We present a new linear inversion formalism for the scalar inverse source problem in three-dimensional and one-dimensional (1D) spaces, from which a number of previously unknown results on minimum-energy (ME) sources and their fields readily follow. ME sources, of specified support, are shown to obey a homogeneous Helmholtz equation in the interior of that support. As a consequence of that result, the fields produced by ME sources are shown to obey an iterated homogeneous Helmholtz equation. By solving the latter equation, we arrive at a new Green-function representation of the field produced by a ME source. It is also shown that any square-integrable (<i>L</i><sup>2</sup>), compactly supported source that possesses a continuous normal derivative on the boundary of its support must possess a nonradiating (NR) component. A procedure based on our results on the inverse source problem and ME sources is described to uniquely decompose an <i>L</i><sup>2</sup> source of specified support and its field into the sum of a radiating and a NR part. The general theory that is developed is illustrated for the special cases of a homogeneous source in 1D space and a spherically symmetric source.
© 2000 Optical Society of America
(000.3860) General : Mathematical methods in physics
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(350.5610) Other areas of optics : Radiation
Edwin A. Marengo, Anthony J. Devaney, and Richard W. Ziolkowski, "Inverse source problem and minimum-energy sources," J. Opt. Soc. Am. A 17, 34-45 (2000)