied to interpolate the field samples of the number of DoF into oversampled fields to calculate the approximation error. Numerical examples verify the accuracy of the proposed methods for calculating DoF.