Abstract

The problem of reconstructing a strip electric current from its radiated field collected over a bounded finite rectilinear observation domain, orthogonal and centered with respect to the source, is dealt with. In particular, the study is developed for a two-dimensional, scalar geometry and focuses on the estimation of achievable performance in terms of the number of degrees of freedom (NDF) and depth resolution. This is a classical problem that we contributed to in the past by addressing a Fresnel zone configuration. Here, the plan is to expand those results by removing the geometrical limitations due to the Fresnel approximation. The main idea is to rewrite the involved radiation operator as a Fourier-type integral operator by introducing a suitable variable transformation. This allows applying simple Fourier-based reasoning to estimate the achievable point-spread function, which in turn is used to estimate the NDF and depth resolution. The obtained NDF and depth resolution estimations are compared to those returned by numerical computation of the relevant singular value decomposition, and very good agreement is found. Moreover, it is shown that the results obtained for the Fresnel zone are a particularization of the new findings when such an approximation holds true.

© 2019 Optical Society of America

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