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Inverse source problem and minimum-energy sources.

E A Marengo1, A J Devaney, R W Ziolkowski

  • 1Department of Electrical and Computer Engineering, University of Arizona, Tucson 85721, USA. emarengo@ece.arizona.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 21, 2000
PubMed
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We introduce a new inversion method for inverse source problems, revealing minimum-energy sources obey Helmholtz equations. This enables unique decomposition of sources into radiating and non-radiating components.

Area of Science:

  • Physics
  • Applied Mathematics
  • Electromagnetics

Background:

  • The scalar inverse source problem is crucial in various fields like acoustics and electromagnetics.
  • Understanding source characteristics, especially minimum-energy (ME) and non-radiating (NR) components, is essential for accurate field reconstruction.

Purpose of the Study:

  • To develop a novel linear inversion formalism for the scalar inverse source problem in 1D and 3D spaces.
  • To derive new results concerning minimum-energy sources and their fields.
  • To establish a method for uniquely decomposing sources and their fields into radiating and non-radiating parts.

Main Methods:

  • A new linear inversion formalism is presented for the scalar inverse source problem.
  • The study analyzes properties of minimum-energy (ME) sources, showing they satisfy a homogeneous Helmholtz equation within their support.

Related Experiment Videos

  • A Green-function representation for ME source fields is derived by solving an iterated Helmholtz equation.

    • Main Results:

    • Minimum-energy sources are demonstrated to satisfy a homogeneous Helmholtz equation in the interior of their support.
    • Fields generated by ME sources are shown to obey an iterated homogeneous Helmholtz equation.
    • Any square-integrable, compactly supported source with a continuous normal derivative possesses a non-radiating (NR) component.

    Conclusions:

    • The developed inversion formalism provides new insights into ME sources and their fields.
    • A procedure is established to uniquely decompose a source and its field into radiating and NR components.
    • The theory is illustrated with examples of homogeneous sources in 1D and spherically symmetric sources.