  In this paper, we develop a theoretical framework for analyzing the
measurable information content of an unknown scene through an active
electromagnetic imaging array. We consider monostatic and multistatic array
architectures in a one-dimensional setting. Our main results include the
following: (a) we introduce the space-bandwidth product (SBP), and show that,
under the Born approximation, it provides an accurate prediction of the number
of the degrees of freedom (DoF) as constrained by the geometry of the scene and
the imaging system; (b) we show that both monostatic and multistatic
architectures have the same number of DoF; (c) we show that prior DoF analysis
based on the more restrictive Fresnel approximation are obtained by
specializing our results; (d) we investigate matched-filter (back-propagation)
and pseudoinverse image reconstruction schemes, and analyze the achievable
resolution through these methods. Our analytical framework opens up new avenues
to investigate image formation techniques that aim to reconstruct the
reflectivity function of the scene by solving an inverse scattering problem,
and provides insights on achievable resolution. For example, we show that
matched-filter reconstruction leads to a significant resolution loss for
multistatic architectures.
