Use of Radon's projection theory in electromagnetic inverse scattering

In a wide variety of electromagnetic profile reconstruction or shape imaging techniques, a need often arises to deduce the three-, two-, or one-dimensional distribution of different physical quantities from their projections, e.g., in radio-astronomy, structural biology, roentgenology, geophysics, and also in electromagnetic imaging. Investigation of such problems in various specialized areas resulted in the establishment of the new interdisciplinary subject known as "reconstruction from projections." The underlying theory, which was first rigorously formulated by Radon, will become of increasing importance to radar target mapping, wave-imaging, and related electromagnetic inverse problems; therefore, a tutorial exposition is timely and well suited for this issue. Major emphasis will be placed on showing how Ludwig's theorems on support, determinacy, and self-consistency can be used favorably to analyze the data-limited reconstruction cases. The derived theorems will be applied to the specific case of physical optics far field inverse scattering, clearly proving that the Bojarski and the Kennaugh identities constitute a Fourier-Radon transform pair.