## New aspects of the inverse source problem with far-field data

JOSA A, Vol. 16, Issue 7, pp. 1612-1622 (1999)

http://dx.doi.org/10.1364/JOSAA.16.001612

Enhanced HTML Acrobat PDF (389 KB)

### Abstract

The time-dependent inverse source problem with far-field data is investigated within a limited-view Radon inversion framework, analogous to that of a limited-view computed tomography reconstruction problem. We investigate the domains in the Radon and Fourier spaces within which data are available for the reconstruction of the space–time structure of the source. Using a linear inversion formalism we derive a filtered backprojectionlike procedure to reconstruct the minimum-energy source consistent with prescribed far-field data. The source inversion technique developed in the paper is illustrated with a numerical example. The paper also contains a new description of nonradiating sources in the time domain.

© 1999 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

**History**

Original Manuscript: October 26, 1998

Manuscript Accepted: January 26, 1999

Published: July 1, 1999

**Citation**

Edwin A. Marengo, Anthony J. Devaney, and Richard W. Ziolkowski, "New aspects of the inverse source problem with far-field data," J. Opt. Soc. Am. A **16**, 1612-1622 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1612

Sort: Year | Journal | Reset

### References

- J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
- N. Bleistein, J. K. Cohen, “Nonuniqueness in the inverse source problem in acoustics and electromagnetics,” J. Math. Phys. 18, 194–201 (1977). [CrossRef]
- A. J. Devaney, E. Wolf, “Radiating and nonradiating classical current distributions and the fields they generate,” Phys. Rev. D 8, 1044–1047 (1973). [CrossRef]
- A. J. Devaney, R. P. Porter, “Holography and the inverse source problem. Part II: inhomogeneous media,” J. Opt. Soc. Am. A 2, 2006–2011 (1985). [CrossRef]
- E. Heyman, A. J. Devaney, “Time-dependent multipoles and their application for radiation from volume source distributions,” J. Math. Phys. 37, 682–692 (1996). [CrossRef]
- P. R. Smith, T. M. Peters, R. H. T. Bates, “Image reconstruction from finite number of projections,” J. Phys. A Math. Nucl. Gen. 6, 361–382 (1973). [CrossRef]
- A. K. Louis, “Incomplete data problems in x-ray computerized tomography. I. Singular value decomposition of the limited angle transform,” Numer. Math. 48, 251–262 (1986). [CrossRef]
- A. D. Yaghjian, T. B. Hansen, “Time-domain far fields,” J. Appl. Phys. 79, 2822–2830 (1996). [CrossRef]
- F. G. Friedlander, “An inverse problem for radiation fields,” Proc. London Math. Soc. 3, 551–576 (1973). [CrossRef]
- M. Bertero, C. De Mol, E. R. Pike, “Linear inverse problems with discrete data. I: general formulation and singular system analysis,” Inverse Probl. 1, 301–330 (1985). [CrossRef]
- I. J. LaHaie, “The inverse source problem for three-dimensional partially coherent sources and fields,” J. Opt. Soc. Am. A 2, 35–45 (1985). [CrossRef]
- H. E. Moses, “Solution of Maxwell’s equations in terms of a spinor notation: the direct and inverse problem,” Phys. Rev. 113, 1670–1679 (1959). [CrossRef]
- H. E. Moses, “The time-dependent inverse source problem for the acoustic and electromagnetic equations in the one- and three-dimensional cases,” J. Math. Phys. 25, 1905–1923 (1984). [CrossRef]
- R. W. Deming, A. J. Devaney, “A filtered backpropagation algorithm for GPR,” J. Env. Eng. Geo. 0, 113–123 (1996). [CrossRef]
- S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).
- D. N. Ghosh Roy, Methods of Inverse Problems in Physics, 2nd ed. (CRC Press, Boca Raton, Fla., 1991).
- M. Bertero, “Linear inverse and ill-posed problems,” in P. W. Hawkes, ed., Advances in Electronics and Electron Physics (Academic, New York, 1989), Vol. 75, pp. 1–120.
- R. P. Porter, A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. Am. 72, 1707–1713 (1982). [CrossRef]
- E. A. Marengo, A. J. Devaney, E. Heyman, “Analysis and characterization of ultrawideband, scalar volume sources and the fields they radiate,” IEEE Trans. Antennas Propag. 45, 1098–1107 (1997). [CrossRef]
- E. A. Marengo, A. J. Devaney, E. Heyman, “Analysis and characterization of ultrawideband, scalar volume sources and the fields they radiate: Part II—square pulse excitation,” IEEE Trans. Antennas Propag. 46, 243–250 (1998). [CrossRef]
- K. T. Ladas, A. J. Devaney, “Generalized ART algorithm for diffraction tomography,” Inverse Probl. 7, 109–125 (1991). [CrossRef]
- G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, San Diego, Calif., 1985).
- A. K. Louis, “Ghosts in tomography—The null space of the Radon transform,” Math. Methods Appl. Sci. 3, 1–10 (1981). [CrossRef]
- A. K. Louis, “Orthogonal function series expansions and the null space of the Radon transform,” SIAM J. Math. Anal. 15, 621–633 (1984). [CrossRef]
- K. T. Smith, D. C. Solmon, S. L. Wagner, “Practical and mathematical aspects of the problem of reconstructing objects from radiographs,” Bull. Am. Math. Soc. 83, 1227–1270 (1977). [CrossRef]
- A. J. Devaney, “Nonuniqueness in the inverse scattering problem,” J. Math. Phys. 19, 1526–1531 (1978). [CrossRef]
- K. Kim, E. Wolf, “Non-radiating monochromatic sources and their fields,” Opt. Commun. 59, 1–6 (1986). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.