## Inverse source problem and minimum-energy sources

JOSA A, Vol. 17, Issue 1, pp. 34-45 (2000)

http://dx.doi.org/10.1364/JOSAA.17.000034

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### Abstract

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

© 2000 Optical Society of America

**OCIS Codes**

(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

**History**

Original Manuscript: March 17, 1999

Revised Manuscript: August 23, 1999

Manuscript Accepted: September 2, 1999

Published: January 1, 2000

**Citation**

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)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-1-34

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