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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 2, Iss. 11 — Nov. 1, 1985
  • pp: 1937–1942

Holographic shape determination of reflecting objects

R. P. Porter  »View Author Affiliations

JOSA A, Vol. 2, Issue 11, pp. 1937-1942 (1985)

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A general and practical method is developed for shape determination of specular reflectors from their scattered fields. Even though this problem has been of interest for many years, and even though a unique solution is believed possible, a general method has eluded us. The method presented here uses the observation that a class of incoming and outgoing waves that satisfy the boundary conditions of the object can be found. Holographic imaging of the scattered field is a practical approach for finding these eigenfunctions for the scatterer. As an example, we invert the scattered field from a sphere, precisely determining its radius.

© 1985 Optical Society of America

Original Manuscript: December 2, 1984
Manuscript Accepted: July 24, 1985
Published: November 1, 1985

R. P. Porter, "Holographic shape determination of reflecting objects," J. Opt. Soc. Am. A 2, 1937-1942 (1985)

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  1. W. A. Imbriale, R. Mittra, “The two-dimensional inverse scattering problem,” IEEE Trans. Antennas Propag. AP-18, 633 (1970). [CrossRef]
  2. W. M. Boerner, F. H. Vandenberghe, M. A. K. Hamid, “Determination of the electrical radius ka of a circular cylindrical scatterer from the scattered field,” Can. J. Phys. 49, 804 (1971). [CrossRef]
  3. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805 (1965). [CrossRef]
  4. P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417 (1969). [CrossRef]
  5. R. P. Porter, “Diffraction-limited scalar image formation with holograms of arbitrary shapes,” J. Opt. Soc. Am. 60, 1051 (1970). [CrossRef]
  6. R. P. Porter, “Image formation with arbitrary holographic type surfaces,” Phys. Lett. 29A, 193 (1969).
  7. R. P. Porter, A. J. Devaney, “Generalized holography and practical solutions to inverse source problems,” J. Opt. Soc. Am. 72, 1707 (1982). [CrossRef]
  8. R. P. Porter, A. J. Devaney, “Holography and the inverse source problem,” J. Opt. Soc. Am. 72, 327 (1982). [CrossRef]
  9. R. P. Porter, “Determination of structure of weak scatterers from holographic images,” Opt. Commun. 39, 362 (1981). [CrossRef]
  10. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 11.3.
  11. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153 (1969). [CrossRef]
  12. D. J. N. Wall, “Methods of overcoming numerical instabilities associated with the T-matrix method,” in Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the T-Matrix Approach, V. K. Varadan, V. V. Varadan, eds. (Pergamon, New York, 1980), p. 269.

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