## Holography and the inverse source problem. Part II: Inhomogeneous media

JOSA A, Vol. 2, Issue 11, pp. 2006-2012 (1985)

http://dx.doi.org/10.1364/JOSAA.2.002006

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### Abstract

The inverse source problem for a monochromeatic source imbedded in a nonabsorbing inhomogeneous medium is investigated within the framework of the reduced scalar wave equation. The Porter-Bojarski integral equation previously formulated for sources imbedded in vacuum is generalized to this case, as are the class of nonradiating and minimum-energy sources considered in Part I [ J. Opt. Soc. Am. 72, 327 ( 1982)].

© 1985 Optical Society of America

**History**

Original Manuscript: July 1, 1985

Manuscript Accepted: July 24, 1985

Published: November 1, 1985

**Citation**

A. J. Devaney and R. P. Porter, "Holography and the inverse source problem. Part II: Inhomogeneous media," J. Opt. Soc. Am. A **2**, 2006-2012 (1985)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-2-11-2006

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### References

- R. P. Porter, A. J. Devaney, “Holography and the inverse source problem,” J. Opt. Soc. Am. 72, 327–330 (1982). [CrossRef]
- A Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1967), p. 189.
- R. P. Porter, “Diffraction-limited, scalar image formation with holograms of arbitrary shape,” J. Opt. Soc. Am. 60, 1051–1059 (1970);“Image formation with arbitrary holographic type surfaces,” Phys. Lett. 29A, 193–194 (1969). [CrossRef]
- N. N. Bojarski, “Inverse scattering,” Naval Air Systems Command Rep., Contract N00019-73-C-0312 (Naval Air Systems Command, Washington, D.C., 1973), Sec. 11, pp. 3–6.
- This form of the integral equation was derived by N. Bleistein, J. Cohen, “Nonuniqueness in the inverse source problem in acoustics and electromagnetics,” J. Math. Phys. 18, 194–201 (1977). [CrossRef]
- C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer, New York, 1969), Chap. III. [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, G. Sherman, “Nonuniqueness in inverse source and scattering problems,” IEEE Trans. Antennas Propag. AP-30, 1034–1037 (1982). [CrossRef]
- R. P. Porter, “Determination of structure of weak scatterers from holographic images,” Opt. Commun. 39, 362–365 (1981). [CrossRef]
- A. J. Devaney, “Inverse source and scattering problems in ultrasonics,” IEEE Trans. Sonics Ultrason. SU-30, 355–364 (1983). [CrossRef]
- R. Courant, D. Hilbert, Methods of Mathematical Physics (Interscience, New York1966), Chap. III.
- A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1965), Vol. I, Apps. BII and BIV.
- M. Fischer, K. J. Langenberg, “Limitations and defects of certain inverse scattering theories,” IEEE Trans. Antennas Propag. AP-32, 1080–1088 (1984). [CrossRef]
- I. J. LaHaie, “Inverse source problem for three-dimensional partially coherent sources and fields,” J. Opt. Soc. Am. A 2, 35–45 (1985). [CrossRef]
- A. J. Devaney, “The inverse problem for random sources,” J. Math. Phys. 20, 1687–1691 (1979). [CrossRef]

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