Holography and the inverse source problem
JOSA, Vol. 72, Issue 3, pp. 327-330 (1982)
http://dx.doi.org/10.1364/JOSA.72.000327
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Abstract
The inverse source problem for monochromatic sources Re[ρ(r, ω)e^{-iωt}] to the scalar-wave equation is investigated. It is shown that a unique solution to the inverse source problem can be obtained by imposing the constraint that the solution minimize the source energy E = ∫ d^{3}r|ρ(r, ω)|^{2}. For certain recording geometries the time derivative of the real image produced by a point-reference hologram is shown to be directly proportional to the time-reversed minimum energy source Re[ρ*ME(r, ω)e^{-iωt}] in the short-wavelength limit.
© 1982 Optical Society of America
Citation
R. P. Porter and A. J. Devaney, "Holography and the inverse source problem," J. Opt. Soc. Am. 72, 327-330 (1982)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-72-3-327
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References
- 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).
- 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. The form of Bojarski's integral equation employed in this paper is that given in Ref. 5.
- A. J. Devaney and E. Wolf, "Radiating and nonradiating classical current distributions and the fields they generate," Phys. Rev. D 8, 1044–1047 (1973).
- N. Bleistein and J. Cohen, "Nonuniqueness in the inverse source problem in acoustics and electromagnetics," J. Math. Phys. 18, 194–201 (1977).
- A. J. Devaney and G. C. Sherman, "Nonuniqueness in inverse source and scattering problems," IEEE Trans. Antennas Propag. (to be published).
- We use the definitions of the spherical harmonics and spherical Bessel and Hankel functions employed by A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1965), Vol. I, Apps. BII and BIV.
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1972), p. 440.
- K. Gottfried, Quantum Mechanics (Benjamin, New York, 1966), p. 90.
- For a discussion on time reversal in holography see W. Lukosz, "Equivalent-lens theory of holographic imaging," J. Opt. Soc. Am. 58, 1084–1091 (1968).
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